Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Ein weiteres Beispiel einer Matrix aus Ravens Progessiv Matrices
Im deutschen Sprachraum sind derzeit folgende adaptierte und überarbeitete Versionen des „Culture Fair
Intelligence Test“ verbreitet:

 „CFT-1 Grundintelligenztest Skala 1“, im Altersbereich von 5;3 bis 9;5
Jahren, und der
„ CFT-20 R Grundintelligenztest Skala 2“ in revidierter („R“) Fassung, für
den Altersbereich von 8;5 bis 19 Jahren und bei Erwachsenen von 20 bis
60 Jahren.

Sie können sowohl als Einzel- als auch als Gruppentest durchgeführt werden. Die neueren Ausgaben des CFT-
20 können wahlweise durch einen Wortschatztest und einem Zahlenfolgetest ergänzt werden.
Die theoretische Fundierung dieser Gruppe von Tests ist die zwei-Faktoren-Theorie der Intelligenz von
Raymond Bernard Cattell. Ein Faktor ist hierbei die kristallisierte Intelligenz, die vor allem erlerntes
Problemlöseverhalten zusammenfasst. Der zweite Faktor ist die fluide Intelligenz als „die Fähigkeit komplexe
Beziehungen in neuartigen Situationen wahrnehmen und erfassen zu können“. Cattell konzipierte die „Culture
Fair Intelligence Tests“, die vor allem die fluide Intelligenz messen sollten, und alle möglichen kulturell und
sprachlich bedingten Einflüsse auf das Ergebnis weitgehend ausschließen sollten. Allerdings existieren auch
Befunde, die diesen Ansichten widersprechen. Demnach ist es möglich, auch die sog. fluide Intelligenz durch
Übung zu steigern. Auch wird die Kulturunabhängigkeit dieser Tests bezweifelt
Cultural Fair Ideas
Celebrate cultures from around the world with a cultural fair.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Putting on a cultural fair can be an entertaining and educational way to display a variety of world cultures in
one location. Plan several main activities that highlight the distinct customs and traditions of each culture
represented at the event, and advertise your prospective schedule well in advance using social and print
media to help attract participants and patrons.
Fashion Show: A cultural fashion show is an entertaining way to display the various forms of dress from culture
to culture. Either put on a show that displays traditional clothing items from each culture represented at the fair
or encourage local designers to use those traditional pieces as inspiration for new, modern garments. Set up a
catwalk in a high-traffic area of the fair, and then either provide chairs for the audience or leave plenty of
standing room. Recruit an emcee to announce the models and describe the garments each one is wearing,
including important information like the origin of the clothing and its use in each particular culture.
Talent Show: Hold a talent show to display various components of each participating cultural group. The
talents could be anything the group finds significant and distinct in its respective culture, ranging from musical
performances to traditional folk dances. Ask the groups to submit their routines before the event so you can
put together an organized act schedule, as well as an informative program to be passed out to the audience.
The talent show doesn't have to be competitive, but if you want to turn it into a competition, recruit several
unbiased judges to score the routines. At the end, award prizes to the best acts.
Food Court: Display the deliciously distinct tastes of the various cultures represented at the fair with a food
court. Encourage each participating cultural group to make and sell several typical dishes representative of
their respective diets. The dishes can be as simple or complex as the vendors wish, but remind participants
that the foods should be easy to prepare for large crowds on location. Provide a designated table or stand to
each group that decides to contribute dishes. Label these areas with clearly written signs or flags to help
patrons identify the origins of the food. Also consider creating a map key to pass out to patrons that displays
where each vendor is located in the food court.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Arts and Crafts Fair: Highlight the artistic achievements of the cultures represented at the fair with an arts and
crafts display area. Have each participating cultural group contribute several typical pieces of folk art to the
display; these can be representative of a variety of mediums, including sculpture, textiles and prints. Find out
what each group plans to contribute so you can properly display the pieces during the event. Set up
designated sections for each group's display, and then offer some background information on each
contribution for patrons to examine as they browse the exhibit.
How to Include Anti-Bias Practices Into the Classroom

Removing bias from the classroom teaches students not to fear or ridicule differences.
An educator can achieve an anti-bias classroom by incorporating a multicultural approach into his teaching. An
anti-bias classroom challenges stereotypes by teaching students how to seek factual evidence to draw
conclusions about people. In a classroom with anti-bias practices, students are expected to treat fellow
students on the basis of fairness and equality. Bias can lead to discriminatory behaviour and, in some cases,
violence.
Educate yourself about bias so that you can recognize it and its effects in your classroom. Examine yourself for
any biases or prejudices that you may have, and either eliminate them or keep them out of the classroom.
Establish ground rules for your classroom. Ask students to help establish the rules or guidelines for appropriate
classroom interaction. Create an environment that encourages students to work together to build a prejudice-
free classroom where they can share ideas openly.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Integrate diversity into every topic. Set aside time during every unit to examine the topic from different
viewpoints. Encourage students to identify two different points of views, the people who may be affected by
the topic, how they are affected, and what their responses or feelings may be. This is an excellent way to teach
students to develop empathy. Use team-building exercises to foster positive relationships among students.
Demonstrate tolerance. Serving as a model of tolerant and non-defensive behaviour establishes the idea that
making mistakes or being different is part of the process of learning -- and living. Do not be afraid to share
personal experiences with children about times when you or someone you know has been on the receiving
end of prejudice or discrimination.
Review classroom materials to be sure they are inclusive. Make sure classroom displays, bulletin boards and
learning materials are accurately representative of all people. Avoid displays or materials that might reinforce
stereotypes.
Develop an "emergency lesson." Anticipate a prejudicial behaviour in the classroom and be proactive by
preparing the emergency lesson to address the prejudice or discrimination displayed. Teachers who do not
firmly and immediately address discriminatory behaviour may cause students to think they condone it.
Anti Bias Activities in the Classroom

Young children often respond to musical activities when learning about diversity.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Young people develop biases for or against different groups of people based on race, ethnicity, gender, class,
sexual orientation or religion. Schoolchildren who have a bias against others sometimes bully or exclude
others. Biases cause children to have problems getting along with and working with others in the classroom. It
also leads to hurt feelings. Teachers can stop bias in their classrooms by having children participate in anti-bias
activities.

Communication Activities: Get children to talk about their own diverse backgrounds, other cultural groups or
prejudice to get a dialogue started about bias or diversity. Have them talk with others or write a poem about
themselves. Ask them to present their poems to the whole class or a group so other students can learn more
about each other's families and cultures. You also could have students prepare an oral report about other
countries or cultures. These presentations should include information about religious and cultural practices,
languages and history. For an anti-bias activity, split your students into groups to talk about their perceptions of
different cultural groups and the formation of these ideas. Start conversations with specific questions about
bias, such as questions about bias in the media or the children's own biases, but let children lead the
discussions. Try to create an open environment in your classroom so children feel comfortable talking about
issues such as prejudice.

Reading Activities: Have students read books on different types of people and groups to expose them to a
wide variety of cultures and show them the differences within cultural groups also have them read books
about topics such as the Holocaust to teach them about the harmful consequences of prejudice. After they
have read books, have them answer questions or talk in a group about the messages in the books. Tailor your
questions to what the books say about the different cultures or prejudice. For an activity about prejudice or bias
within the print media, have students look at advertisements, books, magazines, newspapers, Internet sites and
other types of media for bias against people based on certain categories, such as religion, ethnicity, class,
gender or race. Before having them look for bias, explain what constitutes bias for or against certain groups,
including stereotypical language used for different groups.

Musical Activities: Play different types of music for your students, and let them know about cultural traditions
related to the music and the varieties that exist within each tradition. Give them printouts to sing along or clear
a space for them to dance so that they feel more connected to the music. Sing along to show that you are a
part of creating a more diverse environment within the classroom. To further expose children to different types
of music, have musicians from different cultures come in to talk about their groups' music and demonstrate
instruments. Try to get speakers who know how to present interactive activities so the children can dance, sing
or play instruments as they are learning.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Artistic Activities: Have children create art projects that help them see the diversity in the world or within the
classroom. To personalize your anti-bias activity, get students to make posters about themselves using photos,
magazine images, construction paper and other materials. On the sheet, have them write information about
themselves, such as their ages, interests and family history or background, so others can get to know them and
see how they are different and similar to them. Have the children present the posters to classmates, talking
about the meaning behind different images, and later hang the pieces in the hall or the classroom to remind
students and others about the diversity in your classroom. For another activity, have students create artwork
similar to what they make in other cultures. Bring in experts to teach children how to create animal carvings,
dream catchers or masks. Have them create art during a special event, such as a holiday, and explain the
significance of the artwork.

Group Activity / Pair Activity 3.5:
1. Define culture-fair
2. Define anti-bias
3. Demonstrate how culture-fair and anti-bias approach can be used to improve the learners.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

so4: Implement the planned Numeracy Learning
Programme. 

Learner Tip:
The Learning Programme Guidelines aim to assist teachers and schools in their planning for the introduction of
the National Curriculum Statement. The Learning Programme Guidelines should be read in conjunction with
the National Senior Certificate policy and the National Curriculum Statement Subject Statements.
Section 2 of the Learning Programme Guidelines suggests how teaching the particular subject may be
informed by the principles which underpin the National Curriculum Statement.
Section 3 suggests how schools and teachers might plan for the introduction of the National Curriculum
Statement. The Department of Education encourages careful planning to ensure that the high skills, high
knowledge goals of the National Curriculum Statement are attained.
The Learning Programme Guidelines do not include sections on assessment. The assessment requirements for
each subject are provided in the Subject Assessment Guidelines which come into effect on 1 January 2008.

