I **read a recent article** about the importance of early number talk with children and was pleased that this issue was being brought up. The article shares research on a few of the stark differences in how parents talk with their children about numbers. For example, parents tend to talk to their daughters about half as much about numbers as their sons. Parents also range in how much they use number words around their children from about a dozen times a week, to as much as 1800 times per week.

However, I felt that the list of suggestions the article had at the bottom was incomplete. The article's author essentially makes suggestions which I feel will only help children develop an **instrumental understanding of mathematics**, as opposed to a more useful, interesting, relational understanding.

Here are some more things my wife and I do with our children from a very young age to help them develop a deeper understanding of numbers.

- We play games with our children that involve numbers. We roll dice, we play cards, we solve puzzles together, and we play hopscotch. Through these games, my children gain an understanding of the relationship between numbers and actions we take in the games themselves. We ask questions like "how many ways can you get a 10?" My son recently answered that question with this sequence of answers: 20 - 10, 30 - 20, 40 - 30, 50 - 40, etc...

- We talk about how we use numbers in our day to day life. We talk about fractions of food (that are physically present in front of us), and talk about the relationships between these different fractions. We cook, do our finances, and share as many uses of numbers as we can with our children.

- We look for patterns in numbers. We play with relationships between different numbers. We celebrate discoveries our children make. For example, my eldest son noticed that he only needed to remember the very last digit in a large number to figure out if a number was odd or even. Now, he delights in asking people to give him gigantic numbers like 30,938,309,830,983 and being able to tell right away if the number is odd or even. As a mathematician father, I try hard to balance between giving my sons space to come up with their own discoveries, and expanding where their explorations might go.

- I also try very hard to remember that when my son makes a mistake, with further experiences, it is likely that he will discover these mistakes later for himself. For example, my son was convinced for a long time that numbers went 90, 100, 110, 200. He did not understand place value well enough, but over time, and with further exposure to our use of numbers, this misconception of his has disappeared. He now has a very good understanding of place value up to 1000, although he still does not understand larger numbers (he will say things like 233 hundred thousand, 293 million, 389 billion, and 43), but I am confident that as he continues to be exposed to numbers in his day to day experience, he will understand these numbers better.

- We balance our discussion of patterns in numbers with other types of patterns. We look for patterns in art work, in sidewalks, in tiled floors, and wherever else they may form. We create patterns ourselves in our art work and notice where they came from. We doodle, we draw shapes, we watch clouds, and we look at maps, all of which help my son develop a sense of shape and space.

- We ask for evidence from our sons about why they think something is true, whether or not what they are saying is accurate or not. When they have discovered something, and provided solid evidence for why they think it is true, we celebrate it. We might ask questions like, "How did you discover that?" or "Wow, that's neat. Does it work all the time?"

- We give our children plenty of creative time to explore the world through art work, Lego, blocks, reading, playing games, and other self-exploration activities.

- We see the development of our children's numeracy as a process, rather than a race. I have no interest in accelerating my sons through the elementary school curriculum, instead I focus more on providing opportunities for enrichment.

The key to all of these activities is that we view numbers and quantities as ways of exploring, and we nurture our children's sense of wonder about the world.

Newsletter:

David is a Formative Assessment Specialist for Mathematics at **New Visions for Public Schools** in NYC. He has been teaching since 2002, and has worked in Brooklyn, London, Bangkok, and Vancouver before moving back to the United States. He has his **Masters degree in Educational Technology from UBC**, and is the **co-author of a mathematics textbook**. He has been published in **ISTE's Leading and Learning**, **Educational Technology Solutions**, **The Software Developers Journal**, **The Bangkok Post** and **Edutopia**. He blogs with the **Cooperative Catalyst**, and is the **Assessment group facilitator for Edutopia**. He has also helped organize the first **Edcamp in Canada**, and **TEDxKIDS@BC**.

- Creating a WiiMote interactive white board at my school for under $50.
- 20 reasons not to use a one to one laptop program in your school (and some solutions)
- For whom are Interactive White boards Interactive?
- What is Edcamp?
- Mathematics education blogs
- Forget the future: Here's the textbook I want now
- Eight Videos to Help Teachers Get Started Using Twitter
- Why educators should blog: A helpful flowchart
- There are no aha moments
- Paper use in schools
- 15 things kids can do instead of homework
- Online Geogebra training
- The difference between instrumental and relational understanding
- Why teach math?
- What is The Effect of Technology Training for Teachers on Student Achievement?
- Using Google forms for a "Choose your own adventure" style story
- Ways to use technology in math class
- The Death of the Amateur Mathematician
- We are homeschooling our son
- A Fundamental Flaw in Math Education
- 25 Myths About Homework
- A Restitution Guide to Classroom Management
- Migrating away from Google Reader
- Free tools for math education
- The Role of Immediacy of Feedback in Student Learning

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## Comments

## Comment On Raising Mathematicians

I absolutely love this post of yours! What fantastic examples of what people can do at home to get children really working with and understanding numbers. I've focused on communication in math in my classroom program for the past couple of years (last year in Grade 1/2 and this year in Grade 6), and I've found myself talking a lot to parents about how they can support this math learning at home. I'm going to share your blog post with the primary teachers at my school and our math facilitator as well. You have such great ideas that need to be shared!

What would you suggest for developing math communication skills in junior students? I'd love to hear your ideas!

Aviva

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## I often find (although this

I often find (although this is not always the case) that students struggle with communicating mathematical ideas for a few reasons.

They lack the vocabulary.My recommendation here is to be open-minded about what vocabulary you expect your students to use, and to treat the introduction of vocabulary like you would if you were introducing it in science or social studies - students learn vocabulary that they are able to attach to an experience, and in context.They are afraid of writing something imprecise.Mathematical writing is typically quite terse and very precise, which is incredibly difficult for novices to emulate, so here I would model the use of every day language to describe mathematical ideas. Allow for diagrams to help supplement complicated descriptions. Show students that they can use the language they know already to describe these ideas.They don't really understand the concept they are being asked to explain.If a student can manipulate the symbols to get the desired result, but doesn't understand why what they are doing works, it can be pretty challenging for them to explain it in words. Resolving this one is the most difficult; it essentially requires you to reteach the topic so that students understand it deeper than just as symbol manipulation.## Children should be taught

Children should be taught math in such a way that the children may find serious interest in it. I have seen many Child fear this subject.

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## Re: Raising mathematicians

I really enjoyed reading your article about the various ways to keep your children involved w/ critical thinking and math skills. Another site that I've seen (& will probably use when I have kids of my own) provides "thinking exercises" as "Bedtime stories" can be found on Facebook, called "Bedtime Math Problems" (URL: https://www.facebook.com/bedtimemath).

Great ideas for raising mathematicians.

Thanks,

Audra

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