In my talk at ResearchED Rugby, I discussed how I help students with calculations in physics and how I structure my SLOP (Shed Loads Of Practice) sheets. This blog is an overview of the talk and a list of the types of questions/tasks I include in SLOP sheets. The link for completed SLOP sheets (which currently total one as I’ve only just settled on what I want to include in them) can be found at the bottom in a vain attempt to get you to read this the whole way through. I’d love your feedback and input on these sheets, especially if you fancy helping create more.
You can find a copy of the slides I used here. They contain some examples of student work for some of the techniques.
I try to motivate my students into “showing their working out” by describing the act as “proving you’re not wrong”. This gives them more reason to be clear over what they’re doing. You can explain where marks are awarded during the process of showing their working out as extra incentive. For you, as a teacher, asking for clarity in their working out allows you to diagnose the exact point that students are getting stuck (when this happens) much easier.
My blog about the process I use with my classes (the EVERY method) can be found here. Regardless of what method you use, get students to use it consistently. For the students, having an automatic method to hand can help to reduce the cognitive load associated with performing calculations. As a teacher having a prescribed format can allow you to easily see where a student has gone wrong without too much additional cognitive load for yourself. This is similar to the TLAC technique of “standardise the format”.
I would demo the calculation process, explicitly going through my thinking for all steps, for some simple questions during every lesson where we’re doing calculations. I use the visualiser to either show a perfect model solution or a poor solution created by myself to question the students as to why it’s wrong.
Below is a list of the styles of questions and techniques I try to include on my sheets. They are in the order I tend to use them as I attempt to find a sequence that allows all students to progress. I don’t use all techniques with all classes, but take the “master sheet” and cut out unwanted sections to make something tailored to the current needs of my class. I’d hope that by year 11, I could give students the entire sheet as a revision tool for calculations. These are under development as I’ve trialled different things throughout my NQT year to find out what works for me.
On the sheet, I pick out what I think are important questions (you might think of them as mini hinge questions) that I ask student to “BOX” (draw a box around in their books). When I circulate, I can pick these out quickly and assess whether a student can move forward a bit quicker through the sheet or whether they need reteaching/support/additional practice.
BASICS — I start with basic questions about the formula — definitions, units, what the formula is. The type of questions that make for a simple start so everyone gets some success (and we get to drill some units and definitions).
WORKED EXAMPLES — My preference is to do this live rather than on a sheet, but if you have non-specialists teaching physics, it’s worth including worked examples on the sheet to develop a common language and to ensure students experience perfect solutions.
FADED EXAMPLES — Here I use the scaffold of the EVERY method and slowly remove more and more steps as we move through questions. All of these questions tend to have a similar wording. These completion problems are really useful for the first few times of doing it.
VARY WORDING — The next few questions will be very similar to the completion problems but now with the location of the variables moved around within the question. This is a chance to get students to prove that they know if a variable has units of kg, then it must be mass etc.
VARY UNITS — Similar questions as above, but now with non-standard units that need converting (I may give a hint in brackets for the first few times).
INTERSPERSED DECLARATIVE KNOWLEDGE — throughout the previous questions, I would interleave some simple declarative questions. It stops them mindlessly doing calculations and gets them to think about what the calculations are really about. I might use “Because, But, So” tasks for this too (I’ve blogged about this technique). Equally, this is a chance to address misconceptions (and refute them — see Ben Rogers’ post on refutation texts )
CALCULATE SOME OF THE PIECES — these are now simple multi-step calculations. I’m not saving these as the pinnacle of the sheet, I’m trying to make them common place. It’s part interleaving and part deepening understanding. I might get them to calculate the mass (from density and volume) or the acceleration (from change in velocity and time taken) and then use these in the formula F=ma, for example.
INTERLEAVED CALCULATIONS — I also tend to include more explicitly interleaved questions a bit later in the sheet. A sheet on F=ma might include questions on kinetic energy or work done to emphasise the links. The key thing here is the links between the current content and old content. Think of it as building the schema and linking new learning to old. It shouldn’t just be random questions from old topics (e.g questions on circuits on a sheet about forces would likely be more confusing than useful).
GIVE EXAMPLES OF EVERYDAY OCCURRENCE — throughout the sheet, examples should be as concrete as possible, relating to the experiences of students where possible to make abstract ideas as tangible as possible. Once again, linking the learning to previous knowledge (think of those schema) as often as possible.
SOLUTION ANALYSIS: BECAUSE BUT SO — I’ve blogged about this technique here “Because, But, So” can be used as a framework to get students to analyse an incorrect solution. “The student is wrong because…”, “the student is wrong but…”, “the student is wrong so…”. Equally, getting students to take a model solution and annotate WHY each of the steps should be performed is another route I might take.
REARRANGEMENTS — I would repeat the first few sections with the equation in a rearranged form. I currently get students to substitute then rearrange (see Matthew Benyohai’s blog for the reason why).
SEEING RELATIONSHIPS THROUGH A TABLE OF SIMPLE CALCULATIONS — to get students to think about relationships between variables, I use an activity of simple values for the variables in a table. Using the ideas of minimally different examples from maths (see this blog by Kris Boulton as well as this one by Ben Gordon), I alter the value of just one variable at a time within the rows of the table. I get students to do their working out on a whiteboard so they can quickly make the slight alterations. I want them to keep using my EVERY method, but by using the whiteboard, we can do the calculations much quicker and allow students to easily delve into relationships between the carefully changing variables. I always have questions after the table that probe the nature of the relationship in words e.g. “as force increases, the acceleration….” (I blogged about this in a little more detail here).
GRAPHS — in a similar manner to using a table of simple calculations, I might include a simple graph question to get students to describe the relationship between the variables in the formula we are studying (or an interleaved related one).
GOAL FREE — tasks that set the scene of a problem and allow students to see how much they can work out unguided. These problems have been shown to be really effective. Graphs work really well as goal-free problems. See Adam Robbins excellent blog for more details.
NON-CALCULABLE CALCULATIONS — A recent research paper has pointed to the increased transfer ability that students can achieve by studying numerical problems that are presented without numbers (and are hence non-calculable). Where goal-free has no end point but clear routes to calculations, non-calculables have a clear end point but make you focus on what information you would need to get there.
MULTIPLE CALCULATIONS (WORKED AND FADED) — I might include additional, more complex multi-step calculations later in the sheet (with the possibility of demonstrating worked solutions and giving faded support).
REDUNDANT INFO — to really test understanding, I might set up calculations with redundant information within the question to check students really grasp what they need to perform a given calculation.
ESTIMATES — the idea of non-calculable questions made me think of setting up some questions in a non-calculable manner but asking students to estimate values to perform the calculation.
Here’s that link to my SLOP folder as promised at the top. Please let me know if you have any feedback or would like to help make any more sheets. I’m on Twitter, feel free to contact me on there with any thoughts.