1. Cooperative Learning Statistical Significance and Effect Size By: Jake Eichten and Shorena Dolaberidze

2. This Chapter Examines: The problem of declining math achievement scores in an elementary school where Beth Miller is a first year principal The problem of declining math achievement scores in an elementary school where Beth Miller is a first year principal The effectiveness of cooperative learning strategies in mathematics The effectiveness of cooperative learning strategies in mathematics

3. This chapter is not meant to make you an expert in cooperative learning, but rather observe principal Beth Miller as she undertakes an examination of the problem and develops good questions to facilitate a review which will help her seek out possible solutions. This chapter is not meant to make you an expert in cooperative learning, but rather observe principal Beth Miller as she undertakes an examination of the problem and develops good questions to facilitate a review which will help her seek out possible solutions. This chapter also demonstrates the importance of statistical significance and effect size when using research as a tool for making important decisions. This chapter also demonstrates the importance of statistical significance and effect size when using research as a tool for making important decisions.

4. Who, Where, What, and Why? Beth Miller-First year principal at Pleasant Valley Elementary School Beth Miller-First year principal at Pleasant Valley Elementary School She and staff recognized math deficiencies in grades 3-5 She and staff recognized math deficiencies in grades 3-5 Staff members suggested cooperative learning as a possible solution Staff members suggested cooperative learning as a possible solution Miller put together a research team to develop a plan of action Miller put together a research team to develop a plan of action

5. Two Questions to Guide the Teams Action 1) What kind of cooperative learning strategies are available? 1) What kind of cooperative learning strategies are available? 2) What cooperative learning strategies have been found to enhance achievement in mathematics generally and in problem solving skills specifically with 4th and 5th grade students with widely varying levels of ability? 2) What cooperative learning strategies have been found to enhance achievement in mathematics generally and in problem solving skills specifically with 4th and 5th grade students with widely varying levels of ability?

6. Action for Question 1 The group researched cooperative learning methods that are specifically appropriate for mathematics instruction. They discovered 6 different strategies that were possibilities. The group researched cooperative learning methods that are specifically appropriate for mathematics instruction. They discovered 6 different strategies that were possibilities.

7. Action for Question 2 The team researched 4 studies of cooperative learning techniques that met the following criteria: The team researched 4 studies of cooperative learning techniques that met the following criteria: -Focus on mathematics education -Sample included elementary or middle school children -Experimental and control conditions imposed on the subjects

8. The 4 Studies The four studies that were chosen for review met the previously mentioned criteria and were all found to be statistically significant and had an acceptable effect size. The four studies that were chosen for review met the previously mentioned criteria and were all found to be statistically significant and had an acceptable effect size.

9. Statistical Significance Statistical significance shows the strength of the relationship between 2 variables Statistical significance shows the strength of the relationship between 2 variables Statistical significance gives the researchers confidence that the difference between 2 variables didn’t occur simply because of chance Statistical significance gives the researchers confidence that the difference between 2 variables didn’t occur simply because of chance

10. Statistical Significance Statistical significance is represented as a p value (p=probability) Statistical significance is represented as a p value (p=probability) -An example would be: p <.05, meaning that the probability of an event occurring by chance is less that 5% -The statistical significance of a coin flip would be represented as p =.5, meaning that 50% of the time the result could be due to chance

11. Statistical Significance Example A computer interactive reading program was compared with a traditional reading program using 50 5th graders who were randomly assigned to treatment and control groups A computer interactive reading program was compared with a traditional reading program using 50 5th graders who were randomly assigned to treatment and control groups The researchers reported a difference of 4 points on a reading achievement test in favor of the computer interactive program. The researchers reported a difference of 4 points on a reading achievement test in favor of the computer interactive program.

12. Example Continued How do we know that if we do this study again, the results won’t favor the traditional reading group? How do we know that if we do this study again, the results won’t favor the traditional reading group? Statisticians developed techniques to test for the possibility that a difference in observed scores might have been due to chance Statisticians developed techniques to test for the possibility that a difference in observed scores might have been due to chance

13. Example Continued The researchers found that the statistical significance in this example would be The researchers found that the statistical significance in this example would be p <.01, meaning the results occurring by chance are less than 1%.

14. Why is Statistical Significance Important? When a statistic is significant, it simply means that the statistic is reliable. When a statistic is significant, it simply means that the statistic is reliable. When using research to assist in making important educational decisions, it is important that the data used is reliable. When using research to assist in making important educational decisions, it is important that the data used is reliable.

15. Effect Size Effect size is important for answering the question “How much of a difference did it make?” (Cooperative learning strategies) Effect size is important for answering the question “How much of a difference did it make?” (Cooperative learning strategies) Effect size allows us to compare the magnitude of experimental treatments from one experiment to another Effect size allows us to compare the magnitude of experimental treatments from one experiment to another Effect size is calculated by the mean difference between the treatment and control groups and dividing it by the average standard deviation of the two groups (ES=M1-M2/Av.SD) Effect size is calculated by the mean difference between the treatment and control groups and dividing it by the average standard deviation of the two groups (ES=M1-M2/Av.SD)

16. Effect Size Example Consider a math study with a treatment group mean score of 10 and a control group mean score of 5, and the average standard deviation of the two groups is 10 Consider a math study with a treatment group mean score of 10 and a control group mean score of 5, and the average standard deviation of the two groups is 10 ES=M1(10)-M2(5)/Av.SD(10) ES=M1(10)-M2(5)/Av.SD(10) -The effect size would be.5 The treatment group averaged 1/2 of a SD higher than the control group The treatment group averaged 1/2 of a SD higher than the control group

17. Example Continued Consider another math study that used a different measure of math achievement with the mean difference being 10 and the average standard deviation being 50 Consider another math study that used a different measure of math achievement with the mean difference being 10 and the average standard deviation being 50 The effect size would be.2 The effect size would be.2 The effect sizes would be a common denominator of the two, which will allow for a comparison between the two studies The effect sizes would be a common denominator of the two, which will allow for a comparison between the two studies Study 1’s ES (.5) would indicate that the treatment effect was was greater than than that of study 2’s (.2) Study 1’s ES (.5) would indicate that the treatment effect was was greater than than that of study 2’s (.2)

18. Desired Effect Size

19. Why is Effect Size Important? It answers the question “How much of a difference did the treatment make?” It answers the question “How much of a difference did the treatment make?” When researching materials to assist is making important educational decisions, it is important to understand how well a treatment worked before deciding to implement it into your own setting. When researching materials to assist is making important educational decisions, it is important to understand how well a treatment worked before deciding to implement it into your own setting.

20. Chapter Conclusions As a result of the research Miller and her team conducted, they found: As a result of the research Miller and her team conducted, they found: Two types of cooperative learning that were proven successful for teaching math computation and math problem solving Two types of cooperative learning that were proven successful for teaching math computation and math problem solving Developed an action memo, which they shared with the full staff explaining their findings and their next steps. Developed an action memo, which they shared with the full staff explaining their findings and their next steps.

21. References Haller, E. J., & Kleine, P. F. (2001). Using educational research: A school educational research: A school Administrator's guide (1st ed.). New York, Administrator's guide (1st ed.). New York, NY: Addison Wesley Longman, Inc. NY: Addison Wesley Longman, Inc.