The current study aimed to explore middle school mathematics teachers&rsquo / use of mathematics textbooks and examine their integration of tasks in the textbooks into teaching. The framework of a mixed methods research design guided data collection in this study. A questionnaire called the Use of Mathematics Textbooks Questionnaire was developed and validated to identify the ways teachers benefit from textbooks. The factor analysis revealed four dimensions, namely Reading Student Edition Textbook, Selecting Questions from Workbook, Reading Teacher Edition Textbook, and Selecting Tasks and Problems from Auxilary Books. The results of the study showed that teachers used the student edition textbook for mostly during class and for lesson preparation. Teachers also used the student edition textbook for explaining the topic and the introductory tasks. However, they rarely used it for selecting problems and examples. Teachers read the student edition textbook mostly during and prior to class / and mostly use it for topic explanation, but rarely for problems and examples. They stated that they frequently selected questions from the workbook that were not included in the textbook. However, they occasionally picked questions to use during lessons. They frequently used auxilary books to select questions similar to the ones in the high school entrance exam problems. In examining the process of teachers&rsquo / use of mathematics textbooks, it was argued that there were interpretive processes as teachers engage with and use textbooks. The analysis of interviews and observations showed that teachers read textbooks and select tasks and questions from those books. In their decisions about using tasks from textooks, teachers usually considered the nature of tasks and students&rsquo / characteristics.

published_or_final_version / abstract / toc / Education / Doctoral / Doctor of Philosophy

Statistical Content in Middle Grades Mathematics Textbooks Maria Consuelo (Suzie) Capiral Pickle Abstract This study analyzed the treatment and scope of statistical concepts in four, widely-used, contemporary, middle grades mathematics textbook series: Glencoe Math Connects, Prentice Hall Mathematics, Connected Mathematics Project, and University of Chicago School Mathematics Project. There were three phases for the data analysis. Phase 1 addressed the location and sequence of the statistical concepts. Phase 2 focused upon an examination of the lesson narrative, its components and scope. Phase 3 analyzed the level of cognitive demand required of the students to complete the exercises, and the total number of exercises per statistical concept. These three phases taken together provided insight into students' potential opportunity to learn statistical topics found in middle grades mathematics textbooks. Results showed that concepts, such as measures of central tendency, were repeated in several grades while other topics such as circle graphs were presented earlier than the recommendations in documents such as the National Council of Teachers of Mathematics Principles and Standards (2000) and the Common Core State Standards (2010). Further results showed that most of the statistical content was found in a chapter near the end of the book that would likely not be covered should time run short. Also, each textbook had a particular lesson narrative style. Moreover, most of the statistical exercises required low level cognitive demand of the students to complete the exercises, potentially hindering the development of deep understanding of the concepts.

This diploma thesis deals with the topic of divisibility of natural numbers in mathematics in the 6th year of primary schools. The first, theoretical part of the diploma thesis introduces the concept of didactic situations from the Theory of Didactic Situations in Mathematics by G. Brousseau, the theory of multiple intelligences according to H. Gardner and the theory of cognitive development according to J. Piaget. All chapters are projected into the experimental part. The diploma thesis is focused on the topic of divisibility, therefore a chapter of the same title is included in this part. From the history point of view, the sieve of Eratosthenes and Mersenne prime numbers are described here in two chapters. The practical part of the thesis includes a chapter containing an analysis of various didactic methods used in six sets of mathematics textbooks. Attention is paid to similarities and differences in the sets of tasks. In each textbook the topic of divisibility is compared in regard to the introduction of the divisibility rules. The following two chapters are devoted to an experiment designed to help pupils understand the divisibility rules for numbers 2, 5, 10, 8 and 4. The experiment took place over several days in two parallel classes, each of which was pedagogically led for a long time by a...