4.1 (ac1) – implementing a Numeracy Learning
Programme

How to Implement School Programs
Create educational opportunities for your students.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

School programs allow students to become more involved in the school community and offer enriching
educational opportunities. As a teacher, you have the opportunity to select and start a school program. School
programs can be as varied as organized student government, book clubs, academic clubs or even something
competitive, such as a "mathletes" program or the writing program "Power of the Pen." While beginning a
school program does require planning, it can be a relatively hassle-free process. By working to ensure that
your efforts are well-organized and effective, you can implement a program that enhances students' learning
and enjoyment of school.
Consult the school handbook or administration to determine what specific steps must be taken within your
school. Every school has a slightly different procedure for school-program establishment. This procedure is
likely outlined in your staff handbook. If you cannot locate information about how to begin a school program,
speak to the administration or your department head to ensure that you properly follow the necessary
procedures.
Determine the cost of the program. Take any enrollment fees or materials costs into consideration. Also,
consider whether your program will require travel. If it will, calculate a rough estimate of these costs by
considering the travel distance, type of vehicle and average gas cost. Determine where you will get funding. In
some cases, your school's administration may have funds that they can allocate to your program. If you plan on
fund-raising, develop a cursory plan as to what you might do.
Select students to be serviced by the program. If your program is academic in nature, determine the grade
levels to which the program will be offered. If your program is extracurricular, decide which students the
program would be open to and how you would determine who is eligible to participate.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

The administration will likely want to know how this program will be advantageous to students. Prepare to offer
an explanation as to why this program is worth implementing in your school so that you can adequately defend
your proposed program.
Select staff members to oversee the program. If you do not intend to oversee the program, consider others
who might be appropriate advisers, and approach them about overseeing the program in question.
Plan an implementation schedule. Determine when the program would begin, and create a tentative meeting
and event schedule. While you may change your schedule when and if your program is implemented, this
rough schedule will better allow the administration to decide whether or not to approve your proposal.
How to Apply Piaget's Theory to Teaching Mathematics
A math teacher's guide to using Piaget's approach to learning

Jean Piaget was a forefather of modern child development theory. Surprisingly, this educational academic
began his career in the natural sciences. A quick turn to psychoanalysis brought an interest in human learning
and knowledge acquisition. Piaget's stages of cognitive development encompass growth from birth through
adolescence. They include what he termed the sensorimotor stage (birth to 2 years), the preoperational stage
(approximately 2 through 7), he concrete stage (7 through early adolescence), and the formal operational stage
(adolescence). Educators can use the developmental theories behind each stage to create age-graded
strategies for teaching mathematics.
Preoperational Stage

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Acquire an accurate description of Piaget's theory of preoperational development for children from
approximately age 2 through first grades. In general, children in this stage are beginning to understand how
symbols (such as words or numbers) can represent objects, use make-believe or fantasy thought, are fairly
egocentric in thinking, and do not have a firm grasp on the concept of time.

Choose specific aspects of Piaget's preoperational theory that match mathematics teaching for your age
group/grade. Include concepts that easily translate into teaching strategies. For example, use the idea that the
child now might understand the connection between an object and the symbol that it represents. Set up a
hands-on number lesson in which groups of toys or other objects represent numbers such as five toy cars,
three apples, or seven pieces of chalk.

Write your lesson plan detailing each step and its relation to Piaget's theory. Note the specific stage (i.e.,
preoperational) and theory idea (e.g., make-believe/fantasy, representation). Design a specific learning goal or
object, such as students learning to count to 10 by themselves, or child recognizing written numerals. Make a
bulleted list of materials and a numbered list of steps.

Concrete Operational Stage

Understand Piaget's concrete operational stage. Children in this stage (roughly 7 through early adolescence)
can consider multiple dimensions or aspects of a single object, understand seriation (ordering objects by
increasing or decreasing values), and are able to classify objects. Concrete examples and hands-on
experiences are essential to learning during this stage of development.

Create a lesson plan based on the ideas Piaget theorized about in this developmental stage. Develop learning
objectives/goals, such as the students learning the multiplication tables through nine, or the students
demonstrating knowledge of place value.

Make a written list of materials needed. Because this stage often demands the use of concrete materials, try
items such as pattern blocks, math tiles or counter beads. Write lesson steps, connecting each significant part
to a key Piaget idea (e.g., conservation, seriation, classification).

Set up hands-on mathematics explorations in the classroom to accompany the lessons. For example, if you are
teaching multiplication tables to grade-schoolers, use small math tiles (or other similar objects) on a board to
connect the numbers and representations. Allow the students to work out the solutions on their own with
guidance only as needed.

Formal Operational Stage

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Learn about and understand the formal operational stage (typically the adolescent period). Students in this
stage are capable of creating their own hypothesis, thinking about consequences, use abstract thinking and
reasoning, making inferences, evaluating ideas, and applying one concept to another.
Choose specific concepts of Piaget's theory to connect to math. Try applying pre-existing knowledge to the
math world through well-crafted word problems, providing multiple pieces of information for the students to
clarify and deduce answers from, or using problems that require reasoning skills. Students in this stage should
be able to understand algebraic concepts, and lessons can include the use of variables.
Write a lesson plan. Include a materials list as needed and a numbered step list. Note specific components that
tie to Piaget's ideas with vocabulary such as clarification, evaluation, application or inference.
Pros & Cons of Everyday Math Curriculum
Everyday Math emphasizes cooperative learning.

Everyday Mathematics is a system of teaching mathematics designed by the University of Chicago. The system
has been implemented in many school districts across the nation including New York City school district and
Washington D.C. schools. While the Everyday Mathematics was developed to make learning math more
engaging to Kindergarten through sixth grade students, critics have charged that the learning system does not
arm students with mastery of basic math skills.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Practical Applications: Everyday Mathematics emphasizes math lessons based on practical applications rather
than on rote memorization, such as memorizing multiplication tables. The hope is that the lessons will be more
engaging by matter of relevance to real life. Lessons are often included as part of an activity that is related to
the student's life rather than solving a series of equations. A sample activity may include determining the ratio
of vowels in a teacher's name or examining better prices for goods at the store. Washington D.C. schools found
that students' mathematics scores improved by double in 2007 and 2009 after the district implemented an
Everyday Math curriculum. However, California schools had opposite results after implementing Everyday Math
in the early 1990s.
Reading Emphasis: Because Everyday Mathematics relies on practical application to teach lessons, the system
makes heavy use of word problems to communicate the narrative in which the problem is set. For children who
have difficulty reading, such as children from low-income areas, the emphasis on word problems may increase
the failure rate in mathematics. However, word problems are frequently the Achilles heel of elementary math
students. Everyday Math correctly identifies the lack of practice in understanding word problems in traditional
programs, though perhaps fails in making word problems its central

Group Activity / Pair Activity 4.1:
1. Define learning programme
2. Describe the process of programme implementation.
3. What are the advantages and disadvantages of bringing new learning programmes?

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

4.2 (ac2) - creative and critical thinking and
problem-solving

Much of the thinking done in formal education emphasizes the skills of analysis--teaching students how to
understand claims, follow or create a logical argument, figure out the answer, eliminate the incorrect paths and
focus on the correct one. However, there is another kind of thinking, one that focuses on exploring ideas,
generating possibilities, looking for many right answers rather than just one. Both of these kinds of thinking are
vital to a successful working life, yet the latter one tends to be ignored until after college. We might
differentiate these two kinds of thinking like this:

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Critical Thinking Creative Thinking

analytic generative

convergent divergent

vertical lateral

probability possibility

judgment suspended judgment

focused diffuse

objective subjective

answer an answer

left brain right brain

verbal visual

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

linear associative
reasoning richness, novelty
yes but yes and

In an activity like problem solving, both kinds of thinking are important to us. First, we must analyze the
problem; then we must generate possible solutions; next we must choose and implement the best solution;
and finally, we must evaluate the effectiveness of the solution. As you can see, this process reveals an
alternation between the two kinds of thinking, critical and creative. In practice, both kinds of thinking operate
together much of the time and are not really independent of each other.

What is Creativity?

An Ability. A simple definition is that creativity is the ability to imagine or invent something new. As we will see
below, creativity is not the ability to create out of nothing (only God can do that), but the ability to generate new
ideas by combining, changing, or reapplying existing ideas. Some creative ideas are astonishing and brilliant,
while others are just simple, good, practical ideas that no one seems to have thought of yet.

Believe it or not, everyone has substantial creative ability. Just look at how creative children are. In adults,
creativity has too often been suppressed through education, but it is still there and can be reawakened. Often
all that's needed to be creative is to make a commitment to creativity and to take the time for it.

An Attitude. Creativity is also an attitude: the ability to accept change and newness, a willingness to play with
ideas and possibilities, a flexibility of outlook, the habit of enjoying the good, while looking for ways to improve
it. We are socialized into accepting only a small number of permitted or normal things, like chocolate-covered
strawberries, for example. The creative person realizes that there are other possibilities, like peanut butter and
banana sandwiches, or chocolate-covered prunes.

A Process. Creative people work hard and continually to improve ideas and solutions, by making gradual
alterations and refinements to their works. Contrary to the mythology surrounding creativity, very, very few
works of creative excellence are produced with a single stroke of brilliance or in a frenzy of rapid activity. Much
closer to the real truth are the stories of companies who had to take the invention away from the inventor in
order to market it because the inventor would have kept on tweaking it and fiddling with it, always trying to
make it a little better.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

The creative person knows that there is always room for improvement.

