AMATYC 2007 1

‘Just in Time’ Teaching and Learning

Patricia KubyMonroe Community College Rochester, NY

pkuby@monroecc.edu

http://web.monroecc.edu/pkuby/

AMATYC 2007 2

Crossroads Standard for Pedagogy

• Teaching with technology• Making connections• Experiencing mathematics• Active and interactive learning• Using multiple strategies

Best ways to reach Generation Y (born after 1980) – thrive on change

AMATYC 2007 3

Goal and Objective

• Get my students more involved in the learning process

• Have immediate feedback on their understanding

• Use various teaching methods to reach out to all learning styles and age groups

AMATYC 2007 4

That first statistics class – what do we do?

• Introduce ourselves

• Be sure the students and you are in the right class

• Take attendance

• Pass out the Course Syllabus

• Read the Course Syllabus

• Begin definition of statistics and all of its terms and jargon

AMATYC 2007 5

Something different

• Introduce ourselves

• Be sure the students and you are in the right class

• Take attendance

• Pass out the Course Syllabus + clickers

• Discover who your students are and what they know about statistics

AMATYC 2007 6

Some background information on

MTH 160-003 Statistics I

Fall 2007

AMATYC 2007 7

What is your gender?

39%

61%

Male Female

1. Male

2. Female

AMATYC 2007 8

Type of student?

Full

time

Par

t tim

e

0%

100%1. Full time

2. Part time

AMATYC 2007 9

I am taking Statistics because

I en

joy

mat

h-rela

ted

...

My

maj

or re

quires

it

I nee

d to re

peat

the

...

Sta

tistic

s is

the

most

...

0% 0%0%

100%1. I enjoy math-related courses

2. My major requires it

3. I need to repeat the course

4. Statistics is the most relevant course to everyday life

AMATYC 2007 10

Statistical Terms and Definitions

• Have students read the chapter• Lecture• Use Powerpoint• Etc.

Much material, new words, new concepts, pretty boring start and they probably don’t understand – next class - try a few of these:

AMATYC 2007 11

Which of the following can be concluded from the graph?

1. 23% of those surveyed agreed to participate in the study.

2. Nearly a quarter of those surveyed believe the penny should be kept in circulation.

3. Nearly a quarter of those surveyed want the penny taken out of circulation.

4. The majority of people questioned want to get rid of the penny.

AMATYC 2007 12

Which is not an example of descriptive statistics?

1. The average age of those students surveyed is 22 years.

2. Nearly ¼ of students polled have children of their own.

3. 75% of all students receive financial aid.

4. Approximately one half of the students asked prefer classes that meet on Tuesdays and Thursdays.

AMATYC 2007 13

Which is not an example of inferential statistics?

1. 80% of students travel home for fall break.

2. 4 out of 5 dentists surveyed prefer soft-bristled toothbrushes.

3. The average age of all students at the school is 22 years.

4. 70% of all students participate in extracurricular activities.

AMATYC 2007 14

One third of kindergarten teachers believe knowing the alphabet is an essential skill for their students. In a random sample of 800 kindergarten teachers, 32% listed knowing the alphabet as an essential skill. Identify the variable of interest. 1. ⅓ of kindergarten teachers

that believe knowing the alphabet is essential

2. the 32% of the sample that listed knowing the alphabet as an essential skill

3. 800 randomly selected kindergarten teachers

4. essential kindergarten skills

AMATYC 2007 15

One third of kindergarten teachers believe knowing the alphabet is an essential skill for their students. In a random sample of 800 kindergarten teachers, 32% listed knowing the alphabet as an essential skill. Identify the statistic.

1 2 3 4

25% 25%25%25%1. ⅓ of kindergarten

teachers that believe knowing the alphabet is essential

2. the 32% of the sample that listed knowing the alphabet as an essential skill

3. 800 randomly selected kindergarten teachers

4. essential kindergarten skills

AMATYC 2007 16

The variable, miles traveled to school each day, is an example of what type of variable?

1 2 3 4

25% 25%25%25%

1. nominal

2. ordinal

3. discrete

4. continuous

AMATYC 2007 17

Since student identification number and jean size are numerical, these variables are quantitative.

1 2

50%50%

1. True

2. False

AMATYC 2007 18

What is the variable of interest in this study?

1. E-mail

2. preferred method of communication with companies

3. 32%

4. Workers 1 2 3 4

25% 25%25%25%

AMATYC 2007 19

What people were surveyed?

1. overweight workers

2. health insurance companies

3. business and political leaders

4. small business owners 1 2 3 4

25% 25%25%25%

AMATYC 2007 20

Each evening on the cable news networks, viewers are asked to call in or email their answers to the "Question of the Day". This is an example of what type of sampling?

