The Importance of Problem Solving in Math

When we look at math accomplishment around the world, some countries stand above others in their achievements. Singapore’s record is outstanding, for example, often taking the number one spot in international testing in reading, science and, of course, math.

Digging deeper into the reasons for Singapore’s success, a pattern emerges. This young country has invested most of its resources in developing a high-quality approach to education. Part of this includes drawing from the best practices from around the world in all subjects. Professionals are sent around the world to study the research and practices in different countries and bring their findings back to the ecosystem of their teacher training.

Another reason for their success is the emphasis on problem solving. Where historically math has been taught at elementary levels as primarily computation practice, Singapore was a leader in changing the focus to problem solving. Not only that, but they took from the work of Jerome Bruner’s The Process of Education (1960) to develop their approach of introducing concepts first through concrete experiences, then pictorially, and then finally the abstract or procedural level. This enables a robust form of learning that supports long-term learning, not only memorization or working memory.

Then in the 1990s, a teacher in Singapore created an ingenious approach to problem solving called bar modeling, or tape diagrams in US Common Core parlance. This approach allows a systematic way to solve word problems that is far more efficient that previous strategies, which would often include the tedious guess-and-check approach.

Bar modeling also supports algebraic thinking, in which the unknown is identified, usually with a question mark. That model then allows powerful visualization in problem solving, so when students make a bridge to algebra, it is demystified and scaffolded.

One reason students worldwide might not succeed in math is because they are not challenged in the zone of proximal development (Vygotsky). They are either given tasks that are too challenging, creating frustration, or too easy, leading to boredom. Also, when teachers are unable to challenge students at the appropriate levels, the temptation is to give students too much help too quickly, or give them the answers. This undermines students’ ability to struggle and persevere in problem solving.

This is connected to the mindset work of Carol Dweck and its application to math by Jo Boaler and her team. When struggle is seen as negative and the right answer is paramount, students feel like failures when they struggle. When productive struggle is encouraged, though, and the process, rather that the answer, is emphasized, new patterns emerge. Students persevere, feel successful when they work hard, develop more confidence, and are more willing to take risks in learning. They embrace mistakes as learning opportunities and become more supportive of their classmates. These abilities then carry on through their school careers and life. This is why the first Standard for Mathematical Practice adopted in the US is “Make sense of problems and persevere in solving them.”

Therefore, it’s extremely important to include challenging word problems, and the appropriate scaffolds for student success, as part of students’ math experiences.

The Matholia bar modeling tools and practice activities can fulfill these needs, and the math problems released in the Matholia Loop newsletter have their place in the classroom as well.

Taken from the Practice environment at matholia.com

Susan Midlarsky is a Math Consultant, a Curriculum Writer, and is keenly interested in questions related to learning math. You can find out more about her at susanmidlarsky.com.

The Matholia Team