中学生数学焦虑、信念与成绩关系的研究
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摘要
数学焦虑对学生的数学成绩有着重要的影响，数学焦虑会使个体对数学刺激产生负面的生理反应，对自己解决数学问题的能力怀有错误的信念和消极的态度。学生和公众通常对数学作为课程和个体做为数学学习者有着各自不同的信念，即有着个体差异。
本研究以中学生为研究对象，对国外的有关量表进行了修订并进行了量表施测，对从初一到高三学生的数学焦虑、信念与数学成绩关系进行了探讨，具体的三个研究和结论如下：
1．量表具有较好的信效度，可以用于正式施测。
2．不同数学焦虑水平的被试的数学焦虑和数学成绩有显著差异；不同数学信念水平的被试的数学信念和数学成绩有显著差异；不同数学信念水平的被试的数学焦虑之间存在显著差异；数学成绩的高、中、低三组之间的数学焦虑水平差异显著；数学成绩的高、中、低三组之间的数学信念得分在中等成绩组、高成绩组间差异性显著，其余两个组合：低成绩组与中等成绩组，低成绩组与高成绩组间差异性不显著；数学焦虑不存在性别差异；数学信念性别差异性显著；数学焦虑和数学信念的年级差异性显著。
3．数学信念对数学成绩的影响是通过数学焦虑为中介变量的；数学成绩会直接影响数学信念；数学成绩与数学焦虑之间的影响模式是双向的；数学焦虑与数学信念之间的影响模式是双向的。
Math anxiety has a great influence on the mathematical achievement, math anxiety can rouse a physiological reaction from individuals and produce wrong beliefs and negative attitudes about one's ability to solve mathematical problems. Students
and the public genera have varying beliefs about mathematics as a subject and about
the individual as a learner of mathematics.
This paper revised some scales and measured the participants whose grades vary from grade 1 in junior high school to grade 3 in senior high school, exploring the relation among three factors that are math anxiety, mathematical beliefs and mathematical achievement. I conduct three researches and the conclusions are the follows:
1. These scales had good validity and reliability and can be used in the study.
2.There is significant difference between mathematics anxiety and the mathematical beliefs of the male and female participants. There is significant difference among mathematics anxiety and the mathematical beliefs of the different grades. The results of the study confirmed all the hypotheses except that there exists no gender differences between mathematics anxiety of the male and female participants.
3. Mathematics anxiety is a mediator variable which can mediate the relationship between mathematical beliefs and mathematics achievement; Mathematics had relatively direct effect on mathematical beliefs; there exists a bi-directional influence between mathematics achievement and mathematics anxiety; There also exists a bi-directional influence between mathematical beliefs and mathematics anxiety
本研究以中学生为研究对象，对国外的有关量表进行了修订并进行了量表施测，对从初一到高三学生的数学焦虑、信念与数学成绩关系进行了探讨，具体的三个研究和结论如下：
1．量表具有较好的信效度，可以用于正式施测。
2．不同数学焦虑水平的被试的数学焦虑和数学成绩有显著差异；不同数学信念水平的被试的数学信念和数学成绩有显著差异；不同数学信念水平的被试的数学焦虑之间存在显著差异；数学成绩的高、中、低三组之间的数学焦虑水平差异显著；数学成绩的高、中、低三组之间的数学信念得分在中等成绩组、高成绩组间差异性显著，其余两个组合：低成绩组与中等成绩组，低成绩组与高成绩组间差异性不显著；数学焦虑不存在性别差异；数学信念性别差异性显著；数学焦虑和数学信念的年级差异性显著。
3．数学信念对数学成绩的影响是通过数学焦虑为中介变量的；数学成绩会直接影响数学信念；数学成绩与数学焦虑之间的影响模式是双向的；数学焦虑与数学信念之间的影响模式是双向的。
Math anxiety has a great influence on the mathematical achievement, math anxiety can rouse a physiological reaction from individuals and produce wrong beliefs and negative attitudes about one's ability to solve mathematical problems. Students
and the public genera have varying beliefs about mathematics as a subject and about
the individual as a learner of mathematics.
This paper revised some scales and measured the participants whose grades vary from grade 1 in junior high school to grade 3 in senior high school, exploring the relation among three factors that are math anxiety, mathematical beliefs and mathematical achievement. I conduct three researches and the conclusions are the follows:
1. These scales had good validity and reliability and can be used in the study.
2.There is significant difference between mathematics anxiety and the mathematical beliefs of the male and female participants. There is significant difference among mathematics anxiety and the mathematical beliefs of the different grades. The results of the study confirmed all the hypotheses except that there exists no gender differences between mathematics anxiety of the male and female participants.
