View
220
Download
0
Category
Preview:
Citation preview
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 1/55
INSTITUT PENDIDIKAN GURU
KAMPUS GAYA Peti Surat 10491, 88805 Kota Kinabalu, SabahTel: 088-210646 Faks: 088-217124
TESTING AND EVALUATIONIN
MATHEMATICS
NAME : ARNA BINTI JUNAIDE
IC NUMBER : 851207-12-5130
GROUP : KPLI MATH (NOVEMBER 2009)
CODE AND SUBJECT : MATEMATIK
LECTURER’S NAME : EN BUSTAM BIN DAMAN
DATE :15 APRIL 2011
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 2/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 3/55
7. ANALYSIS AND INTERPRETATION OF ITEM/QUESTION
21
7.1 Difficulty Index (D.I)
21
7.2 Discrimination Index (D.s.I)
23
7.3 Calculation to find Difficulty Index and Discrimination Index
25
7.4 Difficulty Index Analysis
7.5 Conclusion for the items Difficulty Index Analysis
29
7.6 Discrimination Index (D.s.I) Analysis
30
7.7 30% a high-score group and 30% of low-score group
32
7.8 Conclusion for the items Discrimination Index Analysis
32
8. ANALYSIS AND INTERPRETATION OF TEST RESULT
33
8.1 Mean 33
8.2 Median
34
8.3 Mode 35
9. CONCLUSION
36
1.0 INTRODUCTION
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 4/55
Teaching and learning process is a very effective educational system
to see the student’s achievements. It is also known as an activity to help
student to achieve the learning outcome that have been set earlier.
1.1 TEACHING OBJECTIVES
Teaching objective is a process that changing students’ behaviour and
it can be achieved by teachers in one learning process. This changing can be
achieved through teaching and learning activities that are well planned. All
the changes or progress from the student must be assessed from time to
time.
Continuous assessment will determine the effectiveness of teaching
and learning. The students’ progress or change also has to be evaluated and
record time to time. This clearly shows the existence of the relationship
between the objective of teaching, testing, measurement and evaluation.
1.2 MEANING OF TEST
Test is a systematic way to measure changes in an individual’s
behaviour. Referring this to a class, a test is conducted to measure changes
in behaviour related to pupil’s learning activities. It is, in general, a
measuring instrument to obtain information regarding pupil’s achievement inthe cognitive, psychomotor or affective fields.
Test is an important part in learning and teaching process. It is also
one of the techniques to obtain the process of the pupils changing. To
implement the evaluation, teacher must plan and construct a test first. There
have same criteria in construct a question for a test. To legislate a question
paper, it have to follow the specification that have been set which is the test
must be well manage include the whole of the syllabus. This is to ensure all
student have been test using the relevant question from the syllabus and
also from the teaching objectives.
Test also help teacher to find out whether the pupils have successfully
mastered certain skill, and acquired the knowledge which have been learned
before. The test that use to determine the level of achievement of students
is implement by using a paper test. It is divide into two category which is;
1. Objective test
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 5/55
2. Subjective test
1.3 MEANING OF MEASUREMENT
Measurement is a process or system used to determine the
quantitative value of a certain test in learning. This quantitative value isusually expressed in a fixed unit of number, in terms of percentage or grade,
by using a related measuring instrument.
1.4 MEANING OF EVALUATION
Evaluation is defined as a process to determine, obtain and provide
useful information so as to make objective consideration for follow-up action.
In the context of education, evaluation is a system or a process which covers
activities to collect information relating to strategy of teaching-learningactivity and to make analysis and interpretation of result, with the aim to
take appropriate follow-up action such as replanning for more effective
teaching-learning activity thereafter.
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 6/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 7/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 8/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 9/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 10/55
Objective : converting a number in a certain base to a number
in
another base.
Level of Difficulty : Hard
Item no 8 : Express 12435 as a number in base eight.
