Effective Frequency: Do we teach Slope too much?

One of the hardest topics I teach in Algebra 2 is slope. I know what you're thinking-- slope is not an Algebra 2 topic. This is exactly what makes it so hard.

I have this theory, and you can disagree with me in the comments. My theory is that slope is so hard to teach because the word is so familiar. My students may see it first in 8th grade, then definitely in 9th grade, then again as a review in 10th grade before the state test. By the time they get to me in 11th grade, eyes are glaze over at the mere mention of the word. But very few have really mastered the topic.

So why is retention so low? My belief is that slope is either introduced too early before students are ready, and/or too little time is spent on the topic the first time it is introduced. 

This video is about an advertising strategy called "Effective Frequency". When I saw it, I immediately thought about my students. "Sales" is buy-in. "Potential prospects" are our students. 'Advertising" is teaching. "Conversion" is learning. Sometimes I feel like the idea of working hard, completing work, and that school is important is a hard sell. In this way, this video applies directly to teaching. Is slope overexposed? After the 3rd time students see it, is it too late?

Years ago when doing research on negative numbers for my thesis, I came across an eye-opening article from William Schmidt, Richard Houang, and Leland Cogan titled A Coherent Curriculum, The Case of Mathematics. In this article, the number of topics covered per year in the United States is compared to the number of topics covered per year in those A+ countries that the US is always pointing to with a, "Our math scores need to be more like theirs." SIDE NOTE: I wish we would celebrate all the good things about our students rather than focusing on what makes them less than kids in other countries. But that's for another day.

William Schmidt, Richard Houang, and Leland Cogan, A Coherent Curriculum, The Case of Mathematics

Above is a screenshot of the graphic included in the article that shows the progression of topics in A+ countries in grades 1 through 8. Only a few topics are covered each year, allowing teachers and students to get deep into these topics.

William Schmidt, Richard Houang, and Leland Cogan, A Coherent Curriculum, The Case of Mathematics

And here is the graphic from the United States. To be blunt, we're all over the place. Many topics are taught every single year, at least in the grades shown. 

How may times have you said to yourself, "I wish I had more time to spend on this topic because my kids ALMOST get it"? I know I have said it a lot. Do you think student understanding and retention would improve year-to-year if we were allowed this time when first introducing topics?  


  1. I have been saying for years that I think 8th grade is way too early for students to learn slope. In fact, it is introduced quickly in 7th grade. For most students, it is just too abstract for most of the students. Even with bringing it to them with concrete learning it is still hard for them.

    1. 7th grade? I hadn't realized that! Wow, yes, in my opinion that is way too early.