Why is it that so many people feel incompetent in math? Why is it that the statement, “I’m not good at math,” has been a mantra for so many, young and old alike? Why is it that math is seen as a stumbling block for school children throughout their school careers?

We learned to follow specific steps to find solutions, but far too often, little sense-making was expected…I’m sure you’ll agree that if all students had been encouraged to make sense of math ideas when they were kids, we would all be better off today.

Most of us went through a school system that taught math as a set of procedures to follow rather than as a set of tools that could equip us for solving real-life problems. We learned to follow specific steps to find solutions, but far too often, little sense-making was expected. Correct answers were valued, regardless of whether we understood how we arrived at them. And as we progressed through the years, many of us simply did what we had to do to get through each class, rarely grasping the relevance these math processes had for life beyond the classroom.

Now is the time to bring this pattern to an end! Math experts have told us for decades that math should make sense, and the way we get there is by focusing on three important elements:

1. Conceptual understanding,
2. Procedural fluency, and
3. Applications to real life.

Children need to understand that math makes sense. This occurs through many different experiences such as using visual representations or talking about ways in which learned ideas connect with new ideas. Once the math ideas make sense, students need to develop fluency with the basics, such as math facts, multi-digit arithmetic, and problem solving strategies. All the while, they need to see many ways in which the tools of math apply in everyday life.

I’m sure you’ll agree that if all students had been able to make sense of math ideas when they were kids, we would all be better off today.

I recently had the amazing opportunity to travel to Flagstaff, AZ, to work with a group of teachers at the Math in the Mountains conference. My session centered on understanding multiplication of decimals, but staying true to form, I began by putting the problem into context. After all, math makes much more sense when we connect it to something that resembles real life. That said, as the image above reveals, children and adults alike struggle with word problems, and it’s my goal to help everyone make sense of math in their everyday lives!

This strategy looks more like a predictions strategy for reading, but honestly, it’s an amazing way to help students engage with word problems by understanding the numbers rather than just picking them out and “doing” something with them.

As I began the session, I asked the teachers to play a game called Bet Line. This strategy looks more like a predictions strategy for reading, but honestly, it’s an amazing way to help students engage with word problems by understanding the numbers rather than just picking them out and “doing” something with them.

In just a few easy steps, we were laughing together, engaging in comprehension conversations, and preparing to engage in decimal multiplication with understanding. Here’s how Bet Line works, along with an example from my workshop.

1. Introduce the first line of word problem. I showed them the first line, “After his party, Chris has ¾ of a cake left.” I then asked the participants to discuss what they knew so far.
2. Ask, “What do you bet will happen next?” I had the participants predict the next part of the word problem in pairs, and then a few people shared their thoughts with the group.
3. Show the next line of the word problem. When possible, try to make it a little unpredictable to elicit laughter. No one had predicted my next line, “His dog eats 2/3 of what is left.” They once again discussed what they knew so far.
4. Finally, once all the information has been shared, ask them what they bet the question will ask them. The question is the most critical part of a word problem – it defines what one is to “do” with the information. The possibilities span many operations and number sets, depending on the problem at hand. In the case described here, most participants predicted that the question would ask them to figure out how much of the cake was left. However, the question read, “How much of the whole cake does his dog eat?”

Giving students the opportunity to grapple with the language in word problems allows them engage in mathematics with understanding rather then randomly selecting numbers and “doing” something with them.

Because we spent so much time discussing the problem as we went, the participants focused on the language and structure of the problem, which allowed me to then use it as a springboard to discuss why multiplying by a fraction less than one results in a smaller amount than one begins with. This is just how it works with students. Giving them the opportunity to grapple with the language in word problems allows them engage in mathematics with understanding rather then randomly selecting numbers and “doing” something with them.

Try it – you’ll like it!!!