Creative Methods

Several methods have been identified for producing creative results. Here are the five classic ones:

Evolution. This is the method of incremental improvement. New ideas stem from other ideas, new solutions
from previous ones, the new ones slightly improved over the old ones. Many of the very sophisticated things
we enjoy today developed through a long period of constant incrementation. Making something a little better
here, a little better there gradually makes it something a lot better--even entirely different from the original.

For example, look at the history of the automobile or any product of technological progress. With each new
model, improvements are made. Each new model builds upon the collective creativity of previous models, so
that over time, improvements in economy, comfort, and durability take place. Here the creativity lies in the
refinement, the step-by-step improvement, rather than in something completely new. Another example would
be the improvement of the common wood screw by what are now commonly called drywall screws. They have
sharper threads which are angled more steeply for faster penetration and better holding. The points are self
tapping. The shanks are now threaded all the way up on lengths up to two inches. The screws are so much
better that they can often be driven in without pilot holes, using a power drill.

The evolutionary method of creativity also reminds us of that critical principle: Every problem that has been
solved can be solved again in a better way. Creative thinkers do not subscribe to the idea that once a problem
has been solved, it can be forgotten, or to the notion that "if it ain't broke, don't fix it." A creative thinker's
philosophy is that "there is no such thing as an insignificant improvement."

Synthesis. With this method, two or more existing ideas are combined into a third, new idea. Combining the
ideas of a magazine and an audio tape gives the idea of a magazine you can listen to, one useful for blind
people or freeway commuters.

For example, someone noticed that a lot of people on dates went first to dinner and then to the theater. Why
not combine these two events into one? Thus, the dinner theater, where people go first to eat and then to see a
play or other entertainment.

Revolution. Sometimes the best new idea is a completely different one, an marked change from the previous
ones. While an evolutionary improvement philosophy might cause a professor to ask, "How can I make my
lectures better and better?" a revolutionary idea might be, "Why not stop lecturing and have the students teach
each other, working as teams or presenting reports?"

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

For example, the evolutionary technology in fighting termites eating away at houses has been to develop safer
and faster pesticides and gasses to kill them. A somewhat revolutionary change has been to abandon gasses
altogether in favor of liquid nitrogen, which freezes them to death or microwaves, which bake them. A truly
revolutionary creative idea would be to ask, "How can we prevent them from eating houses in the first place?" A
new termite bait that is placed in the ground in a perimeter around a house provides one answer to this
question.

Reapplication. Look at something old in a new way. Go beyond labels. Unfixate, remove prejudices,
expectations and assumptions and discover how something can be reapplied. One creative person might go to
the junkyard and see art in an old model T transmission. He paints it up and puts it in his living room. Another
creative person might see in the same transmission the necessary gears for a multi-speed hot walker for his
horse. He hooks it to some poles and a motor and puts it in his corral. The key is to see beyond the previous or
stated applications for some idea, solution, or thing and to see what other application is possible.

For example, a paperclip can be used as a tiny screwdriver if filed down; paint can be used as a kind of glue to
prevent screws from loosening in machinery; dishwashing detergents can be used to remove the DNA from
bacteria in a lab; general purpose spray cleaners can be used to kill ants.

Changing Direction. Many creative breakthroughs occur when attention is shifted from one angle of a problem
to another. This is sometimes called creative insight.

A classic example is that of the highway department trying to keep kids from skateboarding in a concrete-lined
drainage ditch. The highway department put up a fence to keep the kids out; the kids went around it. The
department then put up a longer fence; the kids cut a hole in it. The department then put up a stronger fence;
it, too, was cut. The department then put a threatening sign on the fence; it was ignored. Finally, someone
decided to change direction, and asked, "What really is the problem here? It's not that the kids keep getting
through the barrier, but that they want to skateboard in the ditch. So how can we keep them from
skateboarding in the ditch?" The solution was to remove their desire by pouring some concrete in the bottom of
the ditch to remove the smooth curve. The sharp angle created by the concrete made skateboarding
impossible and the activity stopped. No more skateboarding problems, no more fence problems.

This example reveals a critical truth in problem solving: the goal is to solve the problem, not to implement a
particular solution. When one solution path is not working, shift to another. There is no commitment to a
particular path, only to a particular goal. Path fixation can sometimes be a problem for those who do not
understand this; they become overcommitted to a path that does not work and only frustration results.

Negative Attitudes That Block Creativity

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

1. Oh no, a problem! The reaction to a problem is often a bigger problem than the problem itself. Many people
avoid or deny problems until it's too late, largely because these people have never learned the appropriate
emotional, psychological, and practical responses. A problem is an opportunity. The happiest people welcome
and even seek out problems, meeting them as challenges and opportunities to improve things. Definition: a
problem is (1) seeing the difference between what you have and what you want or (2) recognizing or believing
that there is something better than the current situation or (3) an opportunity for a positive act. Seeking
problems aggressively will build confidence, increase happiness, and give you a better sense of control over
your life.

2. It can't be done. This attitude is, in effect, surrendering before the battle. By assuming that something cannot
be done or a problem cannot be solved, a person gives the problem a power or strength it didn't have before.
And giving up before starting is, of course, self fulfilling. But look at the history of solutions and the
accompanying skeptics: man will never fly, diseases will never be conquered, rockets will never leave the
atmosphere. Again, the appropriate attitude is summed up by the statement, "The difficult we do immediately;
the impossible takes a little longer."

3. I can't do it. Or There's nothing I can do. Some people think, well maybe the problem can be solved by some
expert, but not by me because I'm not (a) smart enough, (b) an engineer, or (c) a blank (whether educated,
expert, etc.) Again, though, look at the history of problem solving.

Who were the Wright brothers that they could invent an airplane? Aviation engineers? No, they were bicycle
mechanics. The ball point pen was invented by a printer's proofreader, Ladislao Biro, not a mechanical
engineer. Major advances in submarine design were made by English clergyman G. W. Garrett and by Irish
schoolmaster John P. Holland. The cotton gin was invented by that well known attorney and tutor, Eli Whitney.
The fire extinguisher was invented by a captain of militia, George Manby.

And so on. In fact, a major point made by recent writers about corporate excellence is that innovations in
industry almost always come from individuals (not research groups) outside of the area of the invention.
General Motors invented Freon, the refrigeration chemical, and tetraethyl lead, the gasoline additive.
Kodachrome was invented by two musicians. The continuous steel casting process was invented by a
watchmaker (fooling around with brass casting). Soap making chemists turned down the problem of inventing
synthetic detergents: those detergents were invented by dye making chemists.

In a nutshell, a good mind with a positive attitude and some good problem solving skills will go far in solving
any problem. Interest in and commitment to the problem are the keys. Motivation--a willingness to expend the
effort--is more important than laboratory apparatus. And remember that you can always do something. Even if
you cannot totally eradicate the problem from the face of the earth, you can always do something to make the
situation better.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

4. But I'm not creative. Everyone is creative to some extent. Most people are capable of very high levels of
creativity; just look at young children when they play and imagine. The problem is that this creativity has been
suppressed by education. All you need to do is let it come back to the surface. You will soon discover that you
are surprisingly creative.

5. That's childish. In our effort to appear always mature and sophisticated, we often ridicule the creative, playful
attitudes that marked our younger years. But if you solve a problem that saves your marriage or gets you
promoted or keeps your friend from suicide, do you care whether other people describe your route to the
solution as "childish?" Besides, isn't play a lot of fun? Remember that sometimes people laugh when something
is actually funny, but often they laugh when they lack the imagination to understand the situation.

6. What will people think? There is strong social pressure to conform and to be ordinary and not creative.

Here are some overheard examples:

Creative Person: "I like to put water in my orange juice so it's less sweet."
Ordinary Person: "You're weird, you know?"

Ordinary Person: "What are you doing?"
Creative Person: "We're painting our mailbox."
Ordinary Person: "You're crazy."

Creative Person: "Why don't we add a little garlic?"
Ordinary Person: "Because the recipe doesn't call for garlic."

Ordinary Person: "Why are you going this way? It's longer."
Creative Person: "Because I like the drive."
Ordinary Person: "Did anyone ever tell you you're strange?"

The constant emphasis we see in society is toward the ruthlessly practical and conformist. Even the wild
fashions, from those in Vogue to punk rock, are narrowly defined, and to deviate from them is considered
wrong or ridiculous. Some peoples' herd instinct is so strong that they make sheep look like radical
individualists.

So, what will people think? Well, they're already talking about you, saying that your nose is too big or your
shoes are funny or you date weird people. So, since others are going to talk about you in unflattering ways
anyway, you might as well relax and let your creativity and individualism flow.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Almost every famous contributor to the betterment of civilization was ridiculed and sometimes even jailed.
Think about Galileo. And look what happened to Jesus. Quotation: "Progress is made only by those who are
strong enough to endure being laughed at." Solutions are often new ideas, and new ideas, being strange, are
usually greeted with laughter, contempt, or both. That's just a fact of life, so make up your mind not to let it
bother you. Ridicule should be viewed as a badge of real innovative thinking.

7. I might fail. Thomas Edison, in his search for the perfect filament for the incandescent lamp, tried anything he
could think of, including whiskers from a friend's beard. In all, he tried about 1800 things. After about 1000
attempts, someone asked him if he was frustrated at his lack of success. He said something like, "I've gained a
lot of knowledge--I now know a thousand things that won't work."

