Where to Start: Global Strategies
Here are three things teachers can consider when building a culture of mathematics in their room.
Develop a growth mindset with students.
Stanford professor Carol Dweck has shown the benefits of having a growth mindset vs. a fixed mindset. People who have a growth mindset believe that they can improve through their efforts, and see mistakes as learning opportunities. Dweck advises that in order to help develop a growth mindset in students, we should praise their effort, their strategies, their focus, their perseverance, and their improvement – instead of praising intelligence or talent. She reminds us that when kids stumble, we shouldn’t label these as failures, but instead should simply say they haven’t got it yet, but will by continuing to work at it. When this becomes the norm of the class, students will start to encourage others in their class in the same way.
See Carol Dweck’s Ted Talk here.
Develop students’ identity as mathematicians.
After being formally educated in math for a number of years, many students seem to have the idea that math is about remembering facts and algorithms. Paul Lockhart, author of A Mathematician’s Lament, challenges us to change this. He shares that math is about reasoning and understanding, not memorization. Therefore, mathematicians are problem solvers – and this should be the basis of our mathematics instruction. Students can identify as problem solvers, and doing so, then can identify as mathematicians. We can make math engaging by giving students problems to solve, instead of textbook questions to answer. Consider the following question from Lockhart:
Suppose I am given the sum and difference of two numbers. How can I figure out what the numbers are?
Now compare that to a textbook question that asks us to find the sum of 14+17, and find the difference of 231-67. Which is more engaging to students/anyone? Which will help them see themselves as problem solvers/mathematicians?
FYI: If you’d like to read the essay by Paul Lockhard on this topic (a quicker read than the book), you can find it here.
Encourage collaboration.
If we give students challenging questions that have multiple pathways to solve, they will come to deeper understanding when they collaborate with peers and others in their class. To do this, students should be encouraged to engage in discussions with classmates as they discuss math topics, strategies, and ideas. There are at least two implications for this though:
1) Students may need scaffolds to help them have productive conversations.
2) Students need time to have conversations with classmates, which will limit the amount of time that teachers talk/instruct.
In Chapter 5 of the book Visible Learning for Mathematics, there are a number of strategies that teachers can employ to promote collaboration and discussion.
The authors suggest the use of Language Frames to help students have conversations. These are sentence starters and structures that can be provided to students to help them have the types of conversations that will be beneficial to moving their learning forward. Examples of Language Frames are:
In order to solve this problem, I need to know _______________________.
This is a ___________________ problem because I see ________________________.
In order to _____________________, we follow these steps _______________________.
My answer is _____________________. I think this is reasonable because __________________.
A further list of Language Frames can be found on p. 147 of Visible Learning for Mathematics (2017).
The authors also suggest there are other considerations when trying to encourage collaboration in mathematics classrooms that include:
· The questions/tasks need to be complex enough that they require students to work together. If they are too simple, students will solve them individually and there will be no discussion.
· Questions that allow for argumentation/debate are powerful. The act of working towards agreement means that students need to communicate to understand each other, and sometimes negotiate towards understanding. This is a beneficial experience to deepen students’ understanding.
· Ask students to make their thinking visible (whiteboard/poster board, etc.) to other students and their teachers. This provides a way to track thinking and provides some group accountability.
Finally, Chapter 5 lists several ways to support the development of collaborative learning which include:
· Contribution checklists (lists of actions students should consider when being collaborative)
· Allowing student movement in the classroom (studies note the benefits to student achievement of being mobile in class)
· Structuring in peer support opportunities/protocols (grouping students to check in with others before returning to their original group).
Head back to the Math Culture Strategies page.