What does the Equals sign really mean? Stephen shares a story about his son and that Liam thinks that the equals sign means the answer is coming next. Cathy challenges us to think about where that comes from and why it is problematic, particularly when we are moving from arithmetic to algebra.

When we think about the ways we introduce this into math class, it is often through a modelling of a procedure such as, 5+3= and then ask, what is the answer.

Cathy suggests that in fact, what we should be doing is asking:

*What else can we say about this? *
*What else might also be equivalent? *
- And then…prompt the child to share her reasoning around why she thinks this way.

This type of instruction builds a math talk community constructed on shared thinking and reasoning, honouring voice, and diversity of thought.

Stephen began the show with a quote in Cathy’s book, Young Mathematicians at Work: Constructing Algebra, from Galileo:

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual.

This was a theme throughout the show: the humble reasoning of a single child is worth more than an algorithm that has been proven and not understood.

Cathy also compares this with the power that plays in a classroom. If the purpose of the math classroom is for students to try to figure out what *the* answer is that the teacher holds in her head, then we have denied our learners the opportunity to think, reason, share understanding and socially construct meaning.

Join us this week on The Math Pod on April 18th at 8:00 pm EST on voicEd.ca Radio when we begin to delve into the world of variables and the unknown! Join the Twitter chat using #TheMathPod.

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