I felt the common thread in all the articles and videos was the concept of number sense and how crucial it is that we, as teachers, spend a significant amount of time developing it with our students. In Dylan's example, we were able to see how without any help, he came to an answer using a method he developed. He was consistent in its usage and accuracy and was able to explain what he did. The explaining is the best part. I'm forcing myself to ask students to explain or justify their answers in all subjects these days. It's time consuming, but it pays off.
I also viewed Jane's thinking on the Mountain View, Slater School site. I like the questioning process and how Jane recorded the question, the data - the teacher suggested she look at an old worksheet to remind herself what "data" meant- the problem, the answer, and finally putting a check mark at the end to indicate that she had checked her work. You can see that this is process they use daily in that math class that elicits detailed and thoughtful responses. It was interesting to see how quickly Jane added the two numbers 12 + 2 to get 14. That part was the fastest and she did not speak while doing it. What was key was the way that she could explain "why" she did what she did and she was able to say "why" subtracting would not get you to the correct answer. (The teacher asked that question at the very end.)
I was pleased to hear, from the Spark's article, that counting (or the speed at which a child can count and solve arithmetic problems) is not the best indicator for success in math later in life. Rather understanding sets of numbers and how to manipulate them is more important and a better indicator. In my own room, I have seen tremendous growth with students who struggled with counting (and still do) when it comes to their overall number sense. I feel that the accessibility of manipulatives, ten frames, part-part-whole mats and other tools has increased my students' ability to see sets of numbers and to understand equations. I also spend a great deal of time on math vocabulary, ensuring that they know equal means same, sum is the answer when adding, etc. While counting is important - number sense, or better, set sense is more valuable for long term growth.
Susan, I appreciate your post. I like that you mention making number sense a bigger emphasis because I feel the same way. To often teachers rush through because they feel that all their students are proficient, but when the same concepts reoccur the next year, that teacher has to take more time going over it which leaves less time for other concepts. In Dylan's case, he had his own way of making sense of the problem. It was very interesting to read his thought process behind taking the 9 from the 2 and not the 2 from the 9. Crazy!
ReplyDeleteSusan, I agree with your comment on how crucial number sense is. I was seriously stumped on Dylan's logic and reasoning. But with an understand of place value and number sense, it is amazing what students can come up with on their own. I agree that Dylan's logic is a great example as to why teachers need to provide students with manipulatives, ten frames, math vocabulary, number sense, etc... in order to support student's individual learning. Great article and great post!
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