# The Master Plan for Precalculus: (3) Skills

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

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

Although math classrooms over-focus on procedural skills, they should not be entirely cut from the curriculum. There’s a reason they’ve become so important in the math classroom. By making skills 40% of the grade, I can say “a majority of your grade does not come from skills” and yet “you must master a majority of these in order to pass this class” (70% is passing at our school).

Here’s a quiz that’s I’ve made for the near the beginning of the year:

Some things you may or not be able to notice:

Skill Standards are separated into pairs of questions

I don’t expect both questions to cover the entire skill, which is why I intend to give each standard multiple times. See the “Form C” in the top right? That means it’s the third iteration of this quiz. Their grade is then a 0, 1, or 2, depending on how many they show me they know how to do [1]. Their grade will then be either the mode or the latest grade, whichever is higher [2].

Each question is taken from or modeled by a question from the HW in the book

The more similar the questions are to students’ HW, the more likely it is that they’ll do their HW. Many of these are taken straight from their textbook and I’ll point this out frequently throughout the course so students start making the connections.

Each Skill Standard has 3 boxes for grades

One goal of SBG is for students to get better at self-assessment. The first box is for them to predict how well they’ll do, either before they’ve seen the questions or after they’ve tried them. The second box is for them to give themselves a grade as they grade themselves against an answer key [3]. Students are surprisingly bad at giving themselves a grade even though they have the answer key! The third box is the grade that I give them after checking after them. This should help them to get better at assessing themselves.

The Skills Standards are clearly grouped together in one larger box

I’ll explain more about the “understanding” standards, but this reinforces the idea that the skills are closely linked and students should be thinking about how these relate to one another. The final question is my attempt to tie these together in an over-arching “understanding” question.

Here’s how I plan on reporting this to students:

An older version, where you can see the “Math Practice” bar chart filled out on the right.

The newer version has a link with more practice material to the right of their grade (stars).

The coins are my gamification of their grade. I tried to group each set of coins (skills) into a star (understanding). One of the things that contributed to the growth level (at the top) is how much they “improve” from the first time they take a skill. This rewards students who don’t do well the first time around, but study and do better later times. I hope this little incentive encourages those who don’t always “get it” the first time around, as they’re the ones who often need encouragement in math class. Their growth level has no bearing on their grade.

In the next post I’ll explain more what the stars mean.

[1] NOT how many they “get right”. If they show their work, which students are more apt to do in a SBG system like this, they’ll get credit but lose a point in “Attend to Precision” from their math practices grade (see previous post).

[2] I wanted to do just mode, so if they take a quiz 3 times, get a 2, 2, then 1, I’ll reward them for their sustained ability the first two times. However, I didn’t want students to dig holes so deep that they couldn’t get out, so 0, 0, 0, 0 isn’t automatically a failing grade, hence the “latest grade” opportunity.

[3] An idea I’ve gotten from other blogs: orange pens in the back of the room along with an answer key. When students finish their quiz, they leave their own writing utensil at their desk and get instant feedback. They’re not just to mark “right or wrong” but they’re supposed to fix mistakes in work and write how to do it correctly in the orange pen.