Research indicates that many elementary students do not comprehend that the equal sign is an indication that an equality relation exists between two structures. Instead, they perceive the equal sign as an indication that a particular procedure is to be performed. As students mature, and as their exposure to the equal sign and equality relations in multiple contexts increases, most obtain the ability to interpret the equal sign as an indicator of an equivalence relation. Incorrect usages of the equal sign, however, by post-algebra students indicate a tendency for students to regress back to a comprehension of the equal sign as an operator symbol or to ignore the equal sign altogether. The purpose of this project was to develop an instrument that is relevant to objectives associated with the interpretation of the equals relation, and to perform a test reliability analysis to assess measurement reliability and construct validity for the instrument. The model that was utilized to develop items for the instrument followed a general item development and validity assessment model proposed by Cangelosi. This model requires an iterative process that includes a peer review of objectives and instrument items by a panel of experts and a revision of the items based upon recommendations from the panel. A pilot test was synthesized from the revised items and administered to a group of subjects, and an instrument reliability analysis and an item efficiency analysis were performed. The quantitative and qualitative data obtained from this process were used to create the 18-item instrument entitled, Wheeler Test for Comprehension of Equals. The researcher recommends further validity assessments for the instrument across multiple settings and subject groups.

Syftet med denna studie är att undersöka och bidra med kunskap om hur undervisningen om likhetstecknets innebörd kan se ut i ett svenskt klassrum. Det som undersöks är hur en lärare skapar möjlighet för eleverna att urskilja kritiska aspekter av likhetstecknets innebörd genom variationsmönster. Datainsamlingen genomfördes genom stimulated recall i en åk 2 med en lärare som har tio års arbetslivserfarenhet som lärare vid ett undervisningstillfälle. Analysen av datamaterialet gjordes med inspiration från variationsteorin. Resultatet visade att fyra kritiska aspekter gjordes möjliga för eleverna att urskilja. Detta gjordes genom olika variationsmönster som skapades genom användandet av öppna utsagor och olika representationsformer. / The aim of this study is to research and bring knowledge about how the meaning of the equality sign can be taught in a Swedish classroom. The research focuses on how a teacher creates possibilities for the students to discern critical aspects of the meaning of the equality sign through patterns of variation. The data was collected by using stimulated recall during one lesson in a year 2 classroom with a teacher who has been working as a teacher for ten years. The collected material was analysed with inspiration from the variation theory. The result shows that four critical aspects were made visible to the students. This was done through dif- ferent patterns of variation that was created by the use of different forms of representation.

Syftet med denna studie är att undersöka och bidra med kunskap om hur undervisningen om likhetstecknets innebörd kan se ut i ett svenskt klassrum. Det som undersöks är hur en lärare skapar möjlighet för eleverna att urskilja kritiska aspekter av likhetstecknets innebörd genom variationsmönster. Datainsamlingen genomfördes genom stimulated recall i en åk 2 med en lärare som har tio års arbetslivserfarenhet som lärare vid ett undervisningstillfälle. Analysen av datamaterialet gjordes med inspiration från variationsteorin. Resultatet visade att fyra kritiska aspekter gjordes möjliga för eleverna att urskilja. Detta gjordes genom olika variationsmönster som skapades genom användandet av öppna utsagor och olika representationsformer. / The equality sign means that it should be the same, end of discus-sion. -A study about how students are given possibilities to discern critical aspects of the meaning of theequality sign The aim of this study is to research and bring knowledge about how the meaning of the equality sign can be taught in a Swedish classroom. The research focuses on how a teacher creates possibilities for the students to discern critical aspects of the meaning of the equality sign through patterns of variation. The data was collected by using stimulated recall during one lesson in a year 2 classroom with a teacher who has been working as a teacher for ten years. The collected material was analysed with inspiration from the variation theory. The result shows that four critical aspects were made visible to the students. This was done through dif-ferent patterns of variation that was created by the use of different forms of representation.

Elevers uppfattning av likhetstecknet har länge diskuterats inom forskning och ansetts varakritiskt, då förståelsen för tecknets relationella innebörd ofta saknas. Syftet med denna textär att undersöka hur likhetstecknet framställs i svenska läromedel, och diskutera hur det kantänkas påverka elevers uppfattning av symbolen. Detta genom att besvara frågeställningarna;på vilket sätt uppmuntrar läroböckerna i matematik till en relationell förståelse avlikhetstecknet och på vilket sätt uppmuntrar läroböckerna i matematik till en operationellförståelse av likhetstecknet?Studien grundar sig i variationsteorins idéer och resultatet har analyserats kopplat tillvariationsmönster och kritiska aspekter. Kopplingar har även gjorts mellan traditionellaekvationer och en operationell syn på likhetstecknet, samt icke-traditionella ekvationer ochen relationell syn på tecknet. Metoden som använts är en kvantitativ innehållsanalys där sexolika svenska läromedel i matematik, riktade till årskurs 1, analyserats för att få syn på hur devarierar framställningen av likhetstecknet. Resultatet pekar på bristande variation i form avkontrast, generalisering och fusion, då det i störst grad är traditionella ekvationer som fårutrymme i böckerna. Detta kan tänkas bidra till att elever utvecklar en operationell syn pålikhetstecknet snarare än en relationell, vilket i längden kan försvåra övergången frånaritmetik till algebra i matematikundervisningen. / Students' perception of the equals sign has for a long time been debated in research andconsidered critical, as the understanding of the relational meaning of the equals sign is oftenlacking. The purpose of this text is to examine how the equals sign is presented in Swedishtextbooks, and to discuss how it might affect students' perception of the symbol. This is doneby addressing the following questions: in what way do mathematics textbooks encourage arelational understanding of the equals sign, and in what way do they encourage anoperational understanding of the equals sign?The study is based on the ideas of variation theory, and the results are analyzed in relation topatterns of variation and critical aspects. Connections have also been made betweentraditional equations and an operational view of the equals sign, as well as non-traditionalequations and a relational view of the sign. The method used is a quantitative contentanalysis where three different Swedish mathematics textbooks, aimed at grade 1, are analyzedto observe how they vary in the presentation of the equals sign. The results indicate a lack ofvariation in terms of contrast, generalization, and fusion, as the textbooks predominantlyfocus on traditional equations. This may contribute to students developing an operationalview of the equals sign rather than a relational one, which could ultimately complicate thetransition from arithmetic to algebra in mathematics education.