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Figure 5: Gergonne point & Gergonne-Soddy-Incenter line Slightly adapted version of Plenary presented at the SOSI Geometry Imperfect Conference 2-4 October 1996, UNISA, Pretoria. The Gergonne point G of a triangle is the point of concurrency of the three line

Figure 5 Gergonne point & Gergonne-Soddy-Incenter line Slightly adapted version of Plenary presented at the SOSI Geometry Imperfect Conference 2-4 October 1996, UNISA, Pretoria. The Gergonne point G of a triangle is the point of concurrency of the three line

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(meet in the same point) (Figure 1b). connecting opposite vertices are concurrent circle, then the three lines (the diagonals) three points of intersection of the opposite If a hexagon is inscribed in a circle, then the Brianchon's theorem
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Slightly adapted version of Plenary presented at the SOSI Geometry Imperfect Conference, 2-4 October 1996, UNISA, Pretoria. Figure 3: Examples of fractals
Slightly adapted version of Plenary presented at the SOSI Geometry Imperfect Conference, 2-4 October 1996, UNISA, Pretoria. Figure 3: Examples of fractals
Figure 6: Van Aubel rectangle-generalisation In Figure 7, EG is always congruent to FH. Also KM is perpendicular to LN where
Figure 6: Van Aubel rectangle-generalisation In Figure 7, EG is always congruent to FH. Also KM is perpendicular to LN where
Slightly adapted version of Plenary presented at the SOSI Geometry Imperfect Conference 2-4 October 1996, UNISA, Pretoria. Just a brief perusal of some recent issues of mathematical journals like the
Slightly adapted version of Plenary presented at the SOSI Geometry Imperfect Conference 2-4 October 1996, UNISA, Pretoria. Just a brief perusal of some recent issues of mathematical journals like the
By using task-based interviews, Burger & Shaughnessy (1986) characterize
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For example, in a triangular tessellation pattern such as shown in Figure 8.
For example, in a triangular tessellation pattern such as shown in Figure 8.
and explanation that the opposite angles of a parallelogram are equal.
and explanation that the opposite angles of a parallelogram are equal.
ire conceptually important for analysing the geometric properties embedded in Process versus product teaching in geometry The distinction between "processes" and "products" in mathematics education is a Proposals of MASA regarding the South African Mathematics Project, stated:
ire conceptually important for analysing the geometric properties embedded in Process versus product teaching in geometry The distinction between "processes" and "products" in mathematics education is a Proposals of MASA regarding the South African Mathematics Project, stated:
process of proving also has its own product, namely a proof, which should b Jue to limitations of space, we shall here mainly focus on the handling of The distinction between some of the main processes and products of formal made. In addition, they're not even allowed to try their own hand at baking! Benchara Blandford wrote (quoted in Griffiths & Howson, 1974: 216-217): Traditional geometry education of this kind can be compared to a cooking
process of proving also has its own product, namely a proof, which should b Jue to limitations of space, we shall here mainly focus on the handling of The distinction between some of the main processes and products of formal made. In addition, they're not even allowed to try their own hand at baking! Benchara Blandford wrote (quoted in Griffiths & Howson, 1974: 216-217): Traditional geometry education of this kind can be compared to a cooking
Figure 12: Construction & measurement sychologically, constructions like these are extremely important for t ansition from Level 2 to Level 3. It helps to develop an understanding of t ifference between a premisse and conclusion and their causal relationship; ther words, of the logical structure of an "if-then" statement. Logically each 1e above statements can be rewritten in this form. For example, the Il. atement could be rewritten as: "If a quadrilateral has both pairs of oppos des parallel and one pair of adjacent sides equal, then it is a rhombus Cie. h 1 sides equal, perpendicular bisecting diagonals, etc)". Smith (1940) report arked improvement in pupils' understanding of "if-then" statements by letti p pup g y ee a a) a ee ee ee ee ee ee Psychologically, constructions like these are extremely important for the
Figure 12: Construction & measurement sychologically, constructions like these are extremely important for t ansition from Level 2 to Level 3. It helps to develop an understanding of t ifference between a premisse and conclusion and their causal relationship; ther words, of the logical structure of an "if-then" statement. Logically each 1e above statements can be rewritten in this form. For example, the Il. atement could be rewritten as: "If a quadrilateral has both pairs of oppos des parallel and one pair of adjacent sides equal, then it is a rhombus Cie. h 1 sides equal, perpendicular bisecting diagonals, etc)". Smith (1940) report arked improvement in pupils' understanding of "if-then" statements by letti p pup g y ee a a) a ee ee ee ee ee ee Psychologically, constructions like these are extremely important for the
also extremely valuable in constructing counter-examples for false conjectures. Figure 14: Pupil research in geometry However, the development of dynamic geometry has also necessitated a radical
also extremely valuable in constructing counter-examples for false conjectures. Figure 14: Pupil research in geometry However, the development of dynamic geometry has also necessitated a radical
Slightly adapted version of Plenary presented at the SOSI Geometry Imperfect Conference. 2-4 October 1996, UNISA, Pretoria. Formulation The line segments consecutively connecting the midpoints of the adjacent sides Deductive explanation A deductive analysis shows that the inscribed quadrilateral is always a rectangle,
Slightly adapted version of Plenary presented at the SOSI Geometry Imperfect Conference. 2-4 October 1996, UNISA, Pretoria. Formulation The line segments consecutively connecting the midpoints of the adjacent sides Deductive explanation A deductive analysis shows that the inscribed quadrilateral is always a rectangle,
Figure 17: Dynamic transformation of parallelogram into this particular area is needed. understand this even at Van Hiele Level 1 (Visualization), but further research The ability to quickly and efficiently transform geometric configurations with 17. In fact, it seems quite possible that pupils would be able to accept anc
Figure 17: Dynamic transformation of parallelogram into this particular area is needed. understand this even at Van Hiele Level 1 (Visualization), but further research The ability to quickly and efficiently transform geometric configurations with 17. In fact, it seems quite possible that pupils would be able to accept anc
Related topics:
Van Hiele Geometric Thinking LevelsDynamic Geometry SofwareProof and Proving in Mathematics EducationGeometryMathematical reasoning and proof
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