Mathematical task design has been a central focus of the mathematics education research community over the last few years. In this study, six university teacher educators from six different US ...institutions formed a community of practice to explore key aspects of task design (planning, implementing, reflecting, and modifying) in the context of comparing fractions using reasoning and sense-making. By presenting results of their implementation of two tasks with 63 prospective elementary teachers across three institutions and their reflective analysis of the implementation, the authors highlight the importance of collecting and analyzing data and reflecting on this analysis to inform the redesign of tasks. The authors also found that considering different types of tasks (problem solving vs. problem posing) helps illuminate different aspects of prospective elementary teachers' understanding, which can inform task redesign. Finally the authors contribute to the knowledge base on reasoning strategies for comparing fractions and prospective elementary teachers’ knowledge of these strategies.
Background: This article seeks to present findings from the analysis of the TEDS-M reports on the mathematical content knowledge (MCK) and pedagogical content knowledge (PCK) of the pre-service ...teachers in Malaysia Materials and methods: The main objective of this study was to investigate the level of teaching knowledge attained by the Malaysian pre-service primary and secondary teachers. Some 576 primary level pre-service teachers and 389 secondary level pre-service teachers participated in the TEDS-M study. The significance of this study is pertinent as the level of teachers' knowledge influences students’ achievement in schools Results: Results of analysis show that Malaysian pre-service teachers at the primary and secondary performed below the international average for both mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK). Conclusions: The article suggested several steps on how teacher educators could improve the PCK and MCK of pre-service teachers in Malaysia.
PISA (Programme for International Student Assessment) is an international programme which is conducted every 3 years to assess 15 years old students level of proficiency. PISA contains three ...different cognitive tests: mathematic literacy, scientific literacy and reading literacy. Every year that PISA is conducted, the numbers of cognitive test items vary in each test. Therefore it is difficult to develop a standardized procedure for comparison. However, there are some identical items that can be used as a criteria for comparison. The aim of this research is to examine academic achievement of mathematic literacy common items in PISA 2003, PISA 2006 and PISA 2009 applications with respect to mathematical content area and item format. This research is a survey and quantitative study which is conducted by secondary data base. The population of this research is all of the 15 years old students who are attending to schools in 2003, 2006 and 2009 academic years. 15 years old students who participated in PISA 2003, PISA 2006 and PISA 2009 applications and solved the questions regarding mathematic literacy common items are the sample of the research. Relevant statistical analysis was conducted based on research and sub-research questions by using the secondary data base that was prepared by rearranging the national data base of PISA 2003, PISA 2006 and PISA 2009. The findings of the research study demonstrated that the students have poor performance in ‘space and shape’ that is one of the mathematical content area. They have better performance in ‘multiple choice’ items while have poor performance in ‘open-constructed’ items. In general, it was seen that Turkish students have better performance in PISA 2003 and poor performance in PISA 2006.
Only a small percentage of mathematics teacher professional development activities in South Africa include pedagogy and instruction approaches required to teach the content. In the light of the poor ...mathematics results, it is of pertinent importance that teachers need to be developed in terms of the mathematics they teach and the pedagogical component of it. A teachers’ professional development programme that used mentoring as one of the interventions was investigated where the mentor conducted classroom observations and had post–observation conferences with the teachers. The data from the observations, post observation conferences and interviews of both the mentors and the mathematics teachers was used to inform the off-site workshops on mathematics content and the instructional skills required to effectively teach the content. Mentoring supported the teachers in terms of mathematics content and instruction, team teaching and lesson preparation. The teachers’ individual content and instructional needs were also assessed and supported. The study revealed that mentoring that takes cognisance of teachers’ content and instructional needs enhanced their lesson preparation and understanding of mathematics as well as the skills required to teach it effectively. The study recommends mentoring as an effective intervention in professional development programmes especially when it is informed by the teachers’ instructional and content needs.
This study explores in-service high school mathematics teachers’ conception of various forms of complex numbers and ways in which they transition between different representations of these forms. One ...90-min interview was conducted with three high school mathematics teachers after they completed three professional development sessions, each 4 h, on complex numbers. Results indicate that, in general, these teachers did not necessarily have a dual conception of complex numbers. However, they demonstrated varying conceptions with different forms of complex numbers. Teachers worked at an operational level with the exponential form of complex numbers, but there was no evidence to indicate that they had a structural conception of this form. On the other hand, two teachers were very comfortable with the Cartesian form and exhibited a process/object duality by translating between different representations of this form. These results indicate that high school teachers need more opportunities to help them develop a dual conception of each form (
multiple duals
), which in turn can result in developing a dual conception of complex numbers. An interesting phenomenon that we found was that teachers who taught courses such as geometry and international baccalaureate were able to draw from their teaching experiences as they attempted the interview tasks. This particular observation may suggest that teachers’ teaching assignments coupled with appropriate professional development activities could facilitate their understanding of these concepts.
