South African learners underachieve in mathematics. The many different factors that influence this underachievement include mathematics teachers' role in teaching mathematics with understanding. The question arises as to how teachers' mathematical content knowledge states can be transformed to positively impact learners' achievement in mathematics. In this study, different kinds of teachers' knowledge needed for teaching mathematics were discussed against the background of research in this area, which included the work of Shulman, Ma and Ball. From this study an important kind of knowledge, namely mathematical content knowledge for teaching (MCKfT), was identified and a teacher's ability to unpack mathematical knowledge and understanding was highlighted as a vital characteristic of MCKfT. To determine further characteristics of MCKfT, the study focussed on the nature of mathematics, different kinds of mathematical content knowledge (procedural and conceptual), cognitive processes (problem solving, reasoning, communication, connections and representations) involved in doing mathematics and the development of mathematical understanding (instrumental vs. relational understanding). The influence of understanding different problem contexts and teachers' ability to develop reflective practices in teaching and learning mathematics were discussed and connected to a teacher's ability to unpack mathematical knowledge and understanding. In this regard, the role of teachers' prior knowledge or current mathematical content knowledge states was discussed extensively. These theoretical investigations led to identifying the characteristics of MCKfT, which in turn resulted in theoretical criteria for the development of MCKfT. The theoretical study provided criteria with which teachers' current mathematical content knowledge states could be analysed. This prompted the development of a diagnostic instrument consisting of questions on proportional reasoning and functions. A qualitative study was undertaken in the form of a diagnostic content analysis on teachers' current mathematical content knowledge states. A group of secondary school mathematics teachers (N=128) involved in the Sediba Project formed the study population. The Sediba Project is an in-service teacher training program for mathematics teachers over a period of two years. These teachers were divided into three sub-groups according to the number of years they had been involved in the Sediba Project at that stage. The teachers' current mathematical content knowledge states were analysed with respect to the theoretically determined characteristics of and criteria for the development of MCKfT. These criteria led to a theoretical framework for assessing teachers' current mathematical content knowledge states. The first four attributes consisted of the steps involved in mathematical problem solving skills, namely conceptual knowledge (which implies a deep understanding of the problem), procedural knowledge (which is reflected in the correct choice of a procedure), the ability to correctly execute the procedure and the insight to give a valid interpretation of the answer. Attribute five constituted the completion of these four attributes. The final six attributes were an understanding of different representations, communication of understanding in writing, reasoning skills, recognition of connections among different mathematical ideas, the ability to unpack mathematical understanding and understanding the context a problem is set in. Quantitative analyses were done on the obtained results for the diagnostic content analysis to determine the reliability of the constructed diagnostic instrument and to search for statistically significant differences among the responses of the different sub-groups. Results seemed to indicate that those teachers involved in the Sediba Project for one or two years had benefited from the in-service teacher training program. However, the impact of this teachers' training program was clearly influenced by the teachers' prior knowledge of mathematics. It became clear that conceptual understanding of foundation, intermediate and senior phase school mathematics that should form a sound mathematical knowledge base for more advanced topics in the school curriculum, is for the most part procedurally based with little or no conceptual understanding. The conclusion was that these teachers' current mathematical content knowledge states did not correspond to the characteristics of MCKfT and therefore displayed a need for the development of teachers' current mathematical content knowledge states according to the proposed criteria and model for the development of MCKfT. The recommendations were based on the fact that the training that these teachers had been receiving with respect to the development of MCKfT is inadequate to prepare them to teach mathematics with understanding. Teachers' prior knowledge should be exposed so that training can focus on the transformation of current mathematical content knowledge states according to the characteristics of MCKfT. A model for the development of MCKfT was proposed. The innermost idea behind this model is that a habit of reflective practices should be developed with respect to the characteristics of MCKfT to enable a mathematics teacher to communicate and unpack mathematical knowledge and understanding and consequently solve mathematical problems and teach mathematics with understanding. Key words for indexing: school mathematics, teacher knowledge, mathematical content knowledge, mathematical content knowledge for teaching, mathematical knowledge acquisition, mathematics teacher education / Thesis (Ph.D. (Education))--North-West University, Potchefstroom Campus, 2007.

