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.
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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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