Today's school has become more and more digital the last years which means that schools have more access to digital tools than before. For example, digital games are something that is used frequently during mathematic classes. This systematic literature study has the purpose to compile current research about which impact digital games have in school and also see how digital games contribute to students' development of mathematical proficiencies. The results of this study show that students develop mathematical proficiencies through digital games with numerical literacy as the most central. The results also show that students are stimulated by using digital games, this contributes to a positive learning. More research would be desirable about how digital mathematics games can be associated with regular teaching. It would also be interesting to do a qualitative study of teachers’ knowledge about using digital games. / Dagens skola har blivit mer och mer digitaliserad de senaste åren vilket innebär att det finns ett större utbud av olika digitala läromedel än tidigare. Exempelvis är digitala spel något som används frekvent inom skolans matematikundervisning. Denna systematiska litteraturstudie har till syfte att sammanställa aktuell forskning kring vilken inverkan digitala spel har i skolan samt på vilket sätt dessa digitala spel bidrar till elevers utveckling av matematiska förmågor. Resultatet av studien visar att elever utvecklar matematiska förmågor genom digitala spel där räkneförmågan är mest central. Resultatet visar även att elevers matematikintresse stimuleras genom användning av digitala spel vilket bidrar till en positiv inlärning. Ytterligare forskning kring hur digitala spel kan komplettera vanlig traditionell matematikundervisning vore önskvärt. Det vore även intressant att göra en kvalitativ studie om lärares kunskaper kring användning av digitala spel.

Perhaps the most difficult task and challenge teachers today face is being able to adapt teaching to the individual needs and conditions students have in school. The school is moving towards digitalization just like society, and this study thus deals with how teachers can use digitally designed teaching aids to build individualized mathematics teaching. The specific teaching aid Kunskapsmatrisen has been studied to investigate how teachers believe that the aid can meet students’ different conditions and needs in mathematics teaching. The study includes a qualitative analysis based on interviews with active mathematics teachers who have good experiences with the digital teaching aid Kunskapsmatrisen. The result showed that there is a distribution in terms of students’ differences, conditions, and needs in mathematics teaching. This could mean everything from prior knowledge to the students having different wills to learn mathematics. It also turned out that the Kunskapsmatrisen has good opportunities to offer variation in the amount and type of tasks, as well as to meet the students’ knowledge levels. The teacher was also given opportunities to be able to adapt the teaching to the students’ conditions and needs through continuous use of Kunskapsmatrisen. An interesting aspect that was shown was that Kunskapsmatrisen may not be as suitable for students with certain difficulties with mathematics. These students were considered to require more than just Kunskapsmatrisen in the form of interaction and conversation in the classroom or that the teacher was included as a complement. It also turned out that Kunskapsmatrisen perhaps worked best in the students’ own work and not so much for the teaching itself. / Den kanske svåraste uppgiften och utmaningen lärare idag står inför är att kunna anpassa en undervisning efter de enskilda behov och förutsättningar elever har i skolan. Skolan går mot en digitalisering precis som samhället och denna studie behandlar hur lärare kan använda digitalt utformade lär-hjälpmedel för att bygga en individanpassad matematikundervisning. Det specifika hjälpmedlet Kunskapsmatrisen har studerats i förhållande till på vilket sätt lärare anser att hjälpmedlet kan bemöta elevers olika förutsättningar och behov i matematikundervisningen. Studien innefattar en kvalitativ analys baserad på intervjuer med verksamma matematiklärare som har goda erfarenheter kring det digitala lär-hjälpmedlet Kunskapsmatrisen. Resultatet visar att det finns spridning vad gäller elevers olikheter, förutsättningar och behov i matematikundervisningen. Spridningen kan innebära allt från olika förkunskaper till att eleverna har olika vilja till att lära sig matematik. Det visade sig att Kunskapsmatrisen har goda möjligheter för att kunna erbjuda variation i mängd och typ av uppgifter, samt att möta elevernas kunskapsnivåer. Läraren gavs också möjligheter att kunna anpassa undervisningen efter elevernas förutsättningar och behov genom ett kontinuerligt användande av Kunskapsmatrisen. En intressant aspekt som visades var att Kunskapsmatrisen kanske inte lämpade sig lika bra hos elever med vissa svårigheter med matematik. Dessa elever ansågs kräva mer än bara Kunskapsmatrisen i form av interaktion och samtal i klassrummet eller att läraren fanns med som ett komplement. Det visade sig också att Kunskapsmatrisen kanske främst fungerade bäst vid eget arbete och inte så mycket till undervisningen i sig.

