Maybe I am thinking too deeply about trying to decipher “Dylan’s
multi digit subtraction strategy” and the answer is actually very simple, but I
am completely lost. I read it a few times and even tried some problems of my
own but the logic for me just isn’t there. I must be so old fashioned with my
blinders up that my mind wont even accept anything new as far as strategy’s
go. Subtraction has been engrained in my
brain to always go from right to left and borrow from the left side if the
numerator is too small. Dylan’s way of thinking is a powerful example of how
apt children are of adapting original and factual methods for mathematics. It is so necessary to allow children the ability
and power to develop their own ideas before telling and teaching them the
“right way” of doing something. Reading
this article confirmed the notion that there is never just one single way of
doing something. There are multiple
outlets for almost anything and if there is logic behind a method and it can be
proven to work in any condition then it should be validated and accepted. Some children see things differently than
others. Some might instantly understand
the old fashioned method of subtraction while others may not. Some may instantly understand “Dylan’s multi
digit subtraction strategy” and others may not.
That’s why I think it is so beneficial to show children many different
ways of doing something and then decide which way works best for them. I am a very hands-on learner… I can read all the directions in the world
and look at illustrations and maybe even watch a video on the topic of “how to
change a flat tire,” but it is not until I physically change that flat tire
myself that it all makes sense! Everything I have read finally “clicks!” I feel as if young learners are the same way J
It took me a while to understand Dylan's thinking. He starts with the ones' columns and inverses the intergers. He then uses the answer and subtracts it from the tens. Somehow the answer resolves itself even when doing three digit subtraction. I tink it is amazing.
ReplyDeleteIn regards to the pedagogy, I think you are correct that we as teachers must talk and listen to our students and understand their logic if we want to help them understand math concepts.
I had to read the articles on Dylan's strategy a few times too! Finally, I see the consistency, but I'm still amazed at the process he chose to use in order to get the correct answer. I like the way Laura said, "Somehow the answer resolves itself." I am fascinated at just how it resolves itself! After reading and enlarging my screen to see Dylan's writing, I do see the consistency and I see how he avoided a common mistake where he would continue to inverse the integers through the tens and hundreds. Dylan's articles connects well with the Spartk's article in supporting the theory that analyzing student process is a truly crucial step in understanding their number sense and ability to manipulate sets of numbers.
ReplyDeleteJackie, I also had a hard time at first understanding Dylan's strategy, but then I got it. I tried my own problems and I couldn't believe that it worked each time. I was so fascinated by it that I even showed my husband and he also thought it was interesting. When I used to teach math at the primary level, I always had my students explain their logic and reasoning behind their answers, especially if they had the correct answer using a different strategy. It was helpful for me as a teacher because I was able to share these other strategies with my students and noticed that more and more students were able to grasp the concept. Although, my students were bright in their thinking, their strategies weren't as near as complex as Dylan's strategy.
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