What happens when students only know one strategy to solve a problem, and this strategy doesn’t work? Well, at this point they might feel annoyed, frustrated, and even give up. But when they know multiple strategies, it is like students are gifted with a secret weapon – if the first strategy doesn’t work, they can always use another.
However, some teachers have concerns about teaching multiple strategies. A common issue is that students might be overwhelmed or confused. In a recent review, researchers came up with a solution. After reviewing cognitive science research, they outlined three key points to overcome this problem: what, when and how you should support the comparison of strategies.
The research study
In this review, researchers from Vanderbilt and Harvard University explored previous cognitive science studies from the past 15 years looking at how comparison works within mathematical learning. They broke down what to compare, when to compare it and how to support the comparison of strategies.
So, here’s what they found…
What should you compare?
The most common way to compare is to have multiple strategies for solving the same problem. For example, learning two different methods to solve the same algebraic equation.
Over the years, research has constantly shown benefits of using this method. Across five studies, researchers found that presenting students with multiple strategies, rather than just one strategy, constantly led to improved performance. In particular, the three types of knowledge that improved were students’:
- Conceptual knowledge – This is their ability to grasp ideas.
- Procedural flexibility – This is the ability to know how to solve a problem in multiple ways and know which method is the most effective.
- Procedural knowledge – This is the ability to execute and solve a problem. However, the amount of prior knowledge must be taken into account.
When to compare?
Next, the researchers looked at whether multiple strategies should be introduced immediately after starting a new topic, or once the student is familiar with one strategy. In a study, researchers found that learning multiple strategies was more effective when students had some prior knowledge in one of these strategies.
However, being introduced to two strategies simultaneously allows students to be aware of the similarities and differences between them. This was shown in another study, where students who immediately compared strategies gained greater procedural flexibility than those who knew one strategy prior to learning more. The key difference between these two studies is that the second study gave sufficient support to students, giving them more time to learn the material.
Therefore, being introduced to multiple strategies immediately when starting a new topic can be beneficial but requires sufficient support. Without it, students might be overwhelmed, which will slow down learning.
How to support comparison in the classroom
- Present clear examples simultaneously
When providing multiple strategies, give students clear and effective visual aids. For example, include worked examples, which are step-by-step demonstrations of how to solve a problem. Having these examples in their line of sight reduces the likelihood of a cognitive overload. This is because they don’t need to hold onto the information in their limited working memory, and reduces their cognitive load.
- Present the solutions side-by-side
Having the strategies next to each other reduces the need for students to constantly switch to find the information. This also encourages students to find the similarities and differences between the two.
- Encourage discussions about the comparisons
Allow students to explain the differences between the two comparisons. You can do this by asking higher level open-ended questions. Doing this will help prompt students to move from more generic comparisons and encourage them to have deeper level reflections about the two solutions. Having this deeper learning will build on students’ critical thinking skills, as well as increase the likelihood that they remember the information.
- Summarise the key points
Provide students with some of the key differences between the two strategies. Doing this after they reflect on the strategies will help you clear up any misconceptions that may arise. It also reduces the likelihood that students become confused between the two strategies or mix them up.
- Implement them regularly and frequently
Providing students with multiple strategies on a regular basis will help them become more familiar with using them. It will allow them to notice the important underlying structure within each strategy, as well as engage more deeply with the material.
Using multiple strategies is a very effective method to help keep students motivated and also improve their learning. However, how you implement this in your classroom makes a huge difference. Building up knowledge of the various strategies gradually, alongside lots of support, should help yield the benefits and mitigate against the risks of cognitive overload.