Part A: Qualitative Research (30 points) Section 1: Reading, Memo Writing and Categorizing (20 points) This portion of the assignment is designed to help you develop/employ key qualitative research skills. You are to review qualitative data, write memos, segment and then group the data into topics and categories. You must ll four items below and show me your work. Read the case study scenario in Appendix A and the associated data in Appendix B and follow the instructions below. 1. Write Memos. What are memos? Memos are notes about initial impressions of data; qualitative researchers often review data making these notes. Review the data presented in Appendix B and write memos related to your impressions of the data. Be sure to include the memos that you write in your assignment submission. 2. Segment the data. A useful first step in classifying a body of data in many qualitative studies is to break it into segments so that it can be more easily organized. A segment is a word, group of words, or sentence that is comprehensive by itself. That is, it contains one idea or piece of information relevant to the study. The italicized words in the sentences below are examples of segments: Teachers have a complete understanding of the mathematics content. She must have the capabilities of multitasking like placing students, tutoring students, disciplining students . . . all at the same time! To segment the data presented in the transcript, copy and paste the data from Appendix B into a separate document. Identify segments that you think express an individual idea. 3. Provide "topic" labels for each segment. Label each segment in question 2 with a descriptive name for the subject matter. These labels are called topics. At the end of each segment, insert a topic label in parentheses. For example, the segment "complete understanding of the mathematics content" might be labeled "(understanding math)"; the segment being multitasked might be labeled "(multitasking)." Note that any one topic label may apply to multiple segments; in other words, you may not have to think of a unique label for each segment. 4. Group "topics" into "categories". Group topics you feel are similar in nature and label these groups with a term that conceptually describes the topics within it. These labels are called categories. For example, a category may be "Content Knowledge," which would include segments "complete understanding of the mathematics content" (topic: understanding math) and segment "firm grasp of content "(topic: grasp of content). In the end, you might have six or seven categories (an "other" category is acceptable) that together contain all the topics and segments.

3 Section 2: Interpreting and Analyzing Data (10 points) This portion of the assignment seeks to help you gain practice at deriving meaning from qualitative data. Interpreting data requires identifying any patterns you feel represent the major issues that should be reported to the program developer in response to the focus group question ("Based on your experiences this year, what skills do you feel are needed to use the Algebra Computer Program effectively in your classroom?") Your interpretation should be focused on the answers to the following four questions: 1. What is important in the data? (3 points) 2. Why is it important? (3 points) 3. What can be learned from it? (4 points) Using these questions as your guide, provide an interpretation of the data for this exercise. Your response should be at least several paragraphs long. Part B. Quantitative Research (30 points) Section 1: Computing Statistics - Short Answer (5 points) This portion of the assignment is designed to help you practice computing key statistics useful in quantitative research - and to understand meaning from these statistics. 1. Scores on the LSAT are approximately normally distributed. In fact, published reports indicate that approximately 40 percent of all test takers score at or between 145 and 155, and about 70 percent score at or between 140 and 160. The full range of scores is 60 pts. (120-180). Use your knowledge of normal distributions to estimate the mean, median, and the standard deviation of the LSAT. (2 pts.) 2. Back in 1988, a smart college student thought she might want to go to law school and took the LSAT. Her score was 42 and her percentile rank was 95. Obviously, the scoring system has changed since 1988-the scores used to be reported on a different standard scale. Back then, as you can see, a 42 was a high score; now it's not even possible to get a score that low. Imagine that this student decides, in 2008, to apply to law school. She is considering University of Michigan Law School, which reports that the median LSAT score for the 2006 entering class is 168, and that the 25th and 75th percentiles for the class are 166 and 170, respectively. Admission isn't based on LSAT score alone, of course, but assuming her score correlated with her grades, essays, and other admission data, do you think this student has a good chance? To answer this question, you must first convert the 1988 LSAT score to match the current scale, using your knowledge of the normal curve and your answer to Question 1 of this exercise, and then compare it to those of the students entering UM Law School in 2006. (3 pts.)