abstract: This study contributes to the ongoing discussion of Mathematical Knowledge for Teaching (MKT). It investigates the case of Rico, a high school mathematics teacher who had become known to his colleagues and his students as a superbly effective mathematics teacher. His students not only developed excellent mathematical skills, they also developed deep understanding of the mathematics they learned. Moreover, Rico redesigned his curricula and instruction completely so that they provided a means of support for his students to learn mathematics the way he intended. The purpose of this study was to understand the sources of Rico's effectiveness. The data for this study was generated in three phases. Phase I included videos of Rico's lessons during one semester of an Algebra II course, post-lesson reflections, and Rico's self-constructed instructional materials. An analysis of Phase I data led to Phase II, which consisted of eight extensive stimulated-reflection interviews with Rico. Phase III consisted of a conceptual analysis of the prior phases with the aim of creating models of Rico's mathematical conceptions, his conceptions of his students' mathematical understandings, and his images of instruction and instructional design. Findings revealed that Rico had developed profound personal understandings, grounded in quantitative reasoning, of the mathematics that he taught, and profound pedagogical understandings that supported these very same ways of thinking in his students. Rico's redesign was driven by three factors: (1) the particular way in which Rico himself understood the mathematics he taught, (2) his reflective awareness of those ways of thinking, and (3) his ability to envision what students might learn from different instructional approaches. Rico always considered what someone might already need to understand in order to understand "this" in the way he was thinking of it, and how understanding "this" might help students understand related ideas or methods. Rico's continual reflection on the mathematics he knew so as to make it more coherent, and his continual orientation to imagining how these meanings might work for students' learning, made Rico's mathematics become a mathematics of students--impacting how he assessed his practice and engaging him in a continual process of developing MKT. / Dissertation/Thesis / Ph.D. Mathematics 2011

O presente trabalho visa estudar e refletir sobre a identidade docente. O tema é bastante amplo e de extrema relevância, uma vez que a sua discussão não costuma fazer parte do cotidiano da escola. A investigação procurou delinear o que leva uma pessoa a escolher a docência como uma profissão, manter-se nela por um longo período de sua vida e ainda demonstrar através do olhar um brilho quando a ela se refere. Por conseguinte, observar através dos dados obtidos com os docentes envolvidos na pesquisa o que o motiva, o que incita o educador a realizar a sua atividade, o significado e o sentido de ser docente. A pesquisa conta com a participação de educadores da rede municipal de ensino de Estância Velha, e no contato com estes profissionais evidenciou-se, através de suas respostas, que não há como fazer uma separação entre a sua história de vida e suas representações e saberes, e como estas questões refletem pelas suas atitudes no cotidiano escolar, nas diferentes relações. A análise da problemática foi aprofundada através de leituras que consideram a questão da opção pela carreira docente, o modo como o profissional constrói a sua identidade docente. Foram de extrema valia os textos de Miguel Arroyo, Antonio Nóvoa, Selma Garrido Pimenta, Maurice Tardif, José Carlos Libâneo, entre outros. Não há a pretensão de esgotarmos a reflexão sobre o assunto nesta dissertação, no entanto, é um ponto de partida para o entendimento da relação do profissional da área da educação com a sua atividade docente, de forma que possa ser aproveitado nos estudos e reflexões que visam à melhoria da educação. / This work aims to study and reflect on teaching identity. The theme is very broad and very important, since the discussion does not usually form part of the routine of schools. The research seeks to delineate what leads a person to choose teaching as a profession, to remain there for a long period of their life and to demonstrate through the brightness of their eyes, their wish to pursue further reflection on the identity and the knowledge needed for teaching practice. The central focus is the extent of personal choice and the staying on in teaching. It examines, through the data collected from teachers involved in the research, what motivates them, what encourages the teacher to perform his/her activity, the significance and the meaning of being teachers. The research counts on the participation of educators from the municipal teaching network of Estância Velha, and highlights that there is no way to separate the life story from its representations and knowledge, and in which ways these issues reflect upon attitudes in everyday school life in different relations. The analysis of the problem is deepened through readings that regard the issue of choosing the teaching career, as the way the professional builds up his/her teaching identity. It attempts to assume and interpret the contribution of the texts by Miguel Arroyo, Antonio Nóvoa, Selma Garrido Pimenta, Maurice Tardif, José Carlos Libâneo among others. Although the reflection on the issue will not be completed in this dissertation, the objective is to understand the relationship of the professional in the education field with their teaching activity, so that this work might be used in studies and discussions that aim the improvement in education.

