ACP portfolio KJ spring 2016

Name: Krista Jensen
Discpline: Math (Statistics)
Date: 28 April 2016



 Pre-Assessment: Assignment to find a
field of study that contains a confiden

 Confidence intervals for means
 Students will go through the proces
various confidence intervals.
 Assessment strategies include, revi
on SoftChalk.
 Detailed questions relating to Bloom
throughout the lesson and are the b
post assessments.

 Reflection: Teach students to focus on
just regurgitating formulas?

an article related to each students
nce interval.
ss of collecting data and calculating
iew of the obtained articles, class quiz
ms Taxonomy will be given
basis for the questions on pre and
n a mathematical process instead of

Homework Assignment: Fin
field of study that contai

Bloom’s Taxonomy
Knowledge

The confidence interval was?
The confidence level was?
The mean was?

nd an article related to your
ins a confidence interval.

Bloom’s Taxonomy
Comprehension / Analysis

Basic idea of the article?
What conclusions were drawn regarding
the confidence interval?





Discuss article summaries
brought in by the students

Appli
Confidence Levels

Interp

ications
Average

pretations

LESSON – O

Objective 1: O

Understanding the importance of a St
Central Measurement th

KNOWLEDGE KN

Objective 3: O

Confidence Level: How different confidence M
levels affect the confidence interval. Ca

COMPREHENSION & APPLICATION CO

Objective 5:

Calculate and Interpret a

APPLICATION, ANALYS

OBJECTIVES

Objective 2:

tandard Error. Understand the difference between
he standard error and the standard deviation.
NOWLEDGE & COMPREHENSION

Objective 4:

Margin of Error.
alculation and interpretation.
OMPREHENSION & APPLICATION

a 95% confidence interval.
SIS, & SYNTHESIS

1. Go through the data collection proces

Measure the length of screws or length of

2. Calculate the mean & standard error.

Compare to the standard deviation.

“What is the standard error? “
“How does the standard error change with
respect to the sample size?”

Bloom’s: Knowledge, Analysis

5. Calculate the Confidence Interval

“Calculate and interpret the meaning of
the confidence intervals just calculated
in class.“
Bloom’s: Analysis

ss to calculate a confidence interval.

ropes.

3. Confidence Levels

“How do different confidence levels affect the
range of the confidence interval?”

Bloom’s: Comprehension

4. Margin Of Error

“How does combining the standard error and
confidence level allow for calculating a
confidence interval? “
“How does the margin of error change when
the confidence interval changes?”

Bloom’s: Application

Time Instructor Activities Learner A

15 min Guide the students in the data collection process Collect da
Calculate
to four sam

5 min Go over the standard error and how sample size affects Have the s
5 min the standard error. Use the collected data to illustrate the standa
this point.
Ask: “What is the standard error” Blooms: Knowledge Have the s
use in calc
Go over confidence levels and how they impact the size
of the confidence interval using the data collected.
ASK: “How do different confidence level affect the range
of the confidence interval?” Blooms: Comprehension

5 min Go over the margin of error. Discuss how the standard Have the s
5 min error impacts the margin of error. Alter the standard using the
error to illustrate the changes in the margin of error.
Ask: “How does combining the standard error and
confidence level enable the calculation of a confidence
interval?” Blooms: Application

Lecture: calculate the CI, go over how to interpret the Use the in
range for the confidence interval. confidence
ASK:” Interpret the meaning of the confidence intervals
you just calculated in class.” Blooms: Analysis

Activities Lesson Materials

ata using screws, or lengths of an object. Calipers, rulers, screws or
the mean and standard deviation for three other objects that can be
mples (depends on the size of the class. measured. Recording sheets.
NOTE SHEET.
students use the sample data to calculate Calculators
ard error.

students choose three confidence levels to Calculators
culating confidence intervals.

students calculate the margin of error Calculators
sample data and confidence levels.

nformation gathered in class to calculate the Calculators
e intervals.

Explain the affect Interpret
sample size has on confidence i
the margin of error.
comprehension on stude
height
If the confidence level for a analy
95% confidence interval is
Cla
(82.1, 95.6), what is a QUI
probable confidence
interval for a 99%

confidence ?
synthesis

t the An average height of 64
interval inches and a standard
ent’s deviation of 5.4 inches
t. was found for a sample
ysis
size of 35 Students.
ass Calculate a 95%
IZ
confidence interval on
student height.
application

What is the
formula for
calculating the
margin of error?
knowledge

 Draw a connection to previous c
 Review key points of the Confid
 Reinforce the concepts in the qu

 Introduce confidence intervals f

confidence interval calculations
dence interval
uiz

for standard deviations

 Understand the importance of asking the

 Give the students time to practice workin

 “Active learning helps eliminate the illusio

 Get the students to focus on the approac
formulas.

