In response to a tweet about differentiation, I connected it to my honors class. Benjamin Leis asked if I had any posts, and I realized I had been meaning to write one. So here it is.

I teach at a small independent school, and we don’t have tracks of classes. We don’t have A.P. classes. What we do have is in-class differentiation. We have the opportunity for students to take classes at what we call “Skills” level, for students who are taking the class purely for exposure to the material. This is often used for students who have some significant challenges with success in a class, due to learning disabilities or lack of exposure to prerequisite concepts and skills. The class does not count as a college prep class. Often, a student will take a class at skills level one year, then repeat it the next year as a regular college prep class, with greater success due to the extra exposure to the ideas.

Honors is different. Since we are in California, and many of our students are applying to UC schools, we make sure our courses meet UC a-g requirements. This also means that only certain courses can be classified as honors level. Last summer, I prepared the paperwork and got approval for an Honors Precalculus course. So what does that mean?

In my classroom, any student in the class can take the class as an honors class. There are two ways that the class is different for them, but as long as they take on the commitment, they get the honors distinction at the end of the semester. No student is turned away, and all students are encouraged to take on the challenge.

The first way that the class is different is in the way assessments are assessed. I have adopted a version of standards based grading (SBG) in my class. Assessments are scored on a scale from 1 to 4. A score of 4 means that a student can solve problems and is able to apply a concept (or the “how” of the math). Honors students are assessed on a scale from 1 to 6, where a 5 or 6 demonstrates a deeper and more thorough understanding of how that concept works and fits in with other ideas in math (or the “why” of the math). Make no mistake – a student who isn’t taking honors can still receive scores of 5 or 6 (which will improve their semester grade, as they’ve gone above and beyond), but to receive the honors distinction, they’d have to also meet the second requirement.

For the second requirement, each student must complete a research project for each unit and then share their findings with the class in a short summary presentation. For example, when we did our logarithms unit, the honors project was to build a slide rule, and record a short video in which they demonstrated how the slide rule uses logarithms to make arithmetic calculations. When we did our trigonometry unit, students had to develop and explain a trigonometric proof to the class. For matrices, students compared and contrasted using different methods (Cramer’s Rule, Gauss-Jordan elimination, standard algebraic solving linear systems by substitution or elimination) to determine which methods were better, and under what conditions, when solving by hand, with a calculator, or with a computer.

In both requirements, the honors students are expected to demonstrate a more sophisticated and thorough understanding of the math concepts, and to work on how to effectively communicate those ideas. That isn’t to say that the non-honors students aren’t required to understand concepts and communicate, but rather that they do what we have time for in class, whereas the honors students must take some time outside of class to deepen their understanding. For example, in class, we covered the trigonometric identities, and proved a few of them to demonstrate that it could be done. Honors students were required to prove all of the main ones, and demonstrate an understanding of how to prove a challenging one on their own.

Again, there is no restriction on who can elect to take the course with the honors distinction. If a student chooses to do the work, they will get an “H” on their transcript. I would like to see more students of color attempt to take on the challenge, but I would like to see more students of color in my PreCalculus class as well. This is a goal that we have to work on earlier, but that’s a separate blog post.