abstract: A teacher’s mathematical knowledge for teaching impacts the teacher’s pedagogical actions and goals (Marfai & Carlson, 2012; Moore, Teuscher, & Carlson, 2011), and a teacher’s instructional goals (Webb, 2011) influences the development of the teacher’s content knowledge for teaching. This study aimed to characterize the reciprocal relationship between a teacher’s mathematical knowledge for teaching and pedagogical goals. Two exploratory studies produced a framework to characterize a teacher’s mathematical goals for student learning. A case study was then conducted to investigate the effect of a professional developmental intervention designed to impact a teacher’s mathematical goals. The guiding research questions for this study were: (a) what is the effect of a professional development intervention, designed to perturb a teacher’s pedagogical goals for student learning to be more attentive to students’ thinking and learning, on a teacher’s views of teaching, stated goals for student learning, and overarching goals for students’ success in mathematics, and (b) what role does a teacher's mathematical teaching orientation and mathematical knowledge for teaching have on a teacher’s stated and overarching goals for student learning? Analysis of the data from this investigation revealed that a conceptual curriculum supported the advancement of a teacher’s thinking regarding the key ideas of mathematics of lessons, but without time to reflect and plan, the teacher made limited connections between the key mathematical ideas within and across lessons. The teacher’s overarching goals for supporting student learning and views of teaching mathematics also had a significant influence on her curricular choices and pedagogical moves when teaching. The findings further revealed that a teacher’s limited meanings for proportionality contributed to the teacher struggling during teaching to support students’ learning of concepts that relied on understanding proportionality. After experiencing this struggle the teacher reverted back to using skill-based lessons she had used before. The findings suggest a need for further research on the impact of professional development of teachers, both in building meanings of key mathematical ideas of a teacher’s lessons, and in professional support and time for teachers to build stronger mathematical meanings, reflect on student thinking and learning, and reconsider one’s instructional goals. / Dissertation/Thesis / Doctoral Dissertation Mathematics Education 2016

abstract: This dissertation reports three studies of students’ and teachers’ meanings for quotient, fraction, measure, rate, and rate of change functions. Each study investigated individual’s schemes (or meanings) for foundational mathematical ideas. Conceptual analysis of what constitutes strong meanings for fraction, measure, and rate of change is critical for each study. In particular, each study distinguishes additive and multiplicative meanings for fraction and rate of change. The first paper reports an investigation of 251 high school mathematics teachers’ meanings for slope, measurement, and rate of change. Most teachers conveyed primarily additive and formulaic meanings for slope and rate of change on written items. Few teachers conveyed that a rate of change compares the relative sizes of changes in two quantities. Teachers’ weak measurement schemes were associated with limited meanings for rate of change. Overall, the data suggests that rate of change should be a topics of targeted professional development. The second paper reports the quantitative part of a mixed method study of 153 calculus students at a large public university. The majority of calculus students not only have weak meanings for fraction, measure, and constant rates but that having weak meanings is predictive of lower scores on a test about rate of change functions. Regression is used to determine the variation in student success on questions about rate of change functions (derivatives) associated with variation in success on fraction, measure, rate, and covariation items. The third paper investigates the implications of two students’ fraction schemes for their understanding of rate of change functions. Students’ weak measurement schemes obstructed their ability to construct a rate of change function given the graph of an original function. The two students did not coordinate three levels of units, and struggled to relate partitioning and iterating in a way that would help them reason about fractions, rate of change, and rate of change functions. Taken as a whole the studies show that the majority of secondary teachers and calculus students studied have weak meanings for foundational ideas and that these weaknesses cause them problems in making sense of more applications of rate of change. / Dissertation/Thesis / Doctoral Dissertation Mathematics 2016