This literature review looks into the effects of integrating music in mathematics teaching andhow it influences the problem solving ability. A systematic search for scientific articles was madeto investigate the research area. All together 13 scientific articles were chosen, which presentedvarious ways to integrate music in mathematics teaching and which had found different resultsin their studies. Generally, the articles presented positive effects of integrating music inmathematics teaching to develop students’ problem solving ability and mathematical learning.Similarities and differences between the presented articles were compared in the results of thisstudy, which showed common features in the characters of music and mathematics. In this study,problem solving is used in a wide definition which includes arithmetic, communication,reasoning and mathematical concepts

Att möta alla elevers behov i matematikundervisningen kan göras på olika sätt. En väg att gå är genom att använda sig av olika arbetssätt och uttrycksformer. För att få en djupare förståelse så är syftet med denna studie att öka kunskapen kring detta genom beskrivningar från lärare i förskoleklassen om deras matematikundervisning. Det har varit två frågeställningar till hjälp för att få svar på studiens syfte. Frågeställningarna är: - Hur beskriver lärarna deras användning av arbetssätt och uttrycksformer i matematikundervisningen, samt -Vilka möjligheter beskriver lärarna att arbetssätt och uttrycksformer kan ha för lärande. Studiens syfte och frågeställningar har besvarats genom kvalitativa intervjuer med fem verksamma lärare i förskoleklass. Den teoretiska utgångspunkt studien har är den sociokulturella teorin där socialt samspel, medierande redskap och språk är i fokus. Studiens resultat visar på hur lärarna använder olika arbetssätt och uttrycksformer i matematiken. Det visar även vilka möjligheter lärarna ser att dessa har för lärandet. Slutligen framkommer det möjliga hinder med användningen av dessa arbetssätt och uttrycksformer. Resultatavsnittet följs av diskussionsavsnittet där både studiens metod och resultat diskuteras. / To meet all students needs in mathematics, teaching can be done in different ways. One way to do this is by using different working methods and different forms of expressions. The aim of this study is to increase the knowledge about this through the descriptions from teachers in preschool class about their mathematics teaching. Two questions help to answer the aim of the study. The questions are how the teachers describe their use of working methods and different forms of expression in mathematics teaching, and what possibilities the teachers describe that different working methods and different forms of expression can have for students’ learning. The study is based on qualitative interviews with five active teachers in Swedish preschool class (6 years old students). The theoretical starting point of the study is the socio-cultural theory where social interaction, mediating tools and language are in focus. The study illustrates how the teachers use different working methods and forms of expression in mathematics. It also gives examples of what opportunities the teachers see that these have for students’ learning. Finally, in the data, some possible obstacles to the use of these working methods and forms of expression also emerges.

