Teaching Math as a Life-Long Tool

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I don’t know about you…but whenever I get on an airplane, the first thing I usually do is put in my headphones to subtly let everyone around me know that I intend to keep to myself during the flight. However, on those occasions when I strike up a conversation with the person next to me, it doesn’t take long for them to find out that I work with math teachers. And then is happens…I get their math autobiography. And it’s rarely a happy story!

Far too many adults had bad experiences with school math and have carried that negative perception into adulthood. We cannot afford for this to continue!

Way too many adults in the U.S. are eager to tell their horror stories about word problems and fractions and formulas and how math just never made sense. Far too many adults had bad experiences with school math and have carried that negative perception into adulthood. We cannot afford for this to continue! We cannot afford for the next generation of students to go into adulthood without the tool set that everyone recognizes as critical to future career success. We owe it to our students to prepare them for school and for life. They don’t all have to love math – but they all deserve to be comfortable and competent with the logic and thinking skills that mathematics provides.

So, what are we going to do to break this generational cycle of fear of mathematics and the bragging rights that come with it?

For starters, all across the United States, educators are using powerful mathematics standards that aim high for student thinking and understanding. These standards, designed by the best and the brightest mathematics educators, mathematicians, and practicing teachers and leaders, reflect what we know to be in the best interest of our students.

Here’s something you need to know about these standards – they’re really nothing new! Great math teaching and learning always has always been and always will embody the content of these standards. These standards include what math educators and teachers have known for decades about what our students need to know and understand to be successful with mathematics…not just in school, but in life.

To take things further, KP Mathematics offers tools and strategies that help bring state standards to life! Using revolutionary manipulatives that focus on the basic principles and structures of mathematics, students gain conceptual understanding that leads to procedural fluency. The rigor found in the new state math standards is met using these simple tools and the strategies they encompass. Check out our previous posts to learn more about what these revolutionary tools can do for the students in your life!

The Equal Sign Means Relationship, Not Action

Math, Math Content, Math Discourse, Math Standards, Professional Learning, Taking Care of Teachers, Teaching and Learning

Equal Sign Means Relationship

Blog post #1 in the series, Lies We Tell Our Students

The Story

A while back, I was working in a fifth-grade classroom, and as a warm-up, I put the following equation on the board:

8 + 4 = 1 + 11

I then asked the students, “Is this statement true or false?” After waiting several seconds, I asked them to raise their hands to indicate their votes. At that point, two students voted for true, and the other 22 students voted that the statement was false.

Being the good teacher that I am, I asked the students to discuss their thinking, believing that those two students who said it was true would quickly convince the others. However, when I brought the class back together and once again asked my questions, 24 hands went up stating that the answer was false.

“Yikes!” I said, “What’s going on here? This statement is actually true. Can you tell me what you’re thinking?”

“Mrs. Rimbey,” started one of those original two students, ”8 + 4 does not equal 1.”

The Lie

I’ve since come to learn that this is not an isolated case. Many students across the grade levels believe that the equal sign is a symbol that indicates the action of finding the answer, when, in fact, it actually signals a relationship between the expressions on each side. In the vast majority of classrooms, students develop this misconception because virtually every equation they see in the early grades follows the same format: 3 + 3 = 6; 4 x 4 = 16; 20 – 13 = 7; and so forth. The “answer” appears last.

The Truth

So, what do we do about this? We can be sure to provide students with multiple daily opportunities to see equations written in different formats, pointing out that the equal sign indicates an equal relationship, not the action of finding the answer. Provide examples with the “answer first” (e.g., 6 = 2 + 4), with “nothing to do” (e.g., 1000 = 1000), or with “no answer” (e.g., 32 + 42 = 20 + 5).

The Series

This blog post is the first of a series that addresses the lies we tell our students. It’s important to note that these lies are not deliberate untruths. Rather, they are rules, procedures, mnemonics, and tricks we teach kids in an effort to make math easier for them. Sometimes, the lies come in the form of omission, such as the example of the equal sign shared above, where we don’t provide enough varied examples. Sometimes, they come in the form of half-truths, such as addition and multiplication, which always make bigger, which is only true with natural numbers (not including 0).

In Summary

To sum up this week’s Lies We Tell Our Students:

  • The inadvertent lie: The equal sign indicates the action of finding the answer.
  • The truth: The equal sign indicates relationship, not action.

As always, we love hearing from you! Do you think your students fully understand the meaning of the equal sign? Have you tried any of these (or other) strategies with your students? Please share your thoughts in the comments box below.

Next Steps for Teachers: Use a variety of equation structures with students on a daily basis (see examples above). Consider making a set of 4-6 “true-false cards” each day to show the class. Simply write one equation on each card, using a variety of formats, making some true and some false. Then ask the students whether each is true or false and to justify their answers.

Next Steps for Leaders: Discuss the meaning of the equal sign with grade levels, focusing on the notion that the equal sign indicates a relationship, not the action of finding the answer. Although this concept typically appears in the K-1 math standards, this misconception continues to exist in middle school and beyond. Discuss ways to avoid this misconception in each grade level, and then share their ideas across grade levels.

Kimberly Rimbey, Ph.D., works with teachers and leaders to develop system-wide change in mathematics teaching and learning.