3. Mathematics anxiety is a mediator variable which can mediate the relationship between mathematical beliefs and mathematics achievement; Mathematics had relatively direct effect on mathematical beliefs; there exists a bi-directional influence between mathematics achievement and mathematics anxiety; There also exists a bi-directional influence between mathematical beliefs and mathematics anxiety
引文
1．陈英和，耿柳娜，数学焦虑研究的认知取向，心理科学，2002．6
2．中华人民共和国教育部制定《全日制义务教育数学课程标准(实验稿)》，北京师范大学出版社，2001
3．赵继源，数学焦虑的成因及对策，广西师院学报(自然科学版)，2001
4．鞠显英，初中生数学学习分化的原因及教学对策，中国基础教育网(主管单位：教育部基础教育司，北京师范大学)，2001
5．新浪科技，心理学家发现“数学焦虑综合症”，新浪网，2001．5．21
6．专家说中小学数学教学要改，中国青年报，2000．8．10
7．车文博主编，弗洛伊德文集，长春出版社，长春，1998
8．陈淑美，数学焦虑症新解药，光华画报杂志社，第二十三卷第七期，1998
9．林佳颖，中学生数学焦虑的预防与辅导，台湾，1997
10．涂金堂，中学生数学焦虑的预防与辅导，菁莪，第8卷第2期，台湾，1997
11．陈英和，认知发展心理学，浙江人民教育出版社，1996
12．钱铭怡，心理咨询与心理治疗，北京大学出版社，北京，1994
13．J．Flavell著，认知发展，1976
14. Ashcraft, M.H. Cognitive psychology and simple arithmetic: A review and summery of new directions. Mathematical Cognition, 1995,3-34.
15. Ashcraft, M.H.& Kirk, E.P. The relationships among working memory, math anxiety, and performance, Journal of experimental psychology:General,2001,130,224-237
16. Ashcraft, M.H. Kirk, E.P., &Hopko, D. On the cognitive consequences of mathematics anxiety. In C. Donlan(Ed.),.The development of mathematical skill,East Sussex,Great Britain:Psychology Press, 1988,175-196.
17. Ashcraft, M.H.,& Faust, M.W. Mathematics anxiety and mental arithmetic performance: An exploratory investigation. Cognition and Emotion, 1994,8,97-125
18. Campbell, Kathleen T.;Evans, Cay. Education(Chula Vista, Calif.) v. 117(Spring 1997)p.332-8
19. Faust, M.W., Ashcraft, M.H.& Fleck, D.E. Mathematics anxiety effects in simple and complex addition. Mathematical Cognition, 1996,2(1),25-62
20. Eysenck,M.W.,&Calvo,M.G.Anxiety and performance:The processing efficiency theory.Cognition and emotion,1992,6,409-434
21. Hopko, D.R., Ashcraft, M.H., Gute, J., Ruggiero, K.J.,& Lewis, C. Mathematics anxiety and working memory: Support for the existence of a deficient inhibition mechanism. Journal of Anxiety Disorders,1998,12,343-355Carpenter, T. P., Lindquist, M.M., Brown, C. A., Kouba, V. L., Silver, E. A., & Swafford, J. O. (1988). Results of the fourth NAEP assessment of mathematics: Trends and conclusions. Arithmetic Teacher, 35(8), 14-19.
22. Charles, R., & Lester, F. (1982). Teaching problem solving: What, why, & how. Palo Alto, CA: Dale Seymour Publications.
23. Dossey, J. A., Mullis, I. V. S., Lindquist, M. M., & Chambers, D. L. (1988). The mathematics report card, are we measuring up? Trends and achievement based on the 1986 national assessment. (NAEP Report No. 17-M-01).Princeton, NJ: Educational Testing Service.
24. Dweck, C. S., & Bempechat, J. (1983). Children's theories of intelligence: Consequences for learning. In S. G. Paris, G. M. Olson, & H. W. Stevenson (Eds.), Learning and motivation in the classroom (pp. 239-256).Hillsdale, NJ: Lawrence Erlbaum Associates.
