Sequencing of Topics in an Introductory
Course: Does Order Make a Difference
Chris Malone
Winona State University
[email protected]
Co-Authors: John Gabrosek | Phyllis Curtiss | Matt Race
Grand Valley State University
Traditional* Sequence of Topics
Traditional* Sequence of Topics
Descriptive Statistics
Sampling Distributions
Inferential Statistics
Additional Topics
Traditional* Sequence of Topics
Related Work
- Chance, B. L., Rossman, A. J. (2001).
Traditional* Sequence of Topics
Related Work
1
- Chance, B. L., Rossman, A. J. (2001).
1. Data Analysis
Data Collection
Traditional* Sequence of Topics
Related Work
- Chance, B. L., Rossman, A. J. (2001).
1. Data Analysis
Data Collection
2. Bivariate
Univariate Inference
2
Traditional* Sequence of Topics
Related Work
- Chance, B. L., Rossman, A. J. (2001).
1. Data Analysis
Data Collection
2. Bivariate
Univariate Inference
3. Proportions
Means
3
Traditional* Sequence of Topics
Related 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
Traditional* Sequence of Topics
Related Work
- Wardrop, Robert (1995).
Statistics Learning in the Presence of Variation
Traditional* Sequence of Topics
Related Work
- Chance, B. and Rossman, A. (2006).
Investigating Statistical Concepts,
Applications, and Methods
Data: NYC Trees
Data: NYC Trees
Does Foliage Density tend to
be larger for Native Trees
compared to Non-Native trees?
Data: NYC Trees
Data: NYC Trees
61 vs. 56
Yes, Native trees
tend to have
higher Foliage
Density
Data: NYC Trees
Later in the semester…
H O :  Native   NonNative
61 vs. 56
H A :  Native   NonNative
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 NonNative is 56?
Making those illusive connections
A test for a single
proportion is very similar
to a test for a single mean
What we are thinking
Test Statistic =
Testing a Proportion (Native)
Testing a Mean (Age)
What they see
Test Statistic =
But, they don’t
look similar…
One Last Example
Student Task: Determine
whether or not more than
½ the trees in NYC are
Native.
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.
A “Good” Response
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…
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!
What does a complete analysis require?
Descriptive Statistics
Sampling Distributions
Inferential Statistics
Additional Topics
What does a complete analysis require?
Proposed Sequence of Topics
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
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.
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
So, does it work?
New
Traditional
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?
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?
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.
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!
Thank you!
Chris Malone
Winona State University
[email protected]
John Gabrosek | Phyllis Curtiss | Matt Race
Grand Valley State University
Assessment Questions
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.
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 #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.
Assessment Questions
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.
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.