Approach mathematical problem-solving according to George Polya's steps: understand the problem, devise a plan, execute the plan and reflect. Mathematical theorems are based on deductive reasoning. Encourage students to take time to think and try a solution. If that one doesn't work, they can tackle it again from another angle. They learn from their mistakes and become better at deductive reasoning. Computational skills are important, but they take on a supportive role to problem-solving.
Use visuals and manipulatives to aid in the development of deductive reasoning because students must engage several senses in the problem-solving process. Venn diagrams portray relationships between sets. If the reasoning is correct, a student can draw a Venn diagram satisfying the hypotheses and conclusion. Graphic organizers and thinking maps illustrate the process of deductive reasoning. Other visuals, such as attribute blocks, base 10 blocks and pattern blocks, are particularly useful in the lower grades.
Supplement a middle school curriculum with language-dependent and language independent deductive reasoning puzzles to help develop a student's problem-solving strategies and deductive reasoning skills. Regular use of logic puzzles, similar to those encountered in the Logical Thinking Inventory, and language-independent puzzles, such as Sudoku, Shikaku and Hashiwokakero, when combined with reflection and group discussion, require students to analyze problems and justify their reasoning.
Encourage participation in debate to improve critical thinking skills, including deductive reasoning. Students incorporate a wide base of knowledge and learn to apply the information creatively. They are forced to think on their feet as they challenge the reasoning of their opponents.
Divide your class into smaller groups to give students the opportunity to discuss their problem-solving ideas with one another. Giving voice to the reasoning process helps them detect flaws in their deductive reasoning, and listening to others gives the students opportunities to reason along with their classmates.