This study addresses the relation of pre-school teachers’ mathematics content knowledge and their performance—how they perceive mathematical learning situations and whether they are able to plan ...adequate actions that foster children’s learning—in the informal settings of pre-schools. It thus addresses a serious gap in teacher research that has so far mostly been focussed on the formal settings of primary and secondary schools. The paper presents the instruments used to assess the knowledge (a paper–pencil test) and the performance (a video-based assessment), as well as the results of a study involving 354 prospective pre-school teachers. The results indicate that mathematical content knowledge is a significant predictor of the pre-school teachers’ ability to perceive learning situations and to plan educational actions to foster learning. Such evidence not only supports the validity of the knowledge test, but it is also relevant for policy makers because it leads to conclusions about the important opportunities to learn that need to be provided during pre-school teacher training.
This paper shows one of the tales presented to the contest about tales with mathematical
content organized by the Innovation Educative Group “Mathematical Thinking” in 2015.
The tale introduces the ...two digits numbers in a funny way.
En este artículo se muestra uno de los cuentos presentados al concurso de relatos con
contenido matemático organizado por el GIE Pensamiento matemático en 2015 para
alumnos de la ESO, Bachillerato y universitarios. En él se introducen los números de dos
cifras de una forma divertida.
This paper shows one of the tales presented to the contest about tales with mathematical content organized by the Innovation Educative Group “Mathematical Thinking” in 2015. The tale introduces the ...integer numbers in a funny way.
En este artículo se muestra uno de los cuentos presentados al concurso de relatos con contenido matemático organizado por el GIE Pensamiento matemático en 2015 para alumnos de la ESO, Bachillerato y universitarios. En él se introducen los números enteros de una forma divertida.
In a previous study, we validated the fractions schemes and operations trajectory (Norton and Wilkins
2012
; Steffe in J Math Behav 20(3): 267–307,
2002
; Steffe and Olive Children’s fractional ...knowledge. Springer, New York,
2010
; Wilkins and Norton
2011
) with PreK-8 prospective teachers and explored PreK-8 prospective teachers’ understanding of fractions based on fraction schemes and operations (Lovin et al.
2016
). In that study, we found that most of the prospective teachers had constructed the lower-level fraction schemes and operations, but less than half had constructed the more sophisticated ones. In the current study, we explored ways of evoking the more sophisticated fraction schemes and operations, in particular, by implementing simple instructional changes to a mathematics course for PreK-8 prospective teachers. One change focused on fraction language, specifically encouraging the use of iterative fraction language (e.g., 3/5 is three equal-size pieces, each of which is 1/5 of the whole). Another change focused on intentional number choice, specifically emphasizing improper fractions. After focused fraction instruction that included these instructional changes, we found significant increases in PreK-8 prospective teachers’ interiorization of coordinating three levels of units as well as in PreK-8 prospective teachers’ construction of the reversible partitive fraction scheme and the iterative fraction scheme. We conclude with implications for practice and research in mathematics courses intended for PreK-8 prospective teachers.
El legado absoluto Lozano Conde, Laura
Pensamiento matemático,
2017, Volume:
7, 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 has been awarded an honourable mention in the secondary student category. All the information of the contest is available on the website of the Classroom: http://innovacioneducativa.upm.es/museomatematicas.
En esta sección retomamos la publicación de los cuentos presentados al Primer Concurso de Relatos Cortos Matemáticos “π-ensa” organizado durante el curso 2015-2016 por el Aula Taller de las Matemáticas “π-ensa”. Toda la información puede consultarse en la web del Aula: http://innovacioneducativa.upm.es/museomatematicas/. En este artículo se presenta el relato que recibió la mención de honor del jurado en la 2º categoría “estudiantes de ESO”.
This paper reports on a study that explored the subject and pedagogical content knowledge displayed by high school mathematics teachers in the Khomas education region in Namibia. The study was based ...on a quantitative approach using a survey design. A stratified random sampling method was used to select the participants in all the four school circuits in the region. The study population consisted of 79 Grade 12 mathematics teachers from public schools. A sample of 40 mathematics teachers took part in the study, completed a questionnaire and wrote a test. A Microsoft Excel spreadsheet was used to sort the data and produce graphs and tables. A paired t-test was also used to determine if a significant difference existed between the participants' subject content knowledge (mathematical knowledge in our context, (MCK) and pedagogical content knowledge (PCK). The findings revealed that the participants had some deficiencies on MCK topics such as quadratic equations, angles properties and numbers. They also portrayed weak PCK on fractions, simultaneous and linear equations. This shows that a significant difference exists between the teachers' MCK and PCK with t
calculated
= 11.092 greater than the t
critical
(between 2.712 and 2.704) at a significance level, α = 0.01 but also that the participants' MCK and PCK were moderately and positively correlated (r = 0.681, p < 0.01). This study recommends that mathematics teachers in the Khomas region be provided frequently with in-service training to strengthen their shortcomings regarding MCK and PCK (knowledge of mