Math Teachers: Thinking Outside the Algorithm

Middle School math can be frustrating and challenging, especially when the teacher feels that in addition to reaching their own learning milestones, they must backfill the deficits students have when they enter the classroom.  As an educator I have always believed that part of my job was to take my students as far as possible during the year that they spent with me. When teaching math to eighth graders you know that when they leave you they are going on to high school where they will meet many challenges. This is especially true in a Title I school. Because many of my students had a variety of deficits in their math knowledge from previous years, I had to find innovative techniques to help my students learn concepts. Even if your students haven't progressed as far as you wish prior to your class, thinking outside your regular circumstances can open a new way of teaching for you. Instead of focusing on why your students can't just learn the algorithm, maybe there are other ways you can approach the same problem.

In a large urban district where does one find the supplies and techniques to help students? The answer for me was to attend every workshop that was offered. Some paid you to attend. Some offered supplies in exchange for the time spent in the workshop. This is how I obtained two sets of calculators over the years including one set of graphing calculators. I learned how to write mini-grants to obtain other equipment. I was able to obtain protractors, compasses etc through one grant and a computer for my exclusive classroom use from another.

I knew that my job would be easier if I could introduce the math teachers who fed students to me some of the techniques I had learned. When the opportunity arose, I became a math teacher leader for my middle school. I didn’t convince everyone to try new ideas but I convinced many. At the time of standardized testing we found that the test scores for those who tried different techniques were higher than those who continued in a more traditional mode.

The final piece fell into place when I had the opportunity to be trained to use a new Algebra program with my eighth graders. It was concept based and required students to work in groups to discuss math and problem solving. Having my students work to together to discuss mathematics was the final piece falling into place. This wasn’t a magic bullet nor did it go smoothly at first but the bonus for working out the kinks was that my kids loved coming to math class and working on the activities. The final validation came when my students took the Pennsylvania System of School Assessment (PSSA) and thought that I had written the problems on the test because they knew how to THINK mathematically. They all did better on the math section than the other math classes that were being taught traditionally.

I’ve shared these experiences with you so that you understand what I am about to say to those of you who are frustrated teaching students who “don’t get” what you are teaching and are not open to trying new things. I’ve noticed recently that many math teachers respond with negative comments when TER publishes new ideas for teaching math concepts. So I’m going to share with you one of my favorite quotes before writing the conclusion to this article:

“If you always do what you’ve always done, you will always get what you’ve always got.”

--This version of the quote is attributed to Mark Twain.

If my journey in teaching math conceptually has not inspired you to try something new with your students then let me give you a few things to think about. The students we get in our classes are the ones we must teach. We can’t keep complaining about what they don’t know but must find a way to get them to learn how to overcome their deficiencies.

If you are teaching high school math, don’t get hung up on students who don’t have basic arithmetic facts memorized. Tell them to use a calculator. Standardized tests are as old as the hills. Teaching to them doesn’t work and even if it did all you would be teaching your students is how to take a test. Teach the concepts that your students need to know and you will find that they will do at least as well on tests as when you taught to the test. If you are one of those who blame elementary teachers for not knowing enough math, please stop. If you look at the test scores in math for third, fifth and eighth grade more of the younger students are proficient than in upper grades. The difference might just be that in elementary school concepts are taught before algorithms.

Let me leave you with this question. If a student can solve a problem and get the correct answer do they receive credit if they used a viable method without an algorithm?