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Your thoughts are echoed in

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Your thoughts are echoed in my building when it comes to math instruction. My building is in year two of a complete overall of how we view and teach math. Up until last year many of my colleagues and I taught math for procedural understanding and instrumental learning because this was how we were taught and really didn’t know another way. With the mentoring of our math coach we have (and continue to have) a paradigm shift in the area of math instructional. Now our focus is on conceptual and relational understanding in which all approaches to problem-solving are considered.
Most of our math instruction now focuses on real life problem-solving that places a demand on students demonstrating “their” understanding and not on the way the teacher says to do it. The children’s thinking is validated when given opportunities to share their strategies with their peers, and this strategy may be the one that works for the “struggling” math student. Sometimes students’ thinking and approaches to solving problems is so “creative” that teachers also learn and adopt new processes.

One of the most challenging aspects of teaching for conceptual understanding is getting parents to sign on. Some parents do want to help, but they only know how to use the procedures, rules, and tricks they were taught. This comes up quite a bit when parents help with homework and during parent/teacher conferences. Some of our sister schools and districts are still committed to their procedure- based teaching, and we find these students don’t understand why they carry out certain procedures, it’s just how their teacher showed them how to arrive at the correct answer.
The only drawback, if there is one, is students identifying and developing a strategy that will work for “them” consistently. Sometimes when students are exposed to so many routes of problem-solving they are not mature or savvy enough to identify what will in fact work for them.

Thanks for the thought

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Thanks for the thought provoking post. Love reading with the morning coffee!
I really agree with the complete, consistent, correct. Our board has really taken hold of collaborative, problem based math learning as of late, so this is good for me to pass on to my staff.
It made me think of the importance of examining what we value as educators - is curriculum ( or math procedure) the end, or is the end the development of the higher order thinking skills, the learning process, the student discourse? I'm for the latter.
Relates to a post on testing, what are we measuring knowing? Or learning?

Thanks for the though

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Thanks for the though provoking post. Love reading with the morning coffee!
I really agree with the complete, consistent, correct. Our board has really taken hold of collaborative, problem based math learning as of late, so this is good for me to pass on to my staff.
It made me think of the importance of examining what we value as educators - is curriculum ( or math procedure) the end, or is the end the development of the higher order thinking skills, the learning process, the student discourse? I'm for the latter.
Relates to a post on testing, what are we measuring knowing? Or learning?

"For instance, when finding

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"For instance, when finding 25% of 80, the most basic thing we can do is turn the percent into a decimal (0.25) and multiply that decimal by 80. The result is 20. Yet when I presented this problem to a seventh grade class just learning this, one of the students astutely observed that 10% of 80 is 8, and 25% is just 10% + 10% + 5%. They doubled 8 (16), then took half of 8 (4), and added the results (16 + 4 = 20).

SOME TEACHERS MIGHT MARK THAT INCORRECT BECAUSE IT DOESN'T FOLLOW THE EXACT PROCEDURE THEY ASKED FOR..." [emphasis mine].

That makes me want to scream and is the reason I got certified to teach math. When the teacher insists, "Just do it my way..." children frequently stop trusting their own math intuition, stop trying to understand, and that's when the downhill slide in math starts. Even though the teacher should make some attempt to help students see why other procedures ALSO yield the right answer, if a solution is mathematically correct, IT'S MATHEMATICALLY CORRECT.

Ironically, when you say the most basic solution is to convert 25% to a decimal and multiply by 80; for me the "most basic" solution is the one I can do in my head which in this case has to do with the fact that 25% is 1/4; so I would multiply 80 by 1/4 (i.e., divide 80 by 4) and get 20. (This is exactly how my math-hating teenage daughter said she would do it, too...)

Good post; important thoughts. Thanks for posting!

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