We had another great week at The Math Pod! This week we dove into understanding how we build students’ understanding of algebra using variations while creating contexts that are carefully crafted so that they are realizable to students and they don’t get lost in the abstractions that procedural mathematics can lead to.
We need to ensure that our students have opportunities to think like mathematicians so that they can develop denser structures within the terrain of mathematics, thus creating more fluency, flexibility and diversity of ways to think about how to solve complex problems.
Cathy shared three problems in this episode. The frog jumping problem, the foreign coin problem and the handshake problem: all available in her platform, New Perspectives Online.
During the podcast, Cathy also shared her thinking on Patterning and Algebra after we shared a tweet from one of our listeners:
She talked about how so many teachers think of patterning as separate from Algebra, as if they are two discrete units but if there is anything we have learned this year from Cathy it is that all mathematical ideas are connected. She also cautions us about teaching patterning by asking the question, “What’s next?” when we share patterns with blocks or numbers because this makes the assumption that the pattern we see has a next but in fact, it can change at any time. What we are functionally doing is asking the children to guess what we are thinking and that there is one answer. She encourages us, as educators to think beyond this, give the children an opportunity to think broadly and deeply about mathematics and to do so in a math talk community where we can learn from one another–not what the right answer is but rather, what are the many ways we can consider this.
In closing, Stephen drew us back to one of Cathy’s books by sharing this quote by Jonathan Kozol:
“When the guidelines we give teachers are translated into lists of mandated jargon that are given an iconic status in the classroom, I don’t think we are saving time for good instruction. I think we are stealing time for anything that actually contributes to a child’s education.”