Why Math Discussions?

If you haven’t read 5 Practices for Orchestrating Productive Mathematics Discussions you need to. This is basically the mecca of math discussions. Published by NCTM in 2018 it addresses how you can implement math discussions in your classroom.

So, let’s chat about why we need math discussions? Read this quote below about how globalization has changed the demands on the types of thinkers we need in the job force.

The thing is jobs used to allow for people to use basic skills, but now in today’s world we need critical thinkers. We need our students to be able to think, reason, and problem solve. Especially, as the quote says, girls and minorities. So, I ask you…

What opportunities are you giving your students to develop these critical skills needed to be successful in today’s world?

How do you support and engage your students in opportunities to engage with complex problems?

So, now let’s get clear on what we want our students to be able to do. What does it actually look like in a student? Read the quote below.

We want our students to be able to explain and justify with evidence their math thinking! We want them to be able to reason through their ideas and the ideas of their peers. In addition, we want our students to be able to provide evidence and rationale for their math ideas that demonstrates their deep understanding of mathematics. Friends, this can happen… in fact it can all happen through math discussions.

What do you mean ALL Learners Engaged in Math Discussions?

But first, I just want to clarify what I mean by all learners. I mean…

ALL LEARNERS

I’m not trying to be dramatic… okay, maybe a little. But I’m serious, we have to believe that every single child can achieve, be engaged and understand deeply. So, yes. Your learners that are shy, energetic, resistant to math, those that learn differently or take longer to process. Every single learner can be engaged in math discussions.

Engage Every Learning in your Student Centered Math Class with this Ebook!

You can get a head start by downloading my free ebook on the 5 Steps to a Student Centered Math Classroom. Grab it by clicking the picture below!!

5 Tips forEngage All Learners in Math Discussions

#1 Choose a worthy Math Task for Math Discussions

In order to engage your students in a math discussion they need something to talk about. We know there are a few kids in our class who could carry on a discussion about anything. However, we want to use this math discussion to move their understanding of math concepts forward. So that means we must choose a worthy math task. One that has a “low floor’ meaning it allows for students to access the problem with a simple first step. Then, a “high ceiling” in which all learners are challenged within the task. Low Floor High Ceiling tasks are open in nature which allow students to approach problem solving in any way that makes sense to them. If you want to know more about the research of low floor, high ceiling tasks this video from Jo Boaler is helpful.  Find out more about my favorite math task- Problem of the Day at on this post. 

#2 Turn & Talks Engage Students in Math Discussions

Using turn and talks are a great way to get students talking in math discussions.  I suggest using a turn & talk at the beginning of the math discussion to engage every student. It might go something like this…

• a few students share their work from the task.
• ask students to turn and talk about the strategies and models.
• come back together and ask partnerships to share what they talked about to get the discussion rolling.

Be sure to set up clear expectations and procedures for your turn and talks. You don’t want to loose valuable minutes managing student behavior during the turn and talk.  So spend the time at the beginning laying the foundation of a solid procedure & expectations. Then, practice! I like to turn and talk to get to know each other first to practice our procedures and meeting expectations!

#3 Use Opened Ended Prompts to Engage All Learners in Math Discussions

I always start our math discussion off with an open ended question. I LOVE “What do you notice?” or “What do you wonder?” These open ended questions allow students to drive the thinking and discussion. This is also a great prompt to give students for a turn and talk. Be sure you listen closely as students share what they notice. This is the perfect time to do a quick check for understanding and decide the direction you’ll take the math discussion.

#4 Accept All Answers in Math Discussions

Students are often nervous about what to say or how to say it in math discussions. I urge you to accept all answers in math discussions. That will allow students to see that it is safe to share a response that is incorrect. If students are discussing flawed reasoning or a misconception point them to the models to use evidence to explain & ask then to clarify their thinking. It is important that the job of reasoning and explaining stays on the students.

#5 Give Students a Way to Opt-Out in Math Discussions

As you continue to build your students ability to participate in math discussions it is important you give them

a way to opt-out. It is so important we teach students real world skills, and the truth is sometimes you’re not ready to share. I like to make an anchor chart of a few phrases students can use if they aren’t ready to participate. It usually includes, “I need another minute to think.” “Could I get some help please?” “Could you come back to me please?” This allows the classmates to jump in and help and the door open for us to come back to the student.

