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In this article the authors describe their efforts to support teachers' development of deep, connected understandings of school mathematics and to find ways to make use of the teachers' learning as a context for subsequent mathematical and pedagogical development. The authors detail the evolution of their model for Online Asynchronous Collaboration (OAC), which is grounded in current research in mathematics teacher education and that takes advantage of the collaborative nature of the Internet and the permanent nature of the online interactions. They believe that OAC is a promising practice in teacher education and will discuss both the rationale for their design decisions and provide examples of teachers' activity within OAC.

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ONLINE ASYNCHRONOUS COLLABORATION IN MATHEMATICS TEACHER EDUCATION AND THE DEVELOPMENT OF MATHEMATICAL KNOWLEDGE FOR TEACHING

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In this article the authors describe their efforts to support teachers' development of deep, connected understandings of school mathematics and to find ways to make use of the teachers' learning as a context for subsequent mathematical and pedagogical development.

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Abstract

Prospective Teachers (PTs) often enter their mathematics content courses believing that they know enough mathematics to teach elementary school. However, research has shown that much of PTs' knowledge is procedurally based and lacks depth and conceptual understanding. One job of Mathematics Teacher Educators (MTEs) in mathematics content courses is to help PTs become more mathematically proficient, by relearning the mathematics that they believe they already know in deeper, more connected ways. We suggest that one way for MTEs to do this is to incorporate Transformative Learning Theory (TLT) into their mathematics content courses. TLT is an application of andragogy, which are the methods or techniques used to teach adults. Through TLT, learners participate in a process where they are presented with a disorienting dilemma that perturbs their prior understandings. Learners work through the dilemma by critically reflecting on their prior understandings and participating in rational discourse with others. Ultimately, learners are tasked with making connections between their prior understandings and their new knowledge. In this paper, we describe a cycle of transformative learning theory and give examples of incorporating TLT into mathematics content courses for PTs through lessons on proportional reasoning and whole number concepts. We conclude by discussing general considerations and resources for incorporating TLT into mathematics content courses and how this helps PTs develop the five strands of mathematical proficiency (National Research Council, 2001).

Recommended Citation

Johnson, K. & Olanoff, D. (June 2020). Using transformative learning theory to help prospective teachers learn mathematics that they already "know". In A. Appova, R. M. Welder, and Z. Feldman, (Eds.), Supporting Mathematics Teacher Educators' Knowledge and Practices for Teaching Content to Prospective (Grades K-8) Teachers. Special Issue: The Mathematics Enthusiast, ISSN 1551-3440, vol. 17, nos. 2 & 3, pp. 725-769. ScholarWorks: University of Montana. Retrieve (open access) from: https://scholarworks.umt.edu/tme

DOWNLOADS

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Using transformative learning theory to help prospective teachers learn mathematics that they already "know"

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Prospective Teachers (PTs) often enter their mathematics content courses believing that they know enough mathematics to teach elementary school. However, research has shown that much of PTs' knowledge is procedurally based and lacks depth and conceptual understanding.

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Teaching Elementary Students the Magic of Math

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From Stanford Online's "How To Learn Math for Teachers and Parents": Number Talks

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Exploring Fractions and Operations with Cuisenaire Rods

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Exploring Fractions and Operations with Cuisenaire Rods

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When you are talking about factoring, this little game could help.

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Taxman Game

Another gem from my neighbor Tom Sander. The "taxman" game is (apparently) an old programming exercise. But it is also a good game for practicing factors. I have been playing it a bit with Anthony (by hand). Here is a gadget that applies the rules of the game for you.

The rules are simple and fifth-grade friendly:

When you take a number, the taxman gets all the remaining factors.

You are only allowed moves that give the taxman at least one new number.

When you can't move any more, the taxman gets the rest.

It is worth playing without reading anything else - it is not too hard to find a heuristic that beats the taxman. The game was written up in an article by Moniot in the Feb 2007 MAA Horizons - an optimal strategy is not known.

I've gotten up to 121 points on the 20-size board; I am pretty sure this is not optimal. Can you beat the board with 100 squares? What is the best score you can get?

Posted by David at December 7, 2008 05:12 PM

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Another gem from my neighbor Tom Sander. The "taxman" game is (apparently) an old programming exercise. But it is also a good game for practicing factors. I have been playing it a bit with Anthony (by hand). Here is a gadget that applies the rules of the game for you.

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Graphing activities for elementary school teachers to use in class, via Desmos.

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These activities are designed for third- to fifth-grade classrooms, or anyplace where students would benefit from playful exploration of these ideas.

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During COVID, outdoor learning is more valuable than ever!

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Math Learning—and a Touch of Science—in the Outdoor World

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The great outdoors is filled with rich opportunities for math learning—with a connection to science—that can interest and engage children in real-life problem solving.