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?

milestones-002_1

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!

Back to top

Full STEAM (Science, Technology, Engineering, Arts and Math) ahead!

THE DISCOVERY

This past summer,  I bought Rory a YOXO Helicopter construction toy (for only $10 at Chapters!). As soon as we got home, he was dying to dig into it, but I said no (…after watching  Shonda Rhimes’ TED Talk  I might have answered differently)! I wanted him to wait until I had time to help him with it; after all, he was only 4 and a half and couldn’t possibly make a helicopter all by himself!

When we finally did open it, I realized I needn’t have bothered; it is designed so that little people can intuitively build things on their own! Rory looked at the pictures and quickly figured out how to build the helicopter all by himself. He dismissed me immediately and insisted that he didn’t need (nor want!) my help. “I can do it myself!!!!”  resonated throughout the house…and the yard…pretty sure even the neighbours up the street heard his proclamations!

milestones-001

After building the helicopter, he proceeded to tear it apart so he could create something else. This continued until we finally had to put the toy away after he pummeled his brother for trying to destroy his new inventions!

YIPPEE FOR YOXO!

If you’re looking for something to do over the holidays, THIS IS IT!! YOXO is an amazing first step to engaging your child (boy or girl) with STEM. Children gain experience engineering their own creation using the material provided, or by improvising with their own. Unlike Lego, that can only fit other Lego pieces, YOXO is built to incorporate many items – boxes, toilet rolls, even Lego bases can fit into the hatch marks on a YOXO piece. As a result, the possibilities are endless and there is no limit to what can be engineered.

It is appropriate for all age groups. Oliver, only 3, was proud of his creations. Rory, almost 5, wanted more challenge. The colour-coding helped when my 3 year old wanted to follow the instructions, while my older son used the numbers to follow the steps. Other age groups may skip the instructions all together (hmmm…sounds like my husband)!

milestones-002_1

EXPERIENTIAL STEM

STEM (science, technology, engineering and math) or STEAM (includes arts in the acronym) by definition, is experiential; it is taking those subjects, integrating them and then applying them in a meaningful way. If you google STEM, you will find a plethora of lessons or materials that are pushing STEM education right now. The idea of a transdisciplinary curriculum that weaves subjects seamlessly together is not new;  for years, educators have recognized the benefits of an integrated curriculum. 

What is new, is the finding that the majority of the jobs in the future will be in STEM fields, so whatever we can do now to prepare our students for then is important.

“Employment in occupations related to STEM—science, technology, engineering, and mathematics—is projected to grow to more than 9 million between 2012 and 2022. That’s an increase of about 1 million jobs over 2012 employment levels.” Dennis Viloria, 2014

To me, STEM is more than the sum of its parts, it’s a way of thinking.  At a STEM conference, my colleagues and I quickly realized that we wished the acronym STEM didn’t exist because it turns away all those kids with aversions to science or math. We thought a more appropriate name should be DESIGN THINKING. Regardless of what you want to call it, there are lots of things you can do to aid in its development and get children excited about it, even in the early years. YOXO is just one way.

Here are a few other suggestions, so you too can move: Full STEAM ahead!

  1. Nature!!!!
  2. Bloco
  3. Lego
  4. Little bits
  5. Transport toys from Battat
  6. Magnatiles
  7. Maker space 
  8. Design Challenges
  9. Tinker toys
  10. Clipo by Playskool or Funskool

Back to top!

Have more suggestions? Leave them in the comments section!