25. Fennema, E., & Sherman, J. (1976). Fennema-Sherman mathematics attitudes scales: Instruments designed to measure attitudes toward the learning of mathematics by females and males. (Available from Elizabeth Fermema, Wisconsin Center for Educational Research, 1025 W. Johnson St., Madison, WI 53706)
26. Fennema, E. & Sherman, J.A. 1976. Fennema-Sherman mathematics attitudes scales. JSAS Catalog of Selected Documents in Psychology, 6, 31 (Ms. No. 1225).
27. Furinghetti, F. (1996). A theoretical framework for teachers' conceptions. In E. Pehkonen (Ed.), Current State of Research on Mathematical Beliefs Ⅲ. Proceedings of the MAVI-3 Workshop (pp.19-25). University of Helsinki. Department of Teacher Education. Research Report 170.
28. Furinghetti, F. & Pehkonen, E. 2002. Rethinking Characterizations of Belief. To appear in: Beliefs: A hidden variable in mathematics education? (eds. G. Leder, E. Pehkonen & G. Trner). Utrecht: Kluwer.Goldin, G. 2002. Affect, recta-affect, and mathematical belief structures. To appear in: Beliefs: A hidden variable in mathematics education? (eds. G. Leder, E. Pehkonen & G. Trner). Utrecht:
Kluwer.
29. Green, T. F. 1971. The Activities of Teaching. Tokyo: McGraw-Hill Kogakusha.
30. Grigutsch, S. 1998. On pupils' views of mathematics and self-concept: developments, structures and factors of influence. In E. Pehkonen & G. Trner (Eds.) The state-of-art in mathematics-related belief research. Results of the MAVI activities. University of Helsinki. Department of Teacher Education. Research report 195, 169-197.
31. Hembree, R.(1990).The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics education. 1990,21,33-46
32. Kloosterman, P. (1988). Self-confidence arrd motivation in mathematics. Journal of Educational Psychology, 80, 345-351.
33. Lester, F. K., Garofalo, J. & Kroll, D. L. 1989. Self-Confidence, Interest, Beliefs, and Metacognition: Key Influences on Problem Solving Behavior. In: Affects and Mathematical Problem Solving (eds. D. B. McLeod & V. M. Adams), 75-88. New York: Springer-Verlag.
34. Mathematics Views(1998).Literature on Mathematical Beliefs. http://www.uni-d uisburg.de/FB11/PROJECTS/MAVI/.University of Education Freiburg (Germany).
35. McLeod, D.B. & Adams, V.M. (eds.) 1989. Affects and Mathematical Problem Solving. New York: Springer-Verlag.
36. McLeod, D.B. 1992. Research on Affect in Mathematics Education: A Reeonceptualization. In: Handbook of research on mathematics learning and teaching (ed. D.A. Grouws), 575-596. New York: Macmillan.
37. National Research Council (1989). Everybody counts: A report to the nation on the future of mathematics education (summary). Washington, DC: National Academy Press.
38. Newstead, K. (1998). Aspects of children's mathematics anxiety. Educational Studies in Mathematics, 36(1), 53-71
39. Nibbelink, W. H., Stockdale, S. R., Hoover, H. D., & Mangru, M. (1987). Problem solving in the elementary grades: Textbook practices and achievement trends over the past thirty years. Arithmetic Teacher, 35(1), 34-37.
40. Op 't Eynde, P., De Corte, E. & Verschaffel, L. 2002. Framing students' mathematics-related beliefs: A quest for conceptual clarity and a comprehensive categorization. To appear in: Beliefs: A hidden variable in mathematics education?
(eds. G. Leder, E. Pehkonen & G. Trmer). Utrecht: Kluwer.
41. Pajares, M. F. 1992. Teachers' beliefs and educational research: Cleaning up a messy construct. Review of Educational Research 62 (3), 307-332.
42. Pajares, F., & Kranzler, J.(1995a). The role of self-efficacy, self-concept, anxiety, and ability in mathematical problem-solving. Paper presented at the meeting of the Amerecan Educational Research Association, San Francisco.
43. Pehkonen, E. 1994. On Teachers' Beliefs and Changing Mathematics Teaching. Journal für Mathematik-Didaktik 15 (3/4), 177-209.
44. Pietil, A. 2002. Luokanopettajaopiskelijoiden matematiikkakruva: matematiikkakokemukset matematiikkakuvan muodostajina [Pre-service elementary teachers' views of mathematics: The role of mathematics experiences in forming the views of mathematics]. University of Helsinki. Department of Teacher Education. Research Report 238.
