The Museum of Rarely Used Math Manipulatives: What Do We Need?

Today in Kindergarten, we used Attribute Links to play Name My Rule. We sorted shapes based on properties (number of sides, number of ‘points,’ size, color, etc.). Attribute links are a great fit for this game — better than other shape-based math manipulatives we have, like pattern blocks.

The shapes on the LEFT fit my rule. The shapes on the RIGHT do not. So what’s my rule?

For what we are currently teaching in kindergarten — some early understandings about the properties of shapes — this set of manipulatives is fantastic. Unfortunately, they do not serve much of a purpose for the rest of the year. They typically sit in my school’s math office, collecting dust… until…

Come on, come all, to the Museum of Rarely Used Math Manipulatives!

My office mate and I inherited an impressive array of mathematical materials. Our office is full to the brim with books, binders, and, of course, math manipulatives.

We also have an archival closet. It may sound facetious to write that it is full of things that “never see the light of day,” but, in reality, the closet has no windows and also no overhead lighting. It’s a space intended for only the most adventurous — the sort of people that take vacations to visit underground caves, or that consider sneaking into abandoned building a “fun Wednesday afternoon excursion.” This closet feels less like a room in an elementary school and more like the setting for next season of American Horror Story.

But everyone, regardless of their thirst for adrenaline, deserves to share in the delight of these rarely used math manipulatives! That’s why the good people of the #MTBoS (Math Twitter Blogosphere) conceived of the Museum of Rarely Used Math Manipulatives. 

First stop: Place Value Patio. Here, you will find blocks that represent different bases. We have base 2 in red. (Show partially in the photo below.) We have base 3 in orange. We have base 4 in yellow, base 5 in green, base 6 in blue, and base 7 in purple. Bases for everyone!

Next up, we have the Shape Arcade. Here, you will be able to play with pattern blocks that represent 1/4 or 1/12 of a hexagon, pieces of a circle, some colorful “cheeses,” and other geometric shapes. Those last two come courtesy of @Simon_Gregg.

Watch out for that Ten Frame Train passing on your left!

The Museum also offers a wide gallery of Geometric Wonders. There are pre-cut nets that you can fold into 3D shapes — prisms, cones, pyramids, cylinders. There are folding shapes, and shapes that can be filled, and the attribute links, and more.

Then we hit measurement mania. There are balances, and metric weights, and customary weights, and containers to model all different customary and metric capacity units.

Further back in the closet, you may find geoboards tucked neatly into a box, and brittle rubber bands crumbling underfoot.

But this all begs the question: what manipulatives are important to have on hand? 

I believe that it’s not in the manipulative, per se, because they’re only vehicles. It’s about the sort of thinking that the use of these manipulatives encourages. It’s about constructing mathematical understandings, or developing them further.

Manipulatives represent ideas. They’re symbolic; they’re analogies. Sometimes it’s helpful to use the same manipulative to show the connections between ideas, and to build off student familiarity. Whatever you have, use it wisely and use it well.

There are a number of interesting articles about the use of math manipulatives in elementary classrooms, mostly pointing out variables in their use and the thinking encouraged. I’m always drawn back to Deborah Ball’s seminal “Magical Hopes: Manipulatives and the Reform of Math Education” (American Educator, Summer 1992). In the article, Ball plaintively says, “

“My main concern about the enormous faith in the power of manipulatives, in their almost magical ability to enlighten, is that we will be misled into thinking that mathematical knowledge will automatically arise from their use. Would that it were so! Unfortunately, creating effective vehicles for learning mathematics requires more than just a catalog of promising manipulatives. The context in which any vehicle–concrete or pictorial–is used is as important as the material itself.”

-Deborah Ball, “Magical Hopes: Manipulatives and the Reform of Math Education.” American Educator, Summer 1992. Page 46.

It’s not about the manipulatives you have, it’s about how you use them.

That said, I think it is better to use manipulatives repeatedly, to leverage student familiarity with the material and help build connections between mathematical ideas. Simon Gregg (@Simon_Gregg) is a wizard with Cuisenaire Rods. He uses them to explore all basic number operations (including multiplication and division), geometry, geometric measurement, and more. The rods are versatile, and the result is potent.

I’ve seen the use of Base 10 blocks help students make connections between the structure of natural numbers into ones, tens, hundreds, etc., and then decimal fractions like tenths, hundredths, and thousandths, too.

In the main part of our office, we have lots of unifix cubes, tiles, Cuisenaire rods, and Base 10 blocks. There’s a small tub of pattern blocks, and another of centimeter cubes. We also have lots of tools for games, like cards, transparent counters, dice, and spinners.

So, yes, I still have my archive closet full of dusty base blocks and relational geosolids. Yes, it’s annoying to have to hold onto large storage bins full of cups to demonstrate customary capacity measurement (gallons, pints, etc.), especially when I only seem to break them out for teachers once per year. All the same, it wouldn’t make a lot of sense for us to try to teach about equivalent units of capacity with Cuisenaire rods or base 10 blocks. These materials serve a purpose.

As a math teacher and compulsive collector, I delight in my pattern blocks that model 1/4 of a hexagon. They’re fun. They reveal new relationships. There’s so much potential for play — for me — but most of my productive play comes out of years of experience modeling mathematics with the classic pattern blocks. Most students aren’t ready for that, so… back to the Museum they go.

___________

As an addendum: I’ve also started using some virtual manipulatives. My favorites are the ones from the Math Learning Center. I read some research (that I can’t seem to re-locate quickly) that said that virtual manipulatives have the potential to be just as beneficial for learning as concrete manipulatives. The power of using manipulatives is not in the physical touch but in the connections. It’s the learning.

I featured the Number Pieces app in my blog post about listening to English learners in math. I love that these blocks have the ability to ‘magically’ regroup (or decompose) at the touch of a button. It’s an advantage over physical materials.

Most importantly: now, if I have access to a computer or iPad, I have access to base 10 blocks, as well as number lines, rekenreks, and geoboards. It’s so efficient. Meanwhile, my real, live geoboards are back in the Museum of Rarely Used Math Manipulatives. It might be time to let them go.

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