High achiever! Always a high achiever?

158 Pages·2014·3.43 MB·English

by  Elisabet Mellroth

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High achiever! Always a high achiever? er
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High achiever!
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This thesis describes a study based on teacher observations of students who s

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achieve highly on the international competition ‘the mathematical kangaroo’ h
i Always a high achiever?
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although they do not in the national test. The aim with the study was to investigate h

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students’ relative achievement in mathematics over time and how mathematical c
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competencies can be used to explore differences between groups of students on ev
e A comparison of student achievements on mathematical tests
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a non-curriculum based test in mathematics. The study was divided in two parts. ?

with different aims and goals
Study 1 compared students’ (n=568) relative achievement in two national tests |

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in mathematics (years 3 and 6), changes in relative achievement between the 0
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two tests as well as differences in relative achievement between the national test :
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in year 6 and the mathematical kangaroo in year 7 (age 13) were explored. The
study identified two groups of students with high achievements, in only one of
Elisabet Mellroth
the tests, from a sample (n=264) of study 1. Study 2 explored how differences
between those students’ relative achievement on the mathematical kangaroo
could be explained through activation of mathematical competencies.
ISBN 978-91-7063-607-3 Faculty of Health, Science and Technology
ISSN 1403-8099 Mathematics
LICENTIATE THESIS | Karlstad University Studies | 2014:67 LICENTIATE THESIS | Karlstad University Studies | 2014:67
High achiever!
Always a high achiever?
A comparison of student achievements on mathematical tests
with different aims and goals
Elisabet Mellroth
LICENTIATE THESIS | Karlstad University Studies | 2014:67
High achiever! Always a high achiever? - A comparison of student achievements on
mathematical tests with different aims and goals
Elisabet Mellroth
LICENTIATE THESIS
Karlstad University Studies | 2014:67
urn:nbn:se:kau:diva-34516
This thesis is also part of the series Studies in Science and Technology Education
ISSN 1652-5051 at Linköping University
ISSN 1403-8099
ISBN 978-91-7063-607-3
© The author
Distribution:
Karlstad University
Faculty of Health, Science and Technology
Department of Mathematics and Computer Science
SE-651 88 Karlstad, Sweden
[phone]
Print: Universitetstryckeriet, Karlstad 2014
WWW.KAU.SE
To all my students whose strength I have not
discovered, acknowledged or encouraged

Abstract

This study explored changes in relative achievement over time. It also
investigated differences in how two groups of students activate mathematical
competencies. The aim of the study was to investigate students’ relative
achievement in mathematics over time, and how mathematical competencies
can be used to explore differences between groups of students on a non-
curriculum based test in mathematics. The study was divided in two parts.
Study 1 compared students’ (n=568) relative achievement in two national tests
in mathematics (years 3 and 6). Study 1 explored changes in relative
achievement between the two national tests as well as differences in relative
achievement between the national test in year 6 and the mathematical kangaroo
in year 7 (age 13). The study identified, from a sample (n=264) of study 1, two
groups of students with high achievements in only one of the tests, the national
test in year 6 or the mathematical kangaroo. Study 2 explored how differences
between those students relative achievement on the mathematical kangaroo
could be explained through activation of mathematical competencies. The
results in study 1 show that students undergo large changes, both increases and
decreases, in relative achievement between the national tests in years 3 and 6.
Study 2 shows how the two identified groups activate the mathematical
competencies differently on the mathematical kangaroo. 9% of the students
achieve highly in the mathematical kangaroo although they do not in the
national test. The study implicates the importance of using non-curriculum
bounded tests to identify strength in mathematical competencies among
students that not are able to show them through the national test.

Keywords: Achievement, alternative assessment, curriculum based assessment
mathematical competency, mathematical kangaroo, mathematics tests, national
tests.

