“While the world is based on established facts and real objects, what these mean and how to respond to an understanding realities is not a predetermined matter. If learners’ interpretations are to be useful and justifiable, they cannot simply invent their own; sense-making might be grounded in a rigorous investigation, not playful exploration.”
So yes, 63-28=35 … but how we get there matters.
This week my students and I took some brave steps into Number Talks. They have never done them, and I have never taught them.
As we got started, I gave them a humble and realistic disclaimer:
“We’re going to try something new. It’s something that I have read a lot about, but never tried. This could end up being a total mess. If that happens, we’re going to pick ourselves up, lick our wounds, and find a way that we can make this work for us.”
Helluva thing for kids to hear from their new teacher.
At the beginning of our first week we started gently with dot cards.
We then moved into our first talk:
I could see that there were four different methods that students were using to subtract. Most students told me that they used the traditional algorithm. They also told me how interested they were in understanding how solutions that deviated from this subtraction strategy got to the same answer.
So, I put a pin in our thinking, and we started to debrief the solutions. On Friday two of my students helped co-teach some math mini-lessons (one in each of my math classes). I hope that this week we get to the rest of the different subtraction strategies.
If we’re going to move past “facts” and towards “meaning”, and if we’re to move towards thinking and problem solving that is “rigorous” and “justifiable”, then this might be a necessary step.
Like Jo Boaler says at the end of the dot card video, “a lot of people think of math as just one way of doing it and one solution, but really everything, even just the numbers in math can be seen in so many different ways.”