Essential Math You're Not Teaching (But Could Be Tomorrow!)

If you ask a typical group of students, "What is math?", you'll get answers like this:

Addition.
Subtraction.
Multiplication.
Division.
Fractions.
Worksheets.
Pages of thirty problems.
Textbooks.
Homework.
BORING.

Those are the very answers students in my Math Workshop class last fall gave me on their first day. Then I told them something that rocked their worlds: that is all just ARITHMETIC. And arithmetic is just one TEENY, TINY piece of the world of mathematics! There is SO much more! I compare arithmetic to a hammer. It's important, but it is just a tool used to do the REAL work of mathematics. And, it's not the only tool in the toolbox!

One other essential tool is strategic, logical thinking. We all know it's important, but it is often left out of the curriculum, or treated as a lesser part of it. This is ironic, considering our end goal is to produce students who can at least USE math in daily life, and who are prepared for upper level math.

In fact, the Standards of Mathematical Practice in the Common Core state that students should ultimately be able to:

"Make sense of problems and persevere in solving them"
"Reason abstractly"
"Make conjectures"
"Analyze situations"
"Justify their conclusions"
"Distinguish correct logic or reasoning from that which is flawed"
"Look closely to discern a pattern or structure"
"Apply mathematics known to situations arising in daily life"
"Evaluate the reasonableness of their intermediate results"

Obviously, we've got to teach more than basic computation that could be performed by a calculator. But how?

Here are a few suggestions:

• Give students real problems to solve. Problems that do not have one correct solution. Problems that are not immediately identified as addition or subtraction word problems. Problems that require more than arithmetic. Challenge them! In my math workshop, I gave students a real historical problem of European traders going to certain villages in Africa to trade tobacco for sheep. The problem? The people of these villages could not count past two. I gave some students a pile of sheep tickets, and some students a pile of tobacco tickets, and told them to figure out how to trade. (Side note: I included a mini-lecture about how they did not know tobacco was so bad for your health, and no student should view this as encouragement to use tobacco. You might want to change up the example for your students. :) )

• After an activity like the trading, challenge your students to come up with a system that will let them trade more than two sheep at a time. Since it took our number system with place value thousands of years to develop, it's highly unlikely they'll be able to come up with a satisfactory system, and they'll get frustrated. They'll quickly learn to appreciate our system! And they will have exercised their reasoning minds extensively in the exercise.

• Present your students with brain teasers regularly. Many books are available; instead of beginning math or morning work with arithmetic practice, stretch their logic skills! These are the very skills that will help them make sense of the algorithms of arithmetic, in addition to being necessary to higher math.

• Look for the math in art. Patterns, perspective, shapes...it's all math! Join art appreciation and geometry in your lessons.

• Play games. We have evidence of strategy games existing before the time of Christ. These same games continue to be played around the world. They're simple enough that very young children of five and six can learn and play them, yet challenging enough that there are mathematicians who have dedicated their careers to studying the game theory behind them. You might have a MasterMind game in class, or Othello, or other games in which there is no chance (no dice, no spinning, etc.): just logic and strategy. My math workshop students were amazed to find that they could play games for a whole period and count it as math! Sometimes as teachers we feel that's not "real math", too; but that is just because we were likely ourselves products of math education that emphasized arithmetic and very little else.

I recently began creating sets of math strategy games to use with my students. In case you're in an arithmetic rut yourself, I have one game to share with you now. It's called Achi, which I consider particularly appropriate for our students who are bilingual with Spanish, because it makes me think of a sneeze every time we play. ¡Achís! :) It's actually from Ghana, dating back to at least 300 C.E., and is related to tic-tac-toe. Challenge your students to develop their skills with this game and others, and watch how they'll use those math skills in class, and transfer them to other disciplines!

Click on the image to pick up your copy of Achi!