A. 3068
B. 3608
C. 6038
D. 6308 (Level: Understanding)
9. Item number : 9
Topic : Number Bases
Subtopic : 1.1 Number bases in Two,Eight and Five
Objective : Addition of two binary numbers
Level of Difficulty : Easy
Item no 9: 1011012 + 111012 =
A. 10010102
B. 10110102
C. 10111102
D. 11110002 (Level: Understanding)
10.Item number : 10
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 11/55
Topic : Number Bases
Subtopic : 1.1 Number bases in Two, Eight and Five
Objective : Subtraction of two binary numbers
Level of Difficulty : Easy
Item no 10: 1010102 – 1112 =
A. 100112
B. 1000112
C. 1010012
D. 1011012 (Level:
Knowledge)
11.Item number : 11
Topic : Graphs of Functions II
Subtopic : 2.1 Graph of function
Objective : Drawing the graphs of functions
Level of Difficulty : Easy
Item no 11: Which of the following graphs represents y = 4-X2?
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 12/55
(Level: Understanding)
12.Item number : 12
Topic : Graphs of Functions II
Subtopic : 2.1 Graph of function
Objective : Finding the value of y or x from the graph
Level of Difficulty : Easy
Item no 12: Which graph represents y = -1/2 X – 1?
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 13/55
(Level: Understanding)
13.Item number : 13
Topic : Graphs of Functions II
Subtopic : 2.2 solving the equation graphically
Objective : Finding the value of y or x by using the equation
graphically.
Level of Difficulty : Medium
Item no 13: which graph represent y=X2 – X – 6?
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 14/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 15/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 16/55
B. 4 D. 16 (Level:
Synthesis)
16.Item number : 16
Topic : Graphs of Functions II
Subtopic : 2.1 Graph of Functions
Objective : Sketching the graph of a linear function
Level of Difficulty : Medium
Item no 16: The diagram shows a Cartesian plane.
Which of the straight lines, A, B, C or D, represents the graph of y = -2x -5?
(Level: Understanding)
17.Item number : 17
Topic : Graphs of Functions II
Subtopic : 2.1 Graph of Functions
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 17/55
Objective : Sketching the graph of a linear function
Level of Difficulty : Easy
Item no 17: The following points satisfy the equation y = 3X – 1 except
A. (-2, -7)
B. (0, -1)
C. (1, -2)
D. (2, 5)
(Level: Understanding)
18.Item number : 18
Topic : Graphs of Functions II
Subtopic : 2.3 Region representing inequalities in two
variables
Objective : Identifying the shaded region in the graph
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 18/55
Level of Difficulty : Easy
Item no 18:
The inequality represented by the shaded region in the graph is
A. y< -2x + 2
B. y> -2x + 2
C. y ≤ -2x + 2
D. y ≥ -2x + 2 (Level:
Knowledge)
19.Item number : 19
Topic : Graphs of Functions II
Subtopic : 2.3 Region representing inequalities in two
variables
Objective : Identifying the shaded region in the graph
Level of Difficulty : Medium
Item no 19: The diagram shows a Cartesian plane.
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 19/55
Which of the regions, A, B, C or D, satisfies the inequalities x + y ≤ 4 and y ≥
x?
(Level: Understanding)
20.Item number : 20
Topic : Graphs of Functions II
Subtopic : 2.3 Region representing inequalities in two
variables
Objective : Shading the region representing the given
inequalities
Level of Difficulty : Hard
Item no 20:
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 20/55
Which of the following sets of inequalities define the shaded region in the
diagram?
A. 4x + 3y ≥ 12, x – y ≤2, y < 3
B. 4x + 3y ≤ 12, x – y ≥2, y < 3
C. 4x + 3y ≥ 12, x – y ≥2, y ≤ 3
D. 4x + 3y ≥ 12, x – y >2, y ≤ 3
(Level:
Application)
21.Item number : 21
Topic : Transformations III
Subtopic : 3.1 Combination of Two Transformations
Objective : Identifying the centre of the rotation.
Level of Difficulty : Medium
Item no 21: The diagram shows two right-angled triangles, P and Q, drawn
on a grid of
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 21/55
squares.
Q is the image of P under an anticlockwise rotation of 90. Which of the pointsA,B,C or D, is the centre of rotation?
(Level: Understanding)
22.Item number : 22
Topic : Transformations III
Subtopic : 3.1 Combination of Two Transformations
Objective : Combination of Two isometric transformations
Level of Difficulty : Medium
Item no 22: The diagram shows two trapeziums, P and Q, drawn on a grid of
squares.
