Task based worksheets - Describe/discuss/draw what you think geometry is?

Findings and Analysis

Question 6: Describe/discuss/draw what you think geometry is?

5.2.2 Task based worksheets

A grading system of 0 - incorrect, 1- partially correct and 2 - correct was used to mark the worksheets.

Table 23: Grading of respondents based on the Pythagorean Theorem worksheets

Identifying Pythagoras

Half circles Magic Triangle

the sides Puzzle

Question 7 4

s

1 5 6 5 5.1 5.2 5.3 5.4

Write your What can Remember Find the When you Write your The The The sums of Any other Why do you

answers in you the formula area of all add the two answers in numbers numbers the numbers combination think this is the diagram conclude for a circle! the half smaller half the figure written in written in written in of numbers called a

below. from the What circles. circles below the middle the the 4 written Pythagorean

activities in formula Show all together (central) correspondi corners of within the Tree?

steps 3 and would you necessary what do you boxes? ng boxes? each square? squares?

4 in terms of use for a working out. notice?

~ ^the ^small, half circle?

Q medium and

0u ^large

"'

square?

1 M27 2 2 2 0 2 2 2 2 2 2 0

2 M03 2 2 2 1 2 2 2 0 0 0 2

3 ^M23 ² ² ² ² 0 1 0 0 2 0 1

4 Ml9 2 2 2 2 2 2 2 2 2 2 2

5 ^Ml4 ² ² ² ² ² ² ² ² 0 2 1

6 ^MOl ² ² ⁰ ¹ ² ² ² ² ² ² ¹

7 M04 2 2 2 2 2 1 0 0 0 0 1

8 ^M07 ² ² ¹ ² ² ² ² ² ² ² ²

9 M26 2 2 2 2 2 2 0 2 0 0 2

10 ^Ml3 ² ² ² ² ² ² ² ² ² ² ²

Table 24: Average per question based on the Pythagorean Theorem worksheet

Identifying the

I

Pythagoras Puzzle

I

Half circles

I

Magic Triangle Average

sides

Question7 4

s

¹ ⁵ 6 5 5.1 5.2 5.3 5.4

Write your answers What can you Remember Find the When you Write The The The Any Why do you

in the diagram conclude from the the area of all add the your numbers numbers sums of other think this is

below. activities in steps 3 formula for the half two answers written written the combinat called a

and 4 in terms of a circle! circles. smaller in the in the in the numbers ion of Pythagorean the small, medium What Show all half circles figure middle correspo written numbers Tree?

and large square? formula necessary together below (central) nding in the 4 written

would you working what do boxes? boxes? corners within

use for a out. you of each the

half circle? notice? square? squares?

Incorrect 0% 0% 10% 10% 10% 0% 30% 30% 40% 40% 10%

Partially 0% 0% 10% 20% 0% 20% 0% 0% 0% 0% 40%

Correct 100% 100% 80% 70% 90% 80% 70% 70% 60% 60% 50%

---

Correct

per I ^100% I ^100% I ^80% I ^68% I ^50% I ^79.6%

worksheet

The worksheet based tasks were answered in alignment with the relevant DOEs that contained high user interaction and visual aspects, with the aim of achieving a better understanding of the geometric concept. The PS Ts achieved full marks for questions 4 and 5 (Table 24 ). They averaged 80% for the exploration of the Pythagorean Theorem via the Half circle worksheet, while the average for the Magic triangle worksheet was 68%. The Pythagorean Tree worksheet (50% average) relies heavily on visual representation as compared to the other worksheets, which require one to observe the size of the squares that are created as the tree grows. These worksheets stress the Pythagorean concept as it gives rise to other discoveries such as Pythagorean triplets and so forth. It was noted that the average percentages indicate an increase in difficulty from the first worksheet: Identifying the sides - 100% - to the last worksheet: Pythagorean Tree - 50% - as the arrangement of these worksheets required the participants to exercise their HOTs as they progressed. This indicates analytical progression in which one is required to develop, similar to the Low threshold-high ceiling approach expressed by Mark, Cuoco, Goldenberg and Sword's (2010) instructional design principle. Similarly, the CAPS (2011) for Senior FET phase (Grades 7-9) states that,

"geometry topics are much more inter-related than in the Intermediate Phase, especially those relating to constructions and geometry ... hence care has to be taken regarding sequencing of topics" (p.27).

Table 25: Grading of respondents based on the Circle geometry worksheet

Theorem7 A B

c

^D ^TOTAL ^%

If a line is drawn from the centre of If an arc subtends an angle at the If a quadrilateral is cyclic, then the The angle between a tangent to a a circle perpendicular to a chord, centre of a circle and at any point opposite angles are supplementary, circle and a chord drawn from the then it bisects the chord. on the circumference, then the (Opp. Ls of cyclic quad are supp.) point of contact is equal to an angle

~ (Perpendicular from centre to angle at the centre is twice the in the alternate segment. (tan.-chord 8 100%

0 ^chord) ^measure ôf ^the ângle ât ^the ^theorem)

u circumference.

""

1 M27 2 2 2 1 7 88

2 M03 2 1 2 1 6 75

3 ^M23 ² ¹ 0 2 5 63

4 ^Ml9 ² ² ² ¹ ⁷ 88

5 Ml4 1 0 2 2 5 63

6 MOl 2 2 2 2 8 100

7 M04 2 2 2 2 8 100

8 ^M07 ² ² ² ² 8 100

9 M26 2 2 2 2 8 100

10 Ml3 2 2 2 2 8 100

Fifty per cent of the PSTs (derived from Table 25) scored full marks for the selected theorems. This finding correlates to the 50% of the PSTs who possess geometry knowledge from school to university. The geometry gap bridged from school to university can be depicted from the lowest score achieved for the circle geometry theorems which was 63%.

Table 26: Percentages incorrect, partially correct and correct per question based on the circle geometry theorems

Theorem7 A B

c

^D ^Average

If a line is drawn from the centre of If an arc subtends an angle at the If a quadrilateral is cyclic, then the The angle between a tangent to a a circle perpendicular to a chord, centre of a circle and at any point opposite angles are supplementary, circle and a chord drawn from the then it bisects the chord. on the circumference, then the (Opp.Ls of cyclic quad are supp.) point of contact is equal to an angle (Perpendicular from centre to angle at the centre is twice the in the alternate segment. (tan.-chord

chord) measure of the angle at the theorem)

circumference.

Incorrect 0% 10% 10% 0% 5%

Partially 10% 20% 0% 30% 15%

Correct 90% 70% 90% 70% 80%

Table 26 shows that theorems labeled B and D were poorly answered, as the least number of PSTs got these theorems correct. However 90%

were correct in proving the theorems labeled A and C. The average of incorrect and partially correct answers was 20%; thus, the average knowledge of the selected geometry theorems was 80%.

The set of worksheets together with the use of technology required the PSTs to prove the selected theorems or concept. It would be expected that 100% knowledge should be displayed. Average knowledge of the Pythagorean Theorem that is taught in the GET is 79,6%, while that of the circle theorems taught in the FET phase is 80%. If one does not understand the very concept of the theorem, it becomes difficult to apply it (procedural) and make sense of the application (conceptual). In some cases, the person would be able to apply the theorem to mediocre questions but find great difficultly when posed with a non-routine question, because of the lack of understanding of the theorem.

Dalam dokumen Exploring pre-service teachers' views on the use of technology based teaching methods for teaching geometry. (Halaman 82-87)