Fear of failure is one of the major obstacles to creativity and problem solving. The cure is to change your
attitude about failure. Failures along the way should be expected and accepted; they are simply learning tools
that help focus the way toward success. Not only is there nothing wrong with failing, but failing is a sign of
action and struggle and attempt--much better than inaction. The go-with-the- flow types may never fail, but
they are essentially useless to humanity, nor can they ever enjoy the feeling of accomplishment that comes
after a long struggle.

Suppose you let your fear of failure guide your risk taking and your attempts. You try only three things in a year
because you are sure of succeeding. At the end of the year the score is: Successes 3, Failures 0. Now suppose
the next year you don't worry about failing, so you try a hundred things. You fail at 70 of them. At the end of the
year the score is Successes 30, Failures 70. Which would you rather have--three successes or 30--ten times as
many? And imagine what 70 failures will have taught you. Proverb: Mistakes aren't fun, but they sure are
educational.

Myths about Creative Thinking and Problem Solving

1. Every problem has only one solution (or one right answer). The goal of problem solving is to solve the
problem, and most problems can be solved in any number of ways. If you discover a solution that works, it is a
good solution. There may be other solutions thought of by other people, but that doesn't make your solution
wrong. What is THE solution to putting words on paper? Fountain pen, ball point, pencil, marker, typewriter,
printer, Xerox machine, printing press?

2. The best answer/solution/method has already been found. Look at the history of any solution set and you'll
see that improvements, new solutions, new right answers, are always being found. What is the solution to
human transportation? The ox or horse, the cart, the wagon, the train, the car, the airplane, the jet, the SST? Is
that the best and last? What about pneumatic tubes, hovercraft, even Star Trek type beams?

What is the best way to put words on paper? The word processor? Is that the last invention? How about voice
recognition, or thought wave input?

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

On a more everyday level, many solutions now seen as best or at least entrenched were put in place hastily
and without much thought--such as the use of drivers' licenses for ID cards or social security numbers for
taxpayer ID numbers. Other solutions are entrenched simply for historical reasons: they've always been done
that way. Why do shoe laces still exist, when technology has produced several other, better ways to attach
shoes to feet (like velcro, elastic, snap buttons, and so on)?

3. Creative answers are complex technologically. Only a few problems require complex technological solutions.
Most problems you'll meet with require only a thoughtful solution requiring personal action and perhaps a few
simple tools. Even many problems that seem to require a technological solution can be addressed in other
ways.

For example, what is the solution to the large percentage of packages ruined by the Post Office? Look at the
Post Office package handling method. Packages are tossed in bins when you send them. For the solution, look
at United Parcel. When you send a package, it is put on a shelf. The change from bin to shelf is not a complex
or technological solution; it's just a good idea, using commonly available materials.

As another example, when hot dogs were first invented, they were served to customers with gloves to hold
them. Unfortunately, the customers kept walking off with the gloves. The solution was not at all complex: serve
the hot dog on a roll so that the customer's fingers were still insulated from the heat. The roll could be eaten
along with the dog. No more worries about disappearing gloves. (Note by the way what a good example of
changing direction this is. Instead of asking, "How can I keep the gloves from being taken?" the hot dog server
stopped thinking about gloves altogether.)

4. Ideas either come or they don't. Nothing will help. There are many successful techniques for stimulating idea
generation. We will be discussing and applying them.

Mental Blocks to Creative Thinking and Problem Solving

1. Prejudice. The older we get, the more preconceived ideas we have about things. These preconceptions often
prevent us from seeing beyond what we already know or believe to be possible. They inhibit us from accepting
change and progress.

Example problem: How to connect sections of airplanes with more ease and strength than using rivets. A
modern solution is to use glue--glue the sections together. We probably wouldn't think of this solution
because of our prejudice about the word and idea of glue. But there are many kinds of glue, and the kind used
to stick plane parts together makes a bond stronger than the metal of the parts themselves.

Another problem: How can we make lighter weight bullet proof windows? Thicker glass is too heavy. Answer:
Use plastic. Again, we are prejudiced against plastic. But some plastics are not flimsy at all and are used in
place of steel and in bullet proof windows.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Another problem: Make a ship's hull that won't rust or rot like steel or wood. Solution: Use concrete. Our
prejudice is that concrete is too heavy. Why not make lightweight concrete? That's what's done.

Final example: How to divide a piece of cake equally between two kids so they won't complain that one kid is
preferred over the other: "You gave him the bigger piece; you like him better! Waaaah!" Solution: Put the kids in
charge of dividing the cake. Our prejudice is that immature, selfish kids can't do the job. But the solution, one
cuts the cake, the other has first choice of pieces, works very well.

2. Functional fixation. Sometimes we begin to see an object only in terms of its name rather in terms of what it
can do. Thus, we see a mop only as a device for cleaning a floor, and do not think that it might be useful for
clearing cobwebs from the ceiling, washing the car, doing aerobic exercise, propping a door open or closed,
and so on. (Later on in the semester, we will be doing "uses for" to break out of this fixation.)

There is also a functional fixation of businesses. In the late nineteenth and early twentieth centuries the
railroads saw themselves as railroads. When automobiles and later airplanes began to come in, the railroads
didn't adapt. "That's not our business," they said. But if they had seen themselves as in the people
transportation business rather than in the railroad business, they could have capitalized on a great opportunity.

Similarly, when the telephone began its rise, some of the telegraph companies said, "That's not our business;
we're telegraph companies." But if they had said, "Hey, we're in the communication business, and here's a new
way to communicate," they would have grown rather than died. Compare Western Union to AT&T. And have
you heard of those big calculator companies Dietzgen or Pickett? No? Well, they were among the biggest
makers of slide rules. But when electronic calculators began to rise, they didn't know what business they were
in. They thought they were in the slide rule business, when they were really in the calculator business. They
didn't adapt, they didn't accept the challenge of change and opportunity, and they fell.

And there's a functional fixation of people, too. Think a minute how you react when you see your pastor
mowing his lawn, or your auto mechanic on a television show promoting a book. Stereotyping can even be a
form of functional fixation--how many people would laugh at a blonde quoting Aristotle? Too often we permit
only a narrow range of attitudes and behaviours in other people, based on bias, prejudice, hasty generalization,
or limited past experience. Think of those statements like, "I can't believe he said that," or "Imagine her doing
that," and so on. But recall the proverb, "The goal of my life is not to live down to your expectations."

3. Learned helplessness. This is the feeling that you don't have the tools, knowledge, materials, ability, to do
anything, so you might as well not try. We are trained to rely on other people for almost everything. We think
small and limit ourselves. But the world can be interacted with.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

If you are in need of information, there are libraries, bookstores, friends, professors, and, of course, the Internet.
And there are also city, county, and state government agencies with addresses and phone numbers and web
sites. There are thousands of government agencies that really exist and that will talk to you. Contact the EPA if
you're working on air pollution or pesticides. Get some government publications. Call your state senator or
federal congressman for help on bills, information, problems. Contact the manufacturer of a product to find out
what you want to know about it.

If you are technologically poor, you can learn. Learn how to cook, use tools, make clothes, use a computer. You
can learn to do anything you really want to do. All you need is the motivation and commitment. You can learn
to fly an airplane, drive a truck, scuba dive, fix a car--name it.

4. Psychological blocks. Some solutions are not considered or are rejected simply because our reaction to
them is "Yuck." But icky solutions themselves may be useful or good if they solve a problem well or save your
life. Eating lizards and grasshoppers doesn't sound great, but if it keeps you alive in the wilderness, it's a good
solution.

Perhaps more importantly, what at first seem to be icky ideas may lead to better solutions--de-ickified
analogues of the original. When doctors noted that some unsophisticated natives were using giant ant heads
to suture wounds, they imitated this pincer-closing technique by inventing the surgical staple.

Psychological blocks prevent you from doing something just because it doesn't sound good or right, which is a
pretty ridiculous thing. Overcoming such blocks can be really beneficial. Navy commandos in Vietnam
overcame their blocks and put on women's panty hose when they marched through the swamps and jungle.
The pantyhose cut down on the friction and rubbing from the plants and aided in removing the dozens of
leeches after a mission. Overcoming the block to using your own blood to write a help note could save your life
someday if you got kidnapped.

Positive Attitudes for Creativity

1. Curiosity. Creative people want to know things--all kinds of things-- just to know them. Knowledge does not
require a reason. The question, "Why do you want to know that?" seems strange to the creative person, who is
likely to respond, "Because I don't know the answer." Knowledge is enjoyable and often useful in strange and
unexpected ways.

For example, I was once attempting to repair something, without apparent success, when an onlooker asked
testily, "Do you know what you're doing?" I replied calmly, "No, that's why I'm doing it."

Next, knowledge, and especially wide ranging knowledge, is necessary for creativity to flourish to its fullest.
Much creativity arises from variations of a known or combinations of two knowns. The best ideas flow from a
well equipped mind. Nothing can come from nothing.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

In addition to knowing, creative people want to know why. What are the reasons behind decisions, problems,
solutions, events, facts, and so forth? Why this way and not another? And why not try this or that?

The curious person's questioning attitude toward life is a positive one, not a destructive one reflecting
skepticism or negativism. It often seems threatening because too often there is no good reason behind many
of the things that are taken for granted--there is no "why" behind the status quo.

