Back Talk highlights the learning of one or two students and their approach to solving a math problem or prompt. Each article includes the prompt used to initiate the discussion, a portion of dialogue, samples of student work (when applicable), and teacher insights into the mathematical thinking of the students. This article describes how David used repeated addition to solve a multiplication problem. It reveals his processes of solving the problem mentally, of finding the repeated patterns in a problem context, and of representing the problem with a drawing.
This article investigates two children's intuitive thinking in solving multiplication problems from different educational backgrounds. One of the children is in a southern elementary school in the US. He was given the same problems both in first and second grades. The other child was a first grader in a southwest region of China, and she was given the same problems. The findings reveal a variety of intuitive thinking in solving the multiplication problems through addition beyond direct modeling and counting strategies. The authors also discussed how different educational backgrounds in early elementary mathematics education may affect children's intuitive ideas and reasoning in solving multiplication problems. The study implies the importance of understanding children's intuitive ideas of multiplication and highlights potential opportunities for developing children's understanding of multiplicative thinking and algebraic thinking in earlier stages of arithmetic learning.
This study explores the evolution of a professional learning community (PLC) of Chinese teachers over a multi-year period. A group of 16 teachers participated in a three-semester PLC over the 2008-2009 school years to develop master mathematics teachers in a school district in Beijing, China. The goal of the PLC, as identified by the teachers, was to improve instruction for greater student autonomy, creativity, and problem solving as they developed their master capacity building skills and networked relationships. This paper explores what has happened to these 16 teachers six years later, specifically considering how they may have used technology to further their development as master teachers. This study shows the potential of a PLC for self-adaptive, emergent behaviors and understandings that are instructional for transforming teaching practices, sustaining changes in teaching practices and preparing students for 21st century engagements.
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