Download Handout - DigitalCommons@CalPoly

CSU Symposium on University Teaching
May, 2009
SCAFFOLDING STUDENT ACTIVITIES OUTSIDE OF CLASS
Beth Chance, Karen McGaughey, Allan Rossman
Department of Statistics, Cal Poly – San Luis Obispo
([email protected])
Our Goals:
 Want to shift how we spend time in class to more of a “learn-by-doing” environment where
we can provide proactive support in the areas where students are most in need of help
(e.g., reinforcing the difficult concepts, making connections, communication skills,
discussion/debate/exploration/feedback, technology)
 Need to increase and better structure how students spend time outside of class
o Meaningful activities, practice, exploration
o Sufficient support, guidelines, motivation
 Assessment for learning
o Just-in-time learning (e.g., Novak, 1999): Immediate feedback to student and
teacher on what was and was not understood that day
Strategy 1: Reading Quizzes
Sample Email:
Hello everyone,
This is to notify you that you are required to do the Reading Quizzes next week (Week 6 of the quarter). The
quizzes are posted under the Assignments link, in the folder labeled "Reading Quizzes". There is a quiz for each
section of required reading for next week. The quiz for each reading section MUST be completed by 9:10am on
the following dates:
Section 9.1 Monday, May 4 @ 9:10am
Section 9.2 Monday, May 4 @ 9:10am
Section 9.3 Wednesday, May 6 @ 9:10am
Access to the quizzes will expire after the above dates and times; you will no longer be able to access the
quizzes.
Each quiz consists of 1-4 multiple choice or T/F questions covering the required reading. You may save your
answers and return to your quiz at a later time. However, once you have submitted your answers you will not get
another chance.
If you have any questions, let me know asap.
Happy reading! -Dr. McGaughey
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CSU Symposium on University Teaching
May, 2009
Reading Quiz Examples
Directions: These questions cover the reading in Section xx.x in the text. Please read the section, then do your
best to answer the questions below. Questions are concept-based questions. They will not cover the computation
portion of the reading, but rather the big ideas presented in each section. Each question is worth 1 point. You may
save your work and return to this quiz at any time before the due date/time. When you have completed the quiz
submit your answers. You will receive immediate feedback containing a brief discussion along with the correct
answer.
Due: Monday, May 4 at 9:10am.
Question #1:
The following histogram shows the scores on the
first exam for 50 students in Psychology 101. For
this exam, we can say that
a. the mean and median scores are the same
b. the mean score is greater than the median score
c. the mean score is less than the median score
d. there is not enough information to determine the
relationship between the mean and the median
scores.
Question #2:
The three dotplots shown display sample data sets that have standard deviations of 1.1, 4.5 and 7.7. Which of
the three dotplots corresponds to the data set with the standard deviation of 4.5?
a.
b.
c.
Question #3:
The histograms shown here are approximate sampling distributions. Each histogram is based on 500 samples
of size n. All three histograms were constructed by sampling from the same population, but the sample sizes
were different. Which histogram was based on samples with the smallest sample size, n?
a.
b.
c.
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Question #1:
Correct Feedback: Correct!!!
Incorrect Feedback: Incorrect. In a negative skewed (left skewed) histogram, the mean will be below the
median since the small values in the tail will tend to pull the mean down (to the left). The correct answer is (c).
Question #2:
Correct Feedback: Correct!!!
Incorrect Feedback: Incorrect. The standard deviation is a measure of the variability in the data. It can be
defined as the ‘typical’ distance of the data observations from the mean. The data in Sample 3 are clustered
more closely together than the other two samples, thus, Sample 3 has less variability (smaller standard
deviation, 1.1) than Sample 1 and Sample 2. The data in Sample 2 is more spread out than the data in
Sample 1 and Sample 3, thus Sample 2 has the largest standard deviation (7.7). Thus, Sample 1 has the
standard deviation of 4.5. The correct answer is (a).
Question #3:
Correct Feedback: Correct!!!
Incorrect Feedback: Incorrect. The sampling distribution generated from the smallest sample size will
exhibit the most variability. The correct answer is (b).
Strategy 2: Practice Problems
Example 1: Recall the data collected in the “Preliminaries” section about how many letters you could
memorize in 20 seconds. Every person received the same sequence of letters, but they were presented in
two different groupings. One group received JFK-CIA-FBI-USA-SAT-GPA-GRE-IBM-NBA-CPR
and the other received JFKC-IAF-BIU-SASA-TGP-AGR-EIB-MN-BAC-PR
Similar studies have shown that those receiving the letters already organized in recognizable chunks are able
to memorize more than those with the less memorable groupings.
a) Explain why this study is an experiment and not an observational study.
b) Identify and classify the explanatory and response variables in this study.
