Calculus (and Vectors) is a course that uses almost all the math knowledge a student has learned from Kindergarten to Grade 12 Advanced Functions. I find myself, on almost a daily basis, saying to my students, “remember in grade so and so when you learned about such and such? This is why! So you can tackle this calculus skill!”. This isn’t exactly true, of course, but my students seems to enjoy hearing about how all math is connected and built upon itself. Where was I? It seems I’ve gone “off on a tangent” (YES! Calculus pun in a calculus post!), oh yeah, not only does calculus use a student’s prior math knowledge, it ASSUMES that all students can recall this prior knowledge with no review or assistance. I (as well as every other calculus teacher anywhere) realize that this is NOT the case, so I often have mini side-lessons during a calculus lesson (example: the other day we came across a limit that required us to use difference of cubes factoring, which of course only one student in the room remembered how to do, so I did a quick reminder lesson before proceeding). At this point I really hope you’re still reading as I realize that this hasn’t been the most griping opening for a blog post (except for the pun, that was gold!). Here’s the question that has plagued me for years: WHAT CAN WE DO ABOUT THIS? Well this year I tried something new.
To start the year, I made our first three classes together work periods for my students to complete these Khan Academy activities as well as a printed take-home assignment (for those of you who know Khan Academy, I only required my students to answer 3 questions correctly per activity, to save them time). All of this practice led up to a 40 question multiple choice diagnostic test. My goal was to identify the specific areas of need for each of my students, prior to starting any calculus material. I created a spreadsheet that, after inputting a student’s multiple choice answers, sorted the results into the 8 categories being assessed. Below is a screenshot of the results for a sample class. I also looked at their Khan Academy progress, as well as their take home assignment.
After all this, I shared each student’s results with them and their parents, highlighting the areas where I feel they need to improve upon (see below for a sample of what I sent) and I provided them with a recommended questions list. The idea being that they will work on their areas of weakness now, early in the school year, before the grade 12 year becomes chaotic.
So now here we are in mid-October, our course is in full swing and my students’ lives are becoming increasingly busy. The questions I have are:
- How am I going to know if this process worked? (and to what extent?)
- Did it have a lasting affect on my students? (How will I measure this?)
- Should I continually refer back to this? (i.e. as practice before we start a new unit that uses certain skills), or it this their responsibility as 17 year olds who are about to go off to university?
With this being the first time I’ve tried this process, I’d like to know how I can maximize (pun intended) its effectiveness for my students this year as well as improve it in future years.
I’d love some feedback on this, and not just from math teachers 🙂
If you or another teacher would like a copy of the test I used and/or the blank spreadsheet, email me at [email protected] and I’d be happy to share.