Advisory committees of mathematics consider abstract algebra as an essential component of the mathematical preparation of secondary teachers, yet preservice teachers find it challenging to connect ...the topics addressed in this advanced course with the high school algebra they must someday teach. This study analyzed the mathematical content knowledge that developed in preservice teachers during a semester course in abstract algebra utilizing Lerman's "person-in-practice-in-person" lens. This unit of analysis provided insights into the situated nature of the algebra learned by illuminating how the goals of the instructor and preservice teachers impacted the community of practice created in the university classroom and how participating in that community impacted the preservice teachers' mathematical identities.
This article is devoted to the development of algorithms for the adaptation of mathematical educational content and their implementation in the e-learning system. The adaptation of a mathematical ...content consists in the selection of an optimal edition of the material that best suits the individual characteristics of the student. The novelty of the work is the organization of the adaptation algorithms of the educational content in a three-level system: "introductory content adaptation" (an adaptation of the content of introductory materials of the discipline based on the initial level of students) - "current adaptation of the content" (an adaptation of the mathematical content based on current effective actions of students in the electronic course) - "appraisal-correcting adaptation" (an adaptation of normative parameters of the level of assimilation of materials, taking into account the results achieved by students). The introduction of the proposed three-stage system makes it possible to implement in individual educational trajectories and to form for each student a personal space of mathematical educational content that adapts to its level of mastering the material, which helps to improve the quality of instruction in mathematical disciplines. An approbation of the proposed algorithms was carried out in the adaptive e-course in discrete mathematics, implemented at Siberian Federal University in Russia.
This article discusses key issues surrounding the nature and development of professional knowledge for effective teaching of mathematics, especially at the secondary school level. In the education ...research community it is generally accepted that teachers need more than knowledge of the content they will teach; an additional construct, pedagogical content knowledge, has been proposed to describe the knowledge teachers need in order to make the content comprehensible to learners. Studies demonstrate that mathematical content knowledge (MCK) and pedagogical content knowledge (PCK) predict students' mathematics achievement gains, and that PCK has the greater influence on achievement. However, the relationship between these two types of knowledge, and how their development might be influenced by studying university level mathematics, remains unclear. The article reports on an Australian study of the knowledge for teaching mathematics of prospective secondary school teachers, which found that MCK is a statistically significant predictor of PCK, and vice versa, although in each case only a small proportion of the variance in the outcome variable was explained. A higher level of prior mathematical experience was also associated with higher levels of MCK, but not PCK. These results suggest that although university level study of mathematics may be beneficial in developing secondary school MCK, it does not have a significant influence on PCK and is therefore inadequate, on its own, for preparing effective teachers of secondary school mathematics.
This article describes the implementation of STAD (Student Team-Achievement Division), a complex technique of cooperative learning. The main aim of this technique is to respond to diversity through ...personalized learning objectives and activities. For this purpose, each student is assigned to a cooperative group. Thus, students can progress at their own pace and develop their full potential, both intellectual and social, taking advantage of cooperation.
The study was carried out with a group of sixth-grade students of La Carriona-Miranda Primary School (Avilés, Asturias), during the academic year 2011/12. STAD was applied to emphasize the conceptual understanding of mathematical contents (in this case, length measures).
The implementation of this technique has created a good climate of cooperation in the classroom, has motivated the students to complete the tasks assigned, has enabled the acquisition and development of social skills, and has improved academic performance, mainly in those students who had greater learning difficulties.
En este artículo se describe el proceso de puesta en práctica de la técnica compleja de aprendizaje cooperativo TELI (Trabajo en Equipo-Logro Individual). El principal objetivo que se persigue con la aplicación de esta técnica es atender la diversidad del alumnado por medio de la personalización de los objetivos didácticos y las actividades de aprendizaje, de tal forma que cada estudiante, integrado en un equipo cooperativo de base y aprovechando las ventajas de la cooperación, pueda progresar a su propio ritmo desarrollando al máximo sus potencialidades tanto intelectuales como sociales.
El estudio se llevó a cabo con un grupo de estudiantes de sexto curso de educación primaria del Colegio Público de Infantil y Primaria de La Carriona-Miranda (Avilés, Asturias), durante el curso escolar 2011–2012, para trabajar un contenido matemático (en este caso, las medidas de longitud). Su implementación práctica ha permitido crear un buen clima de convivencia en el aula, motivar al alumnado para la realización de la tarea, facilitar la adquisición y desarrollo de habilidades sociales y mejorar los rendimientos académicos, fundamentalmente de aquellas alumnas y alumnos que presentan mayores dificultades de aprendizaje.
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