Teachers who use the problem solving approach to mathematics should talk about the problems with the students, and encourage them to talk about the problems with each other. Provide children with the proper language to use when discussing mathematical concepts. Let students describe the problem in their own words, then give them the academic language. Make a word wall with words and phrases like simplify, equal to, less than and product. Model how you would solve a problem by explaining it out loud to the class. Have the students explain how they solved problems to you and to each other.
When using a problem-solving approach to mathematics, encourage students to share their answers with each other and explain how they arrived at their answer. By allowing students to explain their reasoning, other students can benefit from seeing how different strategies can be used to arrive at the same answer. Even wrong answers, provided with logical reasoning, can be used as a learning experience. Teachers can explain why what seemed like a logical approach may not have given a student the correct answer. Talking about how answers are found also allows students and teachers to see where mistakes were made, and to correct them.
Inquiry in the classroom is essential to good learning experiences. When students begin to ask questions, their interest and motivation is raised and they become more engaged in the learning process. Encourage students to ask questions about math lessons. Formulate key questions that will lead students to correct discoveries about the relationship between numbers or to lead them to a strategy for solving a problem. Children who ask questions are more likely to understand why the rules in math work, rather than just memorizing the rules and applying them when told.
During mathematics instruction, ask students to do more than just write out the problems. Let students work in groups and have them draw out the problem. They can act out word problems, or make a model of what is being described. Let students make pictures, use graph paper or color-code their work. Encourage them to make tables or graphs and look for patterns. Model these strategies during direct instruction often so that when students are working individually or in groups they have the strategies to use to solve their problems.