 Need to memorize fewer formulas.

 It is important to push yourself out of you

e right QUESTION
ng through problems

on of understanding.”

ch/process and why they are using specific

ur comfort zone.





BOPPPS LESSON PLAN

COURSE: Math 1342 (Statistics)
Lesson Title: Confidence Intervals for means

Bridge: Have the students talk about the articles they found that contained a confidence interval.
Specifically, what was the confidence interval explaining? How was the confidence interval used to make assertions?

If the students did not complete the task of getting an article I could bridge into the lesson by asking the question, “How do you determine if one product is
better than another, or one medication is better than another?” This will lead them into talking about using a quantifiable value to compare like products. I will
focus the discussion toward using a midpoint and the variance for a value to draw conclusions.
Estimated time: 5 minutes
Course Student Learning Outcome: Calculate and understand confidence intervals

Learning Objectives: By the end of this lesson, students will be able to
Objective 1: Central measurement. Review the average and the importance of identifying a central location of the data.
Blooms: Knowledge
Objective 2: Standard error. Go over how the standard error is different from the standard deviation. Explain the common mistakes made using the
two calculations interchangeably.
Blooms: Knowledge and Comprehension
Objective 3: Confidence level. Go over confidence level and explain how different confidence levels impact a change in the area covered under a
distribution curve.
Blooms: Comprehension and Application
Objective 4: Compilation of the confidence level and the standard error to get the margin of error.
Blooms: Comprehension and Application
Objective 5: Use all of the pieces of a confidence interval to calculate the average value you would expect given a specific confidence level. Calculate
the 95% confidence interval of student’s class heights using the previous class objectives.
Gather the data and calculate the average, and standard deviation. Determine the level of confidence. Use the statistical values to compute and then
interpret the confidence interval.
Blooms: Application, Analysis and Synthesis

Pre-Assessment: A week prior to class the students would be assigned the task of finding an article relative to their field containing a confidence interval.
After the opening discussion (bridge in) the students would turn in a brief summary explaining the parts of the confidence interval found in their articles.
Estimated time: 5 minutes
Participatory Learning:

Time Instructor Activities Learner Activities Lesson Materials

15 min Guide the students in the data collection process Collect data using screws, or lengths of an object. Calculate Calipers, rulers, screws or

the mean and standard deviation for three to four samples other objects that can be

(depends on the size of the class. measured. Recording

sheets. NOTE SHEET.

5 min Go over the standard error and how sample size Have the students use the sample data to calculate the Calculators

affects the standard error. Use the collected data to standard error.

illustrate this point.

Ask: “What is the standard error”

Blooms: Knowledge

5 min Go over confidence levels and how they impact the Have the students choose two confidence levels to use in Calculators

size of the confidence interval using the data calculating confidence intervals.

collected.

ASK: “How do different confidence level affect the

range of the confidence interval?”

Blooms: Comprehension

5 min Go over the margin of error. Discuss how the Have the students calculate the margin of error using the Calculators

standard error impacts the margin of error. Alter the sample data and confidence levels.

standard error to illustrate the changes in the margin

of error.

Ask: “How does combining the standard error and

confidence level enable the calculation of a

confidence interval?”

Blooms: Application

5 min Lecture: calculate the CI, go over how to interpret the Use the information gathered in class to calculate the Calculators

range for the confidence interval. confidence intervals.

ASK:” Interpret the meaning of the confidence

intervals you just calculated in class.”

Blooms: Analysis

Post-assessment: Use a quiz set up in Soft Chalk. I would allow the students to work together. (The classroom assessment is also the new instructional

technology that I am trying out.)

Estimated time: 5 minutes

Summary: Draw a parallel from the class activity to the articles that were discussed in class. Talk about the relevance of understanding basic analysis in

everyday situations (hospital, large purchases, getting loans, understanding medications, etc.)

Estimated time: 50 minutes

ATTACH ANY LESSON MATERIALS (SLIDES, HANDOUTS, ETC.)

Math 1342
Statistics

CONFIDENCE INTERVALS



Objectives

Confidence Intervals

Formula for Confidenc
unknown standard dev

Margin of Error and ho
sample size

ce Intervals with an
viation

ow it responds to changes in

Confidence Interval fo

A point estimate is an estimate for a
The best point estimate of the popul

The confidence level of an interval e
interval estimate will contain the pa

A confidence interval is an interval
using the point estimate for the me
the estimate.

or µ when σ is known

a specific numerical value of a parameter.
lation mean (µ) is the sample mean ()

estimate is the probability that the
arameter.

estimate of a parameter determined by
ean along with the confidence level of

Formula for Confiden

The margin of error is the largest differe
parameter and the sample estimate of th
In simplest terms it is a measurement of
There are two margins or error.

