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ALI Staff | Published January 07, 2020

While rote memorization has long been the norm in math learning, it’s not the only way to teach this fact-based subject.

Other math strategies that can instill the concepts, skills, and thought processes necessary for a student’s long-term mathematical success are out there and worth a try.

Intentional discourse or mathematical discourse is one such option that allows students to engage with the material in a different way.

It can take learning beyond those flashcards into a much broader understanding of what math *really *is. For those looking to reinvigorate their mathematical curriculum, this could be the perfect option.

Math discourse provides students with the opportunity to talk about math. They get to compare and contrast methods, argue for their rationale, and critique the work of others.

Through conversation and collaboration, students can work together to make sense of the math and to understand the ‘why’ versus making math learning about memorizing answers.

Through the four steps of questioning, conjecturing, defining, and explaining– students can share their mathematical reasoning and open up a conversation — a discourse. They may have to defend their choices or admit they’re not entirely correct and rethink, but this happens through conversation.

Students get to work through it all together, solidifying connections that were once confusing and making new concepts more memorable.

Math learning has always been about the steps necessary to get from an equation to an answer. You start with a question and complete a set of steps to find the solution, and while it wasn’t always required to show your work, you did need to move along a somewhat rigid path to get the question right.

This is still true, but the rigidity of the process can waver when frequent intentional discourse is part of your math strategies.

When you use mathematical discourse, students get to:

- Talk about the ‘how’ and ‘why’ of mathematics, enhancing verbal skills as they sharpen their math learning.
- Build a stronger connection to concepts through the productive struggle of solving a problem.
- Learn about alternate pathways to getting an answer right that are also valid. They gain the ability to break out of the routine and find a route that works better for them.

To have a conversation about math, you need to know what words to use. You need to have the correct vocabulary. As math strategies become more complex, vocabulary becomes even more critical. Knowing what words to use creates an even playing field where all students can discuss math.

There’s no confusion as to what someone is trying to say. For that reason, building up a mathematical vocabulary with students is just as important as teaching them the actual processes for finding answers.

Give students the right tools in which to talk about math, and they can talk about math.

Giving students enough time to have a solid discourse about math is also important.

Wait time is often overlooked as we think Math is about getting the correct answer as fast as possible. This outlook on math learning is outdated and doesn't lead to student success– it can have the opposite effect.

Make sure students have time to really think about a question before you solicit an answer. Also, let students discuss among themselves so they have time to all get their ideas out (smaller groups are better in this case).

You also need to listen to your students so you can build on shared ideas and key points organically happening with their own discussions.

As the teacher, it may fall on you to jumpstart in-class conversations about math. Especially in younger grades, students don’t have the capabilities fully developed to ask open-ended questions in a way that gets people talking. (But with practice, they will get comfortable and gain the confidence to initiate conversations as time goes on)

Some math activities you can do that kickstart intentional discourse include:

- Asking a comparative question — How is a right triangle different from an isosceles or equilateral triangle?
- Asking a leading question — Who wants to tell me how they solved this problem?
- Asking a follow-up question — Would you solve this problem in the same way? Who wants to offer up a different approach?
- Asking a contrasting question — Who got a different answer? What approach did you take?

None of these questions have a hard, right answer to them. It’s not like shouting out the solution to an equation on a flashcard. Instead, questions like these focus on approach and strategy.

They allow students to agree or disagree with each other, but only if they can explain why. These are all conversation starters.

It’s the same for any teaching strategy or anything new introduced into the classroom; there’s always a period of adjustment that can be fraught with negative feelings.

Mathematical discourse is no different, but what’s encouraging is that most frustrations can be reduced or eliminated with practice.

We’re not all gifted orators, and having productive conversations can be challenging at first. There’s also the shift in working through math using words rather than just numbers, which can get frustrating for students, too.

What’s important from the teacher’s side is to recognize this as a productive struggle that you can guide students through with support and strong classroom management skills.

Students don’t have to start out doing this all on their own; you can help get them to the type of answers you’re looking for while they get the hang of it.

Another hurdle is participation.

Will your shy students automatically speak up when you open the floor to discussion?

Maybe not right away. Maybe never. Mathematical discourse works best when everyone participates, so set the expectation early on that each student must contribute.

Keep an eye out for those who hold back and encourage them to share. If you have a lot of students who struggle to speak up in front of the class, shift to think-pair-share math activities to get a peer-to-peer dialogue going.

As you might guess, intentional discourse will look different depending on the grade level you’re working with.

Early learners, for instance, might conduct a “turn and talk,” while high school students identify flawed logic in a complicated equation through a written response.

Specific strategies vary, but no matter the age of your students, discourse is beneficial to their mathematical growth.

Mathematical discourse is a massive shift in math learning, but it can create a noticeable difference in your classroom.

No longer will you be up to your elbows in worksheets and flashcards. Students will still do the math but can now talk through it at math stations or in small groups.

You can spend class time letting students share how they solved the problems, allowing each to have a confidence-boosting win as they discuss their mathematical approach.

It’s also a chance to create a different classroom environment.

Math is a tough subject, and with so much being right or wrong, without a gray area, learning math can be a tense time.

Through math discourse, you can create a space that encourages questions and comments, that makes it safe to get it ‘wrong’ because you're all working together to get it ‘right.’

This atmosphere can take away math anxiety and even show students why learning math is fun.

It’s exciting to think about math as a conversation versus rote memorization.

Although students will still need to get those math facts right, with mathematical discourse, they can talk their way through understanding the concepts in ways that will stick with them forever.

They can become *real* math learners on every level.

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