The effect of a professional development program workshop about problem solving on mathematics teachers’ ideas about the nature of mathematics, achievements in mathematics, and learning in mathematics

  1. Cerda, Gamal
  2. Pérez, Carlos
  3. Giaconi, Valentina
  4. Perdomo- Díaz, Josefa
  5. Reyes, Cristián
  6. Felmer, Patricio
Journal:
Psychology, Society & Education

ISSN: 1989-709X 2171-2085

Year of publication: 2017

Volume: 9

Issue: 1

Pages: 11-26

Type: Article

DOI: 10.25115/PSYE.V9I1.460 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Psychology, Society & Education

Abstract

Results are presented about the effect of a professional development workshop (hereinafter PDW) for mathematics teachers regarding their beliefs about mathematics (N=82). The workshop, titled RPAula, was aimed at primary school teachers and it focused on problem solving (hereinafter PS). The teachers beliefs under study are related to the nature of mathematics, the learning of mathematics and achievement in mathematics, as well as to the type of practices, experiences, and assessments of the importance of PS and the use of PS in the classroom.The results showed that by participating in the PDW, teachers weakened their ideas about mathematics being a rigid, structured and eminently formal process. Likewise, participation in the PDW also lessened teachers’ perceptions of their leading roles during the learning process, increasing their appraisal of PS practices that are student-centered. It was also noted that teachers’ perception that access to mathematics learning is a fixed condition or an unalterable fact associated with students’ innate abilities, gender or ethnic stereotypes, also diminished. In addition, teachers reported improvements in their self-perception of competence and self-efficacy to implement PS in the classroom with their students. These findings and their implications for mathematics learning and teaching are discussed in this article.

