The content of math education &
the evaluation of results in Japan:
Relationship between Assessment & Curriculum
GINSHIMA, Fumi
[email protected]
Curriculum Director &
Deputy Director of Dep. for Curriculum Research
National Institute for Educational Policy Research,
JAPAN
1
Table for Gr. 8 Items & scores (a part of)
in the National report
2
Average % Correct of the Same Gr. 4 Items
in 2007 and 2011: Japan
Speakers
Average % Correct of the Same Gr. 8 Items
in 2007 and 2011: Japan
Speakers
5
TIMSS Grade 8:
ACROSS CONTENT AREAS–2011
Country
Aver. Number Algebra
Geometry
Data/
Chance
U.S.
509
+5
+3
–24
+18
Australia
505
+8
–16
–6
+29
C Taipei
HK SAR
609
586
–11
+2
+19
–3
+16
+11
–25
–5
Japan
S. Korea
Malaysia
N.Z.
Singapore
Thailand
570
613
440
488
611
427
–13
+5
+11
+4
0
–2
0
+4
–10
–16
+3
–2
+16
–1
–8
–5
–2
–12
+9
+3
–11
+25
–4
+4
TIMSS Grade 8:
MATHEMATICS COGNITIVE DOMAIN–2011
Country
Aver.
Knowing
Applying
Reasoning
U.S.
509
+10
–6
–6
Australia
505
–1
+1
+1
C Taipei
HK SAR
609
586
+2
+5
+5
+1
0
–6
Indonesia
Japan
S. Korea
386
570
613
–8
–12
+3
–2
+4
+4
+2
+9
–1
Malaysia
N.Z.
440
488
+4
–7
–21
+3
–14
+6
Singapore
611
+6
+2
–7
Thailand
427
–4
+1
+2
Grade 8: Geometry; Reasoning
Highest score: 72% Japan
International Average: 19 %
C. Taipei 70%
Korea: 69%
Singapore: 55%
.....
Speakers
Grade 8: Geometry; Reasoning
Highest score: 86% Japan
International Average: 33%
Korea: 85%
Singapore: 80%
HK: 75%
.....
Grade 4:
Geometric Shapes and Measures; Reasoning
Highest score: 45% Northern Ireland
International Average: 15%
Japan: 32%
HK: 33%
Korea: 28%
.....
Speakers
Grade 8:
Numbers; Fractions/Decimals; Reasoning
Highest score: 53%
International Average: 23%
HK: 47%
Singapore: 45%
Korea: 44%
Japan: 43%
.....
Grade 8: Numbers; Applying
Highest score: 86%
International Average: 37%
Singapore: 83%
C. Taipei: 82%
HK: 77%
Japan: 65%
.....
Speakers
Responses
Country
A
B
C
D*
Korea
2.7%
6.9%
4.2%
86.0%
Singapore
Taipei
Hong Kong
4.8
2.9
4.0
5.5
7.7
8.7
6.5
7.0
10.0
83.1
82.0
77.0
Japan
Malaysia
Australia
15.4
18.6
30.2
11.1
23.0
23.0
8.2
11.5
5.4
65.3
45.9
33.8
Thailand
U.S.
New Zealand
24.2
32.5
27.3
31.2
26.1
27.8
12.6
10.7
16.0
29.5
29.1
26.2
Indonesia
31.4
38.4
7.8
21.3
• it is important that using assessment
viewpoints to review the tasks in the
textbook, those are for lessons or for
homework.
Task in Textbook
&
Item used in lesson
lesson
Assessment Item
assessment
15
• Instruction and assessment are related to
each other.
• Before the class, it is important that teachers
have the concrete image of the students who
get some ability through the lesson.
• And, it is also important that teachers have
the plan how to assess it in the class.
Assessment is not an end in itself
but just a means to an end.
So, we have to pay a lot of attention to
design the assessment.
