Week 3: Report and Reflection

What I was primarily fascinated with this week was the way our brain learns and interprets math. In the video below Brain Crossing, Jo Boaler explains what brain crossing is, she says that pathways of our brain light up when we think about symbols and numbers and other pathways light up when we visualize, draw, or estimate with numbers. And when both of these pathways cross, when we think of numbers and start visualizing and drawing them, that is the most powerful math learning.

https://www.youtube.com/watch?v=qZBjub36Bvs

In class Friday we preformed two activities that got us using visualizing and drawing with numbers. The first activity the class divided in half and on separate boards created addition and subtraction problems we thought to be difficult and then had to rank the other groups questions from hardest to easiest. Between the two groups rankings, there was a commonality that fractions seemed to be ranked the hardest because of different denominators. Personally, on the spot I can not remember how to solve fractions at all, having not taken math in about 6-7 years. So for me to find this the hardest was stemmed from not understanding the underlying principles to find an algorithm that could be written on the board.

Board reads: "Too much extra work to make them all the same" and "the common denominator is extremely hard to find."

Our second activity was with base-ten blocks and using these manipulatives to show the different outcomes of ways we can find answers. For example, we were asked to represent with the blocks 56-23. They way I would approach this was to have my 5 longs and 6 units and take away 2 longs and 3 units to come up with my answer. Mathieu presented a different method to the class where he took another set of 2 longs and 3 units and compared it to his 5 longs and 6 units and took away from that to get his answer. His method was more of a visual comparison, where mine was more of an approach of applying the logic that we new each long represented 10 units. In the end, we both came up with the same answer, just in different ways.

These examples in class all relate back to the main ideas represented in this weeks reading. That there are many procedures, or algorithms, for adding, subtracting, multiplying, dividing, etc. The traditional methods we use is just one algorithm and not necessarily better than the others. It is valuable for students to participate in learning activities like the ones above so that they have the opportunities to invent their own procedures and to see the procedures others come up with. It was valuable to the class when Mathieu presented his different approach with the base-ten blocks.

As teachers we should be aware of the alternative and multiple algorithms our students may come up with. We should not worry about how to present these algorithms or how many to present to our students, as long as procedures are taught with meaning to the principles of operation, students can invent their own algorithms themselves. We should let students continue the use of their invented algorithms, and encourage them to record in whatever way is meaningful to them as long as it is understandable by someone who is reading it. Our role is to provide students with the understanding to the underlying principles of the problems and with the appropriate language used in mathematics so that they are able to think more holistically about numbers and how they work.