Developing Mathematics Lessons

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# Developing Mathematics Lessons - PowerPoint PPT Presentation

Developing Mathematics Lessons. “The Big Ideas”. Explaining Investigating Exploring Interpreting Analyzing Describing Deriving Reasoning. Justifying Proving Conjecturing Calculating Examining Constructing Grappling Engaging . The Verbs of Doing Mathematics.

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## Developing Mathematics Lessons

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### Developing Mathematics Lessons

“The Big Ideas”

Explaining

Investigating

Exploring

Interpreting

Analyzing

Describing

Deriving

Reasoning

Justifying

Proving

Conjecturing

Calculating

Examining

Constructing

Grappling

Engaging

The Verbs of Doing Mathematics
Instrumental vs. Relational Understanding
• What are some key ideas from the article?
• What quotes did you make note of?
• What questions do you have?
Instrumental vs. Relational Understanding – Key Ideas
• Instrumental is easy way out for teachers – easier to give rules than to explain why
• Rules don’t necessarily lead to ability to apply
• Relational understanding can be reconstructed
• There could be a place for both types of understanding
Instrumental vs. Relational Understanding - Quotes
• The analogy comparing learning to navigate a town
• The kind of learning which leads to instrumental mathematics consists of the learning of an increasing number of fixed plans, by which pupils find their way from particular starting points (the data) to required finishing points (the answers to the questions).
• In contrast, learning relational mathematics consists of building up a conceptual structure (schema) from which its possessor can (in theory) produce an unlimited number of plans for getting from any starting point within his schema to any finishing point.
Instrumental vs. Relational Understanding - Questions
• When is it okay to give instrumental explanations? Is it ever okay?
• What type of understanding do I value?
• What is my definition of mathematics?
• Our role as mathematics teacher needs to change from providing students with instrumental knowledge to facilitating opportunities for students to construct relational knowledge
What I do in my Classroom
• What are some key ideas from the article?
• What quotes did you make note of?
• What questions do you have?