In teaching natural deduction in symbolic logic, I found it very effective to provide students with algorithms for constructing derivations/proofs. These algorithms involved a lot of reasoning backwards from conclusions (both final and intermediate) to be reached. In my own case, I was a poor student in grade 10 Euclidean geometry, until I figured out on my own an informal algorithmic approach to proving theorems.

Dear Wuttichai Phoodee

An instructional approach that effectively promotes students’ mathematical reasoning ability is one that emphasises exploratory, inquiry-based learning over rote memorisation. This involves engaging students in problem-solving tasks that require justification, explanation, and multiple solution pathways. Teachers adopting this approach encourage students to articulate their thinking, challenge assumptions, and build arguments using mathematical language. Tasks are often open-ended, allowing students to investigate patterns, formulate conjectures, and engage in meaningful mathematical discourse. This constructivist method helps students internalise concepts by linking new information to prior knowledge and real-world contexts.

Moreover, the integration of collaborative learning structures further supports the development of reasoning skills. When students work in pairs or groups on complex tasks, they are required to communicate their ideas, evaluate different viewpoints, and refine their reasoning through dialogue. Effective teachers act as facilitators, guiding students with probing questions rather than providing direct solutions. Formative assessment strategies, such as think-alouds, reflective journals, and diagnostic questioning, are employed to make students’ thinking visible and to inform responsive teaching. Such an approach nurtures a classroom culture where reasoning is valued over speed and correctness, fostering deeper understanding and long-term mathematical competence.

I hope this helps.