4 Section 2: Computing Descriptive Statistics - Case (15 points) This portion of the assignment is designed to help you appreciate the need for computing key statistics and to get further practice at computing these items. An excerpt from a research plan focused on the effect of peer tutoring on the reading comprehension of failing seventh-grade English students is in Appendix C. The data for this study are included in Appendix D. Please review the data in Appendix D and then answer the following questions. 1. What is the mean of each group? (2 points) 2. What is the range of each group? (2 points) 3. What is the mode and median of each group? (2 points) 4. Draw a graph of each distribution. (You may use excel). Include a copy of your graphs. Are the distributions skewed? If so, in which direction? (4 points) Using the data labelled "Data for Question 5", please do the following: 5. Please calculate the z-scores for the following values in the experimental group (5 points). You may use excel or calculate the values by hand. In either case, show your work. (Please use the range of values listed below and not the values in Appendix D) Data for Question 5 Experimental Group - Selected Values 34 36 38 39 39 40 40 41 41 41

5 41 41 42 42 42 43 44 44 45 Section 3 - More Practice (5 points) This portion of the assignment is designed to help appreciate the relationship between populations and samples. As discussed in the text, we can estimate the mean of a population by taking several samples and computing their means. The sample means won't all be the same, but they will form a normal distribution around the population meana few will be a lot higher, a few will be a lot lower, and about 68 percent will be within one standard deviation of the mean for the whole population. To illustrate this principle, estimate the mean length of a sentence. To begin, use the three paragraphs in Appendix E as your three samples. 1. Count the number of words in each sentence, then compute the mean length of sentence for each sample. (Include numbers as words; where 10 would be one word or 100.55 would be one word. Include abbreviation - like "i.e." - as a word. Count symbols like +/- as a word). NOTE YOU MAY USE THE WORD COUNT FUNCTION IN MS WORD IF YOU LIKE. (1.5 points). 2. Next, compute the mean of the sample means. This is the estimate of the population mean. (1 point). 3. The standard deviations for the three samples are 17.10 (Sample 1), 19.31 (Sample 2), and 7.65 (Sample 3). With this information, compute the standard error of the mean. (1 point) 4. Knowing the standard error of the mean allows you to state the confidence limits for your estimate of the population mean. In other words, 95 percent of all sample means will fall between two valueswhat are those two values? (1.5 points)

6 Section 4: Interpreting Measures of Relationship (5 points) This section of the assignment is designed to cultivate skills related to interpreting meaning from quantitative data. As part of a larger study, Speed and Gangestad (1997) collected ratings and nominations on a number of characteristics for 66 fraternity men from their fellow fraternity members. The following paragraph is taken from their results section: . . . men's romantic popularity significantly correlated with several characteristics: best dressed (r = .48), most physically attractive (r = .47), most outgoing (r = .47), most self- confident (r = .44), best trendsetters (r =.38), funniest (r = .37), most satisfied (r = .32), and most independent (r =.28). Unexpectedly, however, men's potential for financial success did not significantly correlate with romantic popularity (r = .10). (p. 931) Please address these questions: 1. Explain what is meant by correlation coefficient using one of the correlations above as an example. (2 points) 2. Provide your thoughts on the meaning of the pattern of results. (You could speculate on the meaning of the pattern of results, taking into account the issue of direct causality. You could also indicate what kinds of conclusions could NOT be drawn). (3 points)

Appendix A: Scenario for Part A, Section 1 Recently a researcher was contacted by the developer of a computer-based algebra program to learn more about how teachers were actually using the program. The program was based on sound individualized learning principles. Content paralleled that of the curriculum regularly used in the schools, but the delivery of instruction was substantively different. Computer labs had been constructed in the schools, and hardware and software had been installed so that each student in a class had access to his or her own computer. Sequential lessons provided the framework within which students worked individually. Each lesson provided a discussion of specific objectives, an explanation and demonstration of the objectives, and several opportunities to demonstrate mastery. Movement from lesson to lesson was dependent on mastery of the objectives of previous lessons. The researcher conducted a series of observations over the course of the school year and noted wide variations in program implementation. Some teachers were using the program precisely as designed, whereas others were using it to supplement the normal curriculum. In informal conversations, teachers expressed some frustration with implementation that appeared to be focused on problems related to the transition from a traditional instructional model to one consistent with an individualized instructional approach. As a result of this information, the researcher conducted several focus groups in which a semi- structured interview protocol was used to collect data. One question focused on teachers' perceptions of the skills the program required them to have: "Based on your experiences this year, what skills do you feel are needed to use the Algebra Computer Program effectively in your classroom?" The researcher tape recorded the responses and conversations of the focus groups and transcribed the tapes verbatim. I have provided you with a document in Appendix B that lists some excerpts from transcripts of interviews from a research project.

