Using Desirable Difficulties to Teach Mathematics

Mathematics is a challenging subject for many students. But what can be more challenging is teaching mathematics to students. Humans of any age are inclined to take the path of least resistance. That means that we are programmed to look for shortcuts that favor quick wins. The problem is that mastering mathematics isn’t a quick-win game. It takes years of mastering fundamental skills that build on one another. So, how can teachers strike a balance between the two?

The answer is in desirable difficulties or teaching strategies that are designed to build long-lasting learning over quick performance boosts. The reason is that in rapid success activities, we tend to mistake familiarity for learning. Real learning moves at a slower pace.

Use Daily Retrieval Practices in Multiple Choice Format

Retrieval practice is a great way to build deep learning. The problem is that we tend to quiz weekly, which is too infrequent for most learners. Additionally, we tend to rely on open-ended quiz questions to test true learning rather than selection luck. While open-ended questions have their merit, student motivation increases with the multiple-choice format. Therefore, using regular retrieval practice as a desirable difficulty in learning that is softened by the multiple-choice format can help students stay motivated while mastering long-term mathematics goals.

Mixed Practice Provides the Best Results

Traditional math textbooks and curriculum tend to be organized sequentially. We’ve always taught mathematics in a certain order. And while our left-brains love the organization, it compartmentalizes learning. One common struggle that happens time and again with mathematics students is that they know a formula or process in one scenario but fail to apply it in another. Let’s say, for example, the volume of a three-dimensional shape.

When a student knows the right formulas but not the right context for application, the problem very well might be sequential learning without enough mixed practice. There is even an argument to be made that math textbooks should be organized with mixed math in mind so that students routinely practice different math skills together.

Leave Room for Learning

The power of desired difficulties is in the learning process. We have to allow students to experience the challenge of learning in order to make it stick long term. In practice, that means it might be briefly uncomfortable for students and teachers. But easy doesn’t stick, so finding the right balance between easy wins that motivate students and real learning is necessary.

Teachers should always allow time to think between questions before requiring an answer. Students need time to receive the information, process it, and formulate an answer. Also, keep in mind they may need time to reread the material.

Final Thoughts on Desirable Difficulties

The idea that learning should be easy has been widely debunked. In fact, the best academic performance comes from the most difficult scenarios. When we force our brains to work out a problem, we create a neural pathway. The more opportunities that students get to create neural pathways through mixed practice, the stronger the learning becomes.

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