Hello mathletes,
Last class was a pretty solid lesson on alternative algorithms for addition, subtraction, multiplication & division. Just to quickly recap, there was skip counting to add or subtract, partial addition/subtraction, compensation addition/subtraction, constant sum addition and constant difference subtraction. I have no idea how I went through my entire years of schooling without being taught these methods. All I could think during class was "why am I learning this for the first time?".
My favourite concept was the idea of 'friendly' numbers. Numbers have not been friendly to me in the past so my first thought when I heard this term was "whatchu talkin' bout, Willis?". After being enlightened, at one point in class we were told to multiply 28 x 25 mentally. At first, I looked at that and had a brief panic attack. Once composed, I first turned 25 into the friendly number of 100 by multiplying it by 4. From there I knew that 28 x 100 was 2800. After that, I just needed to divide by 4 since I multiplied by 4 earlier in the question and bam! I arrived at the correct answer of 700. Mind...blown.
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| A live action shot of skip counting to add |
What we are being encouraged to do, and I completely agree with it, is to encourage the use of alternative algorithms. They can be thought of as tools in a toolbox. Some equations lend themselves to being solved more easily with certain algorithms and it's up to us to recognize which tool fits the situation. For me, trying to do 28 x 25 was most easily done by finding the friendly number and going from there. In class, each person who spoke up used a different algorithm to arrive at the answer. So, you could say...'different strokes' for different folks.
This point leads into something that we also talked about this week in class and which I think is important: respect for diversity of learning. Not every student will be able to comprehend the world of math with the same clarity. For some it will be crystal clear & for others it will be clear as mud. Encouraging the use of alternative algorithms gives students the choice to use the method(s) that make the most sense to them. Teaching them principles like these will do more for them than trying to drill into their heads "the correct formula". It also inspires a creativity of thought that math isn't especially known for. It can be a great confidence booster for them once they learn to use these strategies effectively and the confidence that comes from being able to succeed in math is will be what keeps them from running away from it.
Stay hungry, mathletes...hungry for numbers.
Hi Adam,
ReplyDeleteI really enjoyed reading your blog post, especially the "watch talking about willis" comment. I was in complete shock and aw as well when we learned these methods of addition and subtraction. I personally really like using the number line and have been using that to teach my grade 3 student. I think it was really interesting when we were asked to individually multiple 25 x 28, and then hearing the different ways we all came up with an answer. I think that just shows how when we have our own classrooms we have to teach to 25-30 individuals and that requires us to give them multiple tools to use to solve problems. This is exactly what you discussed in your last paragraph and I think as teachers we are incredibly aware of diversity(in numerous ways) in the classroom and that will make us great teachers in the future.