"Mathematics is a very broad and multidimensional subject that requires reasoning, creativity, connection making and interpretation of methods" Jo Boaler, in the Introduction, page xii
This makes me think of the language curriculum and the forward in the math curriculum more than the overall and specific expectations in the math strands. Teaching literacy comprehension strategies through math and teaching math using the comprehension strategies we would use for any graphic or informational texts is true integration of these two subjects. It is curriculum mapping at its best. This is integration that makes sense and is meaningful for students. This allows us to think of math as more than right and wrong solutions. What does this translate into in our classrooms for our students? It means each and everyone in the classroom including the educator can be part of the process by doing the creative and critical thinking required to solve problems. When we pose problems that only have one right answer, we unintentionally reward speed over thinking. The students who can quickly get to the right answer are rewarded because the need for others to continue the thinking is non-existent. Wouldn't it be interesting to create learning goals for what critical and creative thinking looks like in math, what it means to make connections, what it means to analyze and evaluate?
If we want students to see that math is more than just the right answer could a strategy such as this one might work? Intentionally pose a problem that allows students to struggle and debrief the struggle and the thinking rather than the solution and how we reached it. Would students that have always been made to feel that they are not math-smart feel empowered when they see that all their friends struggled too? Would this make them think that constructive struggle makes them critical and creative thinkers rather than failures at math? What does constructive struggle look like, feel like and sound like in a math classroom? Has anyone debriefed a math struggle? What is the criteria for a constructive struggle?
This makes me think of the language curriculum and the forward in the math curriculum more than the overall and specific expectations in the math strands. Teaching literacy comprehension strategies through math and teaching math using the comprehension strategies we would use for any graphic or informational texts is true integration of these two subjects. It is curriculum mapping at its best. This is integration that makes sense and is meaningful for students. This allows us to think of math as more than right and wrong solutions. What does this translate into in our classrooms for our students? It means each and everyone in the classroom including the educator can be part of the process by doing the creative and critical thinking required to solve problems. When we pose problems that only have one right answer, we unintentionally reward speed over thinking. The students who can quickly get to the right answer are rewarded because the need for others to continue the thinking is non-existent. Wouldn't it be interesting to create learning goals for what critical and creative thinking looks like in math, what it means to make connections, what it means to analyze and evaluate?
If we want students to see that math is more than just the right answer could a strategy such as this one might work? Intentionally pose a problem that allows students to struggle and debrief the struggle and the thinking rather than the solution and how we reached it. Would students that have always been made to feel that they are not math-smart feel empowered when they see that all their friends struggled too? Would this make them think that constructive struggle makes them critical and creative thinkers rather than failures at math? What does constructive struggle look like, feel like and sound like in a math classroom? Has anyone debriefed a math struggle? What is the criteria for a constructive struggle?
I agree with the intentionally posing problems that allow students to struggle but not in the way that they will want to abandon the task. I have been working on this with a couple different classes to help them develop community as they will see each other going through some sort of struggle; get them talking to each other; questioning each other. I think we need to not jump in too quickly when students are struggling but rather ask them redirecting questions and move on. In debrief we talked about what made the task difficult/challenging? Student's response included: didn't understand certain word/phrase, not sure where to start, not sure what the problem is asking, partner wasn't helpful for this task. Then I ask them to think about what they need in order to solve the problem? Which lead to criteria for deconstructing a problem.
ReplyDeleteI think the struggle is what makes us feel so accomplished when we overcome it - at least for me. I don't think I am alone in setting goals for myself and the satisfaction I get in reaching them as well as what I learn through the process is the most rewarding.
ReplyDeleteI look at the quote you chose and more than the struggle I look at it as we need to focus on understanding each other's thoughts and making sense of them in our own mind. We should encourage students to communicate to each other once they have had a chance to synthesize the information they are given for themselves. Is this not the true meaning of mathematics and problem solving? I thought the research in blue to be fascinating yet logical ... of course when students learn ways to work and think logically and through reasoning they are more productive! This is a life skill that transcends anything we will ever teach students in our math classroom.