8 Appendix B: Data for Questions in Part A, Section 1 Each paragraph below lists an excerpt from an interview during the focus group sessions. The number beside each paragraph is a unique number assigned to each 'interviewee.' 2 The teacher must have a complete understanding of the mathematics content. She must have the capabilities of being multitasked like placing students, tutoring students, disciplining students . . . all at the same time! The teacher needs to be flexible and willing to individualize the program for each student. 4 You must have a firm grasp of content and be able to switch from topic to topic without difficulty. You must be able to spot and correct errors on the screen, and you must be able to explain concepts in a variety of ways so students who cannot follow the speaker can follow you. You really need to be aware of what is going on so that you can keep students on task and monitor the class to be sure the equipment is being cared for properly. 6 Good organization skills to track each student and keep up with their pace so that you know when they are spending too much time on a lesson. Some students don't ask for help and will continue failing if you don't know when to step in. The task is more physically demanding than a regular classroom. After a day of tutoring individuals and going from station to station where everyone is on a different concept it can be draining but I feel much more effective than delivering a concept to a group. 7 You must be able to rapidly switch gears to aim instruction at the individual students in words they understand, rather than aim it toward the overall group as you would in a traditional classroom. Because you are dealing predominately one on one, you must be able to tailor your vocabulary, your presentation, your entire methodology to a single student knowledge core. 8 You must have a really good knowledge of math. It is also really important to be able to manage everything going on. 11 Nerves of steel. There are moments when 30 children have questions, and you can't get to any of them quickly enough. 16 You must be well organized and able to run a structured classroom in order to handle all the situations and problems that must be taken care of in this classroom. The teacher needs to be able to plan thoroughly in order to coordinate the textbook notes and homework assignments along with the computer lessons, which correlate with the course outline. There is also a need to be able to manage student behavior in order to keep the students on task and focused. In the hands of an experienced effective teacher this program will live up to its potential and really give the students a good head start and a strong foundation in Algebra. However, the administrators must not see it as a cure-all for weak teachers who cannot teach or manage a classroom. The

9 teacher must not expect to just put the students on the computers and let the computers do all the teaching, as this is taking away from the effectiveness of this program. The teacher must be able to help the students pull together what they are learning in the computer lessons and transfer that knowledge to traditional lessons and tests that they will run into later on in this class as well as in other math classes. 23 A teacher should have a good knowledge of algebra and algebraic methods and should be able to translate and simplify instructions from the program to the students. I almost forgot something really important-you also need basic computer skills. 24 Flexibility is the most important attribute that a teacher can have while using this program. I've learned a lot over this past year, and I have had to adjust the order of lessons, the structure of the class, and the grading procedures many times to best benefit the students' learning. Excitement is also a key to effectively using the program. If the teacher is excited about the program, they are more apt to learn more and pass the excitement on to the students. I really don't think that one has to have any special skills to effectively use the program because it is very user-friendly. Being able to solve complex math problems is important so that you can help students work through them. Oh, I just remembered one more very important skill-a teacher has to be able to maintain order in the classroom. Otherwise, the students will not benefit from the program and the equipment will get stolen and/or destroyed. 25 I feel you need more planning time and the ability to multitask. 26 There are only three things you really need: organization, patience, and flexibility.

