The Need for Daily Problem Solving

December 17, 2019

Daily problem solving practice is essential for children’s mathematical growth, but is frequently met with resistance. Too often, word problems stimulate student groans, chair slouching, and bathroom requests. Some children refuse to draw diagrams; others won’t work at all.

Negative attitudes towards word problems usually stem from children repeatedly failing to answer them correctly. Still, most students are closer to becoming good problem solvers than they realize. Their insecurities are not the product of poor critical thinking skills, but instead only associating personal success with correct answers. This mentality is justified in mathematical domains such as standard algorithms and basic number facts, but shouldn’t always be linked to problem solving.

To build a house, a carpenter needs a blueprint as well as various tools, raw materials, and skills. If they lack any of the aforementioned, the house can’t be constructed. To solve word problems, students must read, think, draw, calculate, and persevere. If they struggle to do any of the five, they will frequently get answers wrong, while not realizing that they might be making progress. Some of these skills and traits take months or even years to develop, leading to extensive problem solving futility.

Attentive math teachers realize this unfortunate reality and thus strive to create daily success associations. They celebrate accurate drawings and write problems with friendly numbers, so that students spend less time on computation and more time with critical thinking. Simultaneously, they constantly seek ways to build their students’ working stamina. These efforts and intentionality are essential for children to succeed, because they are not only battling student anxiety but also a society that magnifies it.

American culture rarely celebrates the qualities that great problem solvers possess. We love fast food, overnight delivery, high speed internet, and quick solutions, but often mock deep focus, practice, and perseverance. We scoff at slow deliberators found quietly reading in a park, or solving Sodoku puzzles on metro commutes, wondering why they aren’t on their phones listening to music, texting, or checking social media like normal people. We also tend to denigrate the struggling artist. If they were really talented, we reason, they’d be able to make a living through their passion. Practicing for hours on end is only a noble pursuit when the end product is monetary success.

Revering speedy results and talent is detrimental to all math learning, but is especially harmful to problem solving. These traits lead to short attention spans and the false belief that meeting challenges can come cheaply. Adults have acquired this perspective and, sadly, passed them along to their children.

The expert teacher knows that this mentality is not conducive to becoming a great problem solver, and must work to change pervasive attitudes that students bring with them to class. Because solving complicated math problems requires patience and deep focus, they constantly attempt to build their students’ powers of concentration and perseverance.

This begins by ensuring them a highly academic environment. Children cannot be expected to think deeply in noisy classrooms with constant interruptions and distractions. At the beginning of the school year, a class might collectively focus on a single problem for three to five minutes, but with consistent routines and structures, the teacher gradually increases their students’ endurance to work and deliberate much longer.

Ideally, children would go home every night and engage in critical thinking through brainteasers and logic puzzles. Their parents would play them in chess, help them budget allowances, and ask them time and distance problems on long family drives. This rarely occurs, however, and is becoming less and less common.

Knowing that many children don’t experience such things outside of school, the best math teachers engage students in critical thinking every day, strategically positioning problem-solving time after their fluency block, but before the lesson. Fluency activates student energy and confidence through an outpouring of success and effusive teacher praise. With their energy released and confidence maximized they are prepared for a more cerebral approach to mathematics. When executed well, problem-solving time has a calming effect, while providing students opportunities to apply previously learned topics in a thinking, reasoning context.

Whenever time allows they engage students in the Read, Draw, Write process for ten to 15 percent of the lesson, helping them become expert drawers and thinkers. They do this through modeling but never procedural instructions. The word problem content varies, but it tends to be most valuable when it applies recently taught concepts, often from the previous day’s lesson.