Durante el curso 2015-2016 el Aula Taller de las Matemáticas π-ensa convocó el Primer
Concurso de Relatos Cortos Matemáticos π-ensa. Toda la información puede consultarse en
la web del Aula: ...http://innovacioneducativa.upm.es/museomatematicas/. En este artículo se
presenta el relato vencedor en la 1ª categoría (estudiantes de Bachillerato ó Universidad).
Along the course 2015-2016 the mathematical Workshop π-ensa celebrated the first
Contest of Short Tales with mathematical content “π-ensa”. All the information about the
contest is included in the web page of the Workshop:
http://innovacioneducativa.upm.es/museomatematicas/. This paper presents the winner
tale in the first level (High School or University students).
Preservice mathematics teachers are subject to multiple influences when they make in-the-moment instructional decisions in classroom settings. Little is known about which influences make a ...significant contribution to decisions regarding the mathematical content knowledge (MCK) that preservice teachers decide to enact. The process by which mathematics preservice teachers manage multiple influences when making those decisions also requires particular examination. This study investigated six secondary mathematics preservice teachers' content-related decisions and actions in ten lower secondary algebra lessons using a combination of lesson observations and stimulated recall interviews. The study uncovered five influences, each comprising a number of influencing elements, that led the preservice teachers to intentionally enact or alternatively to intentionally withhold certain aspects of their MCK during algebra lessons. Combinations of harmonious influences were regularly accommodated by preservice teachers, while other combinations of influences competed for the preservice teachers' attention at different points in their lesson. The findings reveal that simply possessing content knowledge does not mean that preservice teachers are prepared to impart that knowledge to their students in the classroom context. The multi-faceted nature of content-related decision-making for preservice teachers suggests that content knowledge development should not be attended to in isolation within teacher education programs but should be located in teaching contexts wherever possible. Author abstract
In an effort to expand our knowledge base pertaining to pre-K-8 prospective teachers’ understanding of fractions, the present study was designed to extend the work on fractions schemes and operations ...to this population. One purpose of our study was to validate the fractions schemes and operations hierarchy with the pre-K-8 prospective teacher population to determine whether this population follows the same trajectory as upper elementary and middle school students. A second purpose of our study was to identify which of the fractions schemes and operations our sample of prospective teachers demonstrated evidence of having constructed along with what this tells us about prospective teachers’ understanding of fractions. We were able to validate the hierarchy for this population, meaning that each lower-level fraction scheme/operation appeared to be a prerequisite to the higher-level schemes/operations. We found that although most of the prospective teachers had constructed the lower-level schemes and operations, less than half had constructed the more sophisticated ones. An unexpected result related to the association between the coordination of three levels of units and the iterative fraction scheme is addressed. Prospective teachers’ reliance on procedural knowledge related to fractions also presented a challenge to assessing, in particular, their ability to coordinate three levels of units. We conclude with implications for research and practice in mathematics courses intended for pre-K-8 prospective teachers.
En este número se continúa con la publicación de los relatos premiados en el Primer Concurso de Relatos Cortos Matemáticos “π-ensa” convocado por el Aula Taller Museo de las Matemáticas “π-ensa” ...durante el curso 2015-2016. Este cuento resultó premiado con el Accé- sit en la categoría de estudiantes de ESO. Toda la información del concurso puede consultarse en la web del Aula: http://innovacioneducativa.upm.es/museomatematicas/.
This issue continues with the publication of the awarded tales in the First Mathematical Short Tales Contest “π-ensa” organized by the Mathematics Museum Workshop Classroom “π-ensa” during the 2015-2016 course. This tale awarded the second prize in the secondary student category. All information on the contest is available on the website of the Classroom: http://innovacioneducativa.upm.es/museomatematicas/.
La voluntad de los números Ortega González, Raúl
Pensamiento matemático,
2016, Volume:
6, Issue:
2
Journal Article
Open access
This issue continues with the publication of the awarded tales in the First Mathematical Short Tales Contest “π-ensa” organized by the Mathematics Museum Workshop Classroom “π-ensa” during the ...2015-2016 course. This tale awarded the second prize in the highschool and college student category. All information on the contest is available on the website of the Classroom: http://innovacioneducativa.upm.es/museomatematicas/.
En este número se continúa con la publicación de los relatos premiados en el Primer Concurso de Relatos Cortos Matemáticos “π-ensa” convocado por el Aula Taller Museo de las Matemáticas “π-ensa” durante el curso 2015-2016. Este cuento resultó premiado con el Accésit en la categoría de estudiantes de Bachillerato y Universidad. Toda la información del concurso puede consultarse en la web del Aula: http://innovacioneducativa.upm.es/museomatematicas/.