I do want to note it is important this is not interpreted as lowering the expectations for students, but instead accommodating students until they are ready. I continue to encourage students to participate and remind them participating is the best way to learn. We discuss our expectations for discussions every time we start, so students know they are expected to participate. This approach of allowing students to “opt out” helps build community and develop a sense of belonging in the students. It is my hope they know that we want them to participate when they are ready and there are supports in place to help them become ready.

Looking for other Discussion Resources?

Here is a blog post on discussion stems. 

Check out this blog post about 3 number talk ideas to improve your students’ fact fluency!

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The Math Teacher Collaborative

Are you looking for a community of like minded teachers to collaborate with? We have a weekly live training and opportunities for Q&A! You must join us if you’re looking to deepen your practice as a math educator and collaborate with some other amazing folks. I hope to see you there.

Reach All Learners in your Student Centered Classroom with this Ebook!

Downloading my free ebook on the 5 Steps to a Student Centered Math Classroom. Grab it by clicking the picture below!!

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Problem Solving Definition

Let’s form a common definition. My training and research comes from a book called Children’s Mathematics: Cognitively Guided Instruction. This training opened my eyes to my problem solving definition. So here it is,

Problem solving to me isn’t just an approach that works in math, it helped me develop lessons that allowed me to plan lessons where students could drive the thinking in every subject.

Problem Solving Process

The problem solving process in my classroom is by far the best part of the day – in my opinion and my students. In fact, on the days we don’t do problem solving I hear groans and moans. It’s actually quite beautiful to see their love for math.

On a typical day of problem solving most of our learning happens in a circle. Read about why I love circles here. We use circles to send the message that every single one of us is vital to the problem solving process. You see, this isn’t a routine just for each child to push themselves, but it is a way for us to work together to collectively gain understanding. This process is just as much about our community working together to develop an understanding as it is for the individual.

launching the task

We start in a circle with launching the task. I make strategic moves to help students envision the math problem as a story. We don’t zoom into key words, instead we work toward a total comprehension of what the problem is asking.

grapple time

Next we move onto independent “grapple” time. This time allows students to get up close with the task and challenge themselves to persevere for only 8 minutes. I have found this is the perfect amount of time for most tasks and for most grade levels. During this very quick amount of time I observe. I look for how students are solving, really trying to get inside their thinking. I don’t use this time to one-on-one teach or coach students.
By giving students this time to grapple we show them that they have the ability to do hard things.

share and discourse

Then, we come to the carpet for select 2-3 students to share. I select these students based on what I see students’ current level of solving. The goal is that students will learn from their peers and be nudged along the trajectory toward more advanced models and strategies. 

Steps to problem solving

My problem solving routine is a total of 25-28 minutes. We do this every day within our math block.
And yes, I also teach fluency and my curriculum addressing all math standards. Here is the time break down for each step.

Launch Task (5 minutes) 

Grapple Time (8 minutes) 

2-3 students share (5-10 minutes) 

Student led discourse driving toward deep understanding of students’ shares. (5- 10 minutes) 

As I’ve said before this is the best part of our day and worth every single minute.

If you would like even more details on how I do this, grab my eBook titled
5 Steps to a Student Centered Math Classroom: Empower Students to Love & Understand Math

Problem Solving Examples

Check out this video in my actual real life classroom. Please know this is not perfect example, but it’s a good idea of how you can empower students to have ideas and think in math without directly teaching math strategies.

Another example of what this looks and feels like in my classroom is located here. I’d love to hear your thoughts and feedback in the comments below.

Problem Solving Techniques

These teacher moves are something I will be perfecting for the rest of my life. Isn’t that exciting? I have found a teaching practice that not only helps students learn, but also helps me learn!
Leading a discussion, listening, and questioning are the key skills I’m working to be a better facilitator. 

There is a long list of skills we can teach our students. For example; how to start solving a problem, how to get over a road block in solving, how to analyze a solution of others, and so on. That’s all for another time!
Hint… look for a teacher training designed just for you/with you this summer!

Ready to Implement?

Are you ready to give this a try in your classroom? Or maybe you just want to see how all the pieces fit together? Grab the lesson plan below where I will walk you through each part of how I go about teaching my favorite math routine!

