Today, let’s take a look at how tools are used to support mathematical understandings and how tools can be misused so they are not really effective in terms of meeting early math outcomes.  

Here you can see a few sorting trays designed so that children can create, extend, and copy patterns (green tray), sort and organize items by attribute (yellow tray), and graph (blue tray).  

This red one is divided into quadrants so that more or larger items can be grouped or sorted in other ways (I.e., animals that fly, animals that swim, animals that walk on 4 legs, animals that walk on 2 legs).

These all come in a set and are beautifully made, large enough that children can use smallish items with them but not so smallish that they present choking hazards.

So, if you had these in your room, how would you use them?

The day I saw these in a Head Start classroom, they were sitting out on a table with several bins of small manipulatives nearby.  A few children were playing with them and from my observations, it was clear that they did not know or understand the purpose of the trays.  They were using each tray much the same way they might use a plastic plate, as a receptacle for putting the toys, storing the toys, and moving the toys around.  The teacher never came over and neither modeled how to use the trays nor explained how to use them.

Here you can see how one child was putting dinosaurs into the spaces of the tray in a disorganized fashion.  At no time did a teacher support his play by suggesting alternatives, or sitting next to him and encouraging more purposeful use of the materials.

It reminds us that our role as “set designer” and “provocateur”  demands that we do not put materials out in a haphazard fashion but systematically think about our curricula, materials and environment in thoughtful ways.  We  must observe the children to know where they are developmentally and what they need from us so we can support their growth.

These tools are not meant to be put out on a table at the same time without direction.  They are meant to be used to support developing mathematical competencies.  That is NOT to say that young children should not use them to play.  Of course they should.  In fact, before I used them for their designed purpose, I would allow  the children to explore the trays, one at a time, over a period of time, to see how they explore them organically, without direction.  Eventually, I would take one over to group time and show the children how they can make patterns in the green tray or sort items in the yellow tray.  I would show examples and sit at the math table and work on patterns with the children, creating them and asking the children to extend them.  I might ask children to create their own patterns and see if I can extend them. I would set out very specific manipulative that have 2 or 4 attributes so they can be easily distributed in the sorting trays.

I would set the scene and facilitate the play.  I would use math language throughout these interactions and make it fun.  I would show excitement about the challenges these trays present and pose thoughtful and stimulating questions that the children could answer.  I would encourage the children to “try” and get excited at their efforts.

In short, I would do my job by being the best, most thoughtful teacher I could be.

Think before you set up your materials and arrange your space.  How are you going to be the best teacher you can be?

I bet most of you already use math sentences with your children all of the time.  When you ask a child to set the table for snack and she comes back to report that she has finished, you might look over at her work and notice that there are 2 chairs that don’t have a place setting.  Rather than telling her that she needs to get 2 more place settings for the empty chairs, you probably say something like,

“Hmmmm. It looks like the table is almost set but not all the way.  How many plates did you put out and how many chairs are there?  So there are more chair than plates.  How many more plates to you need to make sure that every chair has a plate?”

You might also use a math sentence when you are taking attendance.

“If Johnny and Sara are absent,

how many children are absent?”

or

“There are 6 boys and 4 girls at school today.  How many children all together are at school today?

The main point of difference between how older children approach math sentences and how younger children approach them is that older children are reading them and answering on paper.  Younger children are exposed to math sentence because the adults verbally present them and then support them as they calculate the answers.

Most 3 years olds are not going to be able to add 6 and 4 in their heads.  The way that they will get to the answer is through scaffolded interactions, perhaps between themselves and the adult or between themselves and other children.   After posing the question about how many children are in school today, the teacher should then allow the children to try and come up with their own strategies for solving the equation first and the let them try to see if it works.  If, after a couple of attempts, it is still unclear, the teacher can provide a strategy, i.e., “Let’s count all of the children together, both the boys and the girls, to find out,” and then point to each child as s/he is assigned a number.  Remember to stress that the last number you say is the total.

Try and think of number sentences as more than simply asking questions or making statements about math and number, and more as a “plan of action” for including more math opportunities into your interactions with your children.  This intentionality will force you to consider ways to present the problems and then support the children as they figure out the answers.