Why Do Students Struggle with Solving Problems?

Literacy Issues

Little Understanding of Mathematics Vocabulary: For some learners, the meaning of terms such as added, sum quotient, divisor, dividend, factor, numerator, denominator, and difference is unknown or confusing. For example, when sixth-grade students were asked to find the difference in a plant’s height during a month’s growth, they did not understand that they were to subtract the initial measurement from the final measurement. Students did report that the term for the answer to a subtraction problem is called the difference. But they did not connect the term to its application or authentic situations. Also, mathematical terms are easily confused or unknown; many students cannot, for example, distinguish the divisor from the dividend in terms of the quantities they represent.

Limited Ability to Read Problems: This difficulty is related to students’ reading levels. If the vocabulary is beyond students’ comprehension, the mathematics of the problem is compromised. Students’ abilities are also limited by difficulty with complex sentence structure and vocabulary.

Limited Verbal Ability to Explain Thinking:  Students who lack verbal skills have trouble expressing or explaining their thinking both aloud and on paper. This error pattern has serious implications for current testing practices in which students must explain their reasoning. Students may also be unable to discuss their thoughts and strategies in group work or with the teacher. Poor verbal skills often discourage students from attempting to take first steps to solve a problem.

Number Sense Issues

Difficulty Focusing on Important Information:  Some students are unable to understand what is being asked in the problem because shapes, numbers, and/or symbols distract them. These students can neither choose the most important information nor compose a plan of action because they do not understand what information is relevant or unnecessary for the solution.

Limited Ability to “Picture” the Situation:  For learners with this difficulty, the problem has no contextual meaning. For example, if students were asked to find the length of a shadow thrown by a ladder leaning on a wall, there might be little understanding of where that shadow could be located if they have limited experiences with ladders. If students have limited experiences with purchasing, they would have no idea what a discount means. Likewise, if students have never ordered a meal from a menu, they will struggle with determining totals and budgets.

Limited Self-Checking Ability:  Some students have little experience in deter-mining whether answers are reasonable. They often ask the teacher whether or not work is correct, or they might accept any answer just to finish a problem. For example, when students were asked how many buses, each with a capacity of 24 passengers, were needed to take 56 children on a field trip, some replied that two and a half buses would be logical. This response revealed a lack of number sense and an inability to picture reasonable situations.

Instructional Issues

Limited Personal Appeal: Most students must want to solve problems. Motivation is limited when learners feel there is little connection and relevance to their experiences. Students then often question the usefulness of mathematics in daily life situations or in their future. Time and energy for problem solving are diminished when students feel unconnected to mathematics.

Limited Time to Solve Problems:  When students feel rushed or do not take sufficient time to think through a problem, errors result. Students must be provided enough time to check their work to thoroughly evaluate each step of the problem-solving process.