Explanatory:
Type:
Response:
Type:
c) Explain how randomization was implemented and why it was important in this study.
d) Explain how blindness was implemented and why it was important in this study.
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Wooden
Type
Example 2: Roller Coaster Speeds
The Roller Coaster Database maintains a web site
(www.rcdb.com) with data on roller coasters around
the world. Some of the data recorded include
whether the coaster is made of wood or steel and
the maximum speed achieved by the coaster, in
miles per hour. The boxplots display the
distributions of speed by type of coaster for 145
coasters in the United States, as downloaded from
the site in November of 2003.
Steel
20
30
40
50
60
70
80
90
100 110
120
Speed
(a) Identify the observational units in this study. Then identify the explanatory and the response variable here.
Also indicate for each whether it is quantitative or categorical.
(b) Summarize what these boxplots reveal about the differences between the speeds of wooden and steel roller
coasters. In particular, is there a tendency for one type of coaster to be faster? Explain.
(c) Do these boxplots allow you to determine whether there are more wooden or steel roller coasters?
(d) Do these boxplots allow you to say which type has a higher percentage of coasters that go faster than 60mph?
Explain and, if so, answer the question.
(e) Do these boxplots allow you to say which type has a higher percentage of coasters that go faster than 50mph?
Explain and, if so, answer the question.
(f) Do these boxplots allow you to say which type has a higher percentage of coasters that go faster than 48mph?
Explain and, if so, answer the question.
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Strategy 3: Investigation Assignments
Example 1:
STAT 252
Winter 2009
(Rossman)
Investigation 1: Backpack weights (assigned Fri Jan 9, due Wed Jan 14)
You may work with one other person on this assignment, handing in one report with both names. Word-processed reports are
much preferred to hand-written ones. Please copy/paste relevant, well-labeled Minitab output into a Word file as appropriate.
A growing problem in American schools involves students who develop back problems, possibly as a result of carrying too much
weight in their backpacks. Chiropractic experts generally recommend carrying no more than 10% of one’s body weight in a
backpack. To investigate how much Cal Poly students carry in their backpacks, student researchers randomly sampled 100
students. They asked these students to report their body weight, and then they weighed how much was carried in their backpack.
These data (in pounds) are in the Minitab worksheet backpack.mtw. [Click on the link to open the file, as long as you are
working on a computer with Minitab software. In case you want to look at the data in Excel, you can click on backpack.xls.]
First create two new variables:
 ratio of backpack weight to body weight
 whether or not the student carries at least 10% of his/her body weight in his/her backpack
Do this by typing the following at the MTB> prompt in the Session window:
MTB> let c3=c1/c2
MTB> let c4=(c3>=.10)
[Note: If you do not see the MTB> prompt in the Session window, then click in the Session window (the top window) and choose
Editor> Enable Commands. When you have created these new variables, you will see their values in the Data window (the
bottom window).]
a) For each of these two new variables, indicate whether it is categorical or quantitative.
b) Produce (and submit) a histogram and boxplot of the weight ratios. [Hint: Choose Graph> Histogram. Select the
“Simple” option and click OK. Then double click on “c3 ratio” to make that choice appear in the “Graph variables” box. Click
OK again. Once the graph appears, copy/paste it into your Word file. Then repeat with Graph> Boxplot.] Comment on
what these graphs reveal about these weight ratios. [Hint: Refer to shape, center, and spread, paying particular attention to the
10% value that forms the basis for chiropractor’s recommendations.]
c) Calculate the mean and standard deviation, and also the five-number summary (minimum, lower quartile, median, upper
quartile, maximum) of the weight ratios. [Hint: Choose Stat> Basic Statistics> Display Descriptive
Statistics. You can then click on “Statistics” and select the ones you want.] Report these values, and include appropriate
symbols for the mean and standard deviation.
d) Conduct a test of whether the sample data suggest the population mean of the weight ratios is less than .10. [Hint: You could
do the calculations by hand, but it’s easier to use Minitab: As we have done in class, choose Stat> Basic Statistics>
1-Sample t.] Report the hypotheses, in symbols and in words, as well as the test statistic and p-value. Also write a sentence
or two summarizing your findings.
e) Check and comment on whether the technical conditions for this t-test appear to be met.
f) Determine the sample proportion who carry at least 10% of their body weight in their backpack. [Hint: Type MTB> tally
c4.] Report this value, along with its appropriate symbol.
g) Produce a 90% confidence interval for the population proportion who carry at least 10% of their body weight in their backpack.
[Hint: You could do the calculations by hand, but it’s easier to use Minitab: As we have done in class, choose Stat> Basic
Statistics> 1-Proportion.] Also write a sentence summarizing what this interval reveals.
h) Check and comment on whether the technical conditions for this confidence interval appear to be met.
