School Mathematical Knowledge Research Articles

EPISTEMOLOGÍA DE LOS PROFESORES SOBRE EL CONOCIMIENTO MATEMÁTICO ESCOLAR: UN ESTUDIO DE CASO

Se buscó conocer la epistemología de los profesores sobre el conocimiento matemático escolar. El estudio se enmarco en la Teoría Socioepistemológica entendiendo la matemática como una actividad humana desde el relativismo epistémico. Este estudio cualitativo utilizó el análisis microscópico para formar categorías y luego analizó dialécticamente esas categorías. El interés investigativo surgió al observar la influencia del eurocentrismo, el mono epistemisismo de la escuela y la ausencia de algunos conocimientos en la enseñanza. La epistemología del profesor influye su enseñanza y afecta el modelo escolar como herramienta de cambio o de continuidad social. Los resultados mostraron que los profesores mayoritariamente entienden la matemática como un conocimiento a priori, asignando a la acción humana el rol de descubrirla, interpretarla o formalizarla.

Estrategias comunitarias de resolución de problemas matemáticos en una comunidad maya en Yucatán

Este artículo está basado en un trabajo de campo de seis meses realizado en la región maya de México, y busca explorar la manera en que se instruyen las matemáticas en una escuela secundaria maya de Yucatán. Estudiamos los enfoques de la comunidad para resolver problemas, específicamente los problemas matemáticos, ya que en esta región los resultados de exámenes estandarizados en matemáticas son bajos, y las tasas de deserción son altas. Sin embargo, los enfoques que históricamente se utilizan en la comunidad para resolver problemas están llenos de recursos y activos culturales que pueden apoyar la enseñanza de las matemáticas y el desarrollo de habilidades afines en las escuelas de la comunidad. Por tal motivo, primero ilustramos la tensión que existe entre los conocimientos matemáticos de la comunidad y la escuela. En segundo lugar, buscamos expandir la definición sobre lo que se considera conocimiento matemático. Finalmente, describimos dos estrategias de la comunidad para resolver problemas matemáticos que conllevan la autonomía y la mentalidad de improvisación.

Influencia del conocimiento profundo del profesor sobre fracciones en el aprendizaje de alumnos de 4o. grado

El objetivo de este estudio es establecer en qué medida el conocimiento profundo del profesor sobre fracciones y el conocimiento sobre la enseñanza de las mismas, ajustados por el nivel socioeconómico y el nivel de conocimientos en matemáticas que se alcanza en las escuelas (SIMCE), influye en el aprendizaje de los alumnos en cuanto a la conceptualización de las fracciones en 4o. grado. Con información de 378 alumnos de 4o. grado de 9 escuelas, así como de sus respectivos profesores de matemáticas, los resultados de los análisis de regresión muestran que el efecto Conocimiento Profundo del profesor es significativo en el aprendizaje por alumno (p = 0.001), más allá de lo explicado por el puntaje SIMCE del colegio, que también es significativo (p = 0.02).

Design and Development of High School Curriculum Learning System Based on the Core Quality of Mathematics

Mathematics plays a unique and irreplaceable role in forming human rational thinking, scientific spirit and promoting human intellectual development. It is worth studying how to cultivate the core quality of high school students. Under the background of Internet +, many Internet education service industries have further developed, and efforts have been made to study the effective integration of subject knowledge and information technology to improve students’ learning effectiveness. Mathematics, as one of the core courses of high school education, highlights its importance. Based on the core quality of mathematics, this paper constructs a new model of high school mathematics knowledge, and designs and implements the framework of high school curriculum learning system. Teachers adjust teaching content and strategies according to the actual situation of students, improve classroom efficiency, gradually achieve high-level teaching goals, and train new talents who can adapt to the needs of the new era in modern teaching.

Epistemic issues in classroom mathematical activity: There is more to students’ conversations than meets the teacher’s ear

We report on a comparative investigation of student mathematical activity in two settings of a secondary mathematics classroom: peer interaction in small group and group interaction with the teacher. Our framework draws on the understanding of school mathematics as activity in between the historicity of knowledge and the situatedness of norms. We propose the term epistemic issue to refer to instances of knowledge about the construction and justification of school mathematics knowledge whose use is traceable in student activity. A major finding points to the presence of a number of epistemic issues during peer work and their omission in the communication of this work to the teacher; a phenomenon we call epistemic shift. To illustrate this finding and the methods of analysis, we take data from a group of students during a lesson of probability and the lesson-based video stimulated recall interview. We finish by discussing some implications for the development of the mathematical culture of the classroom.

