Making Kids Doers of Math Instead of Doing the Math
My biggest fear in education right now is that we are having our kids go through the paces of doing school. We are turning our students through the drudgery of school. Before I started to really question this thinking I saw it in my own class. My students were coming to school going through the paces and then leaving. Sure they enjoyed it, but was I really making them think? What type of work was I making them do? Why was I teaching them these skills?
I then came across this statement by Fosnot:
The purpose of teaching is to learn, but without learning there is no teaching!
I was shocked. Was she saying that if my students didn’t learn then I wasn’t being a good teacher? The answer was yes! And the more that I reflected on this the more I agreed with this statement. Over time, I realized that even though I was teaching different kids, the common denominator was still me. So when I asked questions like, ‘why don’t they get this?’ The answer is because I am not doing a good enough job. I wasn’t making them understand because I was just making them be there instead of embodying the learning.
I see this a lot in math and this is partially because of my lens. In a math class we traditionally stand in front of students, give a lecture, let them work and then test them to see if they understand. How many of our students are really learning? How many of them become mathematicians?
VanDeWalle suggests that, “The goal is to let all students believe that they are the authors of mathematical ideas and logical arguments.”
So then how do we go about doing this?
I would like to propose three key points to this:
- Role of the teacher
- Environment of learning
- Accountable kids
Role of the teacher
I want to first preface that teaching to me is about turning my kids into mathematicians through inquiry and exploration, but I start with this point because as a teacher we have the most critical role to play. We are not to sit back and allow our students free reign but to ignite and actually talk about math. I know, really insightful!
Researchers have suggested that children should be engaged in problem versus talk procedures. But our role is to bring out the math not by telling students information and expecting them to regurgitate it but by creating contexts for learning asking critical questions and debriefing the math. In my research, I found three types of questions that worked the best for creating these conditions:
- Interrogation: Just like the title suggests → a lot of why’s and how comes
- Going beyond: Pushing the thinking beyond the schema the student has created. These questions include, ‘Have you thought? What about this? Can someone else explain?’
- Comparing: Often I compare strategies together to see if students can move from one to the next. This includes, ‘What are the differences? Similarities?’
In order for this process to really work, “Teachers must have the [student learning] in mind when they plan activities, when they interact, question and facilitate discussions.” ~Fosnot
The key to everyone one of these questions is that it was linked to a big mathematical idea. One that was key to the learning of the student. The same goes to the various talk moves that a teacher can make. These should include: Wait time and revoicing. I cannot stress how important these two items are to the success of building mathematicians. Too often we don’t give students enough time.
Creating an environment of learning
In a mathematical environment , students feel comfortable trying out ideas, sharing insights, challenging others, seeking advice from other students and the teacher, explaining their thinking and taking risks. ~VanDeWalle
When students do mathematics in an environment that encourages risk and expects participation, it becomes an exciting endeavour. Students talk more, share more ideas, offer suggestions, and challenge or defend the solutions of others. When a context is real and meaningful for children, their conversation relates to the context. They mathematize the situation. ~Fosnot
These are two fundamental theories that I try to incorporate when thinking about the environment of my classroom. We may not think this is important, but it is. The place in which students learn assists in their learning. We as teachers need to create a place of discovery, a little frustration and a lot of guidance/facilitation. Students need a place where they can make conjectures, think about their solutions and present them to their peers for evaluation.
Making kids accountable:
No one is allowed to be a passive observer. ~VanDeWalle
I love this quote. I think it is exactly the whole idea around accountable talk. Many teachers may think that just because the student is not talking they are not participating, but the key is not to be a passive observer, which doesn’t always involve talking, but listening. However, that has not been the case in school. We have been so use to hearing teachers talk that many of our students are use to being told the answer that they are not used to talking.
In my thesis research I saw that when I asked an Initiate respond and evaluate types of questions (basically questions I already knew the answers to) I got no further discussion happening. My kids just sat there. But when I asked going beyond types or comparing questions, basically critical thinking questions, that was linked to big ideas kids talked about math. They became active users of the information and doers of math not just following the paces.
“Remember no one is allowed to be a passive observer.” ~VanDeWalle
So I guess I want to ask: How do you make your students into Doers versus just doing? This question doesn’t need to be math as it is a broader problem in education. Love to hear your thoughts and ideas.
Originally posted on Jonathan So’s blog, “Mr. So’s Classroom.”
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