The Importance Of Mathematical Thinking

Mathematical thinking is a broad term containing many perspectives and meanings. Each researcher dealing with mathematics education has his or her own perspective on this topic. Most researchers, mathematicians and mathematics educators define mathematical thinking as a process, which contains at least one of the mental and math-related activities such as reasoning, abstracting, conjecturing, representing, and switching between different representations, visualizing, deducing, inducing, analysing, synthesizing, connecting, generalizing and proving (Carroll, 1996; Harel, Selden, & Selden, 2006; Mason, Burton & Stacey, 1982; Romberg & Kaput, 1999; Schoenfeld, 1992; Tall, 1991).

There is a world-wide desire to improve the teaching of mathematics,

That does not mean that teachers should not be asking questions at the lower end of Bloom’s Taxonomy of cognitive rigor. In fact, it is important that a teacher begins a lesson with the questions at the Recall and Understand levels of Bloom’s Taxonomy. However, in order to solve meaningful problems, students must be challenged with higher-level questions that follow the lower-level questions. Students will find difficulty applying their mathematical ideas or analysing a mathematical situation if they are not asked higher-level questions in classroom activities and

Teachers should not neglect their mathematics instruction and their way of delivering it - mathematic instruction is essential in encouraging mathematical thinking. They should differentiate instruction through flexible grouping, invidualizing lessons, compacting, using assignments, and varying question levels. In order to put this into practice, they should:

• Ensure that instructional activities are learner-centred and emphasizes inquiry/ problem-solving

• Use experience and prior knowledge as a basis for building new knowledge

• Use scaffolding to make connections to concepts, procedures and understanding

• Ask probing questions which require students to justify their responses

• Emphasize the development of computational skills

There are however two types of mathematical instructions, namely the skill-based instruction and the concept-based instruction. In skill-based instruction, teachers focus exclusively on developing computational skills and a quick recall of facts. However, in concept-based instruction, teachers encourage students to solve a problem in a way that is meaningful to them and to explain how they solved the problem, resulting in an increased awareness that there is more than one way to solve most problems. Researchers agree that both approaches are important – that teachers should