So ask questions of everyone. Ask the same question of different people just to be able to compare the
answers. Look into areas of knowledge you've never before explored, whether cloth dying, weather
forecasting, food additives, ship building, the U.S. budget, or the toxicity of laundry detergents.

2. Challenge. Curious people like to identify and challenge the assumptions behind ideas, proposals, problems,
beliefs, and statements. Many assumptions, of course, turn out to be quite necessary and solid, but many
others have been assumed unnecessarily, and in breaking out of those assumptions often comes a new idea, a
new path, a new solution.

For example, when we think of a college, we traditionally think of a physical campus with classrooms, a library,
and some nice trees. But why must college be a place (with congregated students and faculty) at all? Thus, the
electronic college now exists, where students "go" to college right at home, online. Correspondence courses
have existed for years, too, beginning with the challenging of the school-as-centralized-place idea.

When we think of an electric motor, we automatically think of a rotating shaft machine. But why assume that?
Why can't an electric motor have a linear output, moving in a straight line rather than a circle? With such a
challenged assumption came the linear motor, able to power trains, elevators, slide locks, and so on.

Problem: We make brandy, and for this special edition of our finest kind, we want a fully-grown pear in one
piece inside each bottle. The bottle is narrow necked. How can we do it? As you think, watch for the
assumptions you are making. Possible solutions (assuming fully grown pear): close the neck or bottom after
insertion, use a plastic bottle like heat-shrink tubing, change to a wide mouth bottle. If we do not assume a
fully grown pear: grow the pear from a bud inside the bottle.

3. Constructive discontent. This is not a whining, griping kind of discontent, but the ability to see a need for
improvement and to propose a method of making that improvement. Constructive discontent is a positive,
enthusiastic discontent, reflecting the thought, "Hey, I know a way to make that better."

Constructive discontent is necessary for a creative problem solver, for if you are happy with everything the way
it is, you won't want to change anything. Only when you become discontent with something, when you see a
problem, will you want to solve the problem and improve the situation.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

One of the hallmarks of the constructively discontented person is that of a problem seeking outlook. The more
problems you find, the more solutions and therefore improvements you can make. Even previously solved
problems can often be solved again, in a better way. A constructively discontent person might think, "This is an
excellent solution, but I wonder if there isn't another solution that works even better (or costs less, etc)."

Another mark of constructive discontent is the enjoyment of challenge. Creative people are eager to test their
own limits and the limits of problems, willing to work hard, to persevere and not give up easily. Sometimes the
discontent is almost artificial--they aren't really unhappy with the status quo of some area, but they want to find
something better just for the challenge of it and the opportunity to improve their own lives and those of others.

4. A belief that most problems can be solved. By faith at first and by experience later on, the creative thinker
believes that something can always be done to eliminate or help alleviate almost every problem. Problems are
solved by a commitment of time and energy, and where this commitment is present, few things are impossible.

The belief in the solvability of problems is especially useful early on in attacking any problem, because many
problems at first seem utterly impossible and scare off the fainter hearted. Those who take on the problem
with confidence will be the ones most likely to think through or around the impossibility of the problem.

5. The ability to suspend judgment and criticism. Many new ideas, because they are new and unfamiliar, seem
strange, odd, bizarre, even repulsive. Only later do they become "obviously" great. Other ideas, in their original
incarnations, are indeed weird, but they lead to practical, beautiful, elegant things. Thus, it is important for the
creative thinker to be able to suspend judgment when new ideas are arriving, to have an optimistic attitude
toward ideas in general, and to avoid condemning them with the typical kinds of negative responses like, "That
will never work; that's no good; what an idiotic idea; that's impossible," and so forth. Hospital sterilization and
antiseptic procedures, television, radio, the Xerox machine, and stainless steel all met with ho-hums and even
hostile rejection before their persevering inventors finally sold someone on the ideas.

Some of our everyday tools that we now love and use daily, were opposed when they were originally
presented: Aluminum cookware? No one wants that. Teflon pans? They'll never sell. Erasers on pencils? That
would only encourage carelessness. Computers? There's no market for more than a few, so why build them?

Remember then that (1) an idea may begin to look good only after it becomes a bit more familiar or is seen in a
slightly different context or clothing or circumstance and (2) even a very wild idea can serve as a stepping
stone to a practical, efficient idea. By too quickly bringing your judgment into play, these fragile early ideas and
their source can be destroyed. The first rule of brainstorming is to suspend judgment so that your idea-
generating powers will be free to create without the restraint of fear or criticism. You can always go back later
and examine--as critically as you want--what you have thought of.

Proverb: "A crank is a genius whose idea hasn't yet caught on."

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

6. Seeing the good in the bad. Creative thinkers, when faced with poor solutions, don't cast them away. Instead,
they ask, "What's good about it?" because there may be something useful even in the worst ideas. And
however little that good may be, it might be turned to good effect or made greater.

Example problem: How can we get college students to learn grammar better? Solution: Spank their bottoms
with a hickory stick. This isn't a good solution, partly because it's probably illegal. But should we just toss it out?
Why not ask what's good about it? (1) it gives individual, attention to the poor performers, (2) it gives them
public attention, (3) it motivates other students as well as the student being spanked, (4) it's easy and costs
nothing. The next question is, Can we adapt or incorporate some of these good things into a more acceptable
solution, whether derivative of the original or not?

We easily fall into either/or thinking and believe that a bad solution is bad through and through, in every
aspect, when in fact, it may have some good parts we can borrow and use on a good solution, or it may do
inappropriately something that's worth doing appropriately. And often, the bad solution has just one really
glaring bad part, that when remedied, leaves quite a good solution. In the above example, changing the
physical spanking to a verbal spanking changes the entire aspect of the solution while keeping all the good
points we identified.

7. Problems lead to improvements. The attitude of constructive discontent searches for problems and possible
areas of improvement, but many times problems arrive on their own. But such unexpected and perhaps
unwanted problems are not necessarily bad, because they often permit solutions that leave the world better
than before the problem arose.

For example, the first margarine was made from beef fat, milk, water, and chopped cow udder. It wasn't
extremely tasty or healthy. Then about the turn of the century a shortage of beef fat created a problem. What
to use? The margarine makers turned to vegetable fats from various plants and the soybean, corn, and
sunflower oils they used are still used today. The margarine is healthier and tastes better.

Or think about exams or papers. When you don't do as well as you want, you think, "Oh no!" But actually, you
have a good insight into what you don't know and still need to learn. You are aware of the geography of your
knowledge in a much more detailed form than before the errors showed up.

8. A problem can also be a solution. A fact that one person describes as a problem can sometimes be a
solution for someone else. Above we noted that creative thinkers can find good ideas in bad solutions. Creative
thinkers also look at problems and ask, "Is there something good about this problem?"

For example, soon after the advent of cyanoacrylate adhesives (super glue), it was noted that if you weren't
careful, you could glue your fingers together with it. This problem--a permanent skin bond--was soon seen as
a solution, also. Surgeons in Viet Nam began to use super glue to glue wounds together.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Another example, also involving glue: 3M chemists were experimenting with adhesives and accidentally came
up with one that was so weak you could peel it right back off. Hold strength, shear strength, all were way below
the minimum standards for any self-respecting adhesive. A glue that won't hold? Quite a problem. But this
problem was also a solution, as you now see in Post-It Notes.

9. Problems are interesting and emotionally acceptable. Many people confront every problem with a shudder
and a turn of the head. They don't even want to admit that a problem exists--with their car, their spouse, their
child, their job, their house, whatever. As a result, often the problem persists and drives them crazy or rises to a
crisis and drives them crazy.

Creative people see problems as interesting challenges worth tackling. Problems are not fearful beasts to be
feared or loathed; they are worthy opponents to be jousted with and unhorsed. Problem solving is fun,
educational, rewarding, ego building, helpful to society.

Miscellaneous Good Attitudes

1. Perseverance. Most people fail because they spend only nine minutes on a problem that requires ten
minutes to solve. Creativity and problem solving are hard work and require fierce application of time and
energy. There is no quick and easy secret. You need knowledge gained by study and research and you must
put your knowledge to work by hard thinking and protracted experimentation. You’ve surely read of the
difficulties and setbacks faced by most of the famous inventors--how many filaments Edison tried before he
found a working one, how many aircraft designs failed in the attempt to break the sound barrier. But planning
to persevere is planning to succeed.

2. A flexible imagination. Creative people are comfortable with imagination and with thinking so-called weird,
wild, or unthinkable thoughts, just for the sake of stimulation. During brainstorming or just mental playfulness,
all kinds of strange thoughts and ideas can be entertained. And the mind, pragmatist that it is, will probably find
something useful in it all. We will look at several examples of this later on.

3. A belief that mistakes are welcome. Modern society has for some reason conceived the idea that the only
unforgivable thing is to fail or make a mistake. Actually failure is an opportunity; mistakes show that something
is being done. So creative people have come to realize and accept emotionally that making mistakes is no
negative biggie. One chief executive of a big American corporation warns all his newly hired managers, "Make
sure you make a reasonable number of mistakes." Mistakes are educational and can lead to success--because
they mean you are doing something.

Sir Francis Pettit Smith, one of the early developers of the screw propeller, tried one design in 1836. During the
test, half of it broke off--what a failure--but then the boat increased in speed substantially, revealing the
efficiency of a new design, formed from a mistake.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

In sum, as Vergil once said, "They can who think they can." Having the proper positive attitude about generating
new and useful ideas and solving problems is really a large part of the whole process.