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 22/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 23/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 24/55
25.Item number : 25
Topic : Transformations III
Subtopic : 3.1 Combination of Two Transformations
Objective : Combination of Two isometric transformations
Level of Difficulty : Hard
Item no 25: The diagram shows a quadrilateral PQRS drawn on a grid of
squares.
Given W is a reflection in the line x= 1 and T is a translation ( ). Find the
coordinates of the image of point Q under the combined transformation TW.
A. (-2, 5)
B. (1,5)
C. (5,-2)
D. (5, 1) (Level: Application)
26.Item number : 26
Topic : Transformations III
Subtopic : 3.1 Combination of Two Transformations
Objective : Combination of Two isometric transformations
Level of Difficulty : Medium
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 25/55
Item no 27: Given V is a reflection in the line x=2 and U is a translation ( ).
Find the coordinates of the image of point (-2, 4) under the combined
transformation UV.
A. (-1, 4)
B. (-1, 9)
C. (4,-1)
D. (9,-1) (Level: Understanding)
27.Item number : 27
Topic : Transformations III
Subtopic : 3.1 Combination of Two Transformations
Objective : understanding the single transformation reflection
Level of Difficulty : Easy
Item no 28: The diagram shows five quadrilaterals drawn on a grid of squares.
Which of the quadrilaterals, A,B,C or D, is not the image of quadrilateral W
under a reflection? (Level: Analysis)
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 26/55
28.Item number : 28
Topic : Transformations III
Subtopic : 3.1 Combination of Two Transformations
Objective : Understanding the transformation of enlargement
Level of Difficulty : Medium
Item no 27: The diagram shows five quadrilaterals drawn on a grid of
squares.
Which of the quadrilaterals, A,B,C or D, is the image of quadrilateral P under
an enlargement?
(Level: Analysis)
29.Item number : 29
Topic : Transformations III
Subtopic : 3.1 Combination of Two Transformations
Objective : Understanding the transformation of enlargement
Level of Difficulty : Easy
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 27/55
Item no 29: The diagram shows five triangles drawn on a grid of squares.
Which of the triangles, A,B,C or D, is the image of triangle P under anenlargement with a scale factor of 2?
(Level: Analysis)
30.Item number : 30
Topic : Transformations III
Subtopic : 3.1 Combination of Two Transformations
Objective : Combination of Two isometric transformations
Level of Difficulty : Hard
Item no 30: In the diagram, trapezium PTUV is the image of trapezium PQRS
under a rotation followed y an enlargement.
Given that the area of trapezium PQRS is 13.5 cm2, find the area, in cm2, of
the shaded region.
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 28/55
A. 40.5 C. 108
B. 81 D. 121.5
(Level: Analysis)
5.0 SCHEMA / ANSWER DISTRIBUTION
ANSWERS DISTRIBUTION
NO OF
QUESTION
A B C D
1 /
2 /
3 /
4 /
5 /
6 /
7 /
8 /
9 /
10 /
11 /
12 /
13 /
14 /
15 /
16 /
17 /
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 29/55
18 /
19 /
20 /
21 /
22 /
23 /
24 /
25 /
26 /
27 /28 /
29 /
30 /
TOTAL 7 8 9 6
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 30/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 31/55
Using these formulae, we can obtain the value of the difficulty Index for a particularitem/question for interpretation and make decision, as illustrated in the following
table;
Difficulty Index
(D.I.)
Interpretation of an
item/question
Decision
0.00 – 0.20 Too difficult Modify
0.21 - 0.40 Difficult Accept
0.41 - 0.60 Average Accept
0.61 - 0.80 Easy Accept
0.81 – 1.00 Too easy Modify
0.00 0.50 1.00
Difficult item Medium Easy
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 32/55
7.2 Discrimination Index
Discrimination Index possesses the power or function to differentiate candidates
between high-score group and low-score group. This index can be calculated by
using the following formulae:
Discrimination Index ( Ds.I.) =
CH = Total number of candidates in the high-score group who answer correctly the
item/question.
CL = Total number of candidates in the low-score group who answer correctly the
item/question
T H+L= Total number of candidates in both groups with high and low score.
