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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 1 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. 2 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. 3 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. 4 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. 5 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. 6 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 7 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. 8