As a tutor, teacher or parent, sometimes it can be difficult to explain how to work out a challenging math problem. We want to explain it in a way that the student understands, and also want to ensure that when it comes to test time, they are able to set up the problem in a way that will help them solve the problem and give them the best chance of answering the question correctly.
In a study of 165 math teachers, researchers found four common elements that assisted students in setting up a complex math problem. These elements are discussed in detail below, and may help you help your student break down and understand a math concept or idea that seems challenging.
Discuss Key Contextual Factors
When presenting a new lesson or concept, it is important that students understand what is going on in the scenario presented to them. If, like in the example in the study, a teacher is having the class calculate different pledges received in a dance marathon, students should know what a dance marathon is and how it works. Understanding the context behind the problem is an important part of having students make sense of what they are trying to figure out. If it’s just a unfamiliar situation, mixed with a bunch of numbers and math symbols, they won’t be able to connect with the problem, and will be less motivated to work hard to solve the problem
Point Out Key Mathematical Ideas
In the research study, the students were asked how much money was raised at a Dance Marathon, based on the different wants money could be raised (upfront pledges vs. participating in the dance off) The teacher guided the students to this theory, and then used the same language they used in order to keep the conversational relatable and on their level. The students were the ones who suggested using graphs and tables, and the teacher went with it. It’s important to be aware of what the students already know, and guide them to the answer without giving too much away. By pointing out key mathematical ideas and helping students use prior knowledge towards a new problem, you can make a challenging problem seem much more manageable.
Develop A Common Language.
The difference between a successful teacher and a not so successful teacher is that one talks, and one guides. Instead of listing the steps and features of solving a problem, ask questions and solicit information from the student. Start with very basic questions and work to more challenging ones, each time getting closer and closer to solving the problem. As you work with the student, use the words they use so that nothing gets lost in translation. In a classroom setting, having students work together, exchange ideas, and then explain the ideas of their peers in their own word is a great way to measure understanding.
Maintaining Cognitive Demand
The last step is a little harder to explain, and probably makes more sense to math professionals than parents or tutors looking for a way to help their child set up a math problem. Basically, this step involves “identifying the boundaries between background info and the material that must be left for the students to unlock.” It deals with how the problem is presented to students, how much information is given and when and how it is given. The study also describes this step as the“ delicate task of making the problem accessible to students without compromising their opportunities to learn significant mathematics.”
There are plenty of online resources for parents, teachers and tutors to help motivate and guide students through multi step math problems. By following these four key steps however, you can give your child a head start by successfully setting the problem up and working through it in a way that will result in the best understanding.