1. AFFECT FACTORS: CASE OF A PEDAGOGICAL APPROACH FOR PROSPECTIVE TEACHERS Hamide Dogan-Dunlap Qianyin Liang University of Texas at El Paso USA hdogan@utep.edu Partially supported by a UTEP/MSP grant.

2. “math is a fear I have not been able to conquer. The fear of math has put a block on my brain. I don’t like math because I feel very dumb when after so many years I still don't comprehend it.” (A prospective elementary teacher)

3. Majority of prospective teachers in the United States show high anxiety and negative perceptions toward mathematics (Ambrose, 2004; Battista, 1994). Their lack of self-confidence and the fear of failure distract them from learning, and adversely affect their performance in the classroom (Mandler, 1989) Many see mathematics as a highly abstract subject requiring rote memorization of procedures, symbols and formulas. Many have a lack of belief in the importance of mathematics, especially at the K-4 level.

4. There have been reports discussing the role of active learning environments in reshaping students’ perceptions and emotions about mathematics (Fennema, 1989; McDonald; 1989).

5. A set of mediating activities as part of a pedagogical approach, named An Integrated, Collaborative, Field-Based (ICFB) Approach, to teaching and learning mathematics has come about in order to address some aspects of the attitude and perception factors our pre-service teachers hold, consequently enhance their mathematical knowledge.

6. An Integrated, Collaborative, Field-Based (ICFB) Approach Figure. Diagram of the ICFB Approach to Teaching and Learning Mathematics implemented in block I courses with elementary prospective teachers. Adopted from an approach implemented in a middle school block.

7. Study We have investigated the changes the various components of the ICFB approach may have on affect factors. Through quantitative and qualitative means. Reporting on the findings of a comparative study using pre-and post-surveys with Likert-scale statements.

8. Participants Participants came from Three Groups (G1, G2 and G3). Even though all three courses were designed to be active, inquiry-based, and learner-centered, G3 section had minimum student collaboration within the course, and very little active learning took place. It was taught mainly in lecture style. It had occasional project activities in worksheet form with problems that could be solved by applying the concepts and techniques that were covered during earlier lectures

9. All three consisted primarily of English speaking Hispanic students (approximately 85%). There were no male students in G1. G3 had three males, and G2 had two. Everyone was specializing in elementary education in G1. In average ten students in groups G2 and G3 were specializing at the middle school level in either science or mathematics.

10. TableTable. Three prospective teacher groups’ mathematics content courses. Groups G1 G2 G3 Year 2004 2005 2003 Sample Size 21 28 41 The same content coverage √ √ √ The same content instructor √ √ ICFB approach implemented √ In Field-Based Block √ Social, constructive/active learning √ √ Mainly Lecture-Based instruction √

11. Analysis The quantitative analysis of 16 Likert scale statements relating to perception, emotion and confidence are discussed in this paper. Statements were ranked on a 5 point scale: 1=strongly disagree to 5=strongly agree. One-way ANOVA with α=0.05 and α=0.1 significance levels is applied in order to document differences in pre- to post-survey responses within groups, and between groups. Spearman-Brown Split-Half reliability measure is applied to pre- and post-survey statements similar in content to test for the consistency of student responses. The measure ranged from.70 to.90 (Garrett, H. and Woodworth, R, 1967).

12. TableTable. Sixteen statements from pre- and post-surveys. S1Math is simply a bunch of procedures to follow S2Math is a tool used to solve problems and/or find solutions S3Math is difficult S4In order to do math you need to think and use logic and reasoning S5I fear math S6I become frustrated with math S7I do not understand math S8I like math S9I do not like math S10From this course, I expect to improve/improved my own math skills and abilities S11From this course, I expect to learn/learned how to teach math S12From this course, I expect to learn/learned how to make math fun for my future students S13From this course, I expect to become/became more comfortable/confident with my abilities in math S14I believe I can learn and understand math S15I am looking forward to teaching math S16I have the ability to learn new tasks.

13. Results There has been a considerable difference observed among the groups. The group that was exposed to the ICFB approach (G1) differed on many statements showing significantly positive changes from pre- to post-survey in comparing to the other two groups.

14. Table. p-values for between and within group comparison of seven statements from one-way ANOVA. Between Group Comparison Within Group Comparison G1-G3 G1-G2 G2-G3 G1 G2 G3 PrePostPrePost PrePostPre-Post S1 0.03* 0.80.01*0.003*0.450.005*0.3 0.2 S3 0.02* 0.40.001*0.1**0.150.330.01*0.90.5 S5 0.01* 0.1**<0.001*0.04*0.150.470.1**0.60.7 S6 0.02* 0.03*0.04*0.05*0.330.960.20.90.2 S7 0.01* 0.03*0.05*0.002* 0.40.110.05*0.1**0.2 S8 0.01* 0.003*0.002*0.001*0.960.210.90.1**0.8 S16 0.5 0.30.1**0.80.760.460.06**0.20.6 * Statistically significant at α=.05. **Statistically significant at α=0.1.

