Decrease Math Anxiety in Your Students: Build Number Sense

When I was seven, I struggled with my math facts.

My arch-nemesis was subtraction. Minus signs on flash cards made me jolt back in horror. I would search my memory, trying hard to summon up the right answer.

Sometimes, I would get it.

Other times, I wouldn’t.

Eventually, I memorized my facts, including those subtraction brats. I even went on to Honors Math down the road. But math always felt like a burden—out of reach, and I know that my early struggles with rote memorization of subtraction facts had something to do with it.

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For our students who struggle severely with their math facts, those unattainable beginnings make ALL of math feel out of reach.

These students arrive at math class with a block firmly in place. It’s unlikely that much of anything could erase their sinking suspicion that they are “just not good” at math.

Unfortunately, by the time these students reach the upper elementary grades—let alone the middle grades—they’ve already developed entrenched patterns of thinking about math. These negative thoughts self-perpetuate, of course; if children think they’re just not good enough at math, they’ll have a low tolerance for working at it, and they’ll give up before they’ve even started.

It’s a long road we face as teachers.

But that road is not impassable.

It’s true that with older students, it’s not going to be as easy. Their patterns of thinking are more entrenched.

Though it’s not hopeless for them. They’ll have to work harder, of course. And so will you.

But they can do it. And so can you.

Students of any age can decrease their math anxiety and create a deeper understanding of number with regular instruction in number sense.

What is number sense?

Number sense is more than input and output. (It’s more than 5 + 7 = 12.)

If a student has excellent number sense, he or she understands the relationships and connections between numbers. A person with great number sense can visualize how a number can be broken down into smaller units. That person can take a look at the number 80 and break that number into eight groups of ten.

The Research

This research overview provides an excellent overview of number sense. It also illuminates key facts from several studies on low, middle, and high-achieving students.

Try and guess: Which group of students (as above) tends to struggle with number sense?

Yep. That’s right. The lower-achieving students.

That’s why we must make extra efforts to teach number sense directly to our students. They won’t “just develop it” without our assistance.

What About “Just Knowing the Facts?”

We all want our students to know their math facts; certainly they will be better able to handle mental calculations with math facts at their fingertips. But what we don’t want to emphasize is speed. When students try to race to recall their math facts - and fail to do so - that’s where the anxiety enters the equation (no pun intended).

Instead, we need to develop games, activities, and strategies that work to solidify student’s grasp of math facts within the context of understanding the connections between numbers.

Try out some of the below, which will likely inspire you to make your own:

Dice games

The simple fact of probability means that your students will encounter different numbers in the same session while using dice. Use manipulatives in combination with the dice to reinforce your students’ visual understanding of the relationship between numbers.

Try some of these exciting dice games with your students:

  • Go Big or Go Home: Create a representation of a jackpot (dollar signs) on one side and a house on the other. Use floor tiles or carpet squares to represent spaces. (This is a great game to get kids out of their seats!) Students roll the dice and advance the correct number of spaces. Use multiple dice if you want to include other operations (subtraction, multiplication). Students can each hold a clipboard and fill in visual representations of their operations.

  • Dance, Dance, Dice. If you’re working with small groups and can allow things to get a little rowdy (without getting out of control), you can use this game to enrapture some of your reluctant math students. Use multiple dice and create addition and/or subtraction tasks. Students can “dance out” the correct number of steps, then fill in a sheet showing the correct visual representation of the problem. (5 jump steps + 2 side-kicks = 7 dance moves.)

  • Whisper and Find: If the idea of a loud classroom game makes you feel faint, you might enjoy a game that requires students to use their teeny tiny indoor voices. Allow students to throw a bunch of dice on a carpet or soft surface. Ask them to find combinations to create target sums and record their sums on answer sheets. Students can borrow dice from other students if they use their “whisper” voices.

Arrays

Use arrays to solidify your students’ sense for which parts equal which whole.

Try out grids in ten or hundred-blocks. Students can color in parts of the arrays to indicate certain numbers.

Additionally, you can use Legos or other manipulatives to build and take away from various number combinations.

Arrays allow students to understand number relationships outside of a vacuum.

We need the numbers to feel real, which brings us to our next technique:

“Number Talks” or “Number Conversations”

Who says you can’t have an in-depth discussion in math class?

Take a large number or difficult sum or multiplication problem and set it as the discussion topic. Break down the problem into different components.

For example: 42,300 can be broken into its place value, such as 4 ten thousands, 2 thousands, and 3 hundreds. This same number can be broken into multiplication problems, such as 4 x 10,000 (place this in one square of the graphic organizer), 2 x 1,000 (place this in another square), and so on.

Always begin with a think-aloud to show how you would break down a number or problem. Demonstrate different strategies so that students realize there is more than one way to do the same thing.

Skip-Counting and Pattern-Building

Skip-counting encourages your students to unintentionally develop good number sense, as they’re having fun.

Get your students active. They can bounce balls for each number they skip-count.

During another session, set them up with partners of similar skill levels. Offer the partnered pairs a non-judgmental opportunity to count up as far as they can go. They can start off by counting by “finger numbers” - 5s and 10s. Later, ask them expand to more difficult numbers.

Your students can really have fun with number sense. And when they’re having fun, the anxiety starts to dissipate. When they move beyond the terror of trying to memorize facts through methods that aren't working for them, they begin to understand that there’s more to math than just facts, yanked out of a hat at will.

Numbers are meant to be played with.  

Once your students realize that they can play with numbers, they’ll slowly transform into playful mathematicians.

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