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National Assessment in Japan
• subject : Japanese, Math (2007- ), Science (2012)
• date :
1st
2nd
3rd
4th
5th
6th
7th
8th
2007 April 24, Tuesday inventory survey
2008 April 22, Tuesday inventory survey
2009 April 21, Tuesday inventory survey
2010 April 20, Tuesday random sampling survey
2011 --- only distributing item booklets for each schools
2012 April 17, Tuesday random sampling survey
2013 April
random sampling survey
2014 April
inventory survey
• examinee :
2007-2009 : 6th grader ( 1.1 million ), 9th grader ( 1.1 million )
2010- :
6th grader ( 0.3 million ), 9th grader ( 0.3 million )
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Results of Assessment
The Ministry announced the overall prefectural and
national results about four months after the survey
in Japan.
A lot of information that were useful for instruction
has come from the results.
Every teacher could use those findings in each
Mathematics class.
It is important continuing discussion about how to
improve students’ ability based on the findings of
the assessment.
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effect of the assessment
• At first, many people concerned about the
harmful effect. For example,
- only the scores of each prefecture may get a lot
of attention,
- teachers may prepare a lot of exercises during
the class only for getting high score at the
assessment.
• However, many people and media discuss about
the results calmly now.
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background
• The government decided to conduct the National
Assessment after it discovered in 2003 that
children’s reading comprehension and writing
ability had deteriorated through the PISA
(Program for International Student Assessment
of the Organization for Economic Cooperation
and Development).
• We have to discuss about how to improve
students ability of thinking.
21
Overall objectives : Math for elementary school
Through mathematical activities concerning
numbers, quantities and geometrical figures,
children should get basic knowledge and skills,
should get abilities to think logically and to think
with good perspectives,
should notice the pleasure of doing activities and
appreciate the value of mathematical methods,
and should get attitude to make use of mathematics
in daily life situations.
22
Question Items
- Type “A” items measure the students’ basic
knowledge and skills.
→ Sample A1(7), 2007
Write the answer.
6＋0.5×2
- Type “B” items measure the students’ ability to
utilize knowledge and skills to solve problems in
everyday life. And, these also measure the students’
ability to develop plans for solving various problems,
to carry out these plans, to evaluate and improve the
plans.
A few items of type “B” were developed to measure
the students’ ability to explain their way of thinking.
→ Sample B5(3), 2009
23
Time table of the test (elementary school)
• Japanese A
• Mathematics A
20 min.
20 min.
• Japanese B
• Mathematics B
40 min.
40 min.
• Questionnaire
30min.
8:35 a.m.-
24
Results of
the
test 2007:
Correct answers (Math A)  Correct answers (Math B)
14
13
12
Math for 6th
grader
11
Correct answers (Math B)
Type A, 19 items
Type B, 14 items
Coefficient of correlation r=0.715
10
9
8
7
6
5
4
3
2
1
Question
0
1
2
3
4
5
6
7
8
9
10
11
12
13
Correct answers (Math A)
14
15
16
17
18
19
25
Math 2007
B 5 (3)
East Park is near Hiroshi’s house. Which of the East and Central Parks
is larger in area? Write the answer and the reason with words and
expressions.
Which is bigger,
East park or
Central park?
Hiroshi’s
house
Write the answer.
East
Park
How do you find
it ?
Write it down by
using sentences
and expressions.
18.2% of children
answered
correctly.
Central
Park
Shop
○ Roads a, b, and c are normal to Road i.
○ Roads a, b, and c are normal to Road j.
26
Math 2007 B 5 (3)
• 18.2% of children answered correctly, it is the
worst score in Math B test.
• 34.4% of children wrote the wrong expression
‘ 70×160 ’.
• 9.4% of children wrote the bigger park’s name
‘East Park’, and nothing about the way to find it.
• 2.0% of children wrote correct expressions and
mistook calculating.
• 3.5% of children wrote nothing.
27
features of the Math test Ⅱ
Ⅱ. Some of the type B Items ask children to
express their way of thinking by using
sentences and mathematical expression.
At this test,
our institute develop the criteria for
classification to mark the answer, and private
company mark each answer.
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The assessment enables teachers,
administrators and researchers who are
involved in education to get a lot of
important useful information.
It involves enormous cost to carry out the
nationwide assessment.
Therefore, it needs to make effective use
of results and items itself to improve
mathematics instruction.
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Thank you
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