Number Talks

I just can’t stop thinking about Number Talks. I love Number Talks, and really see the power that they have in helping students develop conceptual understanding in math. They really help students to see beyond the traditional algorithm toward understanding the meaning behind the math. Students have opportunities to explain their reasoning, and take safe risks, defend their thinking, and learn from their peers. Without this conceptual understanding, any gaps that exist just grow wider and wider. I just cannot think of a better way to start each math class than with a Number Talk.

Some of the benefits of Number Talks include:

  • Helping students understand the different ways that we all can think about math problems. Everyone is honoured in thinking about problems in their own ways.
  • Learning about mathematical strategies that are not prescribed, but work because they make sense.
  • Acknowledging that mistakes are absolutely about mathematical learning
  • Going beyond the strategies toward truly understanding them
  • Reinforcing math ideas by working with them more than once
  • Uncovering misconceptions, conceptual errors
  • Providing key feedback to the teacher of what to focus on next
  • Promoting a sense of ‘okayness’ with the unknown – the idea that math can be messy, and we don’t have to control what students are thinking about. Confusion is okay.
  • Helping students to understand that speed in math does not translate to understanding

With all this in mind, it sounds like they are the perfect solution, without challenges of their own. But the reality is that they do come with challenges that need to be addressed. For instance, often, I am asked questions like,

  • What do I do when the same students keep participating each week?
  • I feel like my Number talks are becoming very repetitive.
  • My students don’t see the value in them.
  • I don’t have time for this.
  • I don’t see the value in them.
  • Why are Number Talks important?

As I have been thinking about these questions, I have started thinking about Number Talks in relation to these challenges.

First, change your mindset that things must be written down to be learned. Students will have plenty of time in later tasks to write down their thinking. But in Number Talks, make sure that students are NOT writing their thinking down – the power of Number Talks comes from the ability to apply mental math strategies and then to verbally EXPLAIN their thinking. LISTEN to the thinking of others and then paraphrase other students. This really helps students to start to develop deeper understandings about WHY their ideas make sense, not just WHAT they need to do to get the right answer.

So how do we do this if only the same students indicate they have a strategy to share? 

My thinking here is that it is is very easy for the educator to always lead the discussion. I do it all the time. Usually it is the teacher asking the questions, paraphrasing the students ideas, listening to the students, choosing the ones who have the confidence to share. But when we do this, we train students not to listen to each other, not to explain ideas to each other, not to learn from each other. I think that we can put this onus back on the students by taking steps to enable them to take the reins with listening, paraphrasing, verbalizing personal ideas, and those of their peers. Caution: this will feel awkward!! Unnatural!! For the teachers and students. It will also take a long time. Be patient. Keep practicing. It is okay to begin the process of helping students to properly explain their thinking. Let students really get that they don’t have to follow a prescribed process to think during a Number Talks.

In terms of participation, always make sure that Number talks are safe. Cold-calling students is not usually the best way to help them feel safe with math – (and so many of us know what anxiety can do to our math brains!!) What I like to do is to have students turn and talk to a partner about their ideas and strategies. It is a much safer strategy, and all students still have the opportunity to participate.

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But what do I do with the students who figure out the answer right away?

Encourage students who think they know the answer and have a strategy, to try it out a new way, a second, third or fourth way! If it is too easy for most, then have other problems at the ready! This is a formative assessment process as well, so pay attention, and really listen to what the students are saying and thinking about. More than checking off an expectation from the curriculum list, pay attention to the student and where they are at. Use this as feedback for where to go next in your math planning.

Start developing anchor charts of student thinking during Number Talks, and keep them posted to help students understand that this thinking can be transferred to other math activities. That way you can sequence them accordingly, and students don’t have time to forget what they have learned.

I really cannot stress the importance of talking, and engaging with peers to enhance the learning process. Some things to keep in mind are that orally describing thinking, translates to better writing about the math. Understanding the meaning of the math helps students to think about the reasonableness of a problem. Help students to be precise with their words – instead of saying ‘timesed’, use multiply – clarify what they are talking about – also a great strategy for ELL students!

Time is okay!

Give time to think, time to formulate ideas. Too many students feel like if they don’t get the algorithm and solve the problem right away, that they are bad at math. So many of us were taught this way as well, and therefore, it just doesn’t feel natural to teach in these powerful ways that promote depth of thinking. It is important to give yourself permission to try this out – and to also see how much better at conceptual understanding even you become!

I also personally believe that either Number Talks need to be done each day, or on consecutive days, if not for any other reason than to keep the thinking fresh in their heads. Keep students practicing the art of explaining their ideas to each other.

(Also – they really support, and are supported by a Feedback-Friendly Classroom!

But I would love to know what you think!

  • What are your experiences with Number Talks?
  • What challenges are you facing with your students?
  • What other strategies do you have for teaching Conceptual Understanding?
  • What successes can you share around Number talks?

 

I would love to learn more from others who have tried Number Talks!

Deborah McCallum

C 2018

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