Bråk beskrivs som ett av de mest komplexa ämnesområden inom matematik. Däremot har en del läromedel tonat ner bråkens betydelse samtidigt som forskning visar att läroböcker utgör en central del av lärares matematikundervisning. Syftet med denna studie är att ge en bild av vad tre läromedel läroböcker erbjuder elever att lära om bråk. Undersökningen har inspirerats av variationsteorin och utgår från fyra kritiska aspekter som utifrån tidigare forskning visat sig vara viktiga för elevers förståelse för bråk. Totalt har sex läroböcker analyserats med hjälp av en innehållsanalys, i syfte att identifiera vilka variationsmönster som används för att synliggöra fyra kritiska aspekter. Dessutom undersöktes vilka lärandeobjekt som förekommer i respektive lärobok. Av resultatet framgår en variation i vilken utsträckning de kritiska aspekterna behandlas och vilka variationsmönster som används för att öka elevers förståelse för de kritiska aspekterna. Framförallt ges elever möjlighet att lära om täljaren och nämnarens funktion genom generalisering som mönster av variation. I läromedlen kunde sammanlagt 19 unika lärandeobjekt identifieras. Däribland återfinns lärandeobjekt om såväl bråk som del av en helhet som bråk som del av antal. Även om inget av de analyserade läromedlen behandlar samtliga lärandeobjekt är det möjligt att utläsa en tydlig skillnad vad gäller såväl omfång som innehåll. Oavsett står det klart att en kombination av flera läromedel kan berika elevers möjligheter att lära bråk. För att en sådan variation ska vara möjlig krävs en stärkt skollag som säkerställer elevers rätt till läromedel. / Research shows that there are a number of reasons students struggle with fractions. On the other hand, some mathematics textbooks still reduce the importance of fraction, while research found mathematics textbooks as a central part of teachers’ math teaching. However, the aim of this study is to depict what three educational materials offer pupils to learn about fractions. The study has been inspired by the theory of variation and is based on four critical aspects that, based on previous research, have been found as critical for students’ understanding of fractions. A total of six mathematics textbooks have been analysed using a content analysis, in order to identify which patterns of variation are used to make the selected critical aspects visible. Furthermore, this study examined which learning objects that appear in each textbook. The results show a variation in the extent each critical aspect is treated and which variation patterns that are used to improve pupils understanding of selected critical aspects. A total of 19 unique learning objects could be identified in the mathematics textbooks. Due to the fact that none of the analysed teaching materials deals with all learning objects, it is possible to distinguish a variation of both volume and content. However, result from this study claims that mathematics textbooks combined would offer greater opportunities to learn obviously. If teachers should be able to overcome a various teaching material it is necessary to strengthen students’ rights to teaching material.

Bibliography: pages 82-84. / This dissertation is concerned with aspects of the role of the textbook in school mathematics. An attempt is made to uncover control strategies used by the teacher in textbook use in the classroom, and those implicit in a mathematics textbook. It is argued that these forms of regulation place constraints on the transformative role sometimes attributed to textbooks. The following research question is addressed: how does the teacher recruit the textbook in the classroom, how is he/she 'recruited' by it and how are both recruited by school mathematics? A case study methodology is described, involving a video-recording of a fifty minute mathematics lesson and a follow-up interview with the teacher. Transcriptions are used and a fine-grained analysis of data is attempted. A literature survey examines other research in the areas of content selection, content control and content expression. Content selection refers to choices and omissions, content control refers to sequencing, pacing and authority in the pedagogic relationship, and content expression includes verbal and textual modes of expressing content. Theoretical ideas are drawn from Bernstein (1976, 1991, 1993) and Dowling (1993). Although these works are methodologically different, they both describe aspects of regulation and control. Of particular interest are Bernstein's notions of classification and framing, and Dowling's ideas on discourse and procedure. The hypothesis is put forward here that there is a dialectical relationship involving the positioning of teacher and textbook. The teacher recruits the textbook to regulate pupils and knowledge, but s/he is at the same time constrained by strategies implicit in the textbook. In other words the teacher both positions and is positioned by the textbook. Both in tum are positioned by school mathematics. The data analysis examines the 'how', 'what' and 'who' of control. It considers the regulation of speech, silence, working and listening, as well as the sequencing, pacing, selecting, presenting and authorising of content. It argues that the teacher both recruits and is 'recruited' by the textbook, and that although the framing is strong and the teacher has a high degree of control in the pedagogic relationship, the classification is also strong and the teacher lacks control over what she can teach and the relationship between contents. The research concludes by suggesting that the transformative role sometimes attributed to the textbook is problematic. The strategies of regulation and control operating in the classroom, implicit in the textbook and in school mathematics, limit the possibilities of how textbooks can be used by the teacher and constrain transformation to a significant degree.

