The Master Master Plan for Precalculus: (4) Understanding Concepts & Going Beyond

I’m changing things big-time next year. This is the fourth post. Click one of the links to go to the other posts.

  1. An Overview
  2. Math Practices
  3. Skills
  4. Understanding & Going Beyond [this one]

One of Michael Pershan’s complaints of SBG has always stuck with me: by breaking math into standards and grading it as such, we compartmentalize math and students see it as a clustering of individual skills. This 20% of their grade is intended to encourage them to make connections. Here’s their view of the gradebook for reference:

See the different stars? I hope students get as excited about it as I am!

See the different stars? I hope students get as excited about it as I am!

There are two “levels” (stars!) that students can earn for each concept standard. The first is for giving an acceptable answer on the quizzes to the “understanding” question, which is intended to group the skills together. Because those questions change every time, students can lose this star if they show that they understand one part of it but not others. This will work similarly to the skills: I’ll either take the mode or latest grade: whichever is higher. When the options are “1 or 0”, then mode makes a lot of sense to me. I intend to make a list of possible “understanding question” and have this available to students so that they can prepare for these, though I won’t promise to cover ever understanding question which may show up on the quiz.

Not every concept is broken down into 3 skills, but I kept the number within the range of 1 to 3 for each concept. Each “concept” is a section of the textbook which should help me as a teacher find good “understanding” questions.

Going Beyond (to Infinity and…)

The second star cannot be obtained just by taking quizzes. Students must do something outside of class to demonstrate a connection between two or more concepts. This could be a project, paper, explanation (through Doceri or similar software), presentation to the class, or anything that is “above and beyond” what I would expect of students. Something like the Google Maps project or the Stop-Motion Parametric Videos project. This makes these projects optional, except for students who want to earn an A. I hope that many students will go for these projects as (1) getting the second star automatically gets you the first star (a funny thing about how the gradebook is setup) and (2) you cannot lose the second star (“Sorry, you know that project you did and took all that time on that I made you redo? Well, your recent quiz renders all of that void and useless.”)


I’m considering making “getting all coins within a concept standard” as a prerequisite for getting the star for that standard. After all, can students understand what they’re doing if they don’t know what to do in the first place? I’m also considering making “getting one star” a prerequisite for getting the second “Going Beyond” star. However, this might discourage students from going for the bigger projects and as long as I’m strict about the projects clearly demonstrating understanding, then I can feel comfortable giving them both stars at once.

Growth Levels

I want the growth levels to be given to students who become better at mathematics while I’m teaching them. Students who “get things the first time around” aren’t growing, so won’t get anything for skills if they master it the first time around. Because of this, I want something for them to “reach for”, so each 2nd star (“Going Beyond”) that they get, they earn a growth level. That way the growth level rewards weaker students who really have to struggle to get skills down as well as stronger students who push themselves beyond the bounds of the course. I hope that everyone can always find some way to be growing in my class, and that they are motivated to that end.

Oh, and as the growth levels go up through different video game characters. I won’t reveal the full list in case a student finds this blog, but I will say that it includes the likes of Mario, Yoshi, Link, Zelda, and Sonic. I’m pumped.


I’m very excited about the new direction that my classroom is going. I hope that students get excited about it as well. Please give me feedback and let me know if you’ve done something similar in your class!

Gotten better at Math? Bwhahaha!

Gotten better at Math? Bwhahaha!



Filed under Teaching

3 responses to “The Master Master Plan for Precalculus: (4) Understanding Concepts & Going Beyond

  1. Pingback: The Master Plan for Precalculus: (3) Skills | Hilbert's Hotel

  2. Pingback: The Master Plan for Precalculus: (2) Math Practices | Hilbert's Hotel

  3. Pingback: The Master Plan for Precalculus: (1) An Overview | Hilbert's Hotel

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