abstract: The research indicated effective mathematics teaching to be more complex than assuming the best predictor of student achievement in mathematics is the mathematical content knowledge of a teacher. This dissertation took a novel approach to addressing the idea of what it means to examine how a teacher's knowledge of mathematics impacts student achievement in elementary schools. Using a multiple case study design, the researcher investigated teacher knowledge as a function of the Mathematics Teaching Cycle (NCTM, 2007). Three cases (of two teachers each) were selected using a compilation of Learning Mathematics for Teaching (LMT) measures (LMT, 2006) and Developing Mathematical Ideas (DMI) measures (Higgins, Bell, Wilson, McCoach, & Oh, 2007; Bell, Wilson, Higgins, & McCoach, 2010) and student scores on the Arizona Assessment Collaborative (AzAC). The cases included teachers with: a) high knowledge & low student achievement v low knowledge & high student achievement, b) high knowledge & average achievement v low knowledge & average achievement, c) average knowledge & high achievement v average knowledge & low achievement, d) two teachers with average achievement & very high student achievement. In the end, my data suggested that MKT was only partially utilized across the contrasting teacher cases during the planning process, the delivery of mathematics instruction, and subsequent reflection. Mathematical Knowledge for Teaching was utilized differently by teachers with high student gains than those with low student gains. Because of this insight, I also found that MKT was not uniformly predictive of student gains across my cases, nor was it predictive of the quality of instruction provided to students in these classrooms. / Dissertation/Thesis / Ph.D. Curriculum and Instruction 2013

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-07-13T11:56:19Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_Taíza para depósito.pdf: 5088338 bytes, checksum: ca374c1d29df553508c46fa091fbda0e (MD5) / Made available in DSpace on 2016-07-13T11:56:19Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação_Taíza para depósito.pdf: 5088338 bytes, checksum: ca374c1d29df553508c46fa091fbda0e (MD5) Previous issue date: 2015-09-18 / Compreendendo que o paradigma sociointeracionista tem apresentado novas perspectivas para o ensino de língua portuguesa e que essas perspectivas podem ou não influenciar o modo como os professores utilizam os livros didáticos, desenvolvemos um estudo cujo objetivo consistiu em investigar como professores de língua portuguesa utilizam livro(s) didático(s) de português, especialmente nas aulas de gramática/análise linguística. Para tanto, referenciamo-nos em discussões teóricas sobre saberes e práticas docentes (cf. CERTEAU, 1998; CHARTIER 2000, 2005; FERREIRA, 2007, TARDIF, 2008; TARDIF; RAYMOND, 2000; SILVA, 2012; 2013), assim como naquelas dedicadas ao ensino de língua portuguesa e/ou o uso de livros didáticos (cf. MENDONÇA, 2006; ANTUNES, 2009; BUNZEN, 2009; ROJO, 2007). Como procedimentos metodológicos, realizamos, inicialmente, uma sessão de grupo focal com professores de língua portuguesa de uma escola da rede estadual de ensino de Pernambuco. Em seguida, realizamos observações de aula e entrevistas com dois dos participantes do referido grupo, os quais foram selecionados tendo como critério a utilização frequente do livro didático em sala de aula. Para analisar os dados, utilizamos a técnica de análise do conteúdo, conforme Bardin (2012). A análise dos dados gerados a partir dos procedimentos mencionados evidenciou que a professora Alice associava o uso do livro adotado a outros manuais e, ao utilizá-los, tentava aproximar suas práticas de ensino de perspectivas mais “inovadoras”. Essa docente, apesar de reconhecer a necessidade de mudança, sentia-se, algumas vezes, desafiada ao tentar incorporá-las em seu cotidiano. Por isso, quando julgava necessário, recorria a práticas de ensino com características mais conservadoras. Já o professor Mário preferia conduzir suas práticas segundo perspectivas mais tradicionais de ensino, as quais eram validadas por seus saberes pré-profissionais. Nesse contexto, o professor Mário, ao utilizar o livro adotado, buscava explorar os recursos por ele disponibilizados que se identificavam com essa perspectiva. Os resultados evidenciaram, ainda, que a professora Alice e o professor Mário apresentavam visões diferenciadas acerca do LDP que adotaram. Entretanto, ambos buscavam construir um uso autônomo desse recurso e de outros que utilizavam, pois, na maioria das aulas, não os usavam linearmente, nem reproduziam fidedignamente as atividades que eles sugeriam. Ao contrário, buscavam adequar o uso desses recursos às urgências de suas práticas cotidianas. Desse modo, os docentes “burlavam” o que era proposto pelos LDs, “fabricando táticas” para usá-los. Por meio dessas táticas, construíam suas “maneiras” particulares de “consumir” as orientações dos livros, sem almejar reproduzir teorias acadêmicas sobre o ensino da língua ou reproduzir as prescrições dos LDPs. Diante disso, percebemos que, no contexto investigado, os LDPs não constituíam recursos que limitavam a atuação dos professores, mas como instrumentos que podem desencadear uma multiplicidade de práticas. Portanto, não convém olharmos os docentes como reprodutores desses materiais, mas, sim, como sujeitos autores de suas práticas, que possuem saberes específicos para conduzir cada situação de ensino no âmbito de suas salas de aulas. / Realizing that the social interactionist paradigm has presented new perspectives for the Portuguese language teaching and that these prospects may or may not influence how teachers use textbooks, developed a study whose objective was to investigate how Portuguese language teachers use the book (s) textbook (s), especially in grammar lessons / linguistic analysis. For this, was used references in theoretical discussions about knowledge and teaching practices (cf. CERTEAU, 1998; CHARTIER 2000, 2005; FERREIRA, 2007, TARDIF, 2008; TARDIF; RAYMOND, 2000; SILVA, 2012; 2013), as well as those devoted to English language education and / or the use of textbooks (cf. MENDONÇA, 2006; ANTUNES, 2009; BUNZEN, 2009; ROJO, 2007). As methodological procedures, we conducted initially a focus group session with Portuguese-speaking teachers in a school of the Pernambuco state. Then we performed classroom observations and interviews with two of the participants of the group, which were selected on the criteria the frequent use of the textbook in the classroom. To analyze the data, we used the technique of content analysis, according to Bardin (2012). The analysis of data generated from the procedures mentioned revealed that the teacher Alice was associating the use of the book adopted with other manuals and, when was utilizing them, was trying to approach her teaching practices to "innovative" perspectives. This teacher, while recognizing the need for change, felt sometimes challenged when trying to incorporate them into their daily lives. Therefore when judged appropriate, resorted teaching practices with more conservative characteristics. However, the teacher Mario preferred to conduct their practices second most traditional perspectives of education, validated by their pre-professional knowledge. In this context, the teacher Mario, by using the adopted book, sought to exploit the resources available identified with this perspective. The results show also that teacher Alice and teacher Mario had different views about the LDP they adopted. However, both seek to build a stand-alone use of this feature and others that used therefore in most classes, not used linearly, not faithfully reproduce the activities they suggested. On the contrary, they seek to tailor the use of these emergency resources to their daily practices. Thus, teachers were "diverting" which was proposed by LDs, "making tactics" to use them. Through these tactics, they built their "ways" private "consume" the guidelines of the books, without aim reproduce academic theories of language teaching or reproducing the requirements of LDPs. Thus, we see that in the investigated context, the LDPs did not constitute resources that limited the actions of teachers, but as instruments that can trigger a variety of practices. Therefore, should not we look at teachers as reproducers of these materials, but rather as subjects authors of their practices, which have specific knowledge to drive every teaching situation within their classrooms.

