Semantics

Semantics is one of the biggest "problems" with math.  I fear that in early primary classes, math is so focused on number sense that when students are asked to start problem solving, words make all of the hard number sense work disappear.  It's as if it never happened!  The solution to this sounds simple (use more language in math at all grade levels) but isn't.

For the past couple of weeks, my students have been looking at the differences and similarities between perimeter and area.  I thought that they totally understood it, but wanted to do an assessment to check.  Thank goodness I did, because something about the phrasing seemed to cause them to forget everything.  AH!  They know what perimeter is, in isolation.  They know what area is, in isolation.  They can find different possible dimensions for a given perimeter, and can find all possible whole-number dimensions for a given area.  But, start to mix it up, and they're lost.

Slowly, as we toil away at different problems, it becomes more clear.  Here is where the importance of exposing students to different semantics comes in, as well as the importance of taking time.  Whereas we used to (well, I used to) drill the students with text book questions over and over and over, now the shift must be that this practice time is transformed in a way that allows the students to work over and over on something that is meaningful; something that is challenging.

Today I got to see the kids work with partners (that they chose, and boy, was I ever impressed in the choices that they made ... pairings I never thought would naturally happen, did!)  They were asked to solve one of these options, each offering a different challenge:

The area is 100 cm squared.  What could the perimeter be?

OR

The perimeter is 100 cm.  What could the dimensions be?

These questions are fairly (somewhat) straight forward.  The kids were comfortable with this.  When I gave them a map of my house, and asked them to pick a room, solve the area and perimeter, and then list other possible dimensions for the perimeter, it seemed to be too much.  The amount of words, even when broken up, were overwhelming.  The words area and perimeter suddenly became forgotten.  They couldn't quite figure out what it was that they needed to do. 

So my take-away questions, after a week of observing are:
- Do they just need more practice?
- Do they really understand the differences between perimter and area yet, or is it still muddy?
- How can I increase their skills and abilities from where they are now, to where I want them to be (able to use all of the skills and strategies we've been working on, by independently choosing the best option for them, whether it be a table, diagram, working backwards, or another option)?

The semantics in math can be overwhelming.  Changing the phrasing can terrify the kids and make them feel uncertain, even if they actually do know what to do.  Exposure to a variety of semantics is necessary, from an early age, with a consistency in what is being asked of them.  In this example, they need to be able to solve area, perimeter, and figure out different possible lengths and widths.  Solving area and perimeter should be kept consistent.  But, the depth of questions, the phrases and wording should be varied, and consolidated as a whole group.  Even in Grade 1! 

It takes time, and that time is bought with the use of layering in planning.  We're going back to some patterning next week, along with perimeter, by looking at a growing perimeter (I stole the question and modified it from a Math Makes Sense strategies toolkit question about a garden that gets bigger each year). 

Have you tried to change the phrasing in your questions?