## Matematisk ekvivalens i en femteklasse - en kasusstudie

##### Master thesis

##### Permanent lenke

http://hdl.handle.net/11250/2455732##### Utgivelsesdato

2017##### Metadata

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##### Sammendrag

This master thesis is a study of a fifth-grade class and their understanding of mathematical
equivalence and if their understanding affects how they solve algebraic word problems.
Within their understanding of mathematical equivalence the equal sign plays an important
part. This study is based on former research about the main topic (Chesney & McNeil. 2014;
Kieran. 1981; Knuth et al. 2006) that detected many pupils in elementary school with an
operational understanding of the equal sign. Therefor the pupils have misconceptions about
the meaning of the equal sign not being a relational mathematical symbol, but they view the
sign as a "do something signal" (Knuth et al. 2006). This interpretation could take part in
weakening the development of the pupils conceptual understanding of mathematical
equivalence and will therefore influence the pupil’s algebraic results.
My two research questions are as follow:
1. What kind of understanding does a fifth-grade class show about mathematical equivalence?
2. How do pupils, with different understanding about mathematical equivalence, solve
algebraic word problems?
In this study, I use a qualitative research design and within the design I take use of case study
and multiple case study as methods. To answer my first research question the students
completed mathematical tasks constructed to reveal their understand of mathematical
equivalence. To increase the validity of this study I analysed the result and compared it to
their general mathematical abilities. To evaluate the pupils understanding I included their
interpretation of the equal sign and its role in mathematics, and I looked at the students’
performance in solving equivalence problems.
To answer my second research question, I completed to task-based interviews with pupils that
previously had been categorized with different understanding of mathematical equivalence.
The pupils had to solve five algebraic word problems and I analysed their performance based
on their task reasoning and strategic choices.
The result of the analysis revealed that about 45 % of the pupils in this fifth-grade class
showed signs of operational understand, and about 48 % was categorized with a good
understanding of mathematical equivalence. The result is coherent with the previous research
mentioned before. One of my findings was that some of the equivalence tasks had higher
failure rate and was therefore more challenging than others. My analysis showed that the
format of the tasks had a direct link with the result and the pupil’s achievements. I also found
a strong connection between the students that showed good understanding of equivalence and
a relational interpretation of the equal sign.
When it comes to the pupils solving of algebraic word problems, the result from the analysis
showed that students with different understanding of mathematical equivalence had different
solving processes. Pupils that was categorized with operational understanding used almost
exclusively strategies that is related to elementary word problems that shows no signs of
understanding the functional relationship between the values. On the other hand, the students
that was categorized with good understanding of equivalence used multiple strategies that
showed understanding of the notion of balancing two sides of an equation. And therefore, the
pupils had a solving process with algebraic content

##### Beskrivelse

Masteroppgave matematikkdidaktikk MA502 – Universitetet i Agder 2017