Submitted by Renata Morais (rmorais@unoeste.br) on 2018-10-18T18:41:33Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Fernanda Miranda Caliani Sá.pdf: 480365 bytes, checksum: ec0fc3af2197b4c44898e83ed0c69d63 (MD5) / Made available in DSpace on 2018-10-18T18:41:34Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Fernanda Miranda Caliani Sá.pdf: 480365 bytes, checksum: ec0fc3af2197b4c44898e83ed0c69d63 (MD5) Previous issue date: 2018-04-11 / The medical professor, as well as in some other areas of teaching in higher education, is not prepared in the undergraduate course to teach and, as a result, his experience in the classroom derives mainly from his specific knowledge in the field in which it operates. Understanding the teaching exercise as a social practice, the professionalization of the teacher must constitute a strategy for the constant rethinking of education in its institutional and social dimensions. The present research has as general objective to identify and analyze the identity and the knowledge of the teaching of the medical professors, in an undergraduate course in Medicine. In view of the proposed objective, we opted for a qualitative methodology. To conduct the research, a semi-structured interview was conducted with twelve doctors, professors of the Medicine Course of a Private Higher Education Institution of the State of Sao Paulo. The collected data were analyzed from a theoretical reference centered on Mikhail Bakhtin's Theory of Materialist Philosophy of Language. Analyzing, critically, the results of the research, we saw the need to reflect on the process of training, performance and development of the medical professional in teaching. Specific teacher training is required to start a career as a teacher, and institutions should promote initial, ongoing pedagogical training actions, allowing for changes in the pedagogical practices of medical professionals in undergraduate medical courses. / O professor de medicina, assim como em algumas outras áreas da docência no ensino superior, não é preparado, no curso de graduação, para ensinar e, em decorrência disso, sua experiência na sala de aula deriva, principalmente, de seu conhecimento específico no campo em que atua. Entendendo-se o exercício docente como uma prática social, a profissionalização do professor deve constituir estratégia para o repensar constante da educação em suas dimensões institucional e social. A presente pesquisa teve como objetivo geral identificar e analisar a identidade e os saberes da docência dos médicos professores, em um curso de graduação em Medicina. Tendo em vista o objetivo proposto, optamos por uma metodologia qualitativa. Para desenvolver a investigação, foi realizada uma entrevista semiestruturada com doze médicos, professores do Curso de Medicina de uma Instituição de Ensino Superior privada do Estado de São Paulo. Os dados coletados foram analisados a partir de um referencial teórico centrado na Teoria da Filosofia Materialista da Linguagem de Mikhail Bakhtin. Analisando, criticamente, os resultados da pesquisa, constatamos a necessidade de realizar uma reflexão sobre o processo de formação, atuação e desenvolvimento do profissional médico na docência. É necessária uma formação docente específica para iniciar a carreira como professor, e as instituições devem promover ações de formação pedagógica, inicial e continuada, permitindo mudanças nas práticas pedagógicas dos profissionais médicos, nos cursos de graduação em Medicina.

