7 minute read
Using retrieval practice in a Mathematics classroom
TEACHING MATHEMATICS
By Katie Jackson, Mathematics Teacher
We all have a preconceived idea as to what a Mathematics classroom should look like. When we were at school, we were taught Maths by block practice. We learned the concept in class, practiced from a textbook and probably had a topic test at the end of that learning episode – let’s take the example of learning fractions. You would probably be taught to add in one lesson, in the next to subtract, then on to multiplying before a few more lessons on dividing fractions.
Blocked practice is important for students when they learn a new concept or skill. Many students easily understand the work and complete the practice with few problems. They mistakenly think they can solve any problem. For example, if students are learning about finding sides in a right-angled triangle using Pythagoras’ theorem, they have a lot of success in block practice as the cue is that all questions in the lesson relate to Pythagoras’ Theorem. These students feel they have mastered the topic but fail to recognise Pythagoras’ Theorem when sitting a test of many mixed-up topics. This is because the cue of knowing what to do in advance is missing. A test may include many different types of triangles and being able to find area, a side in a right-angled triangle or a side in a non-rightangled triangle. This combination of questions means that the cues are missing and the students do not know which method to use. When it comes time for the test, students and teachers mistakenly believe students have mastered the work but the results are often disappointing. This can be a case of students’ grasping the work at the time because of cues from the lesson, which can be classified as performance, but it does not mean they have stored the information into long-term memory and thus the learning has been forgotten.
WHAT IS INTERLEAVING?
Educational scientists have found that blocked practice is initially useful in learning new concepts, but it is not the best way to retain that understanding. The best way to interrupt a cycle of disappointing results in Mathematics is to use interleaved practice, which forces students to choose an appropriate
strategy to solve a problem and helps them to store the information in long term memory. Interleaving is working on mixed Maths topics where the student must firstly identify which concept of Mathematics is relevant and then choose the appropriate strategy to solve the problem. This strategy has been shown to help students not only retain information, but it also helps them to apply their learning to different contexts.
This strategy is particularly useful in Mathematics where students have to use their skills for problem solving. One way of using interleaving in the classroom is to set some homework each week that is not based on the current topic under study – but has previous Mathematical ideas in another order. This forces students to think deeply and to come back to previous learning, effectively interrupting the cycle of forgetting.
TEACHING MATHEMATICS
An alternate way of using interleaving practice is through some of the work of Mathematics teacher, Craig Barton, in his useful website called SSDD problems (Same Surface, Different Deep Structure). The concept is that, the questions all look the same. They could all be on triangles with the same surface structure to the question. When trying to answer the questions, students must think about using the appropriate method to find the answer, which refers to the deep structure. This can be hard, but it helps students to make connections between all the ideas they have learned about triangles and it helps them to see similarities and differences.
Kirschner, Sweller and Clark (2006) define learning as, ‘a change in long-term memory’. Consider that when Maths students are tested only a short time after learning a topic, teachers see performance rather than learning. ”
This is why interleaving is important and why the practice leads to students’ experiencing “desirable difficulties”; a term coined by Robert and Elizabeth Bjork (2011). We are more likely to retain knowledge when the work is neither too easy nor too hard, and by mixing concepts up, students really need to think about what they are doing. This creates stronger connections in their brains, which ultimately leads to longer term, stronger memories.
Subject Study
Study Re-study
Practice test Test
Test
Retrieval practice
Figure 1: Which approach leads to deeper learning?
RETRIEVAL PRACTICE
Another way to boost student performance is known as retrieval practice. Retrieval practice boosts learning by pulling information out of students’ heads, rather than cramming information into students’ heads’, according to cognitive scientist and author, Pooja Agarwal (2019). Some may believe that studying for a test involves reading notes, summarising and learning information by rote, and often cramming before a test. This approach may lead to short-term results but the information is quickly forgotten over time. The diagram above illustrates retrieval practice. It shows an experiment where students were given time to study for a test. The first group studied for the test and were then given time to re-study before the test. The second group had the same first study session but were then given a practice test. This could be as simple as instructing students to write down everything they know about the topic. Both sets of students ultimately sat the same test, but which group do you think performed better? The students who had done the practice test outperformed peers who had more study sessions. This was because the process of retrieving information strengthens learning and understanding and also helps students identify areas that they are unsure about which gives them direction for further revision. Teachers can try these simple but transformative approaches to using retrieval practice in their classrooms. For example, try asking students, “What did we do in class yesterday?” rather than giving them a summary of the lesson with “Here’s what we did in class yesterday”. This simple shift can significantly boost long-term learning. The act of bringing information into your mind from your memory which is the act of retrieving information, improves one’s understanding of the concept. In Mathematics, this is important because students quickly forget previous learning, so the practice of constantly retrieving helps them think about all the concepts that have been learned.
TEACHING MATHEMATICS
Spacing
The idea of coming back to previous learning is called spacing. When the learning of skills and concepts is spaced over time and constantly revisited, this helps to improve how well students grasp the material. Spacing is the opposite of cramming. Once students have learned a new concept, skill or idea, they should give their mind time to forget so that the brain, in subsequent study sessions, must struggle to recall the information previously learned. To maximise outcomes, spaced practice should be combined with retrieval practice to force the brain to search for related information and create new connections which improves the quality of learning.
Frequent low-stakes quizzing is the signature example of retrieval practice. This can be used to begin every maths lesson as it can help students to recall previous learning - not just from the previous lesson, but from work learned weeks, months and even years ago.”
Students can find this difficult at first but as a regular start to the lesson, students soon look forward to the challenge and it helps them to become independent learners as there is no hiding from seeing what they know and don’t know. It also helps them become used to the uncomfortable feeling of not knowing what to do and find small strategies that will help them to begin a question which often leads to the correct answer. The students mark their own work and have time to reflect on what went well and what it is they need to go home and revise that night. The idea of frequent low stakes testing, in the form of daily revision in maths, means that interleaving, spacing and retrieval practice are being met every lesson leading to long term memory strength and better results for the students.
References Agarwal, P.K., & Bain, P.M. (2019). Powerful teaching: Unleash the science of learning. Hoboken, New Jersey: John Wiley & Sons. Barton, C. (n.d.). Same surface, different deep structure: Maths problems from Craig Barton @ mrbartonmaths. Retrieved April 22, 2020, from https://ssddproblems.com/ Bjork, E. L., & Bjork, R. A. (2011). Making things hard on yourself, but in a good way: Creating desirable difficulties to enhance learning. In M. A. Gernsbacher, R. W. Pew, L. M. Hough, J. R. Pomerantz (Eds.) & FABBS Foundation, Psychology and the real world: Essays illustrating fundamental contributions to society (p. 56–64). Duffield, U.K: Worth Publishers Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. Educational Psychologist, 41, 75–86.
