Abstract
When teachers participating in a professional development workshop discuss their experiences during a problem-solving session, they sometimes express a sense of imbalance or discomfort rooted in the contrast between these experiences and their abilities and previous mathematical self-perceptions, beliefs, and knowledge. These are expressions of what we call mathematical tensions, and it is the purpose of this chapter to classify them and to discuss their appearance as a healthy sign of the effectiveness of the professional development workshop. Our data have been taken from the first of eight sessions of a 30-hour workshop held over the course of 1 year, which included 147 elementary and middle school teachers.
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01 February 2020
The published version of this book included multiple errors in code listings throughout the book. These code listings have now been corrected and text has been updated.
Notes
- 1.
Facilitator, multiplier, and teacher trainer are some of the words used to identify the person working with teachers in PD programs. We prefer to use the word monitor, which is regularly used by the ARPA team to mean a person who guides, supervises, and instructs, both in Spanish and English.
References
Adler, J. (1998). A language of teaching dilemmas: Unlocking the complex multilingual secondary mathematics classroom. For the Learning of Mathematics, 18(1), 24–33.
Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In G. Sykes & L. Darling-Hammond (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3–32). San Francisco: Jossey Bass.
Bellei, C., Cabalin, C., & Orellana, V. (2018). The student movements to transform the Chilean market-oriented education system. In R. Cortina & C. Lafuente (Eds.), Civil society organizations in Latin American education: Case studies and perspectives on advocacy. New York: Routledge.
Bellei, C., & Morawietz, L. (2016). Strong content, weak tools: Twenty-first-century competencies in the Chilean educational reform. In F. Reimers & C. Chung (Eds.), Teaching and learning for the twenty-first century. Cambridge, MA: Harvard Education Press.
Berry, A. (2007). Tensions in teaching about teaching: Understanding practice as a teacher educator. Dordrecht, The Netherlands: Springer.
Creswell, J. W. (2008). Educational research: Planning, conducting and evaluating quantitative and qualitative research (3rd ed.). Upper Saddle River, NJ: Pearson/Merrill Prentice Hall.
Desimone, L., Porter, A. C., Garet, M. S., Yoon, S., & Birman, B. F. (2002). Effects of professional development on teacher’s instruction: Results from a three-year longitudinal study. Educational Evaluation and Policy Analysis, 24(2), 81–112.
Felmer, P., Perdomo-Díaz, J., & Reyes, C. (2019). The ARPA experience in Chile: Problem solving for teachers’ professional development. In P. Liljedahl & M. Santos-Trigo (Eds.), Mathematical problem solving. ICME-13 monographs. Cham, switzerland: Springer.
Garet, M. S., Porter, A. C., Desimone, L., Birman, B. F., & Suk Yoon, K. (2001). What makes professional development effective? Results from a national sample of teachers. American Educational Research Journal, 38(4), 915–945. https://doi.org/10.3102/00028312038004915
Grant, S. G. Peterson, P. L. Shojgreen-Downer, A. (1996). Learning to teach Mathematics in the Context of Systemic Reform. American Educational Reserach Journal. Vol. 33, Nº2, pp. 509–541.
Koellner, K., Jacobs, J., Borko, H., Schneider, C., Pittman, M. E., Eiteljorg, E., et al. (2007). The problem-solving cycle: A model to support the development of teachers’ professional knowledge. Mathematical Thinking and Learning, 9(3), 273–303.
Lampert, M. (1985). How do teachers manage to teach? Perspectives on problems in practice. Harvard Educational Review, 55(2), 178–195.
Liljedahl, P. (2014). The affordances of using visibly random groups in a mathematics classroom. In Y. Li, E. Silver, & S. Li (Eds.), Transforming mathematics instruction: Multiple approaches and practices (pp. 127–144). New York: Springer.
Nipper, K., Ricks, T., Kilpatrick, J., Mayhew, L., Thomas, S., Kwon, N. Y., et al. (2011). Teacher tensions: Expectations in a professional development institute. Journal of Mathematics Teacher Education, 14(5), 375–392.