1. The margin or error that occurs

2,

2. A predetermined margin of erro
must be within.
A predetermined margin of erro
book refers to the margin of erro
the margin of error above and so

nce Interval with σ

ence expected between the population
hat parameter.
the accuracy of the results.

in a formula



or. One that you determine your results
or is used to calculate sample sizes. The
or as E. You set a predetermine equal to
olve for .

Confidence Interva

The formula for a confidence interval wit

− , <



another way the equati

±

Where

is the sample mean

,is a t value based on a crit

is called the critical value which

is the standard error where


al with σ unknown

th unknown is:

< < + ,


ion is commonly written is :

± ,

tical value the degrees of freedom (df)

h is 1-confidence level

s is calculated from the sample

Confidenc

This graph
represents the area
for a 95%
confidence interval

ce Interval

The confidence level is 95% meaning the interval
will contain the true population parameter 95%
of the time. The confidence interval covers
95% of the area under the curve.

The critical value = 1 − 0.95 or 0.05

The area left in the tails is the critical value
divided by two or 0.05 2 = 0.025.

For confidence intervals you need to divide the
critical value into both tails.

The graph illustrates that you are adding or
to the
subtracting the standard error ,

mean.

Using the T Table to g

To use the T table (pg 652 in the book) you need to k
level or the critical value for your interval.

Find the 2 value for a 90% confidence interval
= 25 − 1 = 24

= 1 − 0.9 = .1

= 0.05
2

0.05 =1.711

Go to the row with the proper df
Go to the column that has the correct
confidence level. The t value will be
different for a one or a two tailed test.

get Critical Value

know the degreed of freedom (df) and the confidence

l (two tailed ) with a sample size of 25

80% 90% 95% 98% 99%
one tailed 0.2 0.1 0.05 0.02 0.01
df two tailed 0.1 0.05 0.025 0.01 0.005
19 1.328 1.729 2.093 2.539 2.861
20 1.325 1.725 2.086 2.528 2.845
21 1.323 1.721 2.080 2.518 2.831
22 1.321 1.717 2.074 2.508 2.819
23 1.319 1.714 2.069 2.500 2.807
24 1.318 1.711 2.064 2.492 2.797
25 1.316 1.708 2.060 2.485 2.787
26 1.315 1.706 2.056 2.479 2.779
27 1.314 1.703 2.052 2.473 2.771
28 1.313 1.701 2.048 2.467 2.763

95% Confidence Inte

erval (CI) of a Mean

For a 95% confidence interval the true
population mean ( ) will show up in the intervals
approximately 95% of the time.
In the illustration there are nine intervals derived
from samples with one interval not containing
the population mean.
8/9 = 0.89 or 89% of the intervals contain the
true population mean. When there are fewer
samples the results are subject to a higher error
rate.
The point is the mean is population mean is not
always contained in the CI. The higher the
confidence level the more likely the population
mean will be in the CI.

How Confidence

As a confidence level increases an interval w
is larger.

As the confidence level decreases the interv

When the sample size increases the standar
interval will also decrease.

As the sample size decreases the standard e
interval will also increase. more confident ab
make it larger.

Make sure that you understand ho
affect a confidence interval. This w

Intervals React

will also increase. This is because the z value

val will also decrease.
rd error decreases, therefore the confidence

error increases, therefore the confidence
bout an interval containing a parameter you

ow sample size and confidence level
will be on at least one test.

Confidence Interval Article Summary NAME___________________________

Article name: __________________________________________________________________

Basic idea of the article:
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________

The confidence interval was_______________________________________________________

The confidence level was _________________________________________________________

The mean was__________________________________________________________________

What conclusions were drawn regarding the confidence interval?
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________

Data Collection Sample 2 Sample 3 Sample 4

Sample 1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Mean
Standard
Deviation

Reflective Essay
ACP Spring 2016
Krista Jensen

As with any other writing project I have a difficult time getting started. I am much more
comfortable working with a math problem.

The first topic I would like to address is why I took the ACP course. I was not trained as
a teacher, but have always enjoyed teaching. I got experience teaching others starting in college
and then as a professional. I got to train personal at 3M, and Knolls Atomic Power lab on the use
of statistics. I found a lot of joy in seeing others learn and being part of that process.

After moving to Texas I got the opportunity to work at LoneStar. I have enjoyed working
with the students. However, working with the students at LoneStar pose different hurdles than
working with educated professionals. Some students I haven’t been able to get to participate in
class or do their homework. I was hoping through taking the ACP course I would learn different
ways to engage these students, and help them want to participate in the learning process.

When registering for the course I wasn’t sure of my expectations. I was hoping to find the
solution to getting students to participate and wanting to learn. Knowing that was impossible, I
was hoping to come away with some new strategies for engaging my students. I also wanted to
come away with ways to see if my students were truly learning the material and not just going
through the motions.