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Example 2
STAT 221
Fall 2008
(Rossman)
Investigation 6: Which tire? (assigned Wed, Nov 5; due Mon, Nov 10)
You may work with one other person on this assignment, handing in one report with both names. Word-processed reports are
preferred to hand-written ones. Please copy/paste relevant, well-labeled computer output into a Word file as appropriate.
Reconsider the “which tire” situation and the data that we collected in class. You will investigate whether the sample data, for my
two sections combined, provide compelling evidence that more than one-fourth of all Cal Poly students would choose the right
front tire.
a) State the null and alternate hypothesis, in symbols and in words, for testing whether the sample data provide compelling
evidence that more than one-fourth of all Cal Poly students would choose the right front tire.
When results from my two sections are combined, 28 students chose the right front tire in our sample of 66 responses.
b) Check whether the technical conditions required for the validity of the z-test procedure are satisfied.
c) Calculate the appropriate test statistic and p-value. (Feel free to do this by hand or with the Test of Significance applet
available here.)
d) Summarize the conclusion that you would draw, using the  = .05 significance level.
Now suppose that a friend of yours takes a random sample of students at his/her university and asks this same question, finding
that 35% of the sampled students answer with the right front tire.
e) What additional information do you need to determine whether this sample proportion is large enough to provide strong
evidence that more than 25% of all students at that university would choose the right front tire?
f) Conduct the appropriate test (based on a sample proportion of .35 answering “right front”) first with a sample size of 40, then
with a sample size of 100, and finally with a sample size of 400. In each case report the test statistic, p-value, and test decision at
the  = .05 level. (Again feel free to use the applet.)
g) Comment on the effect of sample size on the strength of evidence against the null hypothesis that 25% of the population would
pick right front, even as the sample proportion remains constant with 35% choosing right front. Also explain why this makes
intuitive sense.
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Strategy 4: Pre-Labs
Stat 217 Lab 1 PreLab
Due by 9am Thursday, April 2
Background: A recent investigation reported in the November 2007 issue of Nature (Hamlin, Wynn, and Bloom)
aimed at assessing whether infants take into account an individual's actions towards others in evaluating that
individual as appealing or aversive, perhaps laying for the foundation for social interaction. In one component of
the study, 10-month-old infants were shown a "climber" character (a piece of wood with "google" eyes glued onto
it) that could not make it up a hill in two tries. Then they were shown two scenarios for the climber's next try, one
where the climber was pushed to the top of the hill by another character ("helper") and one where the climber was
pushed back down the hill by another character ("hinderer"). Each infant was alternately shown these two
scenarios several times. Then the child was presented with both pieces of wood (the helper and the hinderer) and
asked to pick one to play with.
Play the following two videos (there is a bit of sound) to see what was shown to the infants for the helper toy and
then the hinderer toy. If you cannot see the two videos below, click here.
If your computer can run QuickTime videos from the web, you may also want to view the third and fourth videos on this
page to see how the objects were presented to the infants.
Pre-lab Instructions: Answer the following questions the best you can with your current knowledge. I will respond to your
answers via email and you should review my comments before lab. When you press the Submit button, you will be taken to a
Verification page. Make sure you complete that for your submission to go through.
Name:
Email:
Step 1: Consider the study design
a) Suggest one question you have about the study design. Something you would like to know as you evaluate the
results.
Step 2: Make a prediction
b) Do you think the infants will be more likely to choose the helper toy or the hinderer toy?
helper
hinderer
Step 3: Begin to consider how you will analyze the data
Based on the above description of the study, identify the following terms in the context of this study.
c) observational units:
d) variable:
e) research question:
Submit
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References
Angelo, T. A., & Cross, K. P. (1993). Classroom Assessment Techniques: A Handbook for
College Teachers. San Francisco, CA: Jossey-Bass.
Chance, B. 2002. Components of Statistical Thinking and Implications for Instruction and
Assessment. Journal of Statistics Education. 10(3).
Hestenes, D., M. Wells, and G. Swackhamer. 1992. Force concept inventory. The Physics
Teacher. 30: 141–158.
Hestenes, D., and I. Halloun. 1995. Interpreting the FCI. The Physics Teacher. 33: 502–506.
Novak, G. M., Patterson, E. T., Gavrin, A. D., & Christian, W. (1999). Just-in-Time Teaching:
Blending Active Learning with Web Technology. Upper Saddle River, NJ: Prentice Hall.
Novak, G. M. (1999). Just-In-Time Teaching. Available online at:
webphysics.iupui.edu/jitt/jitt.html (accessed June 27, 2005).
Posner, G. J., Strike, K. A., Hewson, P. W., and Gertzog, W. A. (1982), "Accommodation of a
Scientific Conception: Toward a Theory of Conceptual Change," Science Education, 66(2),
211-227.
Resnick, L. (1987), Education and Learning to Think, Washington, D.C.: National Research
Council.
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