Formula Sheet – A Toolbox or Takeout Menu?
During the IB Exams, students get a set of equations and constants to use. Part of the motivation behind them is to reduce the amount of memorization required. There’s no sense in students memorizing Planck’s constant or the Law of Cosines in a context that emphasizes application of these ideas.
That said, I’ve heard variations on the following from different students just in the past three days:
- I thought I was right, then I looked at the formula sheet, and realized I was wrong. (She was right the first time.)
- I didn’t study it because I knew it was on the formula sheet.
- I don’t know what formula to use.
If you read my blog, you know that I don’t test formula memorization for all sorts of reasons. You get it. I get it. It has a place, but that place isn’t one I want to be spending my time.
You might also know that I’ve experimented with different versions of resources available to students during a test. I’ve done open note-card, open A4 sheet, open A5 sheet, open computer/closed network, open computer/open network, open notebook, and open people (i.e. a group test) formats.
I believe that the act of students creating their own formula sheets is more effective than handing one to them. The process of seeing how a formula is applied in different contexts and deciding what needs to be remembered is valuable on its own. Identifying that one problem is similar to another for reasons of physics shows understanding. I want to make opportunities for that to happen. Reducing the size of the resource requires students to prioritize. These are all high level skills.
The difficulty is that students see formulas directly as a pathway from problem to solution. Most problems worth solving don’t fit with that level of simplicity. Formula sheets give you the factual information, and rely on the user to know how to connect that information to a problem. The student thinks that the answer is staring at them in the face, and they just have to pick the right one. As teachers, we want students to identify information they need, then look at the reference to get it.
This is part of the reason I like standards based grading, as it justifies assessing students through conversation. A student asks me for a specific piece of information. If it’s how to calculate something, I’ll tell them if the related learning standard is about applying a concept, not calculating a quantity. If their request directly asks for the answer to the question, I don’t tell them. If they ask for a hint, I give them enough to get them moving, and adjust their proficiency level for the related standard according to the amount of help I give them.
In the long run, however, students need to know how to use the resources available to them. This is one of those big picture skills everyone talks about. Students need to know how to use Google to effectively find what they are looking for. They need to know that typing the text of a question into Yahoo Answers is not going to get them the answer they are looking for. I do know that if a student directly says “I can’t remember a formula for [ ]”, and I give them an equation sheet, they can usually find it. If they use the formula sheet as step one, they are not likely to complete the problem on their own. Having the sheet there in front of them makes it far too easy to start a problem that way. Would having students tally the number of times they looked at their sheet be enough of a feedback mechanism to keep this in check?
I don’t know what the answer is right now.
How do you help students treat a formula sheet more like a tool box, and less like a restaurant take-out menu?
Many of my students don’t use any of the reference materials available to them. The students who do, do better overall, on assignments, quizzes, and tests. I agree with the strategy of having these students create their own reference materials: a vocabulary sheet with a definition that is more “how to use” than textbook, with example(s), a step by step on 3×5 card, visuals of parent graphs (they draw the graph), formulas with each part defined (and notes on where/what those parts look like within a problem) and lots more. I watch them create these helps, and like your questioning, I look/ask to see what they feel is important, what they feel they need to remember. I ask questions about the connections they are making between what they are creating (the reference) and how they might use it to help solve future challenges. Then I give a quiz where they have to use the resource to complete the quiz. Again, some do, most don’t. The quiz then becomes it’s own lesson in using the resource. It’s pulling teeth to get many students to use the resource! The quizzes are a start, though, because I don’t even give the hints to questioners who don’t use their helps. Having said that, there are students who don’t create good reference materials. They don’t have good writing, or don’t have coherent thought patterns – I have to design a guided note or activity page, but the realization that this is valuable tool seems lost on students. To overcome this block, I review with them as if I was actually studying, creating brief notes that they take down, think alouds, really. I model using the reference materials they have created (going around the room, picking up their materials). I am open to more good ideas on this –
Good points. Modeling what to do with these resources is important, and is definitely part of the process. The problem isn’t that they don’t know how to use the tool though. The bigger issue, I think, is that it’s just easier to look for a solution on the paper than do the thinking of what they need first, and then get what they need from the sheet.
I had a student today ask me what the highest speed of a running human was. I was about to look it up because I was curious, and then I stopped.
‘Look it up online’, I said.
‘What do I look up?’
‘Try something.’
Once she had some search results to work with, we had a conversation about parsing them for the answer she was looking for.
The step of just asking the teacher is easy. Looking it up is harder, though not necessarily difficult.
The step of looking on the equation sheet for an answer is easy. Deciding what information you have, what you need, and the connection between them – that’s not only more challenging, but a more valuable exercise for students to go through.
I had my students looking at a video two days ago, then we looked at it again to take notes and make drawings – the unit circle basics. I realized the kids weren’t focusing on any of this, and I asked them to predict, based on what the woman on the video did, what she was going to do next, and write that down. Then I played the video a little further and we started looking at the guesses, and why some kids thought one thing and others went a different way. While I have used the three act and 101 questions and 180 pictures with them before, it never occurred to me to let them predict for a video. The whole class was engaged from that point forward. The same thing happened with some material on the board. A young man’s eyes were glazing over. He said he was bored (I told him that’s why they call it a board!) anyway, I had him look at the problem and ask me any question he had. He wanted to know why I replaced the f(x) with y. At that point several others chimed in and said they wanted to know that too. It led to a great class discussion and more questions. There was even a brief discussion about how learning happens. The quiz on translating from radians to degrees and back to radians came out much better, and the kids were excited about what they learned. They really want to pull this stuff from memory….