45. Richardson, F.C.,&Suinn, R.M. The Mathematics Anxiety Rating Scale. Journal of counseling Psychology, 1972,19,551-554.
46. Richardson, F. C.,& Suinn, R.M.:1972,'Is Math Anxiety a Local Phenomenan?A Study of Prevalence and Dimensionality', Journal of Counseling Psychology 29, 39-47
47. Ruffell, M., Mason, J. & Allen, B. 1998. Studying attitude to mathematics. Educational Studies in Mathematics 35, 1-18.
48. Schoenfeld, A. H. (1985). Metacognitive and epistemological issues in mathematical understanding. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 361-379). Hillsdale, NJ: Lawrence Erlbaum Associates.
49. Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of "well-taught" mathematics courses. Educational Psychologist, 23, 145-166.
50. Silver, E. A. (1985). Research in teaching mathematical problem solving: Some underrepresented themes and directions. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 247-266). Hillsdale, NJ: Lawrence Erlbaum Associates.
51. Schoenfeld, A. H. 1985. Mathematical problem solving. Orlando (FL): Academic Press.
52. Schoenfeld, A. H. 1992. Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In: Handbook of research on
mathematics learning and teaching (ed. A. D. Grouws), 334-370. New York: Macmillan.
53. Schoenfeld, A.H. 1987. What's All the Fuss about Metacognition? In: Cognitive Science and Mathematics Education (ed. A.H. Schoenfeld), 189-215. Hillsdale (NJ): Lawrence Erlbaum Associates.
54. Sfard, A. 1991. On the dual nature of the mathematical objects. Educational Studies in Mathematics, 22, 1-36.
55. Thompson, A. 1992. Teachers' beliefs and conceptions: A synthesis of the research. In A. D. Grouws (Ed.), Handbook of research on mathematics learning and teaching (pp. 127-146). New York: Macmillan.
56. Tobias, S. (1978). Overcoming math anxiety.New York: Norton.
57. Sepie, A.C., & Keeling, B.: 1978,'The Relationship between Types of Anxiety and Under-Achievement in Mathematics',Journal of Educational Research 72, 15-19
58. Skemp,R.R.:1986,The Psychology of Learning Mathematics, Penguin, Harmondsworth.
59. Stodolsky, S.S.:1985.'Telling Math:Origins of Math Aversion and Anxiety in Elementary and Secondary School Students', Journal of Educational Psychology 80,210-2
2．中华人民共和国教育部制定《全日制义务教育数学课程标准(实验稿)》，北京师范大学出版社，2001
3．赵继源，数学焦虑的成因及对策，广西师院学报(自然科学版)，2001
4．鞠显英，初中生数学学习分化的原因及教学对策，中国基础教育网(主管单位：教育部基础教育司，北京师范大学)，2001
5．新浪科技，心理学家发现“数学焦虑综合症”，新浪网，2001．5．21
6．专家说中小学数学教学要改，中国青年报，2000．8．10
7．车文博主编，弗洛伊德文集，长春出版社，长春，1998
8．陈淑美，数学焦虑症新解药，光华画报杂志社，第二十三卷第七期，1998
9．林佳颖，中学生数学焦虑的预防与辅导，台湾，1997
10．涂金堂，中学生数学焦虑的预防与辅导，菁莪，第8卷第2期，台湾，1997
11．陈英和，认知发展心理学，浙江人民教育出版社，1996
12．钱铭怡，心理咨询与心理治疗，北京大学出版社，北京，1994
13．J．Flavell著，认知发展，1976
14. Ashcraft, M.H. Cognitive psychology and simple arithmetic: A review and summery of new directions. Mathematical Cognition, 1995,3-34.
15. Ashcraft, M.H.& Kirk, E.P. The relationships among working memory, math anxiety, and performance, Journal of experimental psychology:General,2001,130,224-237
16. Ashcraft, M.H. Kirk, E.P., &Hopko, D. On the cognitive consequences of mathematics anxiety. In C. Donlan(Ed.),.The development of mathematical skill,East Sussex,Great Britain:Psychology Press, 1988,175-196.
