Asilomar #2: What Do We Do With The Seniors?

Session Title

What Do We Do With The Seniors?


Robert Loew, High School Math Teacher


Loew and his colleagues wanted more options for students who finished Precalculus during their third year of high school (or earlier) but who weren’t going on to a STEM major and didn’t want to take Calculus. They came up with two.

1. Math Analysis

College prep. Approved by the University of California for a-g credit.

One semester of “Calculus Lite,” heavy on application, light on theory, including:

  • continuity and limits,
  • average/instantaneous rates of change,
  • the derivative as the rate of change at a point,
  • basic rules for differentiation, including the chain rule,
  • the meaning of extreme values,
  • the meaning and use of the first and second derivatives,
  • the integral as the cumulative effect of change / area under the curve.

One semester of “other math topics,” including:

  • management science,
  • Eulerian and Hamiltonian circuits,
  • critical path scheduling,
  • game theory and negotiation,
  • the prisoner’s dilemma (as it applies to arms negotiation),
  • fair division (as it applies to settling an estate between three heirs),
  • the time value of money,
  • models for saving and investment (as they apply to calculating the value of a stock, the greater fool theory),
  • decision analysis.

Key texts:

2. Problem Solving

Approved for elective credit. These are techniques for solving problems that aren’t neatly defined, for answering the question “what do you do when you don’t know what to do?” The course emphasizes both individual initiative and group collaboration, rewarding creativity and divergent thinking.

Chapter headings:

  • Draw a Diagram
  • Systematic Lists
  • Eliminate Possibilities
  • Matrix Logic
  • Look for Patterns

Class norms/values:

  • open ended inquiry / divergent thinking,
  • tolerance for ambiguity,
  • collaboration,
  • sustained effort,
  • many students will be uncomfortable and “may need to be filtered out.”

Key text:

I applaud this kind of curriculum design but it seems a shame to me that students who aren’t already tolerant of ambiguity or already patient in their problem solving “may need to be filtered out” of a class designed to teach tolerance of ambiguity and patience in problem solving especially since those seniors have likely been indoctrinated with those bad habits by eleven years in the very same school system.


PowerPoint. Texty. Comic Sans.


PowerPoint printouts. An interesting tactic here: he withheld the handouts until the very end and passed them out only in exchange for a completed session review slip. Seems to me to miss the point of handouts as another space to interact with ideas, but whatev.


  • A family of deer skipped across the path as I walked to this session. The grounds here are incredible.
I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. I love the Herr and Johnson textbook (“Crossing the River With Dogs”) that you mentioned for the problem solving option. I use it with my 7th and 8th graders for really great problem solving strategies — it’s written more for the high school level (so it would work perfectly for the course that your speakers suggested) or community college level, but I think that the large majority of the problems are still very accessible for middle schoolers too.

  2. Man, they have a problem with a surfeit of seniors who are done with Pre-Calculus and need more math?

    Would _love_ to be suffering like that, seriously.

    (Oh, and we do have a Contemporary Math class that uses the Crossing the River with Dogs book. Some take concurrent with Algebra II or Pre-Calculus, some take after Algebra II.)

  3. We just this year added a Statistics and Data Analysis (non AP) course to address this very problem. While I like the problem solving course idea, I think that Stats is probably a far more useful course for a vast majority of people than an introduction to Calculus.