Early Math Counts

For the most part, most of us approach problem-solving in much the same way:

1.   identify the problem

2.  consider options for solutions

3.  noodle through the possibilities and pick one

4.  try it out

5.  and find out if it worked.

Sounds easy enough, right?  As intuitive as this approach sounds to our seasoned ears, we learned how to move through this process over many years of trial and error and with a lot of support from the adults around us.  As children, we interacted with the material world testing hypothesis and drawing conclusions based on our rudimentary experiments.

When we couldn’t reach the sink to wash our hands, we figured out how to pull ourselves up onto the counter and balance our hips on the edge of the sink, so both hands were free to turn on the faucet, get the soap, and get washed up.  We eventually  had to figure out the “hand-washing problem” when we were faced with a too-high sink and no grown-up to lift us.

The “too-high sink problem” might have also been scaffolded for us if an adult had been present in the bathroom but not available for lifting.  Perhaps we came out of the toilet area, looking around for help – no takers.  Perhaps we tried to stand on tippy-toes – too short.  Perhaps we reached for the faucet – no way.  Perhaps we tried to sneak out without washing – yuck.  Most likely we observed another older child push himself up onto the counter.  Maybe another grown-up suggested, “Try jumping up.”

It may have taken two or three tries but once we got the hang of it, we never needed a grown-up again.  Problem solved.

In Young Children (March, 2014) in an article entitled, “Integrating Mathematics Problem Solving and Critical Thinking Into the Curriculum” the authors argue that we can teach problem solving skills and strategies to children by scaffolding their learning via an intentional problem-solving process.

To do this, follow these 4 steps:

1.  Reflect and ask

2.  Plan and predict

3.  Act and observe

4. Report and reflect

(French, Conezio, & Boynton 2003)

Imagine you have a dad in your program who works for a large corporation.  He comes to you one day, reporting that his business is moving and has all sorts of interesting items that you might like for your classroom.   He describes some old adding machines that have been in storage for the better part of 30 years complete with 10 cases of paper rolls that have never been opened. He says there are 4 machines to donate.  Perfect. 

The following Monday, he brings the adding machines over to your center.  You put the 4 machines on a table and the children are instantly interested.  However, you immediately realize that trouble is ahead.  All of the children want to use the machines at once.

You have a problem.

Frequently, I see teachers solving these types of problems by using their authority and exerting their control over the children.  A typical “solve” might be “First-Come, First-Served” or “10 minute turns”.  Both of these might work, but by solving the problem for the children, they miss the opportunity to solve it for themselves.

Using the 5 steps above, teachers can scaffold the problem-solving strategy.

1.  Reflect and ask – Bring the group to the rug and begin sorting through the issue. “It looks like everyone noticed that George’s dad brought us some new equipment for our classroom.  What do you think of the new adding machines?”  Discuss.

“There are only 4 machines and we have more than 4 children in our room.  What could we do so that everyone gets to play with the new equipment?”

2.  Plan and predict – “So the kids think we should let George play with the machines first, since his dad donated them.  You also think that George should pick 3 kids to play with him.  Is that right?”

“How do you think this will go?  Do you think the kids are going to be OK with this solution? Tomorrow, we will try this new plan to see how it goes.”

3. Act and observe – “This morning George gets to play with the new machines.  He is going to pick 3 friends to play with him this morning.  Go ahead George.”

Observe the play and the responses from the other children.

4. Report and reflect – Later, at group time say, “It looks like George and his friends enjoyed playing with the adding machines today.  Did you?”

“I noticed that the 4 of you didn’t play with the machines for all of free – play time.  Should we come up with another solution so more kids can have a turn when the first group is done?  How do we decide who gets to play with the machines next?”

Problem-solving builds strong critical thinking skills which are absolutely necessary for strong math skills.  Help your children problem-solve, not by leaving them to do it all alone, but by scaffolding with them.