Other considerations: Motivation, interest, success

The types of problems you choose are important. They can build success and encourage confidence, they can engage and motivate students by capturing their interest, and they can appeal to their sense of "Why do I have to learn this?" by being relevant.

Do students care? Use problems set in contexts that are interesting to them.

Proponents of differentiated instruction say that we can create powerful environments for learning when we give students tasks that are interesting to them, that allow them to use their preferred learning style, and that are challenging but not too hard. Students will obviously be more willing to engage with a math problem if it is connected to their own life, or if it is inherently interesting for some other reason.

Find out what your students are interested in, and change the context of problems to fit their interests. If it’s sports, or music, or clothes, or animals… whatever. Or let them create problems from their own areas of interest.

Try to put 12½ ÷ ¾ into different contexts.


Larger problems are often more interesting to students because they are more significant. They can show students how mathematics is used in the real world.

One typical project uses a scenario of a school that is building a playground. Families in the school will gather on a weekend to put it together. The students need to plan for the supplies that are needed. A list of parts is given, how many of each part, and the cost of each part – or variations on that kind of information. Students then calculate how much the playground will cost, perhaps adjusting the size of the playground to their budget.

Projects like this can be as complex or straightforward as fits your students. What projects do you use?

Building Confidence through Success

The key to keeping students engaged is to move them gradually through the learning progression, giving them the support they need to move ahead. This allows them to experience success at each step of the way, and success breeds confidence.