A few years ago, the pipes in my mom's house had finally rusted through and I was faced with the task of
finding a plumber to get a bid. Knowing how much they charge for small repairs, I knew that doing a whole
house would cost a fortune. I thought, "You know, I'd really like to do this job myself, but I wonder if I can." My
neighbor happened to be around once when I said this, and he said, "Oh, you can do it." Just that simple
expression gave me the positive attitude I needed to do it. So I did.

Characteristics of the Creative Person

 curious
s  eeks problems
 enjoys challenge
 optimistic
a  ble to suspend judgment
c  omfortable with imagination
 sees problems as opportunities
s  ees problems as interesting
p  roblems are emotionally acceptable
c  hallenges assumptions
d  oesn't give up easily: perseveres, works hard

Group Activity / Pair Activity 4.2:
1. Define creativity
2. Why is creativity important to learners
3. Demonstrate through an activity how you can incorporate creativity in numeracy.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

4.3 (ac3) - Children working with number, space,
shape, data and patterns

Fun Math Activities to Learn the Number Four

With a little creativity, students can learn about the number four in a fun, interactive way.

Teaching young children to recognize and name numbers is simple. Additionally, it is important for children
understand the meaning of a number, and an educator must provide opportunities for exploration. One great
way to do this is through hands-on, interactive applications and games involving numbers. Learning to
recognize and name the number four can be great fun.

I Spy

A fun way to teach the number four is to give students an opportunity to find the number four around the
classroom, school and home. You can begin this game by playing a version of I Spy. State to the students, "I spy
the number four, and it's on the cover of a book." Allow students a chance to find the book containing the
number four and place in it the classroom in view for the remainder of the day. Continue the game until kids
find several objects that display the number.

Make a Necklace

To help students practice counting to four, allow them to make a necklace from beads or fruit loops. Have
students place the beads or fruit loops in patterns of four. For example, four red beads and then four blue
beads. Kids can complete this activity by creating patterns by gluing everyday objects onto paper as well.

Four No More

Allow three students to play Four No More, a version of Slap Jack that requires students to be on the lookout
for a four as the deck is dealt on the table. One student should be the dealer and will turn up one card at a time
onto the table. When a four appears, the first student to hit it and say "Four No More" will get to keep the four
and all the cards beneath it. Play continues until the deck is gone and the player with the most fours wins.

For this game, creating your own deck of cards without the face cards and with more fours would be best
practice.

Activities for Kids on Personal Space

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

There are times during play when it is appropriate to enter someone's personal space.
Children with special needs, particularly those with autism-related disorders, may have a difficult time
understanding the concept of personal space. As a result, they may invade the personal space of others
making them feel uncomfortable. They may also allow others to inappropriately enter their spaces. For their
safety and appropriate socialization, parents and teachers must teach children about personal space, how to
respect the spaces of others, and how to protect their own personal spaces.
Space Spin & Tag: This activity is helpful for introducing the concept of personal space and works best with an
individual student or a small group. Have students spread out their arms and spin slowly two or three times.
Explain that the circles are their personal spaces. If they get so close to another person that they would be hit
by that person's arms when they spin, they have invaded that child's personal space. Tell the students that you
will play a game of tag, but instead of touching the other person; you only have to enter their personal space
for them to be "it." Play tag for several rounds so all the students get a chance to be "it."
Personal Space Circles: Have your students spread out and sit on the floor pretzel-style. Give each child a jump
rope. Have her form the rope into a circle around herself on the floor. Explain that this circle represents her
personal space. Have her make the smallest circle she can with the rope. When the circle is close, this
represents the personal space with her family. Explain that family and close friends can move into her space
more because she feels more comfortable with them. Have her make the circle a little bigger. Tell her that with
friends and people she doesn't know as well, she needs more personal space. Have her make the largest circle
she can with her rope. Explain that with strangers, she needs much more personal space because she doesn't
know them. The size of her personal space depends upon how well she knows someone.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Personal Space Role-Play: Once you have introduced the concept of personal space, use role playing to act
out situations when you must share your personal space. As a group, brainstorm a list of times when it is
appropriate to allow someone into your personal space: greeting someone with a handshake, sitting beside
someone on a bus, or when you visit the doctor or dentist. You can also use role-play to allow students to react
to inappropriate invasion of their personal spaces. Students can practice asking others to respect their personal
spaces.
Social Stories: Children with autism-related disorders often use social stories to help them internalize social
skills. However, these stories can be used with any child who struggles with social behaviours. Social stories
are written in first person. If a child often invades others' personal space, he can write about what he does, how
it makes others feel and what he can do differently. A social story about personal space might be, "I sometimes
stand too close to people. It can make them mad or uncomfortable. I need to stand an arm's length away from
people who are not in my family." This helps the student see what he is doing, how it affects others and what he
can do to change the behaviour.
Children's Activities on Shapes

Learning about shapes prepares children for higher math concepts.
Children typically start to identify shapes by the age of 3. Patterns and shapes are considered to be pre-math
skills and help prepare preschool-age children for the higher math concepts they will need as they enter
school. Several activities can successfully introduce shapes to young children and involve simple materials
such as markers, paints, glue and scissors. Most of these activities require adult supervision.
Circles

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Cardboard Roll Binoculars
Items needed:
2 toilet paper cardboard rolls
1 pipe cleaner
String or ribbon
Paint or markers
Scissors
Paint or colour the rolls as desired. For added emphasis on circles, paint circles on the rolls. When they are dry,
use scissors to poke a hole in each of the rolls, an inch from the top. Thread the pipe cleaner through the rolls,
securing them together. This is also the nose piece, so bend it slightly to go over the nose. If desired, poke
small holes in the rolls on the outside edge and pull a string or ribbon through, knotting it on each end, to make
a strap for the neck.
Circle Caterpillar Craft
Items Needed:
2 toilet paper or 1 paper towel cardboard roll
1 pipe cleaner cut in half
String or ribbon
Cut the rolls into 8 equal, circular rings. To incorporate color recognition, have the child paint each ring a
different color. Once paint is dry, poke a hole through each ring and string together on the ribbon. Knot the
ends to hold the links together. For antennae, poke two holes in the first ring, near the top. Thread the pipe
cleaners through. Add eyes.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Rainbow Paper Craft
Items Needed:
Construction paper: red, orange, yellow, green, blue, purple
Glue
Pencil
Draw a 9" circle on the red paper, a 8" circle on the orange, 7" on the yellow; proceed with the remaining
colours, making each circle an inch smaller than the one before. Have the child cut out the circles. Glue them
one top of each other, starting with the red, then orange, yellow and so on. When the glue dries, cut in half and
you have two rainbows.

Squares
Square Collage
Items Needed:
Different coloured sheets of construction paper
Cut several different-sized squares out of the paper and glue onto another sheet of paper. Make a collage or
see what kind of things can be made. A robot? A house?
A city?
Animal Square Puppets
Items needed:
Construction paper, in assorted colours
Craft sticks

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Cut squares from the paper and let the kids draw animal faces on the them. Then glue to the top of the craft
sticks to make little puppets.
Square Puzzle
Craft foam or construction paper
Ruler
Cardboard
Cut the cardboard into a 5 and 1/2 inch by 5 and 1/2 inch square. Then cut four 1/2" squares, six 1" squares,
three 1 1/2" squares, one 2" square and two 2 1/2" squares. These are your puzzle pieces. Let the kids fit them
all together on the cardboard square. They may not overlap each other or the edge of the cardboard.
Triangles

Triangle Fish
2 different colors of construction paper
Cut a large triangle from one color of paper. Cut a medium and small triangle with the remaining color. Lay the
large triangle down, halfway overlapping the medium one with their points both facing the same direction.
Glue together where they overlap. Add the small triangle as a fin on the large triangle. Glue to secure. Decorate
fish. You can also glue the finished product to a craft stick to make a fish puppet.
Tasty Triangles
Small pretzel sticks (6 per triangle)
Gumdrops (4 per triangle)
Connect 3 of the gumdrops with the pretzel sticks in a triangle formation. Then insert a pretzel stick in the top
of each gumdrop and bring together at the top with another gumdrop. 3-D triangles that taste good, too!

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Royal Crown
Paper dinner plate
Glitter Glue (optional)
Beads (optional)
Find the center of the plate and make a dot. Draw lines from the dot down to the inner ring of the plate. (It's OK
if they are not the same size.) Have the child color each triangle. Poke scissors through the center of the plate
and cut down the two sides of each triangle, leaving it attached at the base. Fold the triangles out, so it looks
like a "crown". Have the child decorate with beads, markers and glitter glue.

General Shape Activities
Simple puzzles incorporate shape identification, as well as an introduction to patterns and spacial awareness.
Introduce even the youngest child to pre-math concepts with blocks, which come in many shapes, sizes and
textures.
Cut a variety of different shapes out of sturdy card stock or cardboard, in many different sizes. Put them all in a
bag and let the child try to identify the shape by feel.
Switch up a game of musical chairs; cut out squares or any other desired shape and use them in place of
chairs.
Use a cookie cutter and cut sandwiches into different shapes.
Have a scavenger hunt in the house. See how many shapes can be found in the child's own surroundings. They
might be surprised!

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Group Activity / Pair Activity 4.3:
1. Design a game based on numbers for kids in Grade R
2. Create a game using shapes
3. Design a fun game so that learners may learn to utilize space.

4.4 (ac4) - CHILDREN WORK individually, in
pairs, and in small and large groups. 