Bibliographic References

  • Alcalá, M. (2002). La construcción del lenguaje matemático. Barcelona: Graó.
  • Araya, P., & Varas, L. (2013). Resolución de Problemas de final abierto en clases de Matemática. Santiago: CIAE, Universidad de Chile.
  • Ávalos, B., & Matus, C. (2010). La formación inicial docente en Chile desde una óptica internacional. Informe nacional del Estudio Internacional IEA TEDS-M. Santiago de Chile: Ministerio de Educación.
  • Bandura, A. (2006). Guide for constructing self-efficacy scales. Self-efficacybeliefs of adolescents, 5, 307-337.
  • Díaz, V. & Poblete, A. (2009). Competencias y Transposición Didáctica: Binomio para un efectivo perfeccionamiento en Matemática. Investigación y Postgrado, 24(2), 77-107.
  • Duffy, M. C., Muis, K. R., Foy, M. J., Trevors, G., &Ranellucci, J. (2016). Exploring Relations between Teachers’ Beliefs, Instructional Practices, and Students’ Beliefs in Statistics.International Education Research, 4(1), 37-66. http://dx.doi.org/10.12735/ier.v4i1p37
  • Engeln, K., Euler, M., &Maass, K. (2013). Inquiry-based learning in mathematics and science: A comparative baseline study of teachers’ beliefs and practices across 12 European countries. ZDM The International Journal on Mathematics Education , 45(6), 823-836.
  • Felmer, P., &Perdomo-Díaz, J. (2016a) Novice Chilean Secondary Mathematics Teachers as Problem Solvers.In Felmer, Pehkonen and Kilpatrick (Eds.).Posing and Solving Mathematical Problems: Advances and New Perspectives. Research in MathematicsEducation Series. Springer, pp. 287-308.
  • Felmer, P., & Perdomo-Díaz, J. (2016b) Un programa de desarrollo profesional docente para el nuevo currículo de matemática: La resolución de problemas como eje articulador. Revista Educación Matemática, in Press.
  • Hu, L.-T., &Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods, 3, 424-453.
  • Kloosterman, P & Stage, F. K. (1992). Measuring Beliefs About Mathematical Problem Solving. School Science and Mathematics, 92(3), 109-115.
  • Koellner, K., Schneider, C., Roberts, S., Jacobs, J., &Borko, H (2008).Using the ProblemSolving Cycle model of professional development to support novice mathematics instructional leaders.In F. Arbaugh& P. M. Taylor (Eds.), Inquiry into Mathematics Teacher Education. Association of Mathematics Teacher Educators (AMTE)
  • Monograph Series, (v. 5), 59-70.
  • Leroy, N., Bressoux, P., Sarrazin, P., &Trouilloud, D. (2007).Impact of teachers’ implicit theories and perceived pressures on the establishment of an autonomy supportive climate.European Journal of Psychology of Education, 22(4), 529-545.
  • Liljedahl, P. (2014). The affordances of using visually random groups in a mathematics classroom. In Y. Li, E. Silver, & S. Li (Eds.) Transforming Mathematics Instruction: Multiple Approaches and Practices. New York, NY: Springer.
  • Marrongelle, K., Sztajn, P., & Smith, M. (2013).Scaling up professional development in an era of common state standards.Journal of TeacherEducation, 64(3), 202-211.
  • Mineduc (2012). Bases Curriculares para la Educación Básica. Unidad de Currículum y Evaluación. Ministerio de Educación, Gobierno de Chile.
  • Mineduc (2014). Resultados Evaluación INICIA 2014. Ministerio de Educación, Gobierno de Chile.
  • Muis, K. R. (2004). Personal epistemology and mathematics: A critical review and synthesis of research. Review of educational research, 74(3), 317-377.
  • National Research Council (2001). Adding it up: Helping children learn mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
  • Niss, M. (2002).Mathematical competencies and the learning of mathematics: the Danish KOM project. http://w3.msi.vxu.se/users/hso/aaa_niss.pdf]
  • Perdomo-Díaz, J. Felmer, P., (2016c) El taller RPAula: Activando la resolución de problemas en las aulas. Profesorado: Revista de Currículum y Formacióndel Profesorado, in Press.
  • Polya, G. (1954). How to Solve It. Princeton, Princeton University Press.
  • Preiss, D., Larraín, A., & Valenzuela, S. (2011). Discurso y pensamiento en el aula matemática chilena. Psykhe (Santiago), 20(2), 131-146.
  • Schoenfeld, A. (1985). Mathematical Problem Solving. Academic Press, Inc., Harcourt Brace Jovanovich, Publishers.
  • Stipek, D.J., Givvin, K.B., Salmon, J.M. &MacGyvers, V.L. (2001). Teachers’ beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17, 213-226.
  • Swan, M. (2006). Designing and using research instruments to describe the beliefs and practices of mathematics teachers. Research in Education, 75(1), 58-70.
  • Tang, S. J., & Hsieh, F. J. (2014). The Cultural Notion of Teacher Education: Future Lower Secondary Teachers’ Beliefs on the Nature of Mathematics, the Learning of Mathematics and Mathematics Achievement. In International Perspectives on Teacher Knowledge, Beliefs and Opportunities to Learn (pp. 231-253).Springer Netherlands.
  • Tatto, M. T. (Ed.). (2013). The Teacher Education and Development Study in Mathematics (TEDS-M): Policy, practice, and readiness to teach primary and secondary mathematics in 17 countries. Technical report. Amsterdam: IEA.
  • Toh, T. L., Quek, K. S., Tay, E. G., Leong, Y. H., Toh, P. C., Ho, F. H. &Dindyal, J. (2013). Infusing Problem Solving into Mathematics Content Course for Pre-service Secondary School Mathematics Teachers.TheMathematicsEducator, 15(1), 98-120.
  • Varas, L., Felmer, P., Gálvez, G., Lewin, R., Martínez, C., Navarro, S., Ortiz, A., &Schwarze, G. (2008). Oportunidades de preparación para enseñar matemática de futuros profesores de educación general básica en Chile. Calidad en la Educación, Consejo Superior de Educación, 29, 63-88.