ERIC ED373955: Standard Grade Mathematics Achievements and Competences, Grade 3 to 6.

94 Pages·1993·2.6 MB·English

by  ERIC

DOCUMENT RESUME
SE 054 373
ED 373 955
Devine, Marion; And Others
AUTHOR
Standard Grade Matheiatics Achievements and
TITLE
Competences, Grade 3 to 6.
Scottish Council for Research in Education.
INSTITUTION
ISBN-0-947833-91-9; SCRE-RR-54
REPORT NO
93
PUB DATE
97p.
NOTE
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Elementary Education; Elementary School Mathematics;
DESCRIPTORS
*Elementary School Students; Foreign Countries;
Intermediate Grades; *Low Achievement; *Mathematics
Achievement; Mathematics Education; Mathdmatics
Tests
Scotland
IDENTIFIERS
ABSTRACT
The first Standard Grade'courses have been in place
in Scotland for almost ten years. This document reports on a study
with the following goals: (1) to describe the actual mathematical
competencies of pupils gaining grades 3, 4, 5, and 6 in Standard
in school
Grade Mathematics; (2) to describe the competencies shown
Grade
work by pupils failing to achieve at least grade 6 in Standard
Mathematics; and (3) to identify any changes that.might seem
desirable in grade-related criteria which might lead to improvements
in the teaching of basic competencies in mathematics. Examination
scripts and classroom work of (n=1,188) students in grades 3 to 7
discusses the findings in
were collected and analyzed. This report
.the following areas: number, measure, relationships, shape,
information handling, interpreting a task, doing a task, and
completing a task. Significant differences were found between grades
4 and 5 in examination performance. An appendix contains criteria
(MKR)
descriptors used in analysis of Standard Grade Mathematics.
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Reproductions supplied by EDRS are the best that can be made
*
from the original document.
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Standard Grade Mathematics
Achievements and Competences
Grade 3 to 6
Marion Devine
Harry Black
Donald Gray
gir
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Standard Grade Mathematics
Achievements and Competences
Grade 3 to 6
Marion Devine
Harry Black
Donald Gray
The Scottish Council for Research in Education
SCRE Research Report No 54
ISBN 0 947833 91 9
Copyright
1993-The Scottish Council for Research in Education
First published January 1994
Report arising from the project (reference TRIi/7/19) funded by the Scottish Office Education
Department between October 1991 and March 1993.
The views expressed are those. of the authors and are not necessarily those of the Scottish
Council for Research in Education or the Scottish Office Education Department.
Printed and bound by The Scottish Council for Research in Education, 15 St John Street,
Edinburgh EH8 8JR.
Acknowledgements
members of our
We are grateful for the assistance and insights provided by
essential
advisory committee during the lengthy period of analysis which was an
given to us by members of
part of this study. The guidance and encouragement
HMI and the Scottish Examination Board is also appreciated
of the
We would also like to express our gratitude to the administration section
the
Scottish Examination Board for its co-operation in collecting and organising
large number of examination scripts from both 1991 and 1992.
Special thanks are due to those teachers who allowed us into their classrooms to
with
gather information from both themselves and their pupils.The schools
which we worked most closely are listed below.
admirably with a
Thank you also to Kay Young our project secretary who coped
complex and difficult layout.
Mai ion Devine
Harry Black
Donald Gray
December 1993
Grampian Region
Banff Academy
Ayr Division
Garnock Academy
Renfrew Division
Gleniffer High School.
Central Region
Grangemouth High School
Lothian Region
Inveralmond Community School
Dumfries and Galloway Region
Stranraer Academy
Page
Tables
(v)
Figures
(vii)
1 Introduction
1
Aims of study
1
Method
1
The examination papers
2
Structure of report
4
2 Comparisons
6
Sources of assessment
6
3 Analysis of examination performance
9
Categories of mathematics
9
Presentation of the findings
9
Knowledge and Understanding (Number)
11
Knowledge and Understanding (Measure)
17
Knowledge and Understanding (Relationships)
22
Knowledge and Understanding (Shape)
27
Knowledge and Understanding (Information
Handling)
33
Reasoning and Applications (Interpreting
a task)
38
Reasoning and Applications (Doing
a task)
44
Reasoning and Applications (Completing
a task)
48
Mathematical competences at grade 3, 4, 5
and 6
52
Grade 3 Competences (Credit/General
Level)
52
Grade 4 Competences (General/Foundation
Level)
52
Grade 5 Competences (General/Foundation
Level)
53
Grade 6 Competences (General/Foundation
Level)
54
Significant differences between Grades
4 and 5
4 Classroom Work
56
Introduction
56
Selecting the sample
56
Page
The profile of competences
56
School characteristics
56
Collecting the data
60
Results of classroom study
61
Number
62
Measure
63
Relationships
64
-65
Shape
Information Handling
66
Interpreting a task
67
