Today we spent our day working through math problems using different manipulates. At first, I, like many, was reluctant to see how they could possibly strength my understanding of math facts and rules, on problems that I have long since "mastered"...or so I thought.
By using the various beans and algebraic blocks I was able to represent my thinking in a way that thoroughly strengthened my understanding AND my ability to teach or explain the idea to others. However, I will not try to explain these mathematical concepts in the same way I learned them long ago...No no no, what purely simple strategy to keep with math... to start with concrete examples and explanations THEN move to the abstract ideas, concepts, theories, and rules that math is so full of. The over used expression, "But where will I ever use this rule?" does not hold the same power as before...Still yes, I'll give it to us all...I'm not sure where the heck you'd be forced to use a quadratic equation...but now I can at least show you with real objects what exactly it is and/or what it at least represents. Awwww it feels good to have a picture for it...not just a rule.
I used to accept that math was full of rules, facts, and theories that you simply follow, just because...they are what they are...you are either right or wrong. In fact I used to like it for that reason... I loved that it was like a book of rules that I could follow...but I found myself at dead ends when I couldn't grasp concepts fully in calculus. Instead, I just plugged and chugged along...jumping through the hoops, thinking it would eventually make sense. With the understanding of math that I'm growing now, I look back shocked that I used to like thinking math were that way. My growing understandings of math are now seemingly endless, and I look forward to the knew ways of thinking that I will learn from other teachers, students, and people! Seeing different solutions as equals and learning from them all to strengthen my own tools to solve.
...So in all...
I learned to use manipulatives for quadratic and algebraic expressions!
This a great tool to use in class when teaching students math in a concrete to abstract method.
I'm wondering how to dig concrete examples deeper with higher level math. I won't be teaching higher level math but just out of wonder....how do manipulatives connect to calculus?
How do uphold our expectations of participation in class, but move onto another student if one student is struggling with an answer??
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