1. volunteer sampling

2. convenience sampling

3. stratified random sampling

4. simple random sampling

AMATYC 2007 21

Which is an example of simple random sampling?

1. Distributing 20 surveys to a group of friends

2. Selecting and contacting every seventh student from the list of current students

3. Handing out surveys to all currently enrolled students and asking that they return the completed surveys to the library

4. Using a random number generator to select 20 student identification numbers and having those 20 students complete a survey

AMATYC 2007 22

Which is an example of systematic random sampling?

1. Distributing 20 surveys to a group of friends

2. Selecting and contacting every seventh student from the list of current students

3. Handing out surveys to all currently enrolled students and asking that they return the completed surveys to the library

4. Using a random number generator to select 20 student identification numbers and having those 20 students complete a survey

AMATYC 2007 23

Which is an example of a stratified random sample?

1. Dividing on-campus students according to the dormitory in which they live, then randomly selecting 10 students from each dormitory

2. Dividing the students according to their status as a traditional or nontraditional student, then randomly selecting 1 out of every 200 students in the strata

3. Dividing the students according to their major, then randomly selecting 5 of the majors and including those students in the sample

4. Dividing the students by off-campus or on-campus students, then randomly selecting 10% of each group to include in the sample

AMATYC 2007 24

Which is an example of a cluster sample?

1. Dividing on-campus students according to the dormitory in which they live, then randomly selecting 10 students from each dormitory

2. Dividing the students according to their status as a traditional or nontraditional student, then randomly selecting 1 out of every 200 students in the strata

3. Dividing the students according to their major, then randomly selecting 5 of the majors and including those students in the sample

4. Dividing the students by off-campus or on-campus students, then randomly selecting 10% of each group to include in the sample

AMATYC 2007 25

Dividing the students at a particular college according to their status as a traditional or nontraditional student, then randomly selecting 1 out of every 200 students in the strata is an example of what kind of sampling?

1. systematic random sampling

2. simple random sampling

3. proportional stratified sampling

4. stratified random sampling

AMATYC 2007 26

Which is not an example of multistage random sampling?

1. cluster sampling

2. proportional random sampling

3. stratified random sampling

4. systematic random sampling

AMATYC 2007 27

Classify the following as either an example of probability or statistics: Determining the length of time a certain brand of tire lasts.

1 2

50%50%1. probability

2. statistics

AMATYC 2007 28

Correlation and Regression

Choose method to present – use student data:

1. Scatter diagram

2. Correlation Coefficient

3. Regression Analysis

AMATYC 2007 29

Minitab – Scatter diagram

72706866646260

12

11

10

9

8

7

6

Height

ShoeSiz

eHeight versus Shoe Size

MTH 160-003 Fall 2007

AMATYC 2007 30

Correlation Coefficient: Applets and Minitab Calculation

• Define correlation coefficient, show formula, explain process, -1 ≤ r ≤ 1, r = 1, r = -1, r = 0

• Applets: Scatter diagrams, matching, constructing

Go back - consider the class scatter diagram – then let Minitab do the calculation:

Correlations: Height, ShoeSize

Pearson correlation of Height and ShoeSize = 0.850P-Value = 0.000

AMATYC 2007 31

Regression AnalysisMinitab Calculation and Applet

• Regression Analysis: ShoeSize versus Height • The regression equation is• ShoeSize = - 19.3 + 0.429 Height

• Some predicting with my shoe size, then a short person and a tall person – each try, slope, y-intercept, range, lurking variables

• Reasoning behind name – Regression line, Line of Best Fit, Least Squares Line

• Applet• Clickers to catch any misconceptions

AMATYC 2007 321 2

36%

64%

1. Yes

2. No

Below is a list of ten 2005 movies with the budget cost (in millions of dollars), the box office receipts (in millions of dollars) and the number of Oscar nominations it received. Does it appear that there is a relationship between the budget and the number of nominations?

AMATYC 2007 33

Which is not true about the correlation coefficient?

1 2 3 4

21%

57%

14%

7%

1. An r = 0 indicates no linear relationship between the two variables

2. An r =1 indicates a perfect positive relationship between the two variables.

3. The correlation coefficient must be between -1 and 1.

4. The correlation coefficient measures the strength of the linear relationship between two qualitative variables.

AMATYC 2007 34

In a random sample of eight college women, each was asked her height (to the nearest inch) and her weight (to the nearest five pounds). The scatter diagram is shown below. What is the best estimate for r?

