“From Under Our Big Tree” Weekly Newsletter #7 – 9 to 11 Class (25 Oct 2015)

What does it mean to be a critical thinking mathematician? Does it mean you can crank out the answer to computation after computation? Not anymore. We have computers that can do that for us. What we need to be able to do, what our students need to be able to do, is ascertain whether an answer that our electronic device gives us actually makes sense given the context. We don’t need any more human calculators. We need people who can “feel” the numbers and have a sense about how to use them in various contexts.

So, how do you achieve that? You must experience, through various modes, deciphering the clues and missing information, building number sense and developing an ability to explain your reasoning. This is why we have started the year with number sense games like Damault and Spin & Add. Damault helps to reinforce multiplication facts but my emphasis is not on rote memorization of the facts. That will come with repeated experience, of this game for example. My goal is for students to utilize strategies to learn the multiplication facts, drawing upon patterns within the numbers. For example, 8 x 7 can be thought about as double the 7, then double the 14, then double the 28 (visual learners, click here). A strong understanding of numbers helps this make sense and it provides a strategy that can be used while memorization is taking place. Enough interaction with a concept and memorization will happen.

We have started thinking about estimation and how we can use “getting close by using clues” to our advantage to feeling out the answer to a problem. It is important, before we launch into double digit multiplication and division, for students to be able to get a sense of the direction they are heading in, so when they arrive at an answer, they can self-check to see if they ended up where they thought they should have. For instance, if I am multiplying 37x 57, I could estimate first that the answer is probably going to be close to 1500 because 30 x 50= 1500. So then,  if I get a very different answer when I go in for precision, then I can back-up because that just doesn’t make sense. We don’t just compute for computation sake. We are dealing with real-world problems that require real-world, make sense solutions. Gone are the days of page after page of computation problems. If a student can do 4 problems correctly, they can do 100. But can they apply their understanding across situations and take into consideration all the clues that a situation may have? We will all be observing as this skill develops.

This week, we have started with visual estimation, where the students look at a container of items and without actually getting to count them all, make an initial estimation as to how many are in the container. This week, it was small, beautifully painted wooden elephants. The goal was not to just throw out a random number for how many elephants were there, but to use clues to come up with a reasonable estimate. Some students came up to the container and counted a visible “section” and then multiplied that by how many “sections” they thought there were. Other students remembered an activity we had used the elephants for where each person got a certain amount of elephants, so they multiplied the number of elephants by the number of people and arrived at their answer. All of the answers were within the ballpark, none were outlandish. It was a great start!

Then, we proceeded to close the circle in on how precise our estimations could become by counting the elephants. As we counted, we would stop to revise the predictions, making sure everyone got a chance to explain their reasoning for why they were changing their estimate or sticking with it. In the end, it was a powerful lesson in visual estimation that reinforced the students’ ability to utilize clues and reasoning to arrive at an answer that makes sense within a context. Now, for their Home Project work, they get to go onto the computer to play some computer games around estimation to continue to hone this valuable skill. To support their budding capabilities, please review the website with them because it has helpful information about what estimation is and how to do it. You can also share your experiences with estimation in your life: http://www.mathsisfun.com/numbers/estimation.html 

Happy estimating!