sequencing of topics in an introductory course: does order make a difference co-authors: john...

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Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State University Chris Malone Winona State University [email protected]

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Page 1: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Sequencing of Topics in an Introductory Course: Does Order Make a Difference

Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State University

Chris MaloneWinona State [email protected]

Page 2: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Traditional* Sequence of Topics

Page 3: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Descriptive Statistics

Sampling Distributions

Inferential Statistics

Additional Topics

Traditional* Sequence of Topics

Page 4: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Traditional* Sequence of TopicsRelated Work- Chance, B. L., Rossman, A. J. (2001).

Page 5: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Traditional* Sequence of TopicsRelated Work- Chance, B. L., Rossman, A. J. (2001). 1. Data Analysis Data Collection 1

Page 6: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Traditional* Sequence of TopicsRelated Work- Chance, B. L., Rossman, A. J. (2001). 1. Data Analysis Data Collection 2. Bivariate Univariate Inference

2

Page 7: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Traditional* Sequence of TopicsRelated Work- Chance, B. L., Rossman, A. J. (2001). 1. Data Analysis Data Collection 2. Bivariate Univariate Inference 3. Proportions Means

3

Page 8: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Traditional* Sequence of TopicsRelated Work- Chance, B. L., Rossman, A. J. (2001). 1. Data Analysis Data Collection 2. Bivariate Univariate Inference 3. Proportions Means 4. Testing Confidence Intervals

4

Page 9: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Traditional* Sequence of TopicsRelated Work- Wardrop, Robert (1995). Statistics Learning in the Presence of Variation

Page 10: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Traditional* Sequence of TopicsRelated Work- Chance, B. and Rossman, A. (2006). Investigating Statistical Concepts, Applications, and Methods

Page 11: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Data: NYC Trees

Page 12: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Data: NYC Trees

Does Foliage Density tend to be larger for Native Trees

compared to Non-Native trees?

Page 13: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Data: NYC Trees

Page 14: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Data: NYC Trees

61 vs. 56

Yes, Native trees tend to have higher Foliage Density

Page 15: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Data: NYC Trees

61 vs. 56

Yes, Native trees tend to have higher Foliage Density

Why cannot we just reject Ho based on the fact that the average for Native Trees is 61 and the average for Non-Native is 56?

NonNative

NonNative

NativeA

NativeO

:H

:H

Later in the semester…

Page 16: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Making those illusive connections

A test for a single proportion is very similar

to a test for a single mean

Page 17: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

What we are thinking

Test Statistic =

Testing a Proportion (Native)

Testing a Mean (Age)

Page 18: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

What they see

Test Statistic =

But, they don’t look similar…

Page 19: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

One Last Example

Student Task: Determine whether or not more than ½ the trees in NYC are

Native.

Page 20: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

A “Good” Response

Determine whether or not more than ½ the trees are in NYC are Native.

A “Good” Response:There was a total of 319 trees in our sample. The percent of trees that were Native is about 55%. From the graph you can see it is above 50%. So, yes we can say that more than ½ of the trees in NYC are Native.

Page 21: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

A “Good” Response

Teacher: The 55% you’ve calculated is for your sample, correct?Student: Yes.Teacher: So, does the 55% apply to all the trees in NYC or just the trees from the sample?Student: Well, I thought it was all trees in NYC, but I guess it’s just the 319 we looked at. So, how do we make that leap to all trees?Teacher: That is a very good question. Stay tuned -- I’ll explain a little bit in Ch 5, some more in Ch 6, and we’ll finish in Ch 7!Student: What? I don’t understand this stuff!

A “Good” Response:There was a total of 319 trees in our sample. The percent of trees that were Native is about 55%. From the graph you can see it is above 50%. So, yes we can say that more than ½ of the trees in NYC are Native.

Getting some clarification from the student…

Page 22: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Descriptive Statistics

Sampling Distributions

Inferential Statistics

Additional Topics

What does a complete analysis require?

Page 23: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

What does a complete analysis require?

Page 24: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Proposed Sequence of Topics

Page 25: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Proposed Sequence of Topics

Categorical: Singe Variable

Categorical: Two or More Variables

Numerical: Singe Variable

Numerical: Single Variable across a Categorical Variable

Numerical: Two or More Variables

Page 26: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Proposed Sequence of Topics

Why change?

