Reform some third-grade student's misconception & incorrect belief basis on Gagné's and Schönefeld's Problem-solving frameworks.

Subject Areas : Research in Curriculum Planning

Sepideh Noruzi ¹ , Mahmoud Mehrmohammadi ² , Ebrahim Reyhani ³ , Hashem Fardanesh ⁴ , Mohsen Imani ⁵

1 - PhD student of curriculum development, Tarbiat Modares University, Tehran, Iran.
2 - Full professor of curricumum studies, Modares University, Tehran, Iran.
3 - Associate Professor of Curriculum Planning, Rajaei University,Tehran, Iran.
4 - Associate Professor of Curriculum studies, Modares University, Tehran, Iran.
5 - Assistant professor of curricumum studies, Modares University, Tehran, Iran.

Received: 2017-10-17 Accepted : 2017-10-17 Published : 2017-08-23

Keywords: problem solving, Schoenfeld, Gange, Incorrect belief, Mathematical misconception,

Abstract :

The aim of this Study was modify some of misconceptions and incorrect beliefs about mathematics in third grade students based on some educational implications. The statistic population included all third grade students’ of one school in district 3 of Tehran.  The Sample was comprised of 9 third grade students, based on their pre-test results. Measurement instruments consisted of one researcher-made test, two semi-structured interview, Wechsler intelligence scale for children (IV) and researcher-made stories. Construct and content validity of questionnaire and stories were established by some specialists and experts. Reliability was verified by test-retest and Pearson correlation coefficient was (0.87). The Wilcoxson was used to data analysis through SPSS19 and it revealed a statistically significant difference in between pre-test and post-test. It means, our intervention was successful to improve students’ misconceptions. In addition, interview analysis acknowledged some changes in students’ beliefs about effective factors in success. Using objective, semi-objective and abstract representation in students with high and average working memory and objective, semi-objective representation and drawing pictures by students with weak working memory can help to improve some misconception, and using believe sources like self, others and deductioncan improve incorrect beliefs.

References:

Bakhshalizadeh, S. (2011). Identifying common misconception 4th grade students in mathematics. Retrieved from Tehran: Research project of the academy of Scientific Studies in Education, [persian].

Berk, L. E., & Winsler, A. (1995). Scaffolding Children's Learning: Vygotsky and Early Childhood Education. NAEYC Research into Practice Series. Volume 7: ERIC.

Bull, R., & Espy, K. A. (2006). Working memory, executive functioning, and children’s mathematics. In S. J. Pickering (Eds.), Working memory and education (pp 93-123). New York: Academic Press.

Clerc, J., Miller, P. H., & Cosnefroy, L. (2014). Young children's transfer of strategies: Utilization deficiencies, executive function, and metacognition. Developmental Review, 34(4), 378-393.

Cowan, N. (2005). Working memory capacity. New York: Psychology press.

CTDF. (2012). Second grade mathematics. Tehran: Organization for publish and distribution. Available from: http://www.chap.sch.ir/, [persian].

CTDF. (2013). Third grade mathematics. Tehran: Organization for publish and distribution. Available from: http://www.chap.sch.ir/, [persian].

Desoete, A. (2008). Multi-method assessment of metacognitive skills in elementary school children: How you test is what you get. Metacognition and learning, 3(3), 189.

Desoete, A., Roeyers, H., & Buysse, A. (2001). Metacognition and mathematical problem solving in grade 3. Journal of Learning Disabilities, 34(5), 435-447.

Egan, K. (1989). Teaching as story telling: An alternative approach to teaching and curriculum in the elementary school. Chicago: University of Chicago Press.

Egan, K. (2005). An imaginative approach to teaching. San Francisco.

Eleftherios, K., & Theodosios, Z. (2007). STUDENTS’BELIEFS AND ATTITUDES ABOUT STUDYING AND LEARNING MATHEMATICS. Paper presented at the Proceedings of the 31st Conference on the International Group for the Psychology of Mathematics Education.