A prática de ensino como formação docente do professor de matemática

Este texto tem por objetivo tratar do problema da formação pessoal do professor a partir da noção de relação com o saber sob a compreensão da teoria antropológica do didático. Um dispositivo teórico-metodológico é desenvolvido para proporcionar um quadro de análise que possibilite evidenciar mudanças da relação do professor com um saber matemático escolar. Resultados obtidos a partir da análise da construção de compreensões, sobre a resolução da equação do segundo grau, mostram a potencialidade do dispositivo de formação pessoal por revelar aquisições de novos saberes e procedimentos úteis, bem como novos problemas relacionados, para as práticas de ensino do professor.

“There is One Geometry and in Each Case There is a Different Formula”

In this paper, we analyze two episodes from an inquiry-based didactical research; the complete analysis of our research data is still ongoing. By taking into consideration various developments from the history of the geometry of space-time, our general aim is to explore high school students’ conceptions about measurement of length and time in relatively moving systems, and lead the students to reconsider these conceptions in an attempt of constructing a new metric for space-time. The episodes are extracted from long (focused) interviews with two couples of students, based on a carefully designed fictional scenario. Two main strategies have been identified and are analyzed in the paper: one of them relies on imagination and intuition; the other one makes use of preexisting school mathematical knowledge, in arriving to a simplified formula of a Minkowskian metric.

On Singapore Prospective Secondary school teachers' Mathematical content Knowledge

This paper reports the performance of one entire cohort of Singapore prospective secondary school mathematics teachers in a mathematics proficiency test. 
 The prospective teachers were admitted to the teacher education program specializing in teaching secondary school mathematics. The strengths of the prospective teachers' content knowledge, their errors and misconceptions in school mathematical content knowledge are discussed.

Cultural influences on Ghanaian primary school pupils conceptions in measurement and division of fractions

This paper reports on a study which investigated how pupils’ notions of measuring and sharing in out-of-school setting reflect their conceptions and practices in school. Two focus group interviews were carried out with 16 primary school pupils, eight each from grade 4 and grade 6 in two average achieving schools (one each from rural and urban schools) in Ghana. Qualitative analysis of pupils’ activities on measuring and division of mixed/decimal fractions showed evidence of cultural influences on the participants’ conceptions and practices in the measurement of capacity and division of a mixed/decimal fraction by a whole number in the real-life situation. It did not appeal to grade four pupils to share/divide a half of an object. Findings from the study appear to confirm the local aspect of mathematical knowledge and recommend the need to help pupils to draw on and integrate every day and school mathematical knowledge in the teaching and learning situation.

PISA 2012 공개 문항을 활용한 예비수학교사의 수학내용지식 분석 사례연구

Mathematics preservice teachers' Mathematical Content Knowledge ("MCK") includes not only knowledge for mathematics, but also academic knowledge for school mathematics and mathematical process knowledge. We can consider the items in PISA 2012 as suitable tools to assess process knowledge as well as mathematical content knowledge because these items are developed by competent international educational experts. Therefore, the responses to items with the low percentage of correct answers in conjunction with the mathematical contents were analyzed with focus on FMC. The results showed the reasoning competency in responses using the conditions of the problem and of understanding the conditions after reading the complex problems within the context (i.e. the reasoning and argumentation competency, and communication competency) requires improvements. Furthermore the results indicated the errors due to a lack of ability of devising strategies for problem solving. Based on the foregoing results, the implications towards the directions of the education for the preservice mathematics teachers have been derived.

