Mathematical Thinking Essay

Burton has identified four aspects of Mathematical Thinking which were described as specializing, generalizing, conjecturing and convincing (Burton, 1984) . Similarly, Schielack, Chancellor and Childs (2000) had mentioned several aspects of Mathematical Thinking e.g. symbolism, logical analysis, inference, optimization and abstraction (Schielack, Chancellor, & Childs, 2000). Likewise, Wren (2006) has emphasized observing and inferring, comparing, classifying and sequencing four aspects of Mathematical Thinking for elementary students. He further described characteristics of Mathematical Thinking as:
• The ability to set up clear cut premises and definitions
• The ability to reason coherently and critically and
• The ability to draw implied

(Shatnawi, 1982). Ma’Moon, Mohammad. Mubark tested the above six aspects in the students in the year 11 scientific stream in Jordan .Finally, six aspects of Mathematical Thinking were identified by the study: Generalization, Induction, Deduction, Use of Symbols, Logical thinking and Mathematical proof (Ma’Moon, 2005). In the study, Mathematical proof was the most difficult aspect, while Logical thinking was the least difficult. Using multiple regression analysis, all six aspects were found to be important for Mathematics Achievement. Mathematical proof and Generalization were the most important aspects, Use of symbols and Logical thinking were next in importance, and Deduction and Induction were the least important aspects. Approximately seventy per cent of the variance in Mathematics Achievement was explained by the six aspects of Mathematical Thinking, gender, and school

Identification of important aspects of Mathematical Thinking was one of the most objectives of that study. A model of Mathematical Thinking was developed with the help of experts’ opinion i.e. curriculum designer, mathematicians and teacher educator and then this model was presented to practicing teachers, and teacher educator for their opinions. There was a significant response in favor of mathematical model. Thus, final model which was included generalization, induction, deduction, problem solving, logical thinking and mathematical proofs. This result was important to develop model of Mathematical Thinking with relevant aspects of Mathematical Thinking and thus getting accurate relationship with Mathematics Achievement. Finally, six aspects of Mathematical Thinking were identified in this study i.e. deduction, generalization, induction, problem solving, logical thinking and geometrical proofs. Most of the teacher 80% of teachers agreed that these six aspects were the most important and relevant to the curriculum of textbook for mathematics. From the above discussion, we nearly reached at the aspects of Mathematical Thinking are Deduction, Induction, Logical Thinking, Generalization, Mathematical Proofs and Problem Solving. The literature related each aspects of Mathematical Thinking are presented