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Acknowledgements

There are so many people that have been very important to me in different
ways during this work.
Arne Engström, my main supervisor, for your support and I would especially
like to thank you for your quick response and constructive comments in the
final phase of my work. Jari Appelgren, my second supervisor, I could not have
done this work without your explanations of the statistical methods, followed
by a millions of question that you have always answered with incredible
patience.
Per Nilsson for encouraging me, thanks to you I started to do research.
Inger Wistedt and Marianne Nolte, both for inspiring and encouraging me.
Jorryt van Bommel and Yvonne Liljeqvist for all your support, advice,
encouragement and jokes.
Annika Pettersson my own personal “hopms”, you helped me find laughter and
you shared the joy in the small as well as in the big things during this process. I
love to cry and laugh with you.
Torodd Lunde, Sergio Carlos, Matthias Müller and Ella Cosmovici Idsøe for
every interesting discussion, your critical comments and for sharing your
knowledge.
Thank you to everyone in SMEER at Karlstad university, especially to Shu-Nu
Chang-Rundgren for your support and your encouragement, also an extra thank
you to Daniel Olsson, Teresa Berglund and Jennifer Flint who all joined me on
this journey.
Ann Dyrman for your hawk eyes, thank you.
I want to give a huge thanks to all the teachers who helped me collect my data,
and also a special thanks to the teachers who helped me with the analysis. Of
course also many thanks to all the students who chose to participate in my
study.
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Thank you Karlstad municipality and Älvkullegymnasiet that allowed me to
participate in the research school. Especially I want to thank my bosses Inger
Thysell and Yvonne Toth, you both believed in me and made me feel good.
Thanks to The Swedish National Graduate School Science, Mathematics and
Technology Education Research (FontD) and to all friends and colleagues I
made through FontD in this process.
Jamie Pattle and Lindsay Fallis thanks for your friendship and your English
support.
I most likely forgot to mention someone, so a deep thank you to everyone that
I have spoken to about my work during this process.
At last I want to thank those people who I am afraid have suffered because of
my work, although always supported me. Emma and Carl, thank you for being
my wonderful children, for bringing me back to earth – I love you! And Jonas
you are incredible, always supporting, never complaining, taking care of
everything, and lifting me up when I am down – you are the very best for me!

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Contents

1 Introduction .......................................................................................................... 1
1.1 Main concepts used in the thesis ................................................................ 2
1.1.1 Relative achievement ................................................................................ 2
1.1.2 Mathematical competence and a mathematical competency .............. 3
1.2 Aim ................................................................................................................. 4
1.3 Research questions ....................................................................................... 5
1.4 Structure of the thesis .................................................................................. 5
2 Literature review ................................................................................................... 7
2.1 Curriculum, mathematical competencies and national test ..................... 7
2.2 Assessment .................................................................................................... 9
2.3 Achievement ................................................................................................ 11
2.4 High achievement, measured relatively.................................................... 13
2.5 The Swedish national test in mathematics .............................................. 17
2.6 The mathematical kangaroo ...................................................................... 18
2.7 Different aims in the two tests.................................................................. 19
3 Theoretical framework ...................................................................................... 21
3.1 Mathematical competencies as physical and mental activities .............. 21
3.2 Mathematical competencies ...................................................................... 22
3.2.1 Mathematical competencies – MCRF, KOM, NCTM ...................... 23
3.2.2 Mathematical competencies – Krutetskii and MCRF ........................ 24
3.3 Conceptualising the mathematical competencies ................................... 29
3.3.1 Applying procedures competency ........................................................ 29
3.3.2 Reasoning competency ........................................................................... 30
3.3.3 Communication competency ................................................................ 31
3.3.4 Representation competency .................................................................. 33
3.3.5 Connection competency ........................................................................ 34
3.3.6 Problem solving competency ................................................................ 35
3.4 Competency Related Activities, CRA ...................................................... 36
3.5 Situations for studying mathematical competencies .............................. 37
3.6 Master a competency .................................................................................. 38
3.7 Achievement ................................................................................................ 39
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