The post How Problem Solving Changed my Math Teaching appeared first on Mona Math.

4 Tips to Engage students in Virtual Math Discussions

Anyone else feel like they are teaching a live virtual class to… no one? With student’s cameras off and hesitations to turn their mics on I often feel like talking to myself and my zoom screen. Believe me I get it, it is hard to get students to have a virtual discussion, let alone a full blown virtual math discussion. In fact, when they do finally turn on their mics it seems to be at the exact second as someone else turns on their mic.

I’m right there with you, virtual teaching is hard. Virtual math discussions feel nearly impossible most days between tech issues and student participation.

However, In my 9 months of virtual teaching I have found 4 tips to make virtual math discussions do about. These tips will help engage your students in math discussions virtually!

Tip #1 Choose the right tech tool for Virtual Math Discussions

Tech tools matter when having a virtual math discussion. Read about my top 3 favorite tech tools here!

I have found when I have multiple ways for my students to engage in the virtual math discussion they are more likely to participate.

Here are the ways they can participate in the virtual math discussion:

• in the chat
• with signals on video (I agree, head nods, etc.)
• by turning on their mic
• by accompanying their work with typed explanation.

When I have a tech tool that allows for all these types of participation students are more likely to participate.

When my students are successfully able to complete the work we are discussing they are more likely to “pop on their mic” and participate in our math discussion. Can you imagine not being able to do the assignment and then being graded on how you participate in talking about the assignment you couldn’t complete? 

Math Discussion prompts and sentence stems are always helpful when having a virtual math discussion. Consider using 2-3 to start and build your class’ bank of sentence stems to refer back to. Here are a few more tips on using discussion prompts.

#2 Choose the Right Math Task for Virtual Math Discussions

We know that when students are engaged in the work it is difficult to keep them from talking. In my class our math discussions are much richer when students are excited about the work we are discussing.

Choose a math task that is relevant for your students. It could be as simple as a word problem about the people in your class or a task involving their favorite video game.

Remember, the best math tasks have a “low floor” or an easy first step to get engaged in the problem. They also have a “high ceiling” or multiple ways to extend the problem and explore the math deeply. Choose a task that engages your students and your math discussions will be more robust!

#3 Use Breakout Rooms in your Virtual Math Discussions

Many of my students have told me they don’t want to talk on the virtual whole group math discussion. So, as we continue to build our classroom culture to be supportive and inclusive so students feel safe participating in math discussions, I find ways to ensure all students are able to participate.

I use break out rooms for ways to engage all my learners in math discussions.
First, I use them for use turn and talks. Turn and talks are a math discussion instructional move- used for brief partner shares with a clear talking task.

Also, we use break out rooms for small group shares. In groups of 3-4 students can share their math thinking and reasoning for a “mini math discussion”.

Another way I use break out rooms is to conference with students and “listen in” just like I would while conferencing in person. I use this time to honor students thinking by observing, asking probing questions to truly understand their thinking. 

Breakout rooms allow me to be flexible in the way I structure of math discussions to boost engagement and ensure all students are doing deep math thinking.

#4 Make Models Visible for the Whole Group Share.

We always come back together as a whole class to have a synthesis math discussion. During this time 2-3 students share their strategies & models.

I draw out what my students are sharing. Students can definitely show their work, but it is also key to draw out what the student is describing in the math discussion. Drawing out their thinking provides a visual model to follow how the solver went through each step. Then, you have a record that students can refer back to while during the virtual math discussion.

I use a document camera that I screen share directly to zoom. However, if you don’t have a document camera you can use your phone on a stand to project. There are multiple ways to project your devices on live meeting and I find it to be very help in engaging my students in talking about the actual models and strategies of their peers.

It’s not forever, but it is for right now

This type of teaching isn’t forever, but building our students virtual math discussion skills can only benefit them in the future. In fact, all the technological skills our students are learning is preparing them to be our future leaders in this field and life.

So, if we’re going to have to teach virtually, why not make it as engaging as possible. We are all starved for discussions with new people and missing our friends. So what better time than to embrace the virtual math discussion.

So, I urge you to give virtual math discussions a try. It might not work, it definitely will come with challenges, but it sure is better than teaching to crickets!

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