17. Ashcraft, M.H.,& Faust, M.W. Mathematics anxiety and mental arithmetic performance: An exploratory investigation. Cognition and Emotion, 1994,8,97-125
18. Campbell, Kathleen T.;Evans, Cay. Education(Chula Vista, Calif.) v. 117(Spring 1997)p.332-8
19. Faust, M.W., Ashcraft, M.H.& Fleck, D.E. Mathematics anxiety effects in simple and complex addition. Mathematical Cognition, 1996,2(1),25-62
20. Eysenck,M.W.,&Calvo,M.G.Anxiety and performance:The processing efficiency theory.Cognition and emotion,1992,6,409-434
21. Hopko, D.R., Ashcraft, M.H., Gute, J., Ruggiero, K.J.,& Lewis, C. Mathematics anxiety and working memory: Support for the existence of a deficient inhibition mechanism. Journal of Anxiety Disorders,1998,12,343-355Carpenter, T. P., Lindquist, M.M., Brown, C. A., Kouba, V. L., Silver, E. A., & Swafford, J. O. (1988). Results of the fourth NAEP assessment of mathematics: Trends and conclusions. Arithmetic Teacher, 35(8), 14-19.
22. Charles, R., & Lester, F. (1982). Teaching problem solving: What, why, & how. Palo Alto, CA: Dale Seymour Publications.
23. Dossey, J. A., Mullis, I. V. S., Lindquist, M. M., & Chambers, D. L. (1988). The mathematics report card, are we measuring up? Trends and achievement based on the 1986 national assessment. (NAEP Report No. 17-M-01).Princeton, NJ: Educational Testing Service.
24. Dweck, C. S., & Bempechat, J. (1983). Children's theories of intelligence: Consequences for learning. In S. G. Paris, G. M. Olson, & H. W. Stevenson (Eds.), Learning and motivation in the classroom (pp. 239-256).Hillsdale, NJ: Lawrence Erlbaum Associates.
25. Fennema, E., & Sherman, J. (1976). Fennema-Sherman mathematics attitudes scales: Instruments designed to measure attitudes toward the learning of mathematics by females and males. (Available from Elizabeth Fermema, Wisconsin Center for Educational Research, 1025 W. Johnson St., Madison, WI 53706)
26. Fennema, E. & Sherman, J.A. 1976. Fennema-Sherman mathematics attitudes scales. JSAS Catalog of Selected Documents in Psychology, 6, 31 (Ms. No. 1225).
27. Furinghetti, F. (1996). A theoretical framework for teachers' conceptions. In E. Pehkonen (Ed.), Current State of Research on Mathematical Beliefs Ⅲ. Proceedings of the MAVI-3 Workshop (pp.19-25). University of Helsinki. Department of Teacher Education. Research Report 170.
28. Furinghetti, F. & Pehkonen, E. 2002. Rethinking Characterizations of Belief. To appear in: Beliefs: A hidden variable in mathematics education? (eds. G. Leder, E. Pehkonen & G. Trner). Utrecht: Kluwer.Goldin, G. 2002. Affect, recta-affect, and mathematical belief structures. To appear in: Beliefs: A hidden variable in mathematics education? (eds. G. Leder, E. Pehkonen & G. Trner). Utrecht:
Kluwer.
29. Green, T. F. 1971. The Activities of Teaching. Tokyo: McGraw-Hill Kogakusha.
30. Grigutsch, S. 1998. On pupils' views of mathematics and self-concept: developments, structures and factors of influence. In E. Pehkonen & G. Trner (Eds.) The state-of-art in mathematics-related belief research. Results of the MAVI activities. University of Helsinki. Department of Teacher Education. Research report 195, 169-197.
31. Hembree, R.(1990).The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics education. 1990,21,33-46
32. Kloosterman, P. (1988). Self-confidence arrd motivation in mathematics. Journal of Educational Psychology, 80, 345-351.
33. Lester, F. K., Garofalo, J. & Kroll, D. L. 1989. Self-Confidence, Interest, Beliefs, and Metacognition: Key Influences on Problem Solving Behavior. In: Affects and Mathematical Problem Solving (eds. D. B. McLeod & V. M. Adams), 75-88. New York: Springer-Verlag.
34. Mathematics Views(1998).Literature on Mathematical Beliefs. http://www.uni-d uisburg.de/FB11/PROJECTS/MAVI/.University of Education Freiburg (Germany).
35. McLeod, D.B. & Adams, V.M. (eds.) 1989. Affects and Mathematical Problem Solving. New York: Springer-Verlag.
36. McLeod, D.B. 1992. Research on Affect in Mathematics Education: A Reeonceptualization. In: Handbook of research on mathematics learning and teaching (ed. D.A. Grouws), 575-596. New York: Macmillan.