1. Students carry out a complete statistical analysis over-and-over.

2. More closely mimics what a statistician does. In particular, students identify appropriate analyses using variable types and number of levels.

3. Just-In-Time Teaching: Giving students exactly what they need, in the exact amount, at precisely the right time.

4. Starting with categorical data is easier.

5. This sequence is more intuitive.

Page 27: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

So, does it work?

Assessment Tool Description

> 552 students from Grand Valley State University

> 6 different instructors

> 8 assessment questions -- 5 short answer, 3 multiple choice.

> Exams were scored similar to AP rubric (0-4)

> Fall 2005 used typical sequence, Spring 2006 used proposed sequence

Page 28: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

So, does it work?

NewTraditional

Page 29: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Some Challenges…

1. Sampling Distributions before Means, Std Dev, Histograms, etc

Required Concepts for Inference > What is the expected number of blacks? > What is the chance of seeing less than 15 blacks? > What is your cutoff for “too” few blacks?

Page 30: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Some Challenges…

2. Test Statistic / Unusual Outcome before Normal Distribution

Concerns… > I’m not convinced that covering std. deviation for numerical data helps them understand the denominator above. > Does computing P(Z < - 2) + P(Z > 2) really help me understand the 1/2/3 Rule better?

Page 31: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Conclusions

> Consider what students really need to know, do they need everything we teach them?> Consider how you analyze data. Does your process of analyzing data mimic how you teach? > Students are not making as many connections between topics as we may think.> Our assessment items suggested we did not do worse, which was our first goal.> Most textbooks are not conducive to the proposed sequence.

Page 32: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Conclusions

> Consider what students really need to know, do they need everything we teach them?> Consider how you analyze data. Does your process of analyzing data mimic how you teach? > Students are not making as many connections between topics as we may think.> Our assessment items suggested we did not do worse, which was our first goal.> Most textbooks are not conducive to the proposed sequence.

Thank you!

Page 33: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Thank you!

John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State University

Chris MaloneWinona State [email protected]

Page 34: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Question #3: A computer manufacturer wants to determine if the average temperature at which a brand of laptop computer is damaged is less than 110 degrees.  Thirty computers are tested to find the minimum temperature that does damage to the computer.  Temperature is continuously raised until computers are no longer able to work. The damaging temperature averaged 109 degrees with a standard deviation of 4 degrees. Using significance level α = .05, conduct an appropriate hypothesis test to answer the research question. Show work and draw a conclusion.

Question #2: Suppose that you want to study the question of how many Grand Valley State University students have their own credit card. You take a random sample of 1000 Grand Valley students and find that 246 of these students have their own credit card. Make an appropriate 95% confidence interval that describes credit card ownership among Grand Valley students. Interpret your interval in the context of the problem.

Question #1: As part of its twenty-fifth reunion celebration, the Class of 1980 of the State University mailed a questionnaire to its members. One of the questions asked the respondent to give his or her total income last year. Of the 820 members of the class of 1980, the university alumni office had addresses for 583. Of these, 421 returned the questionnaire. The reunion committee computed the mean income given in the responses and announced, "The members of the class of 1980 have enjoyed resounding success. The average income of class members is $120,000!". Identify two distinct sources of bias or misleading information in this result, being explicit about the direction of bias you expect. Explain how you might fix each of these problems.

Assessment Questions

Page 35: Sequencing of Topics in an Introductory Course: Does Order Make a Difference Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race Grand Valley State

Question #5:A teacher in a history class gives his students pre and post tests to see how much of an improvement students are making in his class. Each test is graded on a 100 point scale. A 95% confidence interval on the mean difference in test scores (pre-test minus post-test) is -10.5 to -6.3. Interpret this interval in the context of student achievement.

Question #4: The Office of Career Services at the local state university wishes to compare the time in days that it took graduates to find a job after graduation for 2003 and 2004 graduates. Separate random samples of 75 graduates from the 2003 class and the 2004 class are selected. Tim at Career Services states, “The sample of 2003 graduates took an average of 7.3 days longer to find a job than the sample of 2004 graduates. This shows that 2004 graduates were able to find jobs quicker.” Explain the fallacy in Tim’s reasoning.

Assessment Questions