I believe in the Ecological Model of education, wherein we celebrate natural diversity of learners and attempt to broach subjects with a more complete understanding by expressing the ideas and language of the subject in multiple ways.
That’s why in my math classroom, tests and quizzes make up slightly less than 25% of the total grade. They are one way (out of many) to show a depth of mathematical understanding – in the ‘real world,’ though, mathematicians who are able to do excellent work more slowly and thoroughly are also celebrated, usually even moreso than quick ones. Mathematicians who are able to show and make comprehensible the techniques they used and the reasoning behind the techniques are as critical to applications in the field as innovators of new branches of study. So why not allow those sorts of mathematicians to shine as well, in the form of Projects that require slow work and excellent communication and craftsmanship? After all, once we graduate from school, projects are what we do, not take tests.
When completing projects, we have resources. Yes, being able to think quickly on one’s feet is useful in determining which resources are necessary for the problem we are currently solving, but I also think practicing the process of drawing upon resources efficiently is useful, and this is why it is not uncommon for my Mid-Term or Final Exams to be open-note, open-resource (textbook, sometimes even the internet!). The amount of content being covered is voluminous – so completing a 50-question exam in two hours is no small feat, even with notes! You are forced to create some organization or mental schemas to delineate your note-seeking, or to just have studied well enough to not need very many notes (which would obviously put you at an advantage – which is what makes open-note a equitable/fair differentiator).
In order to do well on an open-note final exam, then, it is important that one has great habits throughout the year. And now that we mention them, I think habits are something we do even more often in the ‘real world’ than projects… so they should be part of math class anyways!
As part of my attempts to build habits in my students, for the past two years I have had them create a ‘Study Guide’ as the only homework assignment on Thursday nights before their weekly Friday Check-In’s (quizzes). The idea here is that at the end of every week, instead of doing more practice you are given a little time to organize your thoughts on the subject(s) of the week and place them into a document format that would be useful to you in studying for your final. Imagine at the end of the semester, using all of your previously self-created Study Guides as well as your returned quizzes to study for the final!
I’m becoming more sold on the belief that school is really just a way to force kids to adapt habits: you are forced to engage with a topic every day for a short period of time, and over time you don’t even realize that the subtle, 1% shifts over many days begin to really add up. And since I am deepening the belief in this concept, I recently created and added the ‘Mathematical Habits of Scholarship Checklist’. The idea here is that students fill out this sheet during the last 5 minutes of class every day. Now, as we all know, this is valuable time for math teachers to continue to skill-and-drill! But my pushback is twofold: first, becoming meta-cognitively aware of the things you are doing to improve your understanding of math will also improve your math! And secondly, mathematics is about making sense of this world. That means that taking the time to make sense of how various concepts relate to each other and to organize the concepts into your broader conceptions of the world is important – at least as important as continuously completing practice problems. After all, which skill do you (adult reader) use more: completing the square of a quadratic or creating a healthy daily habit of doing what needs to be done to put food on the table? The other cool thing about this is that, at the end of the week students who have filled out the back page of the tracker with fidelity will already have the outline for their Study Guide!
Accordingly, I am having students fill out this tracker for the last five minutes of each day and I collect it when giving them their Friday Check-In. I don’t judge the students on the coding they use for the checkboxes on the front page (I have them rate 1-10 their performance in each of the category boxes) – I just check to see that they actually filled them out and then check how thoughtful are their notes on the back page, and that’s it! Even if students try to ‘play the system’ at the very least we’re giving them the language to talk about it in the future.
Try it in your classroom and tell me what you think!