Are You Ready… For Calculus?

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:

  1. How am I going to know if this process worked? (and to what extent?)
  2. Did it have a lasting affect on my students? (How will I measure this?)
  3. 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.

About Michael Moore

I have taught senior mathematics at Hillfield Strathallan College for 10 years and I'm currently the Subject Coordinator for the Mathematics and Computer Science department.
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7 Responses to Are You Ready… For Calculus?

  1. lara de lazzari says:

    Wow, Mike. Amazing way to start the year.

  2. Adam Caplan says:

    Michael – I appreciate the straightforward approach you described. Identify the problem, try out a solution, validate your own success; sounds like a recipe for ongoing improvement. Thanks for the sharing your resource list and for the helpful screenshots – very informative.

    I always loved the philosophies embedded in Calculus. The idea that you can analyze a function with multiple levels of derivative simultaneously has informed much of the way I see the world operate.

    Good luck kicking off your student diagnostics this year!

  3. Hi Mike,

    You shared a very comprehensive diagnostic, though the highlights for me were your math puns. Kidding!

    Anyways, I love using Khan Academy, and use the platform to flip my classrooms. I appreciate the amount of work this must have been though! The thing I like most about this practice is that you didn’t just test them, but you gave students their results AND talked to them about their areas of need. My grade 4 math diagnostics are hiding now in my filing cabinet… (hangs head). Perhaps diagnostics should engage students in conversation rather than just be material for the teacher. I love that idea.

    I have some questions:
    1. You ask about how you will know if this process worked. Did you get any comments or feedback (even just casually in conversation) from students or parents.
    2. Is it possible for this to be an activity done by the students before they get to school? I wonder if this would allow them more time to address their areas of need. I am not sure if this would fit into the culture of your school. PLUS who wants to work in the summer.
    3. Do you know if any students DID address their areas of weakness? If so how? Did you provide resources or direction to those that needed help?
    4. Finally you ask how you will measure if the process worked AND had a lasting effect. Could you compare the overall scores from last year to this year. I know that learning is SO much more than test scores…but it’s a start?

    Anyways, hope those questions are helpful. Excited to continue to engage with you on this.

    Best of Luck!

    • Hi Michael,
      Thanks for sharing. I want to pick up on something @ibrown said “Perhaps diagnostics should engage students in conversation rather than just be material for the teacher. ” I’m wondering how/if this conversation happened, and what the response was from students? This could be a great opportunity for them to reflect and set their own next steps, with guidance from you. Perhaps they could even communicate with their parents about what they have determined to be their strengths and opportunities for growth?
      Looking forward to seeing how this plays out in the long run.

  4. Love the concept of the Diagnostic Mike, would love if you could share it with me! I like the concept of having students take ownership of their learning by identifying areas of weakness for them.

    I think chunking it down into a half-day session before each unit might allow you to see how effective the ‘refresh’ is.

  5. Allison Macrae says:

    Hi Mike,

    I agree that this is very important. I find the same thing with my grade 9 / 10’s. Regardless of who taught it and how they learned a topic, kids forget what they previously learned, because their brains are developing at such a rapid rate during adolescence.

    I always appreciated the concept of math being taught as a spiral, rather than a ramp. Kids benefit from revisiting an idea over and over throughout the year and over numerous years.

    I too have run diagnostics, assigned makeup work, and hoped that it made a difference and to be honest, I didn’t pay attention to see if it helped. I think the idea of teaching kids to revisit prior knowledge before starting a new unit is helpful, especially when heading to University. I think if you keep anecdotal evidence and reflections on the process, collect some results, ask the students how they felt it went, that by the end of the year you will be able to determine if it was effective. Perhaps this can be your action plan for the year!

  6. Brian says:

    Hi Mike,
    I feel a diagnostic at the beginning helps us realize what different stages our students are it in course preparation. What we do with that information is what decides whether the diagnostic is worth while or not. Having students do more than one during the year can show the growth they have made and students enjoy seeing that as well. I feel it takes a few years to come up with the appropriate diagnostics and follow ups that you do with them to be able to see if they are working or not. I have known some teachers that have a day every two weeks maybe where the students work on those needed skills to get their prior knowledge up to where it needs to be.

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