Det finns en bred variation av hjälpmedel som existerar i syfte att stödja matematikundervisning. Ett av dessa hjälpmedel kan benämnas konkreta material. Syftet med denna studie är dels att undersöka hur forskningsfältet kring konkreta material ser ut, dels att undersöka vilka utmaningar användandet av konkreta material medför. Konkreta material är fysiska (ej digitala) material som går att manipulera i syfte att stödja inlärningen av olika matematiska begrepp. Forskningsfältet har sammanställts genom en systematisk litteraturstudie. Resultatet visar att ett flertal kategorier inom forskningen kan urskiljas, där en kategori specifikt lyfter hur gynnsam användningen av konkreta material är. Resultatet visar också att det finns många utmaningar som läraren måste ta hänsyn till för att användandet av konkreta material ska bli meningsfullt. Diskussionen lyfter att ett flertal av artiklarna skulle gynnas av ett kritiskt perspektiv, samt att fler empiriska studier med ett kritiskt förhållningssätt inom området skulle behövas. / There is a wide variety of aids that exist to support mathematics teaching. One category of these aids can be referred to as manipulatives. The purpose of this study is partly to examine what the research field around manipulatives looks like, and partly to examine what challenges the use of manipulatives entails. Manipulatives are physical (not digital) materials that can be manipulated in order to support the learning of various mathematical concepts. Through a systematic literature study, the research field has been compiled. The result shows that a number of categories can be distinguished within the research, where one category specifically highlights how favorable the use of manipulatives is. The results also show that there are many challenges that teachers must take into account in order to use manipulatives in a meaningful way. The discussion highlights that several of the articles would benefit from a critical perspective, and that more empirical studies with a critical approach in the field would be needed.

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An operational definition of Systemic Reform is used to document a case study of mathematics education reforms occurring in the mathematics classrooms of one middle school in one school division in one state. The middle school had two lead teachers who participated in the training component of a National Science Foundation-funded state-wide Systemic Reform Initiative. Systemic Reform conceptualized reform as combining bottom-up reform with top-down support. Therefore, the research methodology confronted the challenges of the breadth and complexity of Systemic Reform through the use of selective data in the form of artifacts, interviews, and observations from four populations: (1) classroom teachers, (2) building administrators, (3) district administrators, and (4) state-level staff. The study was conducted at four levels over a five-year period to provide the focus for longitudinal data collection to document: (1) the status of mathematics education during the 1995-96 primary data collection year, (2) the evolution of mathematics education reform over the course of the five year period, and (3) the manner in which Systemic Reform occurred. All levels of educators involved made an initial five-year commitment as active participants in the State's Systemic Reform Initiative, but only the Lead Teacher actually carried through with this commitment. After the first year division-level administrators shifted the focus of reform efforts to the elementary schools and discontinued support for the middle schools; after the second year both the division and state-level administrators withdrew all support. Although changes were made at the school level which supported reform in mathematics education (i.e., adoption of constructivist-type instructional materials, purchase of classroom sets of manipulatives and calculators, implementation of block scheduling, and the organization of teachers in interdisciplinary teams) the necessary changes in technology, curriculum and assessment were not in place to support the reform efforts. Through the perseverance of the Lead Teacher some changes in mathematics classrooms were documented, but the lack of consistent administrative leadership/support and emphasis on multiple reforms ended in the all to common bandwagon phenomena at the building, division and state levels so characteristic of change efforts in schools. / Ph. D.

Det finns en bred variation av hjälpmedel som existerar i syfte att stödja matematikundervisning. Ett av dessa hjälpmedel kan benämnas konkreta material. Syftet med denna studie är dels att undersöka hur forskningsfältet kring konkreta material ser ut, dels att undersöka vilka utmaningar användandet av konkreta material medför. Konkreta material är fysiska (ej digitala) material som går att manipulera i syfte att stödja inlärningen av olika matematiska begrepp. Forskningsfältet har sammanställts genom en systematisk litteraturstudie. Resultatet visar att ett flertal kategorier inom forskningen kan urskiljas, där en kategori specifikt lyfter hur gynnsam användningen av konkreta material är. Resultatet visar också att det finns många utmaningar som läraren måste ta hänsyn till för att användandet av konkreta material ska bli meningsfullt. Diskussionen lyfter att ett flertal av artiklarna skulle gynnas av ett kritiskt perspektiv, samt att fler empiriska studier med ett kritiskt förhållningssätt inom området skulle behövas. / There is a wide variety of aids that exist to support mathematics teaching. One category of these aids can be referred to as manipulatives. The purpose of this study is partly to examine what the research field around manipulatives looks like, and partly to examine what challenges the use of manipulatives entails. Manipulatives are physical (not digital) materials that can be manipulated in order to support the learning of various mathematical concepts. Through a systematic literature study, the research field has been compiled. The result shows that a number of categories can be distinguished within the research, where one category specifically highlights how favorable the use of manipulatives is. The results also show that there are many challenges that teachers must take into account in order to use manipulatives in a meaningful way. The discussion highlights that several of the articles would benefit from a critical perspective, and that more empirical studies with a critical approach in the field would be needed.