The value of Discrimination Index can be utilized to determine whether a certain
item /question is suitable and can be used for a test. Table below illustrates a
general method which is normally used to interpret the suitability of certain
item/question from the calculated value of Discrimination Index.
Discrimination Index
(Ds. I.)
Interpretation of an
item/question
Decision
Ds. I. > 0.40 Positive Discrimination
High
Very suitable and can be
accepted
0.20 < Ds.I. ≤0.40 Positive discrimination
Moderate
Modify the item /
question
0 ≤Ds.I . ≤ 0.20 Positive Discrimination
Low
Item/ question needs to
be reconstructed.
D.I. < 0 Negative Discrimination:
Performance of low-score
group is better than high-
score group.
Item/question is bad and
shoul be removed.
CH – CL
½ T H+L
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 33/55
Interpretation of an item/question based on Discrimination Index
According to research, a good item/question which can be used for a test, usually
has values of difficulty index between 0.40 and 0.60, and discrimination index
of values more than 0.40.
In order to measure the values of difficulty index and discrimination index, we
need to arrange the candidates from the highest score to the lowest score, and
record their performance in every item/question which they answer by marking (/)
as correct and (X) as wrong in a specification table such as table. To determine the
number of candidates in the high-score group CH and the number of candidates in
the low-score candidates (CL), we normally allot about 30% of total candidates as
the high-score group , and about 30% as the low-score group. For example, there
are 19 candidates selected to sit for the test, we calculate the number of candidates
to be included in the high-score group and low-score group respectively as follows;
Number of candidates in the high-score group = 30% x 19 ₌ 5
Number of candidates in the low-score group = 30% x 19 = 5
Table shows arrangement and the values of difficulty index and discrimination
index from 19 candidates who answer 30 items in a form 5 Mathematics objective
test.
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 34/55
7.3 Calculation to find Difficulty Index (D.I) and Discrimination Index
( D.S.I)
ITEM DIFFICULTY INDEX (D.I) DISCRIMINATION INDEX
(D.s.I)
FORMULA
E
Difficulty Index, D.I.=
Numbers of candidates who answer correctly(C)
Total candidates who attempt the
item/question (T)
Discrimination Index, D.s.I=
CH – CL
½ T H+L
1
Total correct answer ( C ) =16
Total No of candidates (T )=19
D.I = 0.84
Total no of answers correct
in high-score group (CH) = 5
Total no of answer correct
In low-score group (CL) =3
Total no of candidates in
both group T H+L = 10
D.s.I= 0.4
2
C= 15
T=19
D.I=0.79
CH=5
CL=4
T H+L=10
D.s.I =0.2
3 CH=5
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 35/55
C=18
T=19
D.I=0.95
CL=5
T H+L=10
D.s.I =0
4 C=9
T=19
D.I=0.47
CH=2
CL=2
T H+L=10
D.s.I =0
5 C=13
T=19
D.I=0.68
CH=2
CL=4
T H+L=10
D.s.I =-0.4
6
C=14
T=19
D.I=0.74
CH=4
CL=2
T H+L=10
D.s.I =0.4
7
C=16
T=19
D.I=0.84
CH=4
CL=3
T H+L=10
D.s.I =0.2
8 C=10
T=19
D.I=0.53
CH=5
CL=5
T H+L=10
D.s.I =1
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 36/55
9 C=18
T=19
D.I=0.94
CH=5
CL=4
T H+L=10
D.s.I =0.2
10 C=14
T=19
D.I=0.74
CH=4
CL=4
T H+L=10
D.s.I =0
11 C=13
T=19
D.I=0.68
CH=5
CL=1
T H+L=10
D.s.I =0.8
12 C=10
T=19
D.I=0.53
CH=4
CL=3
T H+L=10
D.s.I =0.2
13 C=7
T=19
D.I=0.37
CH=4
CL=1
T H+L=10
D.s.I =0.6
14 C=6 CH=4
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 37/55
T=19
D.I=0.32 CL=0
T H+L=10
D.s.I =0.4
15 C=9
T=19
D.I=0.47
CH=4
CL=1
T H+L=10
D.s.I =0.6
16 C=8
T=19
D.I=0.42
CH=2
CL=2
T H+L=10
D.s.I =0
17 C=4
T=19
D.I=0.2
CH=3
CL=1
T H+L=10
D.s.I =0.4
18 C=11
T=19
D.I=0.58
CH=4
CL=2
T H+L=10
D.s.I =0.4
19 C=5
T=19
D.I=0.26
CH=3
CL=0
T H+L=10
D.s.I =0.6
20 C=3 CH=3
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 38/55
