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Att strukturera och beräkna matematiska uttryck: En studie om hur elever i årskurs 5 hanterar utvecklade aritmetiska uttryck
Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
2016 (Swedish)Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesisAlternative title
To structure and calculate mathematical expressions : A study on how 5th grade students handle longer arithmetic expressions (English)
Abstract [sv]

En del svårigheter som elever upplever i algebra kan bero på saknad förståelse av strukturen i matematiska uttryck. Struktur, i det här sammanhanget, syftar på hur en matematisk enhet består av delar, och hur dessa delar är relaterade till varandra. Tidigare studier indikerar också att elevers svårigheter inom algebra beror på bristande aritmetiska kunskaper. Inom aritmetiken kan elever ofta använda informella metoder, medan algebraiska aktiviteter kräver en större medvetenhet om matematiska strukturer. Man har därför hävdat att elevers svårigheter att hantera algebraiska uttryck kan bero på saknad förståelse av strukturen i aritmetiska uttryck. 

Syftet med denna studie är att undersöka hur elever i årskurs 5 beräknar och strukturerar utvecklade aritmetiska uttryck, det vill säga, numeriska uttryck med flera räkneoperationer, som exempelvis 5 · 6 + 4 · 2 · 3. I denna studie behandlas numeriska uttryck med tre eller fyra operationer. 

I studien ingick 116 elever från tre olika skolor. Analysen baseras på data från lösningar av uppgifter på ett skriftligt arbetsblad. Arbetsbladet bestod av tio aritmetiska räkneuppgifter, som eleverna arbetade med individuellt. I analysen av data framkom olika metoder, som eleverna använde för att strukturera och beräkna de aritmetiska uttrycken, speciellt fyra metoder var återkommande i flera uppgifter. Genom de olika tillvägagångssätten som eleverna använde för att beräkna matematiska uttryck kunde olika sätt att skapa struktur upptäckas. Många elever utgick från uttryckens ytliga struktur och endast få elever visade förmåga att urskilja uttryckens dolda struktur. 

Abstract [en]

Some of the difficulties students experience in algebra can be due to lack of understanding of the structure in mathematical expressions. Structure, in this context, refers to how a mathematical entity consists of its parts, and how these parts are related to each other. Previous studies also indicate that students’ difficulties in algebra devolve upon a lack of arithmetical knowledge. In arithmetic, students can manage by using informal methods, while algebraic activities require a greater awareness of mathematical structures. It has therefore been argued that students’ difficulties with algebraic expressions are caused by a lack of knowledge of the structure in arithmetic expressions. 

The purpose of this study is to investigate how 5th grade students calculate and structure longer arithmetic expressions, meaning numerical expressions with several operations, for example, 5 · 6 + 4 · 2 · 3. This study covers numerical expressions with three or four operations. 

The study includes 116 students from three different schools. The analysis is based on data from solutions of tasks on a written worksheet. The worksheet consisted of ten arithmetic calculation assignments that the students worked with individually. The analysis of the data revealed different approaches that students used to structure and calculate the arithmetic expressions, particularly four methods were used in several tasks. Through the different approaches that students used to calculate mathematical expressions, different ways to create structure could be discovered. Many students based their calculations on the surface structure of an expression and only a few students seemed to be able to identify the hidden structure of an expression. 

Place, publisher, year, edition, pages
2016. , 39 p.
Keyword [en]
mathematics, arithmetic expressions, structure, students
Keyword [sv]
matematik, aritmetiska uttryck, struktur, elever
National Category
Mathematics Didactics
Identifiers
URN: urn:nbn:se:hj:diva-30590ISRN: JU-HLK-JU-2-20160167OAI: oai:DiVA.org:hj-30590DiVA: diva2:940315
Subject / course
HLK, Mathematics for teaching and learnin
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Available from: 2016-06-22 Created: 2016-06-16 Last updated: 2016-06-22Bibliographically approved

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