Strategies to Enhance Retrieval in the Maths Classroom: Trigonometry

Retrieval practice is becoming increasingly cited as a powerful tool for enabling students of all abilities and ages to improve the depth of their learning, as well as the corresponding learning outcomes.

Teaching that involves retrieval practice can be particularly important in the subject of Maths, which often requires students to remember complex formulae and procedures, many of which use symbols and notations that students aren’t familiar with.

This article details just a few of the many methods that a GCSE Maths tutor like myself has used in the classroom, which help embed long-term learning and reinforce students’ ability to apply the information they have learnt. These strategies are effective from KS3-KS5, but relate directly to how I teach the topic of trigonometry through online tutoring.

Figure 1 - An introduction to the Trigonometry teaching strategy I have created.

Using Reflective Questioning to Break Down Complex Problems

Reflective questioning is a powerful technique that involves prompting students to think about the techniques they are learning to apply, at a deeper level, which guides them to reflect on their learning and the processes used. One example of where I have used reflective questioning to promote retrieval practice is in KS4 Trigonometry.

This topic involves a variety of methods, including Pythagoras’ theorem, the ‘SOHCAHTOA’ mnemonic, cosine, and sine rule, where each method is different in terms of complexity. Despite this, one of the biggest hurdles students face when learning about Trigonometry is not how to apply the methods, but in the first instance, knowing what the appropriate strategy to apply is, depending on the information provided and the answer the question is searching for.

When teaching trigonometry, I will teach one strategy at a time and frame the different strategies, guiding the student to the correct strategy without explicitly explaining why. This can be seen in Figure 1, where the first prompt asks the student to question whether the triangle has a right angle or not, guiding the student to only a couple of the strategies. Thereafter, the student is encouraged to then ask whether the triangle has an acute angle or not, which further guides the student to the correct strategy, and so on.

Using a strategy like this, which teaches the student not only how to answer the question, but how to approach the question, and empowers them to think independently, and takes away much of the uncertainty and anxiety that many students face with Maths. In my experience, using a guided approach results in the student feeling more confident with their chosen strategy.

Using Student-friendly Language

Using student-friendly, interesting language in the classroom can enhance retrieval practice by making the process of learning and, importantly, understanding Maths engaging, relatable, and even enjoyable for students.

One way in which I embed this into the teaching of Trigonometry, is by using a strategy my students know as the ‘childhood strategy’, when labelling sides of a triangle corresponding to the SOHCAHTOA mnemonic, and discerning which sides will be of use to them. This strategy involves asking the student to label the sides as ‘given’, ‘want’ and ‘couldn’t care less!’, again guiding them to the appropriate sub-strategy.

When first teaching the students this language, I ask them to imagine being in a sweet shop, or shopping for toys – common scenarios students of all ages and backgrounds can relate to. They then learn to identify which sweet (side) they have already been given, the sweet (side) they want, and the sweet they couldn’t care less about.

Another example of where I embed this in my teaching of Trigonometry, is guiding the student to different ‘trigonometry worlds’, based on the reflective questions discussed above. Using approaches like this taps into students’ imaginations and takes an almost gamified yet simplified approach, making applying the appropriate method interesting and relatable.

As well as making the learning more enjoyable, using language such as this reduces a lot of the fear that many students find goes hand-in-hand with complex mathematical language, and enables them to get to grips with understanding the method they are applying, and why they have applied it, as opposed to getting caught up with the complexities such topics can present, hence increasing the depth of the learning.

Finally, using student-friendly, engaging language embeds positive connotations and emotions with the learning of Maths, reducing fear and increasing confidence when approaching such complex topics.

The next blog post will continue the theme of enhancing retrieval practice, with a focus on teaching the complex topic of integration.