15. Groups G1 and G2 showed a notable decrease on statement 1, “Math is simply a bunch of procedures to follow,”Math is simply a bunch of procedures to follow G3 displayed a notable increase on the mean scores of its students’ opinions from pre-survey to post-survey.

16. “Math is simply a bunch of procedures to follow” “Math is simply a bunch of procedures to follow” G1 G2 G3 PrePostPrePostPrePost Mean SD 3.5 1.19 3.2 0.89 2.59 1.18 2.26 1.05 2.81 1.12 3.13 1.16 * Statistically significant at α=.05. **Statistically significant at α=0.1.

17. All three groups showed a decrease on the statement, “Math is difficult,” from pre- to post-survey.Math is difficult,” Group G1 is the only group showing a statistically significant decrease on the number of students agreeing with the statement. Groups G1 and G2 showed statistically significant changes on the statement, “I do not understand math.”I do not understand math

18. “Math is difficult.” “I do not understand math” “Math is difficult.” “I do not understand math” G1 G2 G3 PrePostPrePostPrePost Mean SD 4.25* 0.72 3.65* 0.81 3.14 1.18 3.13 1.18 3.56 1.21 3.42 1.08 Mean SD 3.45* 0.94 2.90* 0.83 2.43** 1.03 2.04** 0.88 2.66 1.18 2.41 0.88 * Statistically significant at α=.05. **Statistically significant at α=0.1.

19. Groups G1 and G3 showed a decrease on the statement, “I fear math,”“I fear math,” G1’s decrease is statistically significant. G2 showed a small increase.

20. “I fear math.” G1 G2 G3 PrePostPrePostPrePost Mean SD 3.7** 1.03 3.2** 0.89 2.37 1.28 2.52 1.20 2.83 1.28 2.75 1.21 * Statistically significant at α=.05. **Statistically significant at α=0.1.

21. None of the groups showed a significant change on their opinion of the statement, “I become frustrated with math,” from pre- to post-survey.“I become frustrated with math G1 and G3 however displayed a notable decrease on the number of students agreeing with the statement. Students in G2 did not change their opinion.

22. “I become frustrated with math.” G1 G2 G3 PrePostPrePostPrePost Mean SD 4 0.86 3.65 0.88 2.96 1.29 2.96 1.33 3.28 1.28 2.97 1.24 * Statistically significant at α=.05. **Statistically significant at α=0.1.

23. Groups G1 and G3 did not seem to have very many students changing their opinion on liking mathematics. G2 on the other hand had notably more students changing their opinion favoring an agreement with the statement, “I like math.”“I like math.”

24. “I like math” G1 G2 G3 PrePostPrePostPrePost Mean SD 2.8 0.95 2.76 1 3.5** 0.96 3.87** 0.97 3.51 1.03 3.56 0.91 * Statistically significant at α=.05. **Statistically significant at α=0.1.

25. On statement 16, “I have the ability to learn new tasks,” all three groups reflected similar opinions in both pre- and post- surveys.I have the ability to learn new tasks Group G1 starts with a higher mean in pre-survey, and shows the highest decrease (.31) from pre- to post-survey. This appears to be in contradiction with the behavior G1 had on the other statements; showed significant positive changes on them!

26. “I have the ability to learn new tasks.” G1 G2 G3 PrePostPrePostPrePost Mean SD 4.55** 0.51 4.24** 0.54 4.36 0.49 4.22 0.42 4.4 0.63 4.33 0.64 * Statistically significant at α=.05. **Statistically significant at α=0.1.

27. Conclusions Overall, only the ICFB group (G1) showed notable changes on the six of the seven statements. On the statements addressing negative feelings about mathematics, G1 had significantly fewer numbers of students indicating agreement. G1 also showed an increase in the number of students indicating confidence in their ability to understand mathematics on statements 3,’‘Math is difficult,” and 7 having a post-pre mean difference of -0.55 on statement 7, “I do not understand math.”

28. Furthermore, many students in G1 changed their opinion on mathematics being a bunch of procedure to follow showing a notable decrease on its mean from pre- to post survey. G2 also showed a notable decrease on this aspect of mathematics.

29. G2 showed significant changes on its opinion on two of the seven statements favoring a positive view. More students in G2 also disagreed with the statement “I do not understand math,” indicating an increase in their confidence level.

30. G3 displayed no statistically significant changes on their opinion of any of the seven statements. G3 however had increasingly more students considering mathematics as a bunch of procedures to follow. This may be attributed to the content delivery difference between this group and the other two groups. G3 implemented mainly a lecture mode as opposed to the active collaborative learning G1 and G2 implemented.

31. Implications The implications of the findings for the teaching of mathematics: An approach similar to ICFB man lead to changes in pre-service teachers’ perceptions, confidence and attitudes toward mathematics; Lead to an increase in teachers’ confidence in their ability to learn and think mathematically. Affect Factors Confidence

32. One needs to interpret the results cautiously: Small sample sizes; Groups differed on some factors; The three groups’ pre-survey scores differed significantly; G3 had a different instructor than the instructor who taught the other two groups G1 and G2.

33. Questions/Comments… Hamide Dogan-Dunlap UTEP Mathematical Sciences Department hdogan@utep.edu