If you've been following this blog, then you already know that I'm likely to tell a little story before jumping into the good stuff – I promise, I'll take you to the practical, usable stuff just as soon as I can.
THE STORY – The way my math teachers taught me (back in the day) as compared to the way I teach young students today are very different models of instruction. One of the primary differences with the way we teach today is the emphasis on reasoning and not just focusing on correct answers. As I think back, I remember so many of my math teachers grading papers by simply laying a template over our papers and looking for the penciled in shading peeking through the punched out holes to determine if our answers were right or wrong – I also remember my very clever friend Mary sometimes marking two answers if she was unsure which was correct; she knew one of the two circles she shaded was bound to turn up in the grading hole on the teacher's template.
The problem with the method of instruction I experienced as a young learner of mathematics was – well actually, there are many problems with it – but two that come to mind immediately are (1) how could my teacher possibly use the powerful instructional strategy of error analysis to help me refine my thinking if all he was doing was looking for shaded dots and (2) how could he possibly know why I thought the answer was "C" if he didn't ask me to justify any of my responses? If you're thinking, "he couldn't", you're right!
By emphasizing increased instructional rigor through activities that require students to reason, we do a better job of closing learning gaps and can better prepare our students for the type of math they will do throughout their lives – after all, math in the real world is rarely multiple choice!
The Department of Education in my state has recently refined the expectations for student-reasoning in mathematics. These newly designed reasoning standards do a nice job of reminding us to use a variety of task types to help students develop their mathematical reasoning skills. As I continue my own journey of learning how to better teach students to reason, I came across a quote from Michael Battista (Reasoning and Sense Making, 2017) that reminds me why helping our students to make sense of the math is so important to their mathematical development:
Students who achieve understanding and sense making of mathematics are likely to stay engaged in learning it. Students who fail to understand and make sense of mathematical ideas and rely on rote learning will eventually experience continued failure and withdraw from mathematics learning.
Okay, so here comes the practical, usable ideas I promised you when you started reading....
Transforming Basic Operations into Reasoning Opportunities!
Below are specific examples of how we can transform a rote-type of mathematics question into one that requires students to use reasoning. For each of the four new MCAP reasoning standards, I have included one example of how to change "THIS" to "THAT".
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