Fadai, M. R. (2013). Belief, basic of teaching. Roshd Mathematics Education, 107(29), 16-21, [persian].

Fardanesh, H. (2011). Theoretical Foundations of Instructional Technoligy. Tehran: Samt, [persian].

Francisco, J. M. (2013). The mathematical beliefs and behavior of high school students: Insights from a longitudinal study. The Journal of Mathematical Behavior, 32(3), 481-493.

Gange, E. D. (1985). The cognitive psychology of School Learning. Boston: Little, Brown and Company press.

Gathercole, S. E., Lamont, E., & Alloway, T. P. (2006). Working memory in the classroom. In S. J. Pickering (Eds.), Working memory and education (pp 219-240). New York: Academic press.

Hjalmarson, M., & Salkind, G. M. (2007). Mathematical representations. Gwenanne M. Salkind George Mason University EDCI 857 Preparation and Professional Development of Mathematics Teachers.

Hogan, K. E., & Pressley, M. E. (1997). Scaffolding student learning: Instructional approaches and issues: Brookline Books.

Izadi, M., Reyhani, E., & Ahadi, G. A. (2015). Teaching addition and subtraction: A comparative study on the math curriculum goals and the content of the first-grade math textbook in Iran, Japan, and the USA. Research in Curriculum Planning, 2(19), 55-74, [persian].

Kadivar, P. (2007). Educational psychology. Tehran: Samt, [persian].

Karimi, F., Moradi, A., Kadivar, P., & Nuri, R. K. (2015). Predicting student performance in verbal Math problem based on Cognitive, Metacognitive, and affective Factors. Quarterly journal of education. Quarterly Journal of Education, 31(1), 13-44, [persian].

Leder, G. C., Pehkonen, E., & Törner, G. (2006). Beliefs: A hidden variable in mathematics education? (Vol. 31): Springer Science & Business Media.

Lester Jr, F. K. (2013). Thoughts about research on mathematical problem-solving instruction. The Mathematics Enthusiast, 10(1/2), 245.

Martin, M. O., Mullis, I. V., Foy, P., & Stanco, G. M. (2012). TIMSS 2011 International Results in Science: ERIC.

Marzughi, R. (2005). Metacognition, theories and implications for education. Tehran: Meshkat, [persian].

Mello, R. (2001). The Power of Storytelling: How Oral Narrative Influences Children's Relationships in Classrooms.

Mogonea, F.-R., & Mogonea, F. (2013). The Specificity of Developing Metacognition at Children with Learning Difficulties. Procedia-Social and Behavioral Sciences, 78, 155-159.

Panaoura, A. (2012). Improving problem solving ability in mathematics by using a mathematical model: A computerized approach. Computers in Human Behavior, 28(6), 2291-2297.

Pillen, M., Beijaard, D., & den Brok, P. (2013). Professional identity tensions of beginning teachers. Teachers and Teaching, 19(6), 660-678.

Pound, L., & Lee, T. (2015). Teaching mathematics creatively. New York: Routledge.

Reyhani, E., Ahmadi, G., & Karami Zarandi, Z. (2011). Comparative study of the problem solving process taught in high school mathematics curriculum America, Australia, Japan, Singapore and Iran. Quarterly Journal of Education, 27(1), 115-142, [persian].

Reys, R. E., Lindquist, M., Lambdin, D. V., & Smith, N. L. (2014). Helping children learn mathematics: John Wiley & Sons.

Santagata, R. (2005). Practices and beliefs in mistake-handling activities: A video study of Italian and US mathematics lessons. Teaching and Teacher Education, 21(5), 491-508.

Schiro, M. S. (2004). Oral storytelling and teaching mathematics: Pedagogical and multicultural perspectives. Unites States of America: SAGE publications.

Schoenfeld, A. H. (1985). Mathematical problem solving. London: ACADEMIC Press.

Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D. Grouws (Ed.), Handbook for research on mathematics teaching and learning (pp. 334–370). New York: Macmillan.

Schoenfeld, A. H. (2010). How we think: A theory of goal-oriented decision making and its