# My Precalculus Problem

This is Lucas’s first year in my school. He’s a senior in my precalculus class. After a few assessments his grade begins to tumble. I know little about his previous math education. I meet with him during lunch a few times to help on the content and see that he’s missing several foundational math and reasoning skills. He ends up with a D in my class.

Jennifer is bored in my class. She’s easily getting an A. I can tell that she knows most of the content because she remembers it from algebra II. At some point in the first trimester she asks me if the second trimester will be review as well. I said that a lot of this is not review and that there will less familiar content in the next trimester (which is mostly true). She ends up with an A-.

In the high school in which I teach there is honors precalculus and “regular” precalculus. I teach the regular level. This means that I get kids like Jennifer, kids like Lucas, and everyone in between. I have college bound students and students that will go into a trade. I have students that love math and some that are only there because their parents made them. I get a lot of students that have scooted by with A’s and B’s without trying and would prefer to continue not trying.

So, basically a typical high school class.

The last couple years I’ve struggled to differentiate for the diversity in this class. I’ve failed many of these students because the content either goes too deep or not deep enough. This summer I’m working on solving this problem, or at least minimizing it. The flowchart below is what I’m currently thinking, although I’m sure this will change as I continue to work on it.

My idea is to pre-assess over algebra II skills that are needed for the unit. If students have mastered most of those skills then they take a different track then those that haven’t. I haven’t worked out a full module yet but I’m thinking I have most of the track 1 materials made and need to make most of the track 2 materials.

Most of my direct instruction is on video which means not every student has to be at the same place at the same time. I just need them to be ready for the summative assessment on a certain day.

With this model I can patch the conceptual holes for the kids that need it, and push the kids that don’t.

What problems do you see cropping up with this idea? For example, I’m worried some less motivated kids might intentionally do poorly on the pre-assessment so they have the “easier” track.

Any feedback is welcome and appreciated. Thanks for reading.

### 4 Comments

• Sam Morey

I have been kicking around a similar idea for algebra I. My instinct would be to offer extra credit on the summative assessment for doing well on the pre-assessment. But another idea might be to explain that being on track 1 will require more work because it includes remediation work and content work. That way track 2 is more appealing to the less motivated.

• Zach Cresswell

I always struggle with offering extra credit because there are a lot of kids that would rarely get the shot at it simply because they struggle. BUT, we may have worked this problem out a bit. Check out this conversation. You might have to send Kay a follow request. https://twitter.com/z_cress/status/748221808793485312

• L Park

Students most likely will have different gaps and may not fit neatly into the two groups. I find it helpful to have essential assignments, extra practice assignments and extension assignment ready for each chapter. Students who easily complete essential assignments are given the extension assignment. Students who complete essential assignments without demonstrating understanding or with a significant amount of support are given extra practice assignments. Students who take longer to complete essential assignments but who demonstrate independent understanding don’t do either extra practice or extension. Since all students complete the essential assignment they should all have practiced skills to be assessed and be able to show at least minimal proficiency. This method requires a fair amount of organization, but once implemented really allows you to differentiate for students. Your highest students get the deepest learning by doing all the extensions. Your next highest get deeper than average by doing some extension. Your average learner gets the essentials. Your low students gets the review needed to master essentials. From a management standpoint, you may find it helpful to offer multiple opportunities to take a quiz or test. Students who “test out” can complete extensions individually, review prerequisites for the next section or assist others while you work with students who didn’t pass the assessment or who weren’t ready on test day.

• Zach Cresswell

I think you’re right. Students won’t fit nicely into two groups. But I’m not sure I have the time, energy, or mainly organizational capabilities to pull that off. 🙂 I think I’m looking to strike a balance between this and “everybody gets the same thing at the same time”.