As we began talking about Bloom’s Taxonomy I thought to myself, this does not apply to
Math. In math there may be more than one way to approach a problem but, only one correct
answer. Each approach is based on specific rules and those rules need to be followed or the
student will not get the correct answer. Most Math classes do not reach beyond the knowledge
and comprehension levels of the Blooms Taxonomy (or I believed). This is particularly true
when working with the developmental level courses. We need the students to know how to do
simple arithmetic without the use of a calculator. In Geometry, the students need to be able to
recall formulas and the unit circle. Student’s need the fundamentals before they proceed in their
education.

Now that I have given my rant about how I felt at the start of the ACP course, let me tell
you how I feel about Bloom’s now. As with anyone else I push back on change. I do not like to
fix something that I don’t see as being broken. I learned math easily, the concepts came and I
understood them. I could regurgitate the material when needed. I know now that I did not master
the material. Bloom’s is trying to provide a way to get a student to master the material by making
them think about the process as well as the result.

For many employed in the sciences, it is hard to teach someone that the square root of 49
is seven. It is a known fact. It becomes part of who you are, the knowledge portion of Bloom’s.

To someone that has never been taught that the square root of 49 is seven it may not be that
clear. This is where the strategy of Bloom’s comes in. A way for a student to understand the
square root of 49 is asking, “Is there a value that when multiplied by itself is 49?” This question
is easier to comprehend then, take the square root of 49. After the process is mastered the result
becomes knowledge that can be used later.

I have started asking myself, “How would I break down each problem into baby steps?” I
try and think of my student and how they may struggle with the problem. Many times I ask an
upper level bloom’s question to my students without realizing. This happens more when I am
working individually with students. I ask questions that provoke thought about the problem at
hand.

Provoking thought working with students individually is commendable, but it also needs
to be done for the class as a whole. I think too often we worry about covering all of the material
and forget that the students need to be able to use the material later. Especially with math.

Now, I am focusing more on questions that will allow an entire class to really understand
the process. Understanding the process will inevitably help them in getting the correct result.
Most students struggle with understanding where to start a problem. This indicates a lack of
synthesis between processes and the formulas.

Reading the book Teaching Tips, I read that knowing if a student understands the
material cannot be done by simply going over the material in class. Even though this is a known
fact, the author provided a nice reminder that students don’t always understand what is being
gone over in class. In the past, I have struggled when multiple students get a problem incorrect
on a test because we went over it so many times in class. However, as with many students the
concepts seem easy when someone is explaining them, but they are not as easy when they are
applied independent of aide.

I have come away from the ACP being reminded of old teaching methods as well as new
ideas on how to help my students.

One of the concepts that I particularly like is breaking up a lecture day into segments. It is
important to remember that an individual has limits on their ability to learn by just listening.
They need to have application to solidify a concept. Chapter 14 of the text states, “It takes an
attempt at working through the material to truly understand it.” I believe more than ever that it is
important to give students the time to attempt working through problems in the classroom, where
they get instructional and peer help.

My main take aways from the ACP course have been to focus more on the depth of
questions asked to students. Help them to understand why something is done and hopefully that
will help them to remember how to derive a particular solution. Also, focusing on breaking a

class up into manageable parts. Allow for more participatory learning. Do not just lecture to the
class. The majority of the students will take nothing away from the class.

For future professional development I would like to work on learning some other
software applications for teaching. I also would like to master SoftChalk and learn how to create
my own images to use in the different web based tools.

I would advise other Adjuncts to take the ACP course. I came away with some new ideas
on how to engage my students, and a better understanding of how to help my students master the
material I am teaching.

Krista Jensen
ACP Spring 2016
Calculating Confidence Intervals for sample means

Student Name_____________________________

Category/Points 4 3 2 1
Proper equation
Equation for Equation for Equation without Equation without the
sample mean population mean the standard error critical values

Correct critical values Located the correct Used the proper Correctly calculated Made an attempt at
critical value on the table. (The t-table for the significance finding the correct
proper table. sample sizes < 30, level. significance level.
the z-table for
sample sizes > 30.)

Correct margin of Used the standard Used the formula for Only included the Used the variance in
error deviation of the the population standard deviation the calculation
sample correctly standard deviation in the calculation for instead of the
along with the instead of the the margin of error. standard deviation.
sample size. sample standard
deviation.

Correct Interpretation Correctly applied Correctly applied the Were able to get the Makes an attempt to
the confidence value of the range of main idea of what a interpret the
level into the confidence confidence interval confidence interval
explaining the interval. means but not in with relationship to
range of the relation to the the calculated
confidence calculated confidence interval
interval. confidence interval.

Remark Excellent Good Satisfactory Needs work
(A work) (B work) (C work) (D and lower)