Extensively Researched by Sexy Kim Pinckney, Sexy Gina Hart, and Sexy Philisa Thomas
Please note that this report will folow as the union of two separate research efforts, that eventually join as they speak to one another
Table of Contents
Importance of Research Problem
What findings mean interms of class literature
The Beginning: My question began with thoughts of math and what is required of an effective math student. Within the context of specific problems, I wanted to find out what the most determining factor was. Are math problems more about sex, effort, interest, experience, or the math itself? And so my search began using data from a previously conducted study of fifth and sixth grade students.
Our problem deals with what brings about affective mathematics. In terms of the three most frequently used strategies, did students' ability to explain their strategy use make them more effective math problem solvers?
Kim's Question: I thought my research question was important for a number of reasons. Traditionally, thoughts of schooling evoke ideas of reading, writing, and arithmetic. So, math has always been a part of the basic educational plan
Hazel Markus and Paula Nurius proposed the idea of possible selves that suggests how a student views their self can determine their actions through a relationship of cognition and motivation (954). And from this I was thinking of whether or not such cognitive processes affect ones accuracy in math.
In order for students to develop good study skills, "it is important to know how likely it is that students will reflect on their thinking and how accurately that reflection will be. Similarly, good problem-solving calls for using efficiently what you know" (Schoenfeld 190).
Metacognition-strategy tie in: Alan A. Schoenfeld stated that planning is an important part of the aspects of self-regulation management that are vital to the metacognitive process (Schoenfeld 190).
"Many students have come to believe that school mathematics consists of mastering formal procedures that are completely divorced fom real life, from discovery, and from problem-solving" (Schoenfeld 197). could talk about behavioral implications
"Knowing a lot of mathematics may not do students much good if their beliefs keep them from using it" (Schoenfeld, 198)
"The student is not an empty vessel into which knowledge must be loaded but an active participant in the process of knowledge construction" (Stigler et al 150).
Philisa and Gina's Question: This research problem is important because it can allow for policy and teaching improvements. If understanding and articulating one's problem solving process truly leads to high math scores, teachers might consider devoting more class time to the teaching of strategy use.
Kim's Question:
10/23/00- Once I felt comfortable enough with SPSS to attempt my research, I began the process. First, I had to make a few decisions, one of which was whether or not to use data from the pro-study or the main study. I decided to work with the pro-study children (those students who talk out loud while they work). This group consisted of fifty students and I chose to work using this group as the sample because (1) they were a smaller group from the whole and therefore, I felt it would be easier for me to interpret their data. (2) Also, I was attracted to the fact that these students were the ones that communicate while working. This communication to me seemed like an example of the metacognitive process. This verball factor could possibly lead to some more accurate data (For example, often times teachers might make less acurrate judgements about a students effort if they don't verbalize these efforts. Or a child might not accurrately communicate answers to questions in an interview regarding interest if they had never thought about it. Verbalizing is one indicator of this thought process.) In Stigler et al's "Traditions in School: Mathematics in Japanese and American Elementary Classrooms," the article claims that a reason for the success in Math of Japanese elementary schools over American elementary schools has a direct correlation to the amount of emphasis placed on student verbalization. Two times as much student talking goes on in Japanes that American classrooms (Stigler et al
Next, I set right into my
research. Using the study, I pulled the scores on the math test given
that consisted of twelve questions. The results are as follows:
SCORE
From these results, I divided the sample into two groups. The first group would constitute the "Majority-Right" group and the other group to represent the "Majority-Wrong" group. I divided the groups so that the "Majority-Right" group would really represent the group of students that got a majority correct of the twelve math questions and the same for the "Majority-Wrong" group, that they represent the students that got a majority of the math problems wrong. Therefore, I divided the group where there was a shift in majority right to majority wrong. The high-scorers got at least seven out of twelve problems correct (There were no students who got a total of 6 correct). The low scorers were those that got five or below correct. I was not concerned here with how many students fell into each category because I didn't want to sacrifice the acurracy of the group label. The group of the "Majority-Right" group consisted of forty-one students, while the "Majority-Wrong" group consisted of eight students.