How to Promote Independent Learning in the Primary Classroom

Promote independent learning by creating consistent classroom routines and procedures.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Allowing students to take ownership and initiative in their learning gives them the confidence needed to
succeed as lifelong learners. Creating independent learners requires a structured classroom with clear
expectations, routines and procedures. The teacher must create an atmosphere where children feel confident
as learners, secure enough in their environment to take risks and comfortable enough with routines to work
independently and help others. Children in the primary classroom can actually handle a lot of responsibility if
they are explicitly taught what to do and when to do it.

Establish clear procedures. Students need to know exactly what to do when they finish their work, where to put
finished/unfinished work, how to access supplies, how to enter/leave the classroom and how to get help.
Procedures are unique to each classroom depending on the grade level and the teacher. Teach students these
procedures by modelling for them, then role-playing and practicing procedures on a daily basis until they are
automatic for the majority of students. When students know exactly what to do they develop a sense of
confidence, responsibility and independence?

Set up learning centers in the classroom designed to hold a group of three to five students with supplies to
work on a specific subject or activity. Subjects for centers might include reading, math, art, spelling, geography
or computers. This allows the teacher time to work individually with students or small groups and allows
students time for self-directed and independent learning.

Assign open-ended learning activities. Allowing students to choose what they want to write about, which book
they want to read or what math game they want to play gives them a sense of ownership in their learning. It
also lets them begin to see what their interests are, what they excel at and what they need to work on.

Celebrate successes. Students will respond well to praise and will be motivated to perform their best. Create a
classroom environment where students celebrate each others' successes, willingly help each other and take
pride in a job well done. Post student work around the classroom, allow students to present work and skills
they are proud of, recognize independent learning and praise students often

Get Acquainted Activities for Kids in Pairs

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Once kids are acquainted, they can work together as a team.
Educators and community leaders often use get acquainted activities for kids in pairs to help break the ice with
a new group of children. Everyone gets to know each other and it builds team spirit. Pair children up randomly
or boy-girl, but do not pair up children who were friends prior to coming into the new class. You want to form
new friendships and create a true getting-to-know-you activity.
Summer Break
Children are most often in a new classroom after summer vacation. Create a getting-acquainted activity by
pairing up all the children for a book report project. Each person shares one memorable summer event while
his partner writes an outline of it as if it were a book. After each child recalls his summer, students write and
illustrate the story into a book report form, broken down into setting, characters and plot. The pairs then go in
front of the classroom and present their reports.
Introductions
Break the ice with a new group by having each child introduce the person next to him by making up two
statements about him. One statement is the child's favourite colour, and the other is something he likes. The
children can ask each other what their names are. Make sure nobody has really talked to each other before the
introductions so they are silly and completely impromptu. How it works: Group everyone into quick pairs based
on where they are sitting. One child says, "This is Mary. Her favourite colour is purple and she likes to eat ice
cream." Afterwards, everyone can reveal real things about themselves.
News Reporters

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Pair the children up to play news reporters. Explain to the children that everyone is going to be a news reporter
and find interesting news stories about his partner. The children can ask each other question about their
families, favourite hobbies and sports. After the news reporting session is over, each reporter gives a report
about his partner. Invite the class to ask each news reporter questions about his subject, such as, "What is the
name of his pets?"

Games

Break the group into pairs for a quick game between each pair. One game idea is rock, paper, scissors, where
the children hold up a fist for a rock, an open hand for paper and two fingers for scissors. In the game, rock
beats scissors, paper beats rock and scissors beat paper. Allow the children to play five rounds and then switch
partners until everyone has played each other. A game breaks up any first-day jitters and introduces everyone
to each other with a fun activity.

How to Teach Group Work

As a cooperative learning technique, group work is a great way to motivate and engage students. However,
group work is a difficult technique to teach. Much of the actual teaching of group work is laying down important
principles for the actual work to take place. Here are some tips and principles that help create successful
group work lessons.

Discuss with the class the advantages of group work. Many students are not convinced of the benefits of
cooperative learning. Brainstorm with the class some of the benefits of working as a team and in groups,
especially after school. I have actually started group work in this way by asking this question. A volunteer then
acted as a group secretary and shared the group's answers in class.

Start the lesson by teaching the whole class together. Provide enough ground material that is necessary and
important for carrying out the group task. Explain to the class that their success on the task depends on how
well they understood the material and helped their fellow students.

Go through a trial run of instructions and explanations, modeling wherever necessary. Understanding the task
is critical for success. Encourage students to also ask their peers for help and clarification. Make sure students
understand that you will act as a facilitator as you visit from group to group. Keep the instructions very short
and simple.

Assign group responsibilities. Responsibilities can include a time keeper, a group secretary who takes notes,
and a group helper who is in charge of making sure everybody understands.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Distribute a group accountability page. Group accountability is an important part of group work. On this page,
students should fill out the following information:1. The names of the students in the group and those who
were present2. The group name (if applicable)3. The date4. The group task5. What each member of the group
did6. What each member of the group will do for homework.Make sure that each member records his/her
homework assignment. Collect these pages at the end of the lesson. I usually sign my name verifying that they
truly worked in class. These accountability forms represent 10 percent of their final group contribution grade.
Give a time limit for group work. If you are working on a long-term in-class assignment like research projects,
make sure students know how long you plan on using group work. Make sure students know exactly how
much time will be devoted to group work. I also tell my students 5 minutes before the end of the group work
activity that they need to start finishing up.
Give students time to finish the necessary activity.
Always leave 5 to 7 minutes before the end of the group work activity for summing up the group work activity
and/or allowing students to reflect on what they had learned.

Group Activity / Pair Activity 4.4:
1. Design an individual activity for learners in Grade R.
2. Design a pair activity that is practical for learners.
3. Design an activity that is to be conducted by learners in a large group.

so5: Assess children's progress in the
Numeracy Learning Programme. 

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Learner Tip:
How to Assess a Child's Math Level
It's always a good idea to assess a child's math level at the beginning, middle and end of the school year. Here
is an easy way to assess it.

Other People Are Reading

Instructions
1. Ask the students to identify the numbers 1 through 30 and be sure that they are out of order.
2. Ask the students to perform several simple addition problems.
3. Ask the students to perform several simple subtraction problems. Only very advanced kindergartners
will be able to perform these.
4. Ask the students to copy and extend an ABC pattern with unifix cubes. Then ask them to copy and
extend an ABBC pattern and so on.
5. Show the students a few different numbers and ask which is greatest. Show them a few that are the
same and see if they recognize they are equal.
6. Ask the students to count as high as they can verbally.

5.1 (ac1) – assessing child's progress in the
Numeracy Learning Programme

Ways to Assess in Math Class

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Written tests offer one form of assessment.
Math assessments allow the teacher to determine student understanding of mathematical concepts. Both
formal and informal assessments work for math class, allowing you to see how students perform under
different conditions. Some children excel at written exams, while others get nervous and perform poorly.
Incorporating a variety of assessment methods gives a well-rounded picture of each child's math skills.
Written Evaluations
Traditional paper and pencil assessments remain a common method of evaluating students' math skills. Daily
worksheets or written assignments from the textbook create the main component of practicing and assessing
the math concepts taught in class. Quizzes and tests serve as an evaluation of the students' skills without the
textbook or other aids nearby to help them with the problems. Written evaluations provide a concrete way to
look at math skills in the classroom.
Math Projects
Math projects require the students to apply math skills to a real-world situation. Examples of math projects
include measuring objects around the school, following a recipe or splitting a bag of candy between a small
group of kids. To create a tangible assessment from the projects, include a tracking sheet for the kids to record
their observations and conclusions. For example, design a chart for the students to write down their
measurements.
Rubrics

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

A rubric consists of a rating scale used to assess a student's skills. The scale typically includes between three
and five rating options to indicate if a child doesn't understand the concept at all, has it mastered or falls
somewhere in between. For a math rubric, break down the chapter into specific concepts. If you're studying
money, include things like understanding values of individual coins and the ability to trade in coins for the
same value. Assess each child individually using the rubric, either by casual observation as he works or by
pulling aside each student to observe him doing a task related to the concept. For a money assessment,
present the child with several coins and ask him to choose the correct coins to make a certain amount.
Journals
Journals are traditionally used for language arts class, but they also work as a math assessment. In the journal,
have the students record practice problems and explain how to do specific problems in their own words. The
journal also works as a place to record observations during math projects. Attach assignments or tests into the
journal to turn it into a more comprehensive portfolio to demonstrate the child's math skills. The journal and
portfolio concept creates a tool to use during conferences to let parents know how well

Student Assessment Resources

Educators are always looking for new resources on assessing student learning.
Student assessment has always been a hotly debated topic. Adding to the stress levels of educators is the
federal government's No Child Left Behind Act that requires all students to read and do math at or above
grade level by 2014. In this environment, educators are pressured to "teach to the test" and student assessment
is under intense scrutiny. Teachers can find hundreds of assessment resources online and in print. A few
comprehensive resources offer a good starting point.
Nine Principles of Good Practice for Assessing Student Learning

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

This comprehensive guide from the American Association for Higher Education describes nine key principles of
good practice for student assessment that can be summarized as follows. Assessment begins with educational
values, reflects an understanding of learning as a complex process and has a clear purpose. Assessment
places equal emphasis on both outcomes and the experiences that lead to those outcomes. Assessment is
cumulative rather than isolated. Assessment engages the wider educational community, connects useful
information with issues that people care about and leads to improved educational performance. Finally,
assessment fulfills its responsibilities to students and to the public.