CONCERNING THE MATHEMATICAL QUALITY KNOWLEDGE OF MODERN UNIVERSITY ENTRANTS

The aim of the article is to analyze the dynamics of Unified State Examination GPA on Mathematics in Novosibirsk Region, Russia over the last two years. Methods. For diagnosing the Mathematics quality digestion of general education institution graduates, the authors apply the empirical material; correlation relationship between entrance test results and the results of Unified State Examination is assessed. Results. The research findings include the main causes of low results in Mathematics; one of them is the absence of clear conceptual thinking. The authors give the analysis of residual assessment for school mathematical knowledge during the entrance test results of incoming first-year students (brunches of study: Public and Municipal Administration, Human Resource Management) of Siberian Management Institute, Siberian Affiliate of Russian Presidential Academy of National Economy and Public Administration (Siberian Affiliate of RANEPA). The conclusion is drawn that the result of Unified State Examination isn’t an objective indicator of mathematical knowledge of the incoming first-year students. Scientific novelty. The authors single out the key factors caused low mathematical knowledge quality of school graduates. Correction ways and concrete steps to be taken for improving students’ assimilation of Bachelor’s Programme Science Disciplines are described. Practical significance. The authors note that the research outcomes can be used not only for improving Unified State Examination probity and objectivity of students’ quality assessment but for increasing basic Mathematics education as well

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This paper considers theconcept of qualityeducationand modern ways ofitsdiagnosis,such asthe Unified State Examination (GPA) and the FederalInternet-
 based Exam in vocational education.
 The dynamics of the GPA on mathematics in Russia and Novosibirsk Region during last two years are analyzedin order to estimate the effectiveness of
 using GPA as a knowledge quality indicator.The paper delivers results of assessment of residual school mathematical knowledge based on the entrance
 test results among incoming first-year students (specialties: Public and Municipal Administration, Human Resource Management) of Siberian Branch of
 the Russian Presidential Academy of National Economy and Public Administration (Siberian Branch of RANEPA).
 Empirical material of the main sections of school Mathematics is provided and the correlation between the entrance test results and the results of the
 Unified State Examination is assessed. The conclusion is drawn that the results of the Unified State Examination arenot objective indicators of the incoming
 first-year students� knowledge of Maths.
 It is shownthat the FederalInternet-based Examin vocational educationhasa number of disadvantages, removal of whichwill affect itsobjectivity. The
 authors discussandanalyze the results ofthe FederalInternet-based Exam on Mathematics of studentsof Siberian Branch of the Russian Presidential
 Academy of National Economy and Public Administration (Siberian Branch of RANEPA).
 The hypothesis regarding possible reasons of current situation is put forward and steps to be taken for improving student assimilation of Mathematics
 and Natural Science of Bachelor�s Degree programs are described.

Relationships between Teaching Professional Rank, Course Taking, Teaching Experience and Knowledge of Algebra for Teaching

In this study, we examined the relationships among years of teaching experience, professional rank, number of courses taken, and knowledge of algebra for teaching (KAT). 338 in-service and 376 pre-service secondary mathematics teachers in China completed a KAT questionnaire. Various statistical techniques were employed to examine these relationships. The pre-service participants teachers performed statistically significantly higher in advanced mathematics knowledge than their in-service counterparts. Among the inservice teachers, senior teachers had scored higher in school mathematics and teaching mathematics, compared with junior teachers. Yet participants' advanced mathematics knowledge decreased as their professional rank advanced or their teaching experience increased. The number of courses taken has significantly positive correlation with school mathematics knowledge and advanced mathematics knowledge. The implications of these findings for mathematics teacher education are discussed.

Socioepistemología y empoderamiento: la profesionalización docente desde la problematización del saber matemático

La Matemática Educativa, como disciplina académica, se propone un objetivo mayor: democratizar el aprendizaje de las matemáticas. Para alcanzarlo, habrá que transitar de una perspectiva platónica, centrada en objetos abstractos ajenos a la realidad, hacia una visión socioepistemológica que asume a las prácticas sociales como la base de la construcción del conocimiento matemático de toda persona. Esto precisa de numerosas restructuraciones del sistema educativo, una de ellas es la profesionalización docente. En este artículo, postulamos al empoderamiento como el proceso que atiende a la profesionalización docente desde una mirada socioepistemológica a través de la problematización del saber matemático escolar.

Using School Mathematics to Understand Cultural Activities: How Far Can We Go?

