When teaching physics equations, it’s invaluable to establish a baseline for the pupils. I use two different approaches to this. I sometimes give a baseline test, using 5 questions of increasing difficulty and asking for answers on their mini-whiteboards. If any pupil gets below 3 then I reteach how to rearrange equations to the class quickly before moving on (we’ll call this class, Class 1).

The second approach is to just go straight in and teach from the basics, giving lots of reward for those who may know the answers and reward those for trying their hardest, essentially establishing a new baseline (we’ll call this one Class 2).

From this, in both classrooms, I start with using the units to identify what quantities contribute to the quantity that we are focusing on and how we might go about calculating it. So for example, if we are covering speed calculations for that lesson, we will talk about how speed is measured in metres per second (m/s) and how the forward-slash could be taken to mean that distance divided by time is equal to the quantity of speed. This way, students have a small understanding of what the lesson is going to entail before moving on to operationalising any formulas.

Once students have understood where the units have come from, I then teach them the EVERY method and drill this into them through lots of modelling and examples. I find students can be resistant to using this as I often get complaints such as “It’s long sir!” or “I can work it out without it sir!” but I really insist on its use as it helps for students to order their thoughts and, under exam pressure, select the appropriate equation for their question; particularly when they have a number of different equations at their disposal.

**EVERY** stands for:

**Equation** – Decide which equation you need

**Values** – Select the values required for the equation

**Enter** – Enter the values into the equation

**Results** – Consider the results of your calculation – do they make sense for the scenario?

**Y(units)** – Add the units.

(Check out Dr Millichamp’s blog for more details!)^{[1]}

I then give the students independent Shed Loads of Practice (SLOP). When teaching calculations, I have used two different methods in asking pupils to practice completing equations and it depends on the prior knowledge of the class. Should the class have never seen rearranging equations before, I like to set up practice in a skill acquisition practice scheduling method called Blocked Practice ^{[2]}. This is where students get to practice a particular part of a whole skill which in this example is, operationalising the speed=distance/time equation, and splitting it into parts so that students can get the hang of operationalising the different parts of the formula numerous times. In effect, solely calculating speed before moving onto another way of operationalising the formula, then using the same formula to calculate distance. If we were to use the tennis forehand shot scenario, this would be comparative to practising setting an open stance conducive to hitting a ball 10 times, then building on that knowledge with practising setting an open stance whilst swinging the tennis racket 10 times, then after that practising hitting the ball over the net 10 times.

I found this particularly effective for Class 2 because, as complete novices, it ensures that the cognitive load is reduced for all students in that they only need to figure out how to calculate one value and practice how to do that a number of times in an attempt to have students familiarising themselves with the terminology and use of the formula. I make this super easy for the class by literally giving students values for distance and for time and ask them to use the EVERY method to and I quote “show me how to calculate speed EVERY time”. I have found that this is where I want students in Class 2 to spend the majority of their time as the skill is essentially acquired faster^{[3]}.

However, it is also key to note that while the skill is acquired at a faster rate, it is also forgotten at a faster rate as shown in the graph below^{[4]}. In practice, Blocked practice is great for acquiring the initial skill, however, we must add more to the practice to ensure that students do not forget as quickly.

In classes that have perhaps had more practice at rearranging equations in the past such as Class 1, I schedule SLOP in a slightly different way mainly to ensure that the pupils remain challenged but still practice the skill of rearranging the equation. Early on in practice, I may use a Serial Practice schedule^{[6]}, in which I may plan questions using a scheme such as using two questions relating to each manipulation of the equation i.e calculate speed, then the next two questions “calculate distance”, then the next two questions “calculate time”. This also increases cognitive load by increasing the amount of contextual interference^{[7]}.

Contextual interference is a phrase used in skill acquisition science to describe the extent of variability (the number of pieces of information to process) there is within the practice. The higher the contextual interference, the higher the cognitive load used to problem solve, beneficially^{[8]}. The evidence also shows adding contextual interference increases the likelihood of long term skill retention, and also allows for students to be able to troubleshoot for themselves in metacognition^{[9]}.

