Honors Geometry opens with a challenging start.

It’s always hard to decide just how challenging the first month of Honors Geometry should be. Last year it was too easy. There were too many students who apparently said to themselves, “This course isn’t so hard.” As a result, they avoided a tough choice: do the necessary work, or drop the course. The transition from middle school to high school is always a challenge in and of itself, so any disappointing grades could be attributed to that fact rather than a mismatch between the course and the student.

As a result, we decided to increase the level of difficulty to make it reflect the rest of the course. We opened with a degree of algebraic notation that definitely challenged almost everyone, such as {(x, y) : (x, y) ∈ T ∩ U} or RA, –45°(P) = Q. We created quite rigorous definitions of transformation, isometry, reflection, involution, and other terminology — and expected students to know the definitions and to be able to apply them. We focused on inverses and composition of functions, showing when the composition of two reflections is a translation and when it’s a rotation — and what the amount and direction of said translation is, or what the amount and center of said rotation is. We also expected students to remember important ideas from algebra, such as squaring a binomial, finding the slopes and equations of perpendicular lines, and solving a quadratic equation (and if they didn’t remember these skills and concepts, they were expected to take care of this lapse as soon as possible). Some homework problems were rather intimidating, such as this one:

If and are perpendicular and A, B, and C are points such that Ms(A) = B and Mt(A) = C, find MtMsMtMtMs(A).

So…maybe we went overboard. Maybe. This opening was clearly too challenging for 25% of the class. But I don’t think it needs much tweaking. It wouldn’t be doing students any service to pretend that honors-level math courses in high school are easy. They really should know what they’re in for; they need to know that they’re not in middle school anymore, Toto. And the bottom line is that the students are all working hard, they’re doing their work, and they managed to achieve a median of 85% on the first test. I can’t complain about that!


Categories: Math, Teaching & Learning, Weston