Mathematics and culture are often interconnected, making school mathematics intimately linked to the society in which it is taught. In response to this connection, mathematics educational reform policies indicate that learners should be getting an education which is connected to their cultures. Contexts are seen to be useful insofar as they provide access to school mathematics. This article focuses on the reverse, that is, using school mathematics to deepen our understanding of cultural activities, largely based on the notion that the mathematics content learnt in schools will be transferred by learners to use in their daily lives. We propose that this reverse practice calls for learners who are mathematically, socially and epistemologically empowered through mathematics education. We argue that mathematics classrooms rarely establish mathematics as an essential tool for understanding and changing the world. Critical pedagogy is not being valued as an emerging pedagogic agenda in mathematics education. Also the advanced nature of cultural practices need more advanced mathematical knowledge possibly to respond to the complexity of the practices. The qualitative study from which this article emerges worked with three mathematics teachers and their Grade 9 learners from one rural school (situated very close to a cultural village). An attempt was made to try and connect mathematics concepts to cultural activities. Based on the analysis of data collected over an extended period of ethnographic and participant classroom observation, we argue that school mathematical knowledge can be used to read and understand cultural practices deeper. DOI: 10.5901/mjss.2014.v5n3p146

Towards a Bernsteinian language of description for mathematics classroom discourse

This article aims at developing an external language of description to investigate the problem of why particular groups of students are systematically not provided access to school mathematical knowledge. Based on Basil Bernstein’s conceptualisation of power in classification, we develop a three-dimensional model that operationalises the contextual boundaries, the linguistic features and the structure of knowledge, and their respective relations to power on a not too high level of abstraction. The contribution of this article consists of a systematic connection of classification with the latter two dimensions that abides the generative principles of Bernstein’s internal language of description. Finally, we illustrate the analytical potential of the three-dimensional model through a brief discussion of one classroom episode.

Changes in school mathematics knowledge in Greece: a Bernsteinian analysis

The purpose of this paper is to critically examine the changes that took place in school mathematics knowledge for pupils aged six and seven (first grade of Greek elementary school) and its pedagogical approach, which took shape following the reforms of the mathematics curricula in 1982 and 2003. Our analysis is based on Bernstein’s theoretical framework on pedagogic discourse and Dowling’s theoretical framework on textual domains. The results showed that there are differences between the 1982 and 2003 reforms, in terms both of the content of mathematics knowledge, as well as of the forms of pedagogic interaction between the teacher and the pupil.

The role of contextual, conceptual and procedural knowledge in activating mathematical competencies (PISA)

This paper analyses the difficulties which Spanish student teachers have in solving the PISA 2003 released items. It studies the role played by the type and organisation of mathematical knowledge in the activation of competencies identified by PISA with particular attention to the function of contextual knowledge. The results of the research lead us to conclude that the assessment of the participant’s mathematical competencies must include an assessment of the extent to which they have school mathematical knowledge (contextual, conceptual and procedural) that can be productively applied to problem situations. In this way, the school knowledge variable becomes a variable associated with the PISA competence variable.

Prediction and the Periodical Aspect as Generators of Knowledge in a Social Practice Framework

We start from the assumption that school mathematics knowledge could be better explained if social practices were considered to be generators of knowledge. This perspective changes the way we look at what school mathematics knowledge is and what it takes to teach and learn it. In this article, we will present a teaching situation about periodic functions, which was designed with this perspective in mind. The design was based on the assumption that the scientific notion of periodic function is related with the social practice of prediction. In the situation, prediction as a social practice is transformed into a situational line of argument which redefines that which is periodical. The situation brings into play meanings for the repetition of a movement, which takes place in time in the context of graphs of functions. Our analysis of the situation will focus on the prediction tools that participants generated in order to define that which is periodical. We will conclude with some implications of our observations for the teaching of mathematics.

A construção de saberes matemáticos entre jovens e adultos do Morro de São Carlos

O texto procura compreender as relações entre os conhecimentos matemáticos construídos por jovens e adultos trabalhadores na vida cotidiana e os conhecimentos matemáticos escolares. Para tanto, foi desenvolvida uma pesquisa etnográfica no Morro de São Carlos, Rio de Janeiro, acompanhando a rotina local de um curso de educação de jovens e adultos, assim como aspectos da vida diária dos alunos e da vida comunitária na favela. Os resultados indicaram uma estreita associação entre o uso de habilidades matemáticas no cotidiano com a necessidade de garantir formas de sobrevivência, assim como a importância de fatores afetivo-emocionais como impulsionadores de raciocínio matemático. O mundo da escola e o mundo da vida cotidiana apareceram como separados, assim como os conhecimentos matemáticos pertencentes a um ou outro contexto.