In order to investigate ways pre-service student teachers (PSTs) might learn to teach with high-level tasks and effectively incorporate student thinking into their lessons a teaching experiment was designed and carried out by the cooperating teacher/researcher (CT). The intervention was for the CT to interject into the lessons of the PSTs during moments of opportunity. By interjecting a small question or comment during the lesson the CT hoped to support the learning of both the students of mathematics in the class and the PSTs. This in-the-moment interjecting was meant to enhance and underscore the situated learning of the PSTs within the context of actual practice. Essentially the PSTs learned how to manage and improve the discourse of the classroom in the moment of the discourse. This study utilized both an ongoing analysis of the data during collection in order to inform the instruction provided by the CT and a retrospective analysis of the data in order to develop an understanding of the developmental sequence through which PSTs progressed. The results suggest the interjections provided to the PSTs served multiple roles within the domains of mathematical development for the students of mathematics and pedagogical development for the PSTs. A classification of the interjections that occurred and the stages of development through which PSTs passed will be discussed. Implications from this work include increased attention to the groundwork leading up to the student teaching experience as well as an adjustment to the role of cooperating teacher to be more that of a teacher educator.

Syftet med föreliggande licentiatavhandling är att, utifrån ett specialdidaktiskt perspektiv, bidra med kunskap om lågpresterande elevers grundläggande antals- och taluppfattning, och hur utvecklingen av denna kan stödjas. Den övergripande forskningsfråga som besvaras är vilka aspekter, som ur ett specialdidaktiskt perspektiv, är särskilt betydelsefulla att beakta vad gäller lågpresterande elevers kunskapsutveckling inom grundläggande antals- och taluppfattning. Avhandlingen består av två delstudier. I delstudie 1, som är en systematisk litteraturöversikt, studeras vad som är kännetecknande för lågpresterande årskurs F-3-elever och hur de definieras i forskningslitteraturen. I den andra studien, delstudie 2, undersöks vilket kunnande gällande tals del-helhetsrelationer som förskoleklasselever utvecklar i en undervisningsinsats där konceptuella subitiseringsaktiviteter fokuseras. Specialdidaktikens förebyggande och stödjande roll utgör studiens övergripande förståelseram där de lågpresterande elevernas kunskapsutveckling förstås i förhållande till vilket lärande som möjliggörs i undervisningen. Det matematiska innehållet är grundläggande antals- och taluppfattning med fokus på konceptuell subitisering. Teorier om barns antals- och taluppfattningsutveckling (Baroody m.fl., 2009; Nunes &Bryant, 2007; Sayer m.fl. 2016), inbegripet teorier om subitisering (Clements m.fl., 2019; Kaufman m.fl., 1949) och groupitizing (Starkey &McCandliss, 2014), har utgjort den innehållsliga utgångspunkten. För att tolka specialdidaktikens specifika bidrag och krafter i relation till allmän matematikdidaktisk kompetens har ramverket Mathematical Knowledgefor Teaching (MKT) (Ball m.fl., 2008) använts, mer specifikt de tre delarna specialized content knowledge, knowledge of content and students och knowledge of content and teaching. Resultatet av syntesen visar att den specifika kompetens som krävs i relation till innehållet (specialized content knowledge), är fördjupad kunskap om centrala aspekter och vanliga trösklar i elevers kunskapsutveckling inom grundläggande antals- och taluppfattning för att motverka framtida matematiksvårigheter. Även fördjupad kunskap om elevers individuella variationer vad gäller att förstå och hantera antal och tal (knowledge of content and students) för att tidigt kunna identifiera elever i svårigheter är centralt och slutligen fördjupad kunskap om hur lågpresterande elevers antals-och taluppfattning kan stödjas och svårigheter förebyggas och överbryggas i undervisningen (knowledge of content and teaching). Specialdidaktikens bidrag förstås som krafter som hjälper till att balansera relationen mellan den svagpresterande eleven, läraren och matematikinnehållet i undervisningen, så att lärande möjliggörs. Specialdidaktisk kompetens kan därmed sägas komplettera den allmänna ämnesdidaktiska kompetensen (MKT) genom sitt bidrag med fördjupad kunskap om hur elever som inte utvecklas som förväntat i matematik kan stödjas, i grundläggande antals- och taluppfattning, vilket bildar Specialdidactic Mathematical Knowledge for Teaching eller SMKT.