Proof is incorporated in the VCE Mathematics Study Design 2016-2018 and VCE Mathematics textbooks. Proof is integrated in many areas of study such as arithmetic and number, geometry measurement and trigonometry, algebra and structure, and discrete mathematics (Victorian Curriculum and Assessment Authority [VCAA], 2016). This supports the idea that one of the central goals of school mathematics, notably at the upper secondary level, is the development of proof concepts (Coe & Ruthven, 1994). The incorporation of algebraic proofs in Victorian Mathematics education also refutes the criticism that the focus on algebraic proofs theme is sporadic at the secondary school level (Pedemonte, 2008).
Many different methods of proof are stated in both …show more content…
According to Bell (1976), proof is the topic that shows the widest variation in approaches internationally. He also states that this variation can cause the tension between the awareness among teachers that deduction is essential to mathematics but that only most ablest students can have good understanding of it. In addition, proof is mostly shown in the Specialist Mathematics VCE textbooks Units 1 & 2 and Units 3 & 4 while just a few of it is shown in other textbooks such as Method Mathematics VCE Units 1 & 2 and Units 3 & 4 (Smiths et al, 2015; Evans et al, 2015). This textbook treatment of proof may influence on the teachers’ perspective of the use of proof in the classroom along the level of Mathematics. A study of Bergqvist (2005) shows that teachers underestimated the students’ level of reasoning. They believed that the high level of reasoning of proof are too hard for students to reach. Some teachers argued that only a few of students could use higher level of reasoning, they thus would not use it in teaching. Consequently, students may not develop deductive reasoning skills which demonstrates in the result of VCAA mathematics assessment documents where the incomplete responses of students to “show that” questions were …show more content…
The article of Hanna & Sidoli (2007) emphasizes that visual presentation of proof from technology such as dynamic software play an important role in proof, particularly in geometric problems. Visualisation through computer graphic can also directly show the way to a rigorous proof. In addition, dynamic geometry software helps students to focus their attention on the key aspects of the geometric relationship to be able to interpret relationships and to offer tentative explanations and proofs. Moreover, the use technology helps to generate cognitive conflicts, which motivates students to use deductive reasoning to prove the problems and to feel the necessity of proof (Lee & Chen, 2008). Furthermore, Heinze & Kwak (2002)’s paper shows that if students’ concepts of the geometrical objects are restricted, their ideas of these objects will be inconsistent with mathematic definitions. This results in a low capability of using logic implication which is one of the basic element of deductive reasoning (Heinze & Kwak, 2002). Hence, integration of technology in proof in the VCE Mathematics Study Design and the textbooks should be
Many different methods of proof are stated in both …show more content…
According to Bell (1976), proof is the topic that shows the widest variation in approaches internationally. He also states that this variation can cause the tension between the awareness among teachers that deduction is essential to mathematics but that only most ablest students can have good understanding of it. In addition, proof is mostly shown in the Specialist Mathematics VCE textbooks Units 1 & 2 and Units 3 & 4 while just a few of it is shown in other textbooks such as Method Mathematics VCE Units 1 & 2 and Units 3 & 4 (Smiths et al, 2015; Evans et al, 2015). This textbook treatment of proof may influence on the teachers’ perspective of the use of proof in the classroom along the level of Mathematics. A study of Bergqvist (2005) shows that teachers underestimated the students’ level of reasoning. They believed that the high level of reasoning of proof are too hard for students to reach. Some teachers argued that only a few of students could use higher level of reasoning, they thus would not use it in teaching. Consequently, students may not develop deductive reasoning skills which demonstrates in the result of VCAA mathematics assessment documents where the incomplete responses of students to “show that” questions were …show more content…
The article of Hanna & Sidoli (2007) emphasizes that visual presentation of proof from technology such as dynamic software play an important role in proof, particularly in geometric problems. Visualisation through computer graphic can also directly show the way to a rigorous proof. In addition, dynamic geometry software helps students to focus their attention on the key aspects of the geometric relationship to be able to interpret relationships and to offer tentative explanations and proofs. Moreover, the use technology helps to generate cognitive conflicts, which motivates students to use deductive reasoning to prove the problems and to feel the necessity of proof (Lee & Chen, 2008). Furthermore, Heinze & Kwak (2002)’s paper shows that if students’ concepts of the geometrical objects are restricted, their ideas of these objects will be inconsistent with mathematic definitions. This results in a low capability of using logic implication which is one of the basic element of deductive reasoning (Heinze & Kwak, 2002). Hence, integration of technology in proof in the VCE Mathematics Study Design and the textbooks should be