Five Dimensions of Good Assessment

Linda Suskie of the Middle States Commission on Higher Education distilled the findings of a number of
national organizations and assessment experts into five dimensions of good assessment. Her conclusion,
based on the existing body of research, is that good assessments are used, are cost-effective, yield reasonably
accurate and truthful results, are valued and, finally, good assessments focus on and flow from clear and
important goals.

Winona State University's List of Assessment Rubrics

Winona State University's extensive list of sample rubrics are applicable to various college-level assignments.
You'll find rubrics for assessing essays, debates, computer programming, critical thinking, lab reports, research
papers, writing skills and dance, among others. The site provides sample rubrics from many universities across
the country, including Harvard, Penn State, Clemson, the University of California-Irvine, Purdue and Johns
Hopkins.

Kathy Schrock's Assessment & Rubric Information

Kathy Schrock's Assessment and Rubric Information provides sample assessment tools in the forms of rubrics,
graphic organizers, electronic portfolios and report card comments and progress reports. This site is a resource
for K-12 educators.

University of Texas at Austin Instructional Assessment Resources

The University of Texas at Austin's Instructional Assessment Resources website provides a step-by-step
process for assessing students. The site divides the assessment process into three tasks: planning the
assessment, gathering data and reporting results.

St. John's University Online Resources for Higher Education Assessment

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

This site provides a comprehensive list of links to assessment publications, research, rubrics, benchmarking
studies, reports, glossaries of assessment terms, surveys, portfolio assessment projects and articles, data and
tools to help organize assessment information.

Group Activity / Pair Activity 5.1:
1. Explain the importance of continually assess the numeracy level for learners
2. Conduct an assessment for a group of learners in a group getting the results that are accurate for that
group of students. The group must be comprised of best friends only.

5.2 (ac2) – numeracy Assessment tools and
procedures

Mathematical Assessment Tools
Mathematical knowledge can be assessed using various tools.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

"Foundations for Success," the final report of the National Mathematics Advisory Panel in 2008, identified
slipping mathematical prowess as a serious educational and social concern. From the high mathematical
standards of the 20th Century, America is losing ground and runs the risk of not being able to sustain a work
force with adequate mathematical skills. Currently, technical mathematical talent is imported from abroad to
address this gap. Assessing students mathematical abilities is important, as without the basic skills, they will
have trouble studying algebra, the benchmark of higher mathematical success. There are a number of
assessment tools to measure mathematical knowledge.

Teacher Tests

A standard way to assess a student's mathematical skills and abilities is for the math teacher to prepare a test.
This assessment tool may be used at the end of a chapter to test particular concepts, at designated times
during the year or as a final exam of the year's work. Teachers working in the same school jurisdiction
sometimes share tests, as their students use the same materials to study mathematics.

Standardized Tests

A school district, state or educational assessment organization may design standardized mathematics tests to
assess the acumen of students in a given geographical area. Mathematics is the subject that best lends itself to
standardized tests, as the answers are either "right" or "wrong," so subjective evaluation doesn't enter into
calculating the results. Educators use standardized mathematics tests as an assessment tool to measure the
students against the "norm." Standardized tests change every year, and back-issues are often used to help
students prepare for upcoming assessments.

Computer Tests

As the Internet grows and develops so does the mathematics assessment tools that are available online. No
matter if you want to test kindergarten mathematical skills about basic numbers or get some help studying for
the GMAT, there are resources that can help. Computer-based testing tools have the benefit of providing
instant assessments, which a lot of students find helpful when they are testing their mathematical ability.

Measure of Academic Progress

The Measure of Academic Progress -- or MAP as it is commonly known in education circles -- is a computer-
generated tool that tests students in English, math and science in the primary grades. Each test is unique, in
that if the student is good at mathematics, the assessment questions will get increasingly more difficult. The
same is true if the student is struggling with mathematical concepts.

Elementary Math Assessment Tools

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Elementary math gives students the basic understanding of fundamental mathematical principles that will
later serve them not only in practical situations, but also in the more advanced math classes of junior and
senior high school. These basic skills must be tested, and for this reason several assessment tools have been
designed for teachers to get a good idea of how well their students understand math.
Elementary Math Assessment Tools
Elementary math gives students the basic understanding of fundamental mathematical principles that will
later serve them not only in practical situations, but also in the more advanced math classes of junior and
senior high school. These basic skills must be tested, and for this reason several assessment tools have been
designed for teachers to get a good idea of how well their students understand math.
Assessment Tools for Math

Vary techniques when assessing math skills in students.
Math is a subject that every student must learn in school, and a variety of methods exist for math assessment.
One single assessment procedure does not provide an accurate view of a student's overall strengths and
needs in math, therefore it is beneficial to use multiple techniques and integrate them into everyday teaching.
This provides the most authentic form of math assessment.
Self-Assessment

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Ask the student to assess his own math skills. Self-assessment allows you to gain insight into the student's
views of his mathematical strengths and needs. Conduct interviews with the child and ask him to tell you what
he likes about math and what he struggles with. A written assessment with pre-determined questions about
math feelings or a math journal can also provide the same information as the interview.

Portfolios

Portfolios consist of student-selected work for evaluation. Encourage the student to choose her best math
work, but also work that caused struggles. A key component of a portfolio is the self-reflection that
accompanies the chosen assignment. In this refection, the student evaluates her own work and explains the
process of her math learning. Any positive or negative feelings associated with the math assignment are also
recorded in this section of the portfolio. Assess the portfolio with the child and talk to her about their selections
and learning processes.

Classroom Worksheets and Tests

Worksheets and tests allow a teacher to evaluate a student's math skills in a variety of settings. An educator
develops worksheets that help a student practice the math skill taught in the lesson plan. Worksheets are
completed at both school and home. They are easy to create and provide multiple chances for a student to
practice and learn the skill. Classroom tests are also used to assess a student's knowledge of math skills.
Develop tests that appeal to a variety of learning styles, such as a visual or an auditory learner. This provides
the opportunity for the student to succeed on the test and gives you a better assessment of the child's true
mathematical knowledge.

Standardized Tests

Many states require students to participate in national or state standardized tests. These forms of assessment
are the same tests given to every student in the district or state. Results are provided in the form of a child's
performance in relation to other children his age; they also provide a breakdown of the student's performance
in individual math concepts. Not all children perform well on standardized tests due to the added pressures or
test anxiety; therefore, interpret these results with care.

How to Develop Assessment Tools

An assessment is a diagnostic process that measures an individual's behaviours, motivators, attitudes and
competencies. Assessment tools comprise various instruments and procedures. These tools are largely used in
educational institutions, non-profit organizations and in the corporate world too. The success of designing and
developing assessment tools is brought about by using scientific methods to do so.

Instructions

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Develop assessment tools with the candidates to be assessed in mind. Different scenarios call for different
tools and modes of evaluation. Ensure that the instruments and procedures for assessing are relevant to the
audience, the skills and the task that they are being evaluated for.

Set benchmarks. According to the "Business Dictionary," a benchmark is a "standard, or a set of standards, used
as a point of reference for evaluating performance or level of quality." Take into account all the factors,
attributes and competencies that you want to measure and improve on. Ensure that the benchmarks you
establish are specific and operational. Operational benchmarks will also help you carry out realistic
improvements after the assessment.

Establish methods for gathering evidence. Assessment tools are functional only to the extent that they are able
to gather cognitive, behavioural and statistical outputs of those being assessed. Consider designing a tool that
clearly indicates the competencies, skills, attributes and behaviours of candidates against the benchmarks.
These tools may include comprehensive questionnaires, SWOT (Strength, Weakness, Opportunities and
Threats) analysis and diagnostic models.

Adhere to the principles of assessment, which include the following:

 Validity: The extent to which evidence gathered can be supported.
R  eliability: Consistency that the tools used for one set of candidates can
be used to assess other candidates of the same competencies and
generate the same results.
F  lexibility: Allowing the candidates ample time to understand the terms
of the assessment.
 Fairness: Criteria should not discriminate against an individual or group of
candidate.

Establish a method for assessing and evaluating outcomes against the benchmarks. Effective assessment tools
should be able to interpret the outcome of the measurements. Depending on the purpose of the assessment,
consider using the three major forms of evaluation: goal-based, outcome-based, and process-based.

ECD NQF 4 - Student Guide Knowledge Module 2

ECD NQF 4 - Student Guide Knowledge Module 2

Group Activity / Pair Activity 5.2:
1. Define assessment tool
2. Explain you can use an assessment tool to assess a learner in numeracy.

5.3 (ac3) - assessment standards in the national
curriculum statement

The National Curriculum Statement Grades R - 12 aims to produce learners that are able to:

I dentify and solve problems and make decisions using critical and
creative thinking;
 Work effectively as individuals and with others as members of a team;
O  rganise and manage themselves and their activities responsibly and
effectively;
C  ollect, analyse, organise and critically evaluate information;
 Communicate effectively using visual, symbolic and/or language skills in
various modes;
 Use science and technology effectively and critically showing
responsibility towards the environment and the health of others; and
 Demonstrate an understanding of the world as a set of related systems
by recognising that problem solving contexts do not exist in isolation.

Inclusivity should become a central part of the organisation, planning and teaching at each school. This can
only happen if all teachers have a sound understanding of how to recognise and address barriers to learning,
and how to plan for diversity

How Do Learning Standards Impact Curriculum & Assessment?

Learning standards should guide the process of creating curricula and assessments.

ECD NQF 4 - Student Guide Knowledge Module 2