1 2 3 4

0%

19%

50%

31%

1. r = -0.875

2. r =0.567

3. r = 0.865

4. r = 0.508

AMATYC 2007 35

1. There is a positive linear relationship between the height and weight of the women.

2. In general, the taller the woman the more she will weigh.

3. Taller women must also be heavier.

4. In general, the shorter the woman the less she will weigh.

In a random sample of eight college women, each was asked her height (to the nearest inch) and her weight (to the nearest five pounds). A scatter diagram was constructed. From this scatter diagram, one can conclude all except for which?

1 2 3 4

0% 0%

93%

7%

AMATYC 2007 36

The correlation between the height and weight of 8 college-age women is obtained. The Minitab output is shown below.

1 2 3 4

67%

13%7%

13%

1. There is a strong positive linear relationship between height and weight.

2. There is a weak positive linear relationship between height and weight.

3. There is a strong negative relationship between height and weight.

4. There is a strong positive nonlinear relationship between height and weight.

What does the correlation coefficient indicate about the relationship?

Correlations: Height, Weight Pearson correlation of Height and Weight = 0.865P-Value = 0.006

AMATYC 2007 371 2 3 4

77%

0%

15%8%

1. On average, each additional hour of studying will increase the exam grade by approximately four points.

2. On average, each additional hour of studying will increase the exam grade approximately 69 points.

3. If one studies four hours, the exam grade will be approximately a 69%.

4. The effect of one additional hour of studying can not be determined unless it is known how long one studied.

The regression equation relating x, the number of hours one studied, to y, the exam grade is determined to be ŷ = 4.1x + 68.7. From this equation, one can conclude that

AMATYC 2007 381 2 3 4

93%

0%0%7%

1. approximately 75%

2. approximately 58%

3. approximately 100%

4. approximately 69%

The regression equation relating x, the number of hours one studied, to y, the exam grade is determined to be ŷ = 4.1x + 68.7. Predict the exam grade of someone who studied one and a half hours.

AMATYC 2007 39

The least squares criterion requires that _____.

1 2 3 4

7%

43%

14%

36%

1. the sum of squared differences between the actual y's and the average y's be minimized

2. the sum of the squared differences between the actual y's and the predicted y's be as small as possible

3. the sum of the squared differences between the actual y's and the predicted y's be as large as possible

4. the sum of the differences between the actual y's and the predicted y's be as small as possible

AMATYC 2007 40

Sampling Distributions and the Central Limit Theorem

• Define Sampling distribution, give example

• Applets: normal and non-normal populations

• Discussion

• Write up SDSM and CLT

AMATYC 2007 41

When sampling two at a time, 1000 times repeatedly from a population, the sample size is:

1 2 3

33% 33%33%

1. 1000

2. 2000

3. 2

AMATYC 2007 42

Which of the following is true when sampling, with replacement, from the distribution {1,2,3,4,5,6} with sample sizes of two:

1 2 3

33% 33%33%

1. a mean of any two being 4 is fairly common

2. all of the sample means will be equal.

3. a mean of any two being 3.5 is impossible.

AMATYC 2007 43

1. be normally distributed for n = 2

2. be normally distributed for n = 9

3. be normally distributed for n = 30

4. All of the above are true.

If the parent population is normally distributed, will

x

AMATYC 2007 44

As the sample size increases the ________.

1. Standard error increases and the sampling distribution of sample means becomes shorter and wider.

2. Standard error increases and the sampling distribution of sample means becomes taller and thinner.

3. Standard error decreases and the sampling distribution of sample means becomes shorter and wider.

4. Standard error decreases and the sampling distribution of sample means becomes taller and thinner.

AMATYC 2007 45

Ball-bearings are manufactured such that their mean diameter is 2 inches and their standard deviation is 0.5 inches. Many samples of size 25 are randomly selected and their means are calculated. The distribution of these sample means should:

1. be exactly the same as the parent population.

2. have a similar measure for central tendency but much more dispersed.

3. have a similar measure for central tendency but much less dispersed.

4. randomness makes it too difficult to predict.

AMATYC 2007 46

Student Feedback

• 96% felt more engaged and participative using clickers in the course

• 100% recommended that the instructor continue to use clickers in the class

• It helped me “to see if I was understanding the material”; “to pay attention and participate in class”; “ to learn in a different way”; “stay involved”; “to review for tests”.

• #1 answer – “the anonymity, so I could see if I understood the material – could see the results of your answer and everyone else in class; there was adequate feedback with all of these”

AMATYC 2007 47

Results between pre and post applet/clicker classes

• Applets alone – avg corr/regr test = 90%

• Applets & clickers

Final exam scores are 9.5% pts higher

Comprehensive section scores are

8.7% pts higher

Final averages are 5-6% pts higher

AMATYC 2007 48

• Logistics

• Questions

• Comments