The importance of students' problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in ...developing creative approaches to mathematics. At the same time, there are also claims that students' mathematical content knowledge could be highly related to creativity in mathematics, too. This paper reports on a study that investigated USA and Chinese high school students' mathematical content knowledge, their abilities in mathematical problem posing, and the relationships between students' mathematical content knowledge and their problem-posing abilities in mathematics.
This study examined pre-service primary teachers' (PSPTs) mathematics performance on a set of question items measuring at the sixth grade level in Hong Kong. These items covered the five learning ...strands of the local primary mathematics curriculum - number, algebra, measures, shape and space, and data handling. The participants of the study were 152 PSPTs who had chosen mathematics as a major in an undergraduate teacher education program. Their strengths and weaknesses in particular mathematics topics were identified. Across all four years of the teacher education program, only 6% of the participants were able to provide fully correct mathematical responses to all five items. Further, it is surprising that merely 14% of graduating cohorts achieved a full mark for the mathematical word problem that required them to show their working steps. These findings suggest that issues relating to the preparation of mathematics specialists should be further considered in primary mathematics education.
Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the ...knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content knowledge, horizon content knowledge and specialised content knowledge, have been used to describe aspects of such knowledge.
Purpose: This paper proposes a model for teacher knowledge in mathematics that embraces and develops aspects of earlier models. It focuses on the notions of contingent knowledge and the connectedness of 'big ideas' of mathematics to enact what is described as 'powerful teaching'. It involves the teacher's ability to set up and provoke contingent moments to extend children's mathematical horizons. The model proposed here considers the various cognitive and affective components and domains that teachers may require to enact 'powerful teaching'. The intention is to validate the proposed model empirically during a future stage of research.
Sources of evidence: Contingency is described in Rowland's Knowledge Quartet as the ability to respond to children's questions, misconceptions and actions and to be able to deviate from a teaching plan as needed. The notion of 'horizon content knowledge' (Ball et al.) is a key aspect of the proposed model and has provoked a discussion in this article about students' mathematical horizons and what these might comprise. Together with a deep mathematical content knowledge and a sensibility for students and their mathematical horizons, these ideas form the foundations of the proposed model.
Main argument: It follows that a deeper level of knowledge might enable a teacher to respond better and to plan and anticipate contingent moments. By taking this further and considering teacher knowledge as 'dynamic', this paper suggests that instead of responding to contingent events, 'powerful teaching' is about provoking contingent events. This necessarily requires a broad, connected content knowledge based on 'big mathematical ideas', a sound knowledge of pedagogies and an understanding of common misconceptions in order to be able to engineer contingent moments.
Conclusions: In order to place genuine problem-solving at the heart of learning, this paper argues for the idea of planning for contingent events, provoking them and 'setting them up'. The proposed model attempts to represent that process. It is anticipated that the new model will become the framework for an empirical research project, as it undergoes a validation process involving a sample of primary teachers.
The current study explored the difficulties teachers encounter when teaching common fractions division, focusing on teachers' knowledge concerning this issue. Nine teachers who study towards a M.Ed. ...degree in mathematics education demonstrated the algorithms they apply in order to solve fractions division problems, described how they teach the subject, and attempted to explain a student's mistake, in understanding a word problem involving dividing by fraction. The findings indicate there is a missing link in the teachers' pedagogical capability, stemming from insufficient content knowledge. They presented different solution algorithms and reported using constructivist teaching methods, yet the methods they described couldn't lead a student to understand the logic behind the algorithm they teach (invert-and-multiply - multiplication by an inverse number, in accordance with the requirements of the curriculum). Furthermore, the participating teachers did not possess specialized mathematics content knowledge (SCK) and knowledge of content and students (KCS), enabling them to identify the source of a student's misconception.
There is a consensus that we need to improve the quality of pre-service teacher education, and teachers' mathematical content knowledge is critical for teaching. Identifying opportunities and ...influences that assist pre-service teachers to extend their mathematical content knowledge throughout their teacher education programme is important. This paper reports on qualitative data, collected over 4 years from two typical pre-service teachers whose developing mathematical content knowledge was investigated during their primary and secondary programme. These data were analysed and reported using the four dimensions of the Knowledge Quartet: foundation knowledge, transformation, connection and contingency. The results highlight the consequences of programme structure in order to help pre-service teachers to establish and sustain a positive mathematics learner identity, build teacher identity and develop mathematical content knowledge. Author abstract
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