Nipper, K., & Sztajn, P. (2008). Expanding the instructional triangle: Conceptualizing mathematics teacher development. Journal of Mathematics Teacher Education, 11(4), 333–341.
Pellegrino, J. W., & Hilton, M. L. (Eds.). (2012). Education for life and work: Developing transferable knowledge and skills in the 21st century. Washington, DC: National Research Council of the National Academies, The National Academic Press.
Perdomo-Díaz, J., & Felmer, P. (2017). El taller RPAula: Activando la resolución de problemas en las aulas. Profesorado: Revista de Curriculum y Formación del Profesorado, 21(2), 425–444.
Perdomo-Díaz, J., Rojas, C., & Felmer, P. (2018). La resolución de problemas como estrategia de desarrollo profesional docente: tensiones que generan en el profesor. Educatio Siglo XXI, 36(3), 101–122.
Rouleau, A. (2017). Tensions in the role of mathematics coaches. Proceedings of the 10th congress of European Research in Mathematics Education (CERME). Dublin, Ireland.
Rouleau, A., & Liljedahl, P. (2016). Teacher tensions: The case of Naomi. Proceedings of the 21st international conference on Mathematical Views (MAVI). Milan, Italy.
Swan, M. (2007). The impact of task-based professional development on teachers’ practices and beliefs: A design research study. Journal of Mathematics Teacher Education, 10(4–6), 217–237.
Valenzuela, J.P. & Montecinos, C. (2017) Structural reforms and equity in Chilean schools. In Oxford Research Encyclopedia of Education. Oxford: Oxford University Press.
Acknowledgments
The authors would like to thank the anonymous referees for many suggestions that made the chapter better. P. F. was partially funded by PIA-CONICYT Basal Funds for Centers of Excellence Project FB0003 and Grant PAI AFB-170001. J.P-D. was partially funded by Proyecto de Investigación del Plan Nacional del MICINN con Referencia EDU2017-84276-R.
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Appendix: Selected Problems
Appendix: Selected Problems
Playing with sticks
Using match sticks we can make the following sequence of figures: How many sticks do we need for figure number 7? How many sticks for figure 14? How many sticks for figure 145?
The scale
We have eight balls of the same color and the same size. We know that seven balls weigh the same and one, possibly, is heavier. We also have a scale. How to determine which is the heaviest or if they all weigh the same? How many times should you use the scale? Is it possible to do it using the balance only twice?
The unknown fractions
What are the values of triangle and circle?
The book
Grandfather Anacleto is reading a book when his grandson Malandrín comes to visit him. Malandrín asks him which page he is on. Grandpa tells him: the product of the two pages I’m looking at is 1190. What pages is grandfather Anacleto looking at?
Generous Peter
Peter left his house with a pile of stickers of an Olympic album and he came back without any. His mother asked him what he had done with the stickers, and Peter replied: “to each friend that I met, I gave half of the stickers I had, plus one.” If Peter met six friends, how many stickers did he have when he left his house?
The farmer and his sheep
When farmer Ramón gets up every morning, he takes a look through the four windows of his house, and in each of them, he always sees nine sheep. The sheep are distributed as shown in the figure, and from each window, Ramón is able to see the front paddock and the two paddocks located at the corners. One day Rosa, Ramon’s wife, sold one of the sheep while he was out of the house. She redistributed the sheep in the paddocks in such a way that from each window there were still exactly nine sheep, so that Ramón does not realize one sheep was missing. How did Rosa do it?
The slot machine
Six friends put 23 coins in a slot machine. If each one spent a different number of coins, how many coins did each player deposit?
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Perdomo-Díaz, J., Felmer, P., Rojas, C. (2019). Teachers’ Mathematical Tensions Surfacing During the First Session of a Problem-Solving Professional Development Workshop. In: Felmer, P., Liljedahl, P., Koichu, B. (eds) Problem Solving in Mathematics Instruction and Teacher Professional Development. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-29215-7_19
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