T=19
D.I=0.16 CL=0
T H+L=10
D.s.I =0.6
21 C=9
T=19
D.I=0.47
CH=4
CL=1
T H+L=10
D.s.I =0.6
22 C=12
T=19
D.I=0.63
CH=4
CL=1
T H+L=10
D.s.I =0.6
23 C=7
T=19
D.I=0.37
CH=4
CL=0
T H+L=10
D.s.I =0.8
24 C=8
T=19
D.I=0.42
CH=4
CL=1
T H+L=10
D.s.I =0.6
25 C=9
T=19
D.I=0.47
CH=5
CL=4
T H+L=10
D.s.I =0.8
26 C=6 CH=3
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 39/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 40/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 41/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 42/55
7.6 Conclusion for the Items Difficulty Index (D.I) Analysis
ITEM DIFFICULTY INDEX (D.I) Remarks
1
3
7
9
0.84
0.95
0.84
0.94
-Almost all student can easily
answer the question correctly.
Based on the result
interpretation of the items, this
question need to modify
because the level are too easy.
14
17
19
0.32
0.21
0.26
- The percent that student were
able to answer the question aretoo low. This item are in
difficult category but are still
accept to test because in
making an item/question for
JPU, there are provide 25% or 9
question for difficult
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 43/55
item/question.
For the item that are in easy, medium and difficult category, it will be
save and store in a question bank so that it can be use anytime when it
needed.
7.7 Discrimination Index (D.s.I ) Analysis
ITEM
S
TOTAL
OF
CORRE
CT
ANSWER
(CH)
TOTAL OF
CORRECT
ANSWER
(CL)
CH – CL
½ T H+L
INTERPRETATION
OF AN
ITEM/QUESTION
DECISION
1 5 3 0.4 Positive
discrimination
Moderate
Modify the
item
2 5 4 0.2 Positive
discrimination low
Item needs
to be
reconstructe
d
3 5 5 0 Positive
discrimination low
Item needs
to be
reconstructe
d
4 2 2 0 Positive Item needs
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 44/55
discrimination low to be
reconstructe
d
5 2 4 -0.4 Negative
discrimination
Item is bad
and should
be removed
6 4 2 0.4 Positive
discrimination
Moderate
Modify the
item
7 2 3 0.2 Positive
discrimination low
Item needs
to be
reconstructe
d
8 5 0 0.1 Positivediscrimination low
Item needsto be
reconstructe
d
9 5 4 0.2 Positive
discrimination low
Item needs
to be
reconstructe
d
10 4 4 0 Positive
discrimination low
Item needs
to bereconstructe
d
11 5 1 0.8 Positive
discrimination high
Very suitable
and can be
accepted
12 4 3 0.2 Positive
discrimination low
Item needs
to be
reconstructe
d
13 4 1 0.6 Positive
discrimination high
Very suitable
and can be
accepted
14 4 0 0.4 Positive
discrimination high
Very suitable
and can be
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 45/55
accepted
15 4 1 0.6 Positive
discrimination high
Very suitable
and can be
accepted
16 2 2 0 Positive
discrimination low
Item needs
to bereconstructe
d
17 3 1 0.4 Positive
discrimination high
Very suitable
and can be
accepted
18 4 2 0.4 Positive
discrimination high
Very suitable
and can be
accepted
19 3 0 0.6 Positivediscrimination high
Very suitableand can be
accepted
20 3 0 0.6 Positive
discrimination high
Very suitable
and can be
accepted
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 46/55
21 4 1 0.6 Positive
discrimination high
Very suitable
and can be
accepted
22 4 1 0.6 Positive
discrimination high
Very suitable
and can be
accepted
23 4 0 0.8 Positive
discrimination high
Very suitable
and can be
accepted
24 4 1 0.6 Positive
discrimination high
Very suitable
and can be
accepted
25 5 1 0.8 Positive
discrimination high
Very suitable
and can beaccepted
26 3 0 0.6 Positive
discrimination high
Very suitable
and can be
accepted
27 5 2 0.6 Positive
discrimination high
Very suitable
and can be
accepted
28 4 1 0.6 Positive
discrimination high
Very suitable
and can be
accepted
29 4 2 0.4 Positive
discrimination high
Very suitable
and can be
accepted
30 2 2 0 Positive
discrimination low
Item needs
to be
reconstructe
d
The table above shows the Discrimination Index for each of the item.