As students move through the questions, the contextual interference increases as they find themselves having to identify what the question wants from them. Then they must select a way to manipulate the equation to give the appropriate answer. This is where I really have high expectations in ensuring that students are using the EVERY method, and I really highlight how well organised their calculations are from this to positively reinforce EVERY and increase morale and motivation. Using the tennis forehand example, this would be shown by a certain number of attempts at setting a stance, then some attempts at hitting the ball over the net, then practising setting an open stance whilst swinging the tennis racket and completing this sequence of practice until there have been 30 efforts of practice.

A ramped element of SLOP in these lessons comes from increasing the difficulty of each question (differentiation box checked). So for Class 1 this would be moving from Blocked Practice into the more random Serial Practice. It is key that to continue with improving long term retention of the skill that the next stage for them is using serial practice^{[10]}. Increasing the cognitive load in such a way really tests how well these students know how to operationalise the equation.

However, for Class 2 who have usually mastered this by now, I move onto practice which contains a higher element of contextual interference^{[11]}. This is where when scheduling more practice in my SLOP, students are given questions that are more variable in their nature, whereby students must select the appropriate information from a larger amount of information to be able to work out what a problem is asking of them. If we were to use the tennis forehand example, this would look like asking a pupil to hit the tennis ball using the tennis forehand shot, but putting the ball into a specific area. This could also look like, asking the pupil to hit the tennis ball into a particular area at a higher speed. Or even asking the pupil to score a point against an opponent using the forehand shot.

To conclude my ramblings on using skill acquisition science for learning physics calculations, I think when students understand where the units of a quantity come from, it often paints a simple picture for how a calculation is done. Also, the inclusion of lots of purposeful practice for the equation is paramount for novices and through blocked practice with low contextual interference, initial learning is completed at a faster rate. However, be wary that with low contextual interference, students also forget at a faster rate so therefore offset the likelihood of forgetting by including gradual increases in challenge throughout all SLOP completed on that day.

## References

^{[1]} (n.d.). Thomas Chillimamp – Medium. Retrieved April 23, 2020, from https://medium.com/@tomchillimamp

^{[2]} “Promoting a skills-based agenda in Olympic sports: the … – NCBI.” https://www.ncbi.nlm.nih.gov/pubmed/19449252. Accessed 23 Apr. 2020.

^{[3]} (2013, February 8). Contextual Interference Effects in Learning Three Badminton …. Retrieved April 23, 2020, from https://www.tandfonline.com/doi/abs/10.1080/02701367.1986.10608091

^{[4]} (2013, February 8). Contextual Interference Effects in Learning Three Badminton …. Retrieved April 23, 2020, from https://www.tandfonline.com/doi/abs/10.1080/02701367.1986.10608091

^{[5]} (2013, February 8). Contextual Interference Effects in Learning Three Badminton …. Retrieved April 23, 2020, from https://www.tandfonline.com/doi/abs/10.1080/02701367.1986.10608091

^{[6]} (n.d.). Promoting a skills-based agenda in Olympic sports: the … – NCBI. Retrieved April 23, 2020, from https://www.ncbi.nlm.nih.gov/pubmed/19449252

^{[7]} (2017, October 19). Role of Constant, Random and Blocked Practice in an …. Retrieved April 23, 2020, from https://www.tandfonline.com/doi/full/10.1080/00222895.2017.1383226?src=recsys

^{[8]} (n.d.). Contextual interference – Gwern. Retrieved April 23, 2020, from https://www.gwern.net/docs/spacedrepetition/2004-lee.pdf

^{[9]} (n.d.). (PDF) Systematically increasing contextual interference is …. Retrieved April 23, 2020, from https://www.researchgate.net/publication/46282557_Systematically_increasing_contextual_interference_is_beneficial_for_learning_sport_skills

^{[10]} (n.d.). Systematically Increasing Contextual Interference is Beneficial …. Retrieved April 23, 2020, from https://www.sciencedirect.com/science/article/pii/S1877042811022506

^{[11]} “Systematically Increasing Contextual Interference is Beneficial ….” https://www.sciencedirect.com/science/article/pii/S1877042811022506. Accessed 23 Apr. 2020.

*Featured photo by Tyler Anderson on Unsplash*

Thankyou Tobias, I’m training as a physics teacher GCSE and this has been an area of interest for me throughout. Linking it in with the metacognition makes perfect sense to me. I will absolutely experiment with your method once I can go back in a classroom.