Doing a task
68
Completing a task
69
Low attainers in the classroom
70
5 Points for Discussion
72
Patterns of results
72
..ksS
Classroom concerns
72
Examination concerns
74
Changes to the grade related criteria
76
Different purposes of assessment
77
:>",
4:
References
78
Appendix 1
7
(v)
Page
Tables
Number of scripts analysed for each year
2
1.1
3
Final award by level of paper (1991)
1.2a
3
Final award by level of paper (1992)
1.2b
Number of individual criteria represented in 1991
4
1.3
and 1992 examination papers
se4
Estimated awards (1992) Actual awards (1992)
6
2.1
6
Differences between teacher and SEB grades for each element
2.2
Number of agreements and differences between teacher assessment
7
2.3
.ks
and examination attainment at the level of individual criteria
Agreements and differences between teacher'and researchers
7
2.4
Percentage of pupils successful in criteria available in one year only
11
3.1
Percentage of pupils successful in criteria available in one year only
13
3.2
Percentage of pupils successful at Credit Level competences in Measure
17
3.3
Percentage of pupils successful in criteria available in one year only
17
3.4
Percentage of pupils successful in criteria available in one year only
20
3.5
Percentage of pupils successful in criteria available in one year only
22
3.6
Percentage of pupils successful in criteria available in one year only
24
3.7
Percentage of pupils successful at Credit Level competences in Shape
27
3.8
Percentage of pupils successful in criteria available in one year only
27
3.9
Percentage of pupils successful in criteria available in one year only
28
3.10
Percentage of pupils successful in criteria available in one year only
30
3.11
Percentage of pupils successful in criteria available in one year only
3.12
32
Peftentage of pupils successful at General Level competences in
3.13
34
Informatioa Handling
Percentage of pupils successful in criteria available in one year only
34
3.14
Percentage of pupils successful in criteria available in one year only
3.15
36
Percentage of pupils successful in the criteria available in 1991'
3.16
38
Percentage of pupils successful in criteria available in one year only
40
3.17
Percentage of pupils successful at Credit Level in Doing a task
3.18
44
Percentage of pupils successful in criteria available in one year only
3.19
45
Percentage of pupils successful at Foundation Level competences
47
3.20
in Doing a task
Percentage of pupils successful in criteria available in one year only
3.21
417
*.;
Percentage of pupils successful at Credit Level in Completing a task
3.22
48
Percentage of pupils successful on criteria available in one year only
3.23
48
Percentage of pupils successful in criteria available in one year only
3.24
49
Percentage of pupils successful at Foundation Level competences in
3.25
51
Completing a task
Percentage of pupils successful in criteria available in one year only
3.26
51
Characteristics of schools
4.1
57
Estimated awards for selected pupils
4.2
61
(vi)
8
Page
Figures
Percentage of pupils successful at Credit Level competences
11
3.1
in Number
Percentage of pupils successful at General Level competences
13
3.2
in Number
Percentage of pupils successful at Foundation Level competences
15
3.3
in Number
Percentage of pupils successful at General Level competences
18
3.4
in Measure
Percentage of pupils successful at Foundation Level competences
20
3.5
in Measure
Percentage of pupils successful at Credit Level competences
22
3.6
in Relationships
Percentage of pupils successful at General Level competences
3.7
24
in Relationships
Percentage of pupils successful at Foundation Level competences
26
3.8
in Relationships
Percentage of pupils successful at General Level competences
3.9
28
in Shape
Percentage of pupils successful at Foundation Level competences
3.10
30
in Shape
Percentage of pupils successful at Credit Level competences
3.11
32
in Information Handling
Percentage of pupils successful at Foundation Level competences
3.12
36
in Information Handling
Percentage of pupils successful at Credit Level competences
3.13
38
in Interpreting a task
Percentage of pupils successful at General Level competences
3.14
40
in Interpreting a task
9
(iii)
Page
Percentage of pupils successful at Foundation Level competences
3.15
42
in Interpreting a task
4,4
Percentage of pupils successful at General Level competences
3.16
45
in Doing a task
Percentage of pupils successful at General Level competences
3.17
49
in Completing a task
Number of opportunities offered to the classes visited
4.1
58
Percentage of pupils successful in the classroom (Number)
4.2
62
Percentage of pupils successful in the classroom (Measure)
4.3
63
Percentage of pupils successful in the classroom (Relationships)
4.4
64
Percentage of pupils successful in the classroom (Shape)
4.5
Percentage of pupils successful in the classroom (Info Handling)
4.6
66
Percentage of pupils successful in the classroom (Interpreting a task)
4.7
67
Percentage of pupils successful in the classroom (Doing a task)
4.8
68
:0.Np
Percentage of pupils successful in the classroom (Completing a task)
4.9
69
?e.
10
(viii)