Syftet med studien är att undersöka vilken roll lärarna ger till läromedlet i matematik i deras geometriundervisning i årskurs tre. För att svara på studiens syfte, har en triangulering av två metoder genomförts. Den ena metoden är innehållsanalys och den andra är semistrukturerad intervju. Resultaten visar att lärarna ger sitt matemaikläromedel en central roll i geometriundervisningen i årskurs tre. Resultaten visar också att de resurser lärarna använder sig av i sin geometriundervisning är uppgifter i elevernas arbetsböcker, illustrationer, begreppsförklaringar och att lärarna använder sig av lärarhandledningen som inspiration eller stöd i sin undervisning i geometri. Studiens resultat stödjer tidigare forskning inom användandet av matematikläromedel och även tidigare forskning inom geometriundervisning. / The purpose of this study is to examine what role the teachers give to the textbooks in their geometry-teaching in third grade. A triangulation has been made between two methods to fulfill the purpose of the study. One method is content analysis and the second one is semi-structured interview. The results shows that the textbooks are given a huge role from the teachers in the geometry-teaching in third grade. The results also shows that the resources the teachers use in their geometry-teaching is assignments in the pupils’ textbooks, illustrations, explanations, and that the teachers use the teachers’ manual as an inspiration or as support in their geometry teaching. The result of this study supports previous research within the use of textbooks and previous research on geometry-teaching.

Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2017-12-04T11:55:04Z No. of bitstreams: 1 César Augusto Pimentel de Souza.pdf: 2249653 bytes, checksum: a5e594086976fe654bfb207a8782b87e (MD5) / Made available in DSpace on 2017-12-04T11:55:04Z (GMT). No. of bitstreams: 1 César Augusto Pimentel de Souza.pdf: 2249653 bytes, checksum: a5e594086976fe654bfb207a8782b87e (MD5) Previous issue date: 2017-09-20 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The present study deals with the concepts of Literacy and Mathematical Literacy under the aegis of solving problems from a qualitative, documentary and bibliographical approach. The purpose of this paper is to analyze the convergences and divergences between the guidelines of the PNAIC/2014 Book 4 "Operations in Problem Solving" and a collection of mathematical textbooks for the first years of elementary school (1st, 2nd and 3rd years), focusing on the problems of Additive and Multiplicative Structure. The following French theories were used in the theoretical reference: Gérard Vergnaud's Theory of Conceptual Fields (TCC) and Yves Chevallard's Anthropological Theory of Didactics (TAD). TCC was useful for classifying the types of problems of the Additive and Multiplicative Structure present in Book 4 of the PNAIC/2014 and in the three volumes of textbooks entitled Mathematical Literacy. The TAD, in turn, provided the analysis of the praxeological organizations that are articulated around the types of tasks, techniques, technologies and theories of the problems selected in the textbooks. The results obtained are based on elements and findings that support the idea that there is a partial consonance between the PNAIC’s teacher training book and the textbook. It has been found that some types of TCC problems have not been addressed in Book 4 of the PNAIC and in the Textbooks Collection, and it has also been found, on the basis of the TAD, that although textbook problems are presented with a diversity of contexts and forms, usually demand the same action of the subject in relation to mathematical knowledge. The conceptual and methodological choices identified in the quoted materials are addressed in this research / O presente estudo versa sobre os conceitos de Alfabetização e Letramento Matemático sob a égide da resolução de problemas a partir de uma abordagem qualitativa e de caráter documental e bibliográfico. O objetivo deste trabalho é analisar as convergências e divergências entre as orientações do Caderno 4 do PNAIC/2014 “Operações na Resolução de Problemas” e uma coleção de livros didáticos de matemática destinados ao ciclo de alfabetização (1º, 2º e 3º anos), com foco nos problemas de Estrutura Aditiva e Multiplicativa. Foram utilizadas no referencial teórico as seguintes teorias francesas: A Teoria dos Campos Conceituais (TCC) de Gérard Vergnaud e a Teoria Antropológica do Didático (TAD) de Yves Chevallard. A TCC foi útil para a classificação dos tipos de problemas de Estrutura Aditiva e Multiplicativa presentes no Caderno 4 do PNAIC/2014 e nos três volumes de livros didáticos intitulados como Alfabetização Matemática. A TAD, por sua vez, propiciou a análise das organizações praxeológicas que se articulam em torno dos tipos de tarefas, técnicas, tecnologias e teorias dos problemas selecionados nos livros didáticos. Os resultados obtidos baseiam-se em elementos e constatações que permitem defender a ideia de que existe uma consonância parcial entre o Caderno de formação de professores do PNAIC e o livro didático. Verificou-se que alguns tipos de problemas identificados pela TCC não foram contemplados no Caderno 4 do PNAIC ou na Coleção analisada, e verificou-se também, com base na TAD, que embora os problemas propostos nos livros didáticos se apresentem com uma diversidade de contextos e formas, geralmente demandam a mesma ação do sujeito em relação ao conhecimento matemático. As escolhas conceituais e metodológicas, identificadas nos materiais citados também foram analisadas e pudemos identificar convergências e opções distintas que caracterizam esses materiais

<p>Det verkar råda stor konsensus om att matematikundervisningen är viktig för att Sverige skall kunna hävda sig och kunna konkurrera i en global värld. Samtidigt visar det sig att eleverna i allt större utsträckning har svårt att nå målen för undervisningen. En undervisning, som forskningen visar, är hårt styrd av den matematikbok som används.</p><p>I Finland har det visat sig att vilken lärobok som används i undervisningen får statistiskt signifikanta konsekvenser för elevernas resultat. I uppsatsen undersöks om samma statistiskt signifikanta samband även föreligger i Sverige. 149 skolor omfattande 13 408 elever ingår i den statistiska kvantitativa studien. Till skillnad från i Finland pekar resultaten på att det inte går att dra någon slutsats om samband mellan använd lärobok och elevernas resultat. En förklaring till att det inte går att påvisa någon skillnad kan vara att de två helt dominerande matematikböckerna i årskurs 9, i en kvalitativ utvärdering bedöms som likvärdiga.</p><p>För att göra den kvalitativa utvärderingen av matematikböckerna används en metod utvecklad av The American Association for the Advancement of Science, AAAS, i USA. I uppsatsen visas att metoden är tillämpbar i Sverige och kan fungera som det ”instrument för att bedöma läromedels kvalitet utifrån målen att sträva mot i grundskola och gymnasieskola samt motsvarande mål för annan matematikutbildning” som matematikdelegationen efterlyser (SOU 2004:97).</p><p>Den föreslagna metoden används för att granska de två dominerande matematikböckerna i årskurs 9, Matematikboken Z och Matte Direkt. Den begränsade granskningen visar att de båda böckerna är likvärdiga, men framförallt att de har samma svagheter. Båda böckerna får låga betyg i kategorierna ”Building on Student Ideas about Mathematics” och ”Enhancing the Mathematics Learning Environment”. Något som kan få negativa konsekvenser för elevernas inlärning och för sättet som undervisningen bedrivs på.</p> / <p>Education in mathematics is considered important for Sweden to be able to compete in a global world where knowledge and information is imperative. However, mathematics results are decreasing and students often fail to reach the stipulated educational goals.</p><p>Research shows that in mathematics, what is taught and how it is taught is very dependent on the textbook used. In Finland, it has been concluded that there is a statistically significant difference in students´ results depending on which textbook is used. The objective of this thesis is to evaluate if the same is true in Sweden, i.e. is there a statistically significant difference in students’ results in mathematics depending on which textbook is used in Swedish schools? The evaluation is based on responses from 149 schools comprising 13 408 students. The study indicates that the textbook used does not affect the outcome. One explanation is that when assessing the quality of the two textbooks most commonly used in Swedish schools they can be considered equivalent.</p><p>Since textbooks in mathematics have a large influence on what is taught and how it is taught it is important to be able to assess the quality of the textbooks. The thesis demonstrates that a method for assessing textbooks in mathematics, developed by the American Association for the Advancement of Science, AAAS, can be used in Sweden. The method would be appropriate as the tool the “Matematikdelegationen” (SOU 2004:97) is requesting for evaluation of the quality of textbooks in mathematics.</p><p>Following the method stipulated by the AAAS, a limited evaluation is made of the two textbooks that dominate in Swedish schools in year 9, Matematikboken Z and Matte Direkt. It is striking that both books perform poorly in the same areas, Building on Student Ideas about Mathematics and Enhancing the Mathematics Learning Environment. This can have a negative impact on the pupils´ ability to learn mathematics and might also have a negative effect on the way mathematics is taught.</p>

