Model the Learning

One of my biggest learnings in my role as a board co-ordinator has been around mental math in elementary schools. To be honest, when I first heard the term, I assumed mental math had to do with memorization and just learning multiplication facts.  I now know it to be a procedure very rich in strategy, promoting flexibility of number, and the very important mathematical process  of representing  a problem. Being able to see the math not only contributes to the understanding of the question at hand, but also to assessing the reasonableness of the answer. Visualization and representation of mathematics does not come easily to me - I was the student who became good at math by memorizing procedures. I still have to put a lot of effort into picturing multiplication in an array or area model, or picturing factorization by splitting items into groups, or picturing what happens to fractions as they are operated upon. This past week, I had the opportunity to model the a...

Last month, I was passing through the hallway one of our high schools, when I overheard a teacher delivering a lesson. He was discussing equations of some sort, where a fraction was multiplied by a variable.  In this particular case, he was asking about 2/3 x 6.  He checked the class for understanding: "Do we all know how to multiply a fraction by a whole number?"  Think about that for a second.  What is your go-to method for solving 2/3 x 6? Thinking about fractions Prior to this year, if someone asked how to multiply a fraction by a whole number, I would have given them the “algorithmic“ method of doing so: create a fraction out of the whole number by placing a numerator of six over a denominator of one.  Then multiply my 6/1 fraction by 2/3: multiplying the numerators together and then multiplying the denominators together. This would give me 12/3, which could then be reduced to 4.  Rethinking about fractions For the first tim...