37. National Research Council (1989). Everybody counts: A report to the nation on the future of mathematics education (summary). Washington, DC: National Academy Press.
38. Newstead, K. (1998). Aspects of children's mathematics anxiety. Educational Studies in Mathematics, 36(1), 53-71
39. Nibbelink, W. H., Stockdale, S. R., Hoover, H. D., & Mangru, M. (1987). Problem solving in the elementary grades: Textbook practices and achievement trends over the past thirty years. Arithmetic Teacher, 35(1), 34-37.
40. Op 't Eynde, P., De Corte, E. & Verschaffel, L. 2002. Framing students' mathematics-related beliefs: A quest for conceptual clarity and a comprehensive categorization. To appear in: Beliefs: A hidden variable in mathematics education?
(eds. G. Leder, E. Pehkonen & G. Trmer). Utrecht: Kluwer.
41. Pajares, M. F. 1992. Teachers' beliefs and educational research: Cleaning up a messy construct. Review of Educational Research 62 (3), 307-332.
42. Pajares, F., & Kranzler, J.(1995a). The role of self-efficacy, self-concept, anxiety, and ability in mathematical problem-solving. Paper presented at the meeting of the Amerecan Educational Research Association, San Francisco.
43. Pehkonen, E. 1994. On Teachers' Beliefs and Changing Mathematics Teaching. Journal für Mathematik-Didaktik 15 (3/4), 177-209.
44. Pietil, A. 2002. Luokanopettajaopiskelijoiden matematiikkakruva: matematiikkakokemukset matematiikkakuvan muodostajina [Pre-service elementary teachers' views of mathematics: The role of mathematics experiences in forming the views of mathematics]. University of Helsinki. Department of Teacher Education. Research Report 238.
45. Richardson, F.C.,&Suinn, R.M. The Mathematics Anxiety Rating Scale. Journal of counseling Psychology, 1972,19,551-554.
46. Richardson, F. C.,& Suinn, R.M.:1972,'Is Math Anxiety a Local Phenomenan?A Study of Prevalence and Dimensionality', Journal of Counseling Psychology 29, 39-47
47. Ruffell, M., Mason, J. & Allen, B. 1998. Studying attitude to mathematics. Educational Studies in Mathematics 35, 1-18.
48. Schoenfeld, A. H. (1985). Metacognitive and epistemological issues in mathematical understanding. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 361-379). Hillsdale, NJ: Lawrence Erlbaum Associates.
49. Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of "well-taught" mathematics courses. Educational Psychologist, 23, 145-166.
50. Silver, E. A. (1985). Research in teaching mathematical problem solving: Some underrepresented themes and directions. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 247-266). Hillsdale, NJ: Lawrence Erlbaum Associates.
51. Schoenfeld, A. H. 1985. Mathematical problem solving. Orlando (FL): Academic Press.
52. Schoenfeld, A. H. 1992. Learning to think mathematically: problem solving, metacognition, and sense making in mathematics. In: Handbook of research on
mathematics learning and teaching (ed. A. D. Grouws), 334-370. New York: Macmillan.
53. Schoenfeld, A.H. 1987. What's All the Fuss about Metacognition? In: Cognitive Science and Mathematics Education (ed. A.H. Schoenfeld), 189-215. Hillsdale (NJ): Lawrence Erlbaum Associates.
54. Sfard, A. 1991. On the dual nature of the mathematical objects. Educational Studies in Mathematics, 22, 1-36.
55. Thompson, A. 1992. Teachers' beliefs and conceptions: A synthesis of the research. In A. D. Grouws (Ed.), Handbook of research on mathematics learning and teaching (pp. 127-146). New York: Macmillan.
56. Tobias, S. (1978). Overcoming math anxiety.New York: Norton.
57. Sepie, A.C., & Keeling, B.: 1978,'The Relationship between Types of Anxiety and Under-Achievement in Mathematics',Journal of Educational Research 72, 15-19
58. Skemp,R.R.:1986,The Psychology of Learning Mathematics, Penguin, Harmondsworth.
59. Stodolsky, S.S.:1985.'Telling Math:Origins of Math Aversion and Anxiety in Elementary and Secondary School Students', Journal of Educational Psychology 80,210-2