The math achievement of American students had been stagnant or falling since 2007, according to both national and international measures (NAEP, TIMSS, PISA). While the Common Core State Standards were partially a response to sinking levels of American math proficiency, those standards require a much greater depth of conceptual understanding of mathematics for teachers than previous standards, yet more than half of fifth- through eighth-grade math teachers are not certified to teach math. The federal government and school districts spend millions of dollars on teacher professional development, but little evidence shows what kind of professional development might be the most beneficial for math teachers. This study measured the impact of math content-based professional development on middle school math teachers. Findings suggest that the participating teachers’ content knowledge about ratios and proportional reasoning increased slightly during the study. Exit surveys indicated that the most recent PD session would have an impact on their teaching practice, although the impact would mostly be related to their pedagogy. However, there was little change in teachers’ self-efficacy toward teaching mathematics. As research indicates, content knowledge in math is connected to student achievement, the implication of which is that middle school math teachers can increase their content knowledge through professional development. Given that access to higher-level math courses is critical to college success, and the foundation for those higher-level math courses begins in middle school, it is imperative that all students and their teachers are supported to be successful in math.

Konkreta material kan effektivt stödja elevers matematikförståelse, om det används medvetet av skickliga lärare. Användandet av konkreta material medför en rad utmaningar, vilket kan vara anledningen till att matematikböcker dominerar matematikundervisningen i den svenska skolan. Syftet med denna studie är att bidra med kunskap om hur dessa utmaningar kan hanteras och vad det är som är avgörande för att en matematikundervisning med konkreta material ska vara välfungerande. Följande studie är en kvalitativ fallstudie där en tematisk analys används för att undersöka fem nyckelfall genom observation av matematiklektioner där konkreta material används, med en efterföljande intervju. Resultaten organiserades under tre huvudkategorier: (1) Progression från konkret till abstrakt, där vikten av en tydlig progression från konkret till abstrakt via olika representationsformer identifieras; (2) Konkreta material i undervisning, där vikten av lärares val av material identifieras; samt (3) Betydelsen av eget engagemang samt kollegialt och organisatoriskt stöd, där vikten av organisatoriskt och kollegialt stöd identifieras. Diskussionen lyfter att lärarens roll är mer avgörande än en specifik metod eller ett specifikt material. Dock lyfts även hur förutsättningarna för lärare att skapa en välfungerande matematikundervisning kan påverkas av externa faktorer, såsom kollegialt och organisatoriskt stöd. / Manipulatives can effectively support students' understanding of mathematics when used intentionally by skilled teachers. The use of manipulatives presents a range of challenges, which may explain why textbooks dominate mathematics teaching in the Swedish school system. The purpose of this study is to contribute knowledge on how these challenges can be addressed and what is crucial for successful mathematics instruction using manipulatives. This study is a qualitative case study employing thematic analysis to investigate five key cases through observation of mathematics lessons utilizing manipulatives, followed by interviews. The results were organized into three main categories: (1) Progression from manipulatives to abstract, where the importance of a clear progression from concrete to abstract through various representational forms was identified; (2) Manipulatives in teaching, where the importance of teachers' choices of materials was identified; and (3) The importance of personal commitment and organized and collegial support, where the importance of organizational and collegial support was identified. The discussion emphasizes that the teacher's role is more crucial than any specific method or material. However, it also addresses how the conditions for teachers to create effective mathematics teaching can be influenced by external factors such as collegial and organizational support.