Representing numbers

Rory was writing out numbers the other day and some of them were backward and all I wanted to do was tell him that they were backward and that he should fix them. Instead, I bit my tongue, and silently thought “positive feedback, positive feedback” in my head and then said, “Good job, I see you’ve written the numbers in order from 1-10!”. The experience reminded me of an earlier encounter in a kindergarten classroom, where I was helping a student who was working on the number 3. I forced him to change his backward 3 around, even though he was protesting in frustration. He eventually got it, but from that moment on, I wondered…how important is it for a kindergartener to know how to write numbers symbolically?


Rory writes the numbers 1-10

My conclusion…it’s not! At least not in the early grades! In fact, I don’t even know whether it qualifies as a math skill! I tried my hardest to find evidence to the contrary, but I couldn’t even find one educational math article on how to teach the skill. To further support my claim, if you google ‘how to write numbers’, the first thing that pops up are grammar articles.

So why do we put so much importance into learning how to write numbers? Well, the digits are symbols that are a great way to communicate mathematically. It is a universal language and, once learned, speeds up our representation of problems. As students mature, they graduate from using concrete objects to pictorial representations and eventually to abstract symbols. Knowing how to write numbers is a great way to show one’s thinking in a problem. That being said, I still don’t feel that the ability to write numbers properly, should be assessed as a math skill.

“Children should eventually be encouraged to connect their drawings to symbols, but they should not be forced to do so too soon.” Van de Walle

What is more important, especially in the early years,  is how a child internalizes the number they are learning. What does 5 represent? Can they show it using different objects? Can they show different ways of making 5 (i.e. 2 and 3 or 1 and 4)? Can they visualize it on a number line?

Here’s a video of Oliver (pre-school) to see what he makes of the number 5.

“Models or representations, whether they are conventional or not, give learning something with which they can explore, reason, and communicate as they engage in problem-based tasks.” Van de Walle

Notice even Van de Walle minimizes the importance of conventional number writing. Instead he places the value on any representation and its use in problem-based tasks. I felt very proud of Oliver in his ability to represent the 5 objects in his own way. He has demonstrated that he can represent 5 using concrete objects and pictorial representations. He is using models and making sense of the number; learning how to write the digit 5 does not need to be rushed.

So what can you do to help develop your child’s understanding of number symbols? For sure, you should still teach them to recognize the numbers orally, and visually. Of course you should encourage them to write it in standard form. But, concentrate on the important stuff: expose students to the number by using problem-based tasks. Encourage them to discover the meaning of each number, by coming up with their own way of representing the number. Allow the use of manipulatives to model the number and allow children to choose their own representation to model their thinking. Surround the learning of numbers with real-life scenarios. Most importantly, include opportunities to problem-solve and decompose the number while they are learning about it. For example, how many ways can 5 people be on a bunk-bed? Or how many girls or boys could we sit at this table to have 5 in total? Always ask, “who found a different way?” to encourage the sharing of ideas.

Here’s an example of Rory learning about the number 5 using a real-life problem. He is still being asked to represent the problem, but I’m allowing him to choose the method (drawing or symbols) to show his thinking. If he had chosen to represent it with pictures instead, I would have been okay with that; however, he is comfortable with writing numbers. I could even extend him by introducing him to equations at this point, but the purpose of this lesson was to think flexibly about the number 5 and so we concentrated on that.

Now…fingers crossed I get that cat so we can use the 5th stocking!

Happy holidays everyone!

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