Next, I began to run T-tests to see whether or not a students' interest or non-interest in the word problem were significant in determining the scores on the problems. The T-test compares sample means by calculating Student's t and displays the two-tailed probability of the difference between the means (SPSS Reference Guide 701). In this case, I computed the score just as before, and selected the "Majority Right" group by specifying "select if (score>=7). Then I computed interest (int) by calculating all of the interest mastery level variables, and I computed boring (bor) by calculating all of the non-interest mastery level problems. I ran the T-test for a paired sample of int and bor as follows:
T-test for Paired Samples Pairs Significance Paired Differences
From these results, I could see that the issue of interest was not a significant factor in determining the correctness (right or wrong) of the math problems for the "Majority Right" group.
10/30/00- I ran the same T-test for the "Majority-wrong" group in the same manner. The findings there were:
T-test for Paired Samples Pairs Significance Paired Differences
For this group, too, the interest, non-interest variables were not significant in determining the scores on the math problems.
Gina and Philisa's Question:
Initially Philisa and I became partners because we were both interested in students' perception of performance versus actual performance in reading; however through a great deal of confusion and and clarifications, we eventualy decided that what we might try to pinpoint was the correlation between using peronal experience as a strategy and the number of correct problems. Philisa and I began working on our project under the assumption that personal experience would be a frequently used, and highly effective strategy for solving math problems. Thus we decided to find the number of students who employed "personal experience" as a strategy (noted as either the child explaining use (1) or the interviewer inferring use(2)) versus non use of the strategy (coded as no strategy(0) or unable to see strategy(3)). Using SPSS program we ran a frequency file where we recoded 1's and 2's as using the strategy and 0's and 3's as not using the strategy. Much to our surprise, only 2 of 50 students used personal experience at all. Based on these findings, we decided to run frequencies for all the strategy use in math (with the same yes/no recoding) to see just what strategies were being used.
In the lab session that followed, Philisa and I attempted to run a frequency of the strategies; however, due to errors in programming and misunderstanding that period was spent finding a frequency for all 19 strategies at once and did not help very much except for the valuable lessons in programming that we picked up through our many errors.
We then finally found frequencies for each of the 19 on their own where they were run as frequencies of strictly use and not use (1&2=1) and (0&3=0). We found that "parts"84% , "Key words" 76% and "Re-read for Comprehension" %92 were the top three strategies reported as used. Here "parts" means that the child exibited a strategy where s/he broke the strategy into parts to understand it better, "Key Words" indicated the strategy where the student used key words in the math word problem to understand some aspect of the problem, and "Re-read for comprehension" meant just that. We singled out these top three strategies because, as we had learned in dealing with "personal experience" strategy, not all the strategies would have a significant amount of users to then run other tests on. Thus, these three were the strategies with sufficient significance to find further data about. Then we decided to run an ID to check how many of the students who used the strategy were able to explain that they did in fact use it. In this way were able to see how many explained their use of the strategy, and how many were reported to have used it by the interviewer (subtracting the 1 score (explainers) from the total use seen in the regular frequencies. We hoped that this would lead to some discussion of metacognition.
We then joined with Kim Pinckney's study on recipes for successful math students (in terms of score) and were able to check the scores of the students with metacognition (here the ability to talk about their strategy use) to see if the presence of metacognition leads to higher performance on the math problems.
graph of top 3 strategies
graph of percentage of kids who explained(themselves) strategy use
suggestions were: Stigler (10/25)Japanese School article re: talking about math instead of just doing it; also, 10/4 Siegler artical and Gaskins: understanding and control of strategy
Schoenfeld article for metacognitive suggestions for practice
BRAP article to encourage metacognitive processes
"American teachers place little emphasis on coherence across lessons" (Stigler et al 156).
"Students in American lessons work many more problems than do their Japanese counterparts, and come to emphasize quantity rather than quality of solutions" (Stigler et al 161).
"The Japanese lesson plan emphasizes what students will think, not what the teacher will say or do. . .The teacher divides the lesson into three steps: understanding the problem, investigation, and generalization" (Stigler et al 160).