I’ve been itching to get into some basic abstract algebra goodies. With the help of the Cuisenaire Rods, Simply Fun Sumology number tiles and the Discovery Toys Busy Bugs, I’m able to do that.

Start with wrap around addition.

This type of math is officially called “modular arithmetic.” We are only going to use the numbers 0, 1 and 2.

It begins as regular addition. And since we are only using those three numbers, all our answers have to be either 0, 1 or 2. So when we add 1+2, we wrap around.

If we were to count in our system, we’d say: “0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, …”

The addition table looks like this:

(Notice you could do this with numbers from 1- 12 and it would be clock addition!)

Now things get buggy.

Switch out all the number tiles with some pretty color Cuisenaire Rods. They don’t have to be the “right” rods. We’re only looking at the colors. Here’s the progression I did:

The end result is a very abstract chart!

You can “bug” two things together.

Like this:

(I know – a spider isn’t a bug. But run with me on this, okay?)

Notice that each of these are directly from the “spider table” above.

You can read this as, “Purple spider green equals green,” just like you would say, “Zero plus one equals one.”

We know that if you start counting at one object the number of thing is the same as if you start with something different – but kids don’t. Here are some thoughts on counting that can put you in a different mindset when dealing with children and counting. Continue Reading

One Response to Counting Isn’t an Inherent Concept

[…] Crowder encourages teachers to think deeply about preschool math in Counting Isn’t an Inherent Concept and What is […]

I like your idea of using of the balance – it’s beautifully visual, but I would hesitate to call what you’ve done subtraction. Of course, it’s formally equivalent to subtraction, but this to me looks more like the “missing number”, or complementary addition flavour of the operation, which is not necessarily understood as the same thing by a young learner. i.e. To me, you’ve demonstrated the formal equation 5 + ? = 12, rather than the concept of 12 – 5 = ?.

As you’ve pointed out, 5 + ? = 12 is the same thing as 12 – 5 = ?. If we tell a young learner that they can’t understand this, then they will believe us.

They can understand this. Actually, they are much better at understanding this than we are. They have not been socialized out of understanding what is inherent to them.

Ordinal numbers are “1st, 2nd, 3rd, …” but we need these to count items to arrived at the final cardinal numbers. All this fancy math talk – why not make it fun with some colorful bugs! Continue Reading

Seeing division helps a great deal with understanding division. Especially when it comes to remainders. This video offers a tangible way to do this. Continue Reading

Cups that are “built to scale” stop being just toys and start being the ideal curriculum tool to teach math and arithmetic! Continue Reading

4 Responses to Using Toys as Curriculum Tools to Teach Arithmetic

Bon,

I think it’s a good opportunity to introduce fraction ideas and names from the get-go. For example, 9 divided by 6 is one and one-half rather than one and three left over.
The 3 left over need to be seen, IMO, in relation to the unit container of 6.

I agree, Gary. The trouble I’m having is with the words “divided by” and “goes into.” When you pour sand from one cup to the other, there is another “go into” idea there.

I’m going to need to think on that one some more.

But you are right – the language here would be good to include. Thanks for the comment!

Buy them online at http://www.tinyurl.com/dtedtoys2 – that’s an official site of mine through Discovery Toys (they don’t have an affiliate program so I became a “dealer”). Totally legit – company’s been around for >30 years.

I hope you enjoy them, Makenna – and remember, they are guaranteed for LIFE! (that’s really the best part about them)

Differentiation is the foundation of learning. Curiosity comes in the form of “Why is that different?” And right behind it is “Why is that the same?” Continue Reading

What’s the difference between congruent and similar triangles? This post shows it – AND there’s a video on how to demonstrate and learn congruent triangles with the Discovery Toys Giant Pegboard! Continue Reading

[…] Crowder encourages teachers to think deeply about preschool math in Counting Isn’t an Inherent Concept and What is […]