I am home sick today, so I have a bit of time to actually post to the website this week. Instead of just posting the class newsletter that went home yesterday, I thought I would share with you some reflections from what we’ve been up to in the classroom. I would love to do more of this. I blame any typos on my coughing fits!!!!
Math is so much more than just memorizing rules! To truly be math literate, the students have to be able to understand the why behind their problem-solving.
My goal in teaching math is always to be sure that the students are building a concrete foundation of mathematical thinking. How is that done? They need experiences where they build that understanding through hands-on work, and giving explanations of their work both visually and verbally.
You can see the differences in the student’s work and thinking during a recent math lesson.
We met at the carpet and I gave the students a problem: there are 13 girls and 25 boys on the playground. How many kids are there? I had the kids hold out their hands and imagine the 13 girls in one palm and 25 boys in the other. Then we moved our hand together to show that we wanted to combine these two sets.
Next, I asked the students to think of a way to solve the problem. Then one by one, I had volunteers come up to share their strategies.
The first student showed perhaps the most concrete of all solutions. They drew 13 circles, then 25 circles and counted each circle one by one, starting with one.
This works, and they got the right answer, but not the most efficient way to solve this. But this is where the student's thinking is at for now...and there isn't anything wrong with that. As their teacher, I need to show them other ways to solve this type of problem more effiecently, and give them opportunies to use those other strategies.
Next, a student came up and drew each number as base ten blocks. Then they added each stick of ten by counting by tens, and then the ones to get the correct answer. Drawing the base ten block instead of the tedious circles is a step in the right direction! This shows that they can see a simpl line as representing a stick of ten cubes, showing their abstract thinking at work.
We talked about how drawing the base ten blocks was a bit more quicker and more organized then a bunch of circles. But either solution worked .
I asked the class if anyone had another way…something different.
Next up was a quiet girl in the class who started to draw 13 circles, just like the first person. I stopped her and asked if this was going to be different than the first way and she softly answered, “Kinda.” As hard as it was for me, I just continued to let her draw, watching to see what she was going to do. As teachers, we often what to jump in and save the day…hurry it along, but I am learning to be more patient. It pays off!
And there is was. She did not go on to draw the other set of circles, 25, like I thought she was going to.
Instead she says, “I know that there are 25 boys so I don’t have to draw all those. I can just say 25 and then count on these 13.”
Holy smokes! I did not see this coming. Moving along the concrete to abstract thinking continuum we go!
Again I asked the class: Any other ways to solve this problem?
The last way was as interesting to me as the others. The eager student raised his hand and quickly wrote on the board :
I had him explain his work to the class. Then he said he would add up the tens to get to 30 and then the ones to get 8…altogether 38.
I then asked the kids to add together 2 digit numbers on their own. I encouraged them to use any of the strategies we had gone over, and if they were always drawing out all those circles, to try one of the other ways for today…or even two ways! if they wanted to. They EAGERLY got to work.
When everyone had finished, we were able to put the solutions on the ELMO for everyone to see. ALL students got the right answer…in several different ways. I now have a really valuable piece of assessment. You can look at these solutions they completed and lay them out from the most concrete thinking to the most abstract.
I hope this illustrates in some detail of what goes on in our math lessons. I ask A LOT of questions and the kids do A LOT of explaining and clarifying.
I hope that it shows the richness of the work we do. Can you imagine how different the lesson would have been if I had just said “Okay you add these number here, and these numbers here and then you’re done. Now go to that.”
They certainly wouldn’t be building that foundation of understanding of numbers that they really need.
It may take more time, and more patience to teach this way , but I think it is worth it! I hope you do too.