In school algebra, using different methods including factorization to solve quadratic equations is one common teaching and learning topic at upper secondary school level. This study is about analyzing the algebra content related to solving quadratic equations and the method of factorization as presented in Swedish mathematics textbooks with subject matter content knowledge (CK) and pedagogical content knowledge (PCK) as analytical tools. Mathematics textbooks as educational resources and artefacts are widely used in classroom teaching and learning. What is presented in a textbook is often taught by teachers in the classroom. Similarly, what is missing from the textbook may not be presented by the teacher. The study is based on an assumption that pedagogical content knowledge is embedded in the subject content presented in textbooks. Textbooks contain both subject content knowledge and pedagogical content knowledge. The primary aim of the study is to explore what pedagogical content knowledge regarding solving quadratic equations that is embedded in mathematics textbooks. The secondary aim is to analyze the algebra content related to solving quadratic equations from the perspective of mathematics as a discipline in relation to algebra history. It is about what one can find in the textbook rather than how the textbook is used in the classroom. The study concerns a teaching perspective and is intended to contribute to the understanding of the conditions of teaching solving quadratic equations. The theoretical framework is based on Shulman’s concept pedagogical content knowledge and Mishra and Koehler’s concept content knowledge. The general theoretical perspective is based on Wartofsky’s artifact theory. The empirical material used in this study includes twelve mathematics textbooks in the mathematics B course at Swedish upper secondary schools. The study contains four rounds of analyses. The results of the first three rounds have set up a basis for a deep analysis of one selected textbook. The results show that the analyzed Swedish mathematics textbooks reflect the Swedish mathematics syllabus of algebra. It is found that the algebra content related to solving quadratic equations is similar in every investigated textbook. There is an accumulative relationship among all the algebra content with a final goal of presenting how to solve quadratic equations by quadratic formula, which implies that classroom teaching may focus on quadratic formula. Factorization method is presented for solving simple quadratic equations but not the general-formed quadratic equations. The study finds that the presentation of the algebra content related to quadratic equations in the selected textbook is organized by four geometrical models that can be traced back to the history of algebra. These four geometrical models are applied for illustrating algebra rules and construct an overall embedded teaching trajectory with five sub-trajectories. The historically related pedagogy and application of mathematics in both real world and pure mathematics contexts are the pedagogical content knowledge related to quadratic equations.