News from the Southern 1 Region
Susan Birnie, Southern 1 Regional Director
Summer 2011

As many of us end our school year, it is that time to look back and reflect on what is working and what needs to be improved. In a recent NCTM Teaching Children Mathematics article, A Reflection Framework for Teaching Math (November 2010), there are several questions proposed for teachers to reflect on their practice. These same questions can be easily adapted for coaches and supervisors as they review their work with teachers in the process of improving instruction:

Structure of the Lesson

  • Were the activities mathematically related and coherent and based on the big ideas of mathematics?
  • Did the flow of the lessons facilitate students' deeper understanding of the mathematical concepts?

Multiple representations

  • Were a variety of representations (graphs, pictures, symbols, charts, diagrams, or manipulatives) used during instruction in meaningful ways?
  • Were students able to translate back and forth between different representations to demonstrate their understanding of the concept?

Use of mathematical tools

  • Did students have the opportunity to use appropriate math tools (other than paper, textbooks, or chalkboards) to investigate concepts and solve problems in class?
  • Were connections made between the tools and the mathematical concepts?

Cognitive depth

  • Were selected tasks connected to underlying concepts, or were the tasks mainly focused on memorization?
  • Were some of the tasks open-ended?

Mathematical discourse

  • Did the students consistently participate throughout the math class and play a substantive role in directing the content of math discussions?
  • Were questions focused on mathematical thinking (processes, strategies, and solutions) rather than on correct answers?

Explanation and justification

  • Were students often required to provide explanations and justify their reasoning?
  • Did student explanations focus on conceptual understanding of the concept rather than procedural steps?

Problem solving

  • Were students engaged in problems that allowed them to grapple with mathematical concepts, or were they doing exercises for which they were practicing an already-learned procedure?
  • Did the lesson encourage multiple strategies to solve each problem?
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