10 Appendix C: Excerpt from a Research Plan for Part B, Section 2 Statement of the Hypothesis Although most of the research on peer tutoring has focused on elementary students, it has shown that peer tutoring is effective in promoting the academic performance of both non-remedial and remedial students. Therefore, it was hypothesized that failing seventh-grade English students who participate in a peer tutoring program have higher reading comprehension scores than failing seventh-grade English students who do not participate in a peer tutoring program. Sample The sample for this study will be selected from the total population of approximately 60 seventh- grade students with Fs in English at an upper-middle-class, private, Catholic middle school in Miami, Florida. The population is 98% Hispanic and largely of Cuban-American descent. Students will be randomly selected (using a table of random numbers) and randomly assigned to two groups of 20 each. Each group will become a class, and one class will be designated randomly to receive peer tutoring. Experimental Design The design of this study will be a posttest-only control group design. This design was chosen because it controls for many sources of invalidity and because random assignment to groups was feasible. A pretest is not necessary since all students in the study are assumed to have roughly equal knowledge of the dependent variable, and Stanford Achievement Test scores from annual spring testing were available to check initial group equivalence. Mortality, a potential threat to this design, should not be a problem since the study will last only six weeks. Procedure Prior to the beginning of the school year, 40 of the students who had received an F in English the previous year will be randomly selected and randomly assigned to two groups of 20. By a coin toss, one group will be chosen to participate in peer tutoring. The control group will have regular instruction only. All seventh-grade English students, including the 40 in the study, will be randomly assigned to one of four English classes. The 20 experimental students will be randomly assigned a peer tutor from the eighth grade. All tutors will be members of the National Junior Honor Society with cumulative grade point

11 averages from 3.5 to 4.0. The peer tutors will be trained to ask tutees recall and interpretation questions about reading material and to help tutees recall and apply vocabulary. The tutor/tutee pairs will meet four days a week, after school, for 45 minutes per day. The control group will receive only regular classroom instruction. All students in the experimental and control groups will have the same English teacher for regular classroom instruction, and all classes will learn the same material using the same textbook. After the completion of peer tutoring, the American School Achievement Test: Reading will be administered to all students.

Appendix E: Data for Part B, Section 3 Sample 1: Inferential statistics are data analysis techniques for determining how likely it is that results obtained from a sample, or samples are the same results that would have been obtained from the entire population. Put another way, inferential statistics are used to make inferences about parameters, based on the statistics from a sample (see Chapter 12 to review the distinction between statistics and parameters). In the simplest language, whereas descriptive statistics show how often or how frequent an event or score occurred, inferential statistics help researchers to know whether they can generalize to a population of individuals based on information obtained from a limited number of research participants (see Chapter 5 to review sampling techniques and the importance of a representative sample for making generalizations). Sample 2: As with any normal distribution, a distribution of sample means has not only its own mean (i.e., the mean of the means) but also its own standard deviation (i.e., the difference between each sample mean and the mean of the means). The standard deviation of the sample means is usually called the standard error of the mean. The word error indicates that the various sample means making up the distribution contain some error in their estimate of the population mean. The standard error of the mean reflects how far, on average, any sample mean would differ from the population mean. According to the normal curve percentages (see Figure 12.3), we can say that approximately 68% of the sample means will fall within one standard error on either side of the mean (remember, the standard error of the mean is a standard deviation), 95% will fall between 2 standard errors, and 99+% will fall between 3 standard errors. In other words, if the population mean is 60, and the standard error of the mean is 10, we can expect 68% of the sample means (i.e., means of the scores taken from each sample) to be between 50 and 70 (60 10), 95% of the sample means to fall between 40 and 80 [60 2(10)], and 99% of the sample means to fall between 30 and 90 [60 3(10)]. Thus, in this example it is very likely that a sample mean would be 65, but a sample mean of 98 is highly unlikely because 99% of sample means fall between 30 and 90. Given a number of large, randomly selected samples, we can quite accurately estimate population parameters (i.e., the mean and standard deviation of the whole population) by computing the mean and standard deviation of the sample means. The smaller the standard error, the more accurate the sample means as estimators of the population mean. Sample 3:

14 Based on a test of significance, as we have discussed, the researcher will either reject or not reject the null hypothesis. In other, the researcher will make the decision that the difference between the means is, or is not, likely due to chance. Because we are dealing with probability, not certainty, we never know for sure whether we are absolutely correct. Sometimes we'll make mistakes-we'll decide that a difference is a real difference when it's really due to chance, or we'll decide that a difference is due to chance when it's not. These mistakes are known as Type I and Type II errors.