Based on the table above, the discrimination Index of the item almost
accepted by the student except one item which is item number 5 that should
be removed in the question.
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 47/55
6.9 Conclusion for the Items Discrimination Index (D.s.I)Analysis
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 48/55
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 49/55
8.0 ANALYSIS AND INTERPRETATION OF TEST RESULT.
Analysis and interpretation of test or examination result is considered an
important stage in assessment. This stage is normally done by teachers after the
examination, when the test paper of each student was marked and recorded. The
aim of making analysis and interpretation of the students’ result is to obtain the
feedback of the actual performance of the students and to overcome the
weaknesses identified.
The measurement of basic statistics normally used for norm-referencedevaluation is frequency polygon, mean, median, and mode. The results obtained
from the basic statistics will enable teachers to make correct interpretation on the
students’ performance and prepare report for future reference.
8.1 MEAN
SCORE (X) FREQUENCY (f) f X x fx
6 1
1 x 6 6
9 1
1 x 9
9
12 2
2 x 12
32
13 1
1 x 13
13
14 1
1 x 14
14
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 50/55
15 2
2 x 15
30
16 2
2 x 16
32
17 3
3 x 17
51
18 1
1 x 18
18
20 1
1 x 20
20
22 2
2 x 22
44
23 1
1 x 23
23
27 1
1 x 27
27
N = ∑f = 19
∑fx = 319
Frequency distributions of ungroup scores of mathematics test for form 5
ibnu sina
Mean, X = ∑fx = 319 = 16.79
∑f 19
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 51/55
8.2 MEDIAN
Median for grouped or ungrouped data is the value in the middle of an array
of set of data. It is a value that divided the bottom 50% of a group of data
arranged in ascending order, from the top 50% of the data.
If the scores are expresses as single-valued cumulative distributions, then the
formula to find the median is:
Median, M = ( N + 1 ) th score, N = ∑f = Total frequency
2
SCORE X FREQUENCY (f) CUMULATIVE
FREQUENCY
(cf)
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 52/55
6 1 1
9 1 2
12 2 4
13 1 5
14 1 6
15 2 8
16 2 10
17 3 13
18 1 14
20 1 15
22 2 17
23 1 18
27 1 19
N = 19
Median = 19 + 1 = 10 th score
2
:- the median lies the scores of 16
8.3 MODE
In statistics, the mode of a set of numbers, or in a frequency distributions is
the value which has the greatest frequency, i.e.the value which occurs the most
often.
SCORE X FREQUENCY (f)
6 1
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 53/55
9 1
12 2
13 1
14 1
15 2
16 2
17 3
18 1
20 1
22 2
23 1
27 1
The mode is 17, because it occurs as the most number of scores.
A distribution having only one mode and it is called unimodal .
9.0 CONCLUSION
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 54/55
Testing and evaluation need a few more systematic processes from the
beginning to the end of the process. The existences of systematic steps can
easily forming a set of quality tests. This is due to give a test as a part of
the process of teaching and learning. When implement the tests, teachers
must identify the question whether it meet to the objective of teaching and
learning.
When viewed the result of the difficulty index and discrimination index
for the item that have been constructed in this working paper which have
provided this course, the items are well supervised ad appropriately use by
students for testing purposes. This is because, both of the index did not
shows any difficulties and differentiation that will go too far.
So that, every teacher must have sufficient knowledge in the field of
test construction for students to master the skills they have learned before
to be more effectively and the items/question that were appropriately and
challenging for students ability to grow their brain power.
7/27/2019 Testing and Evaluation in Mathematics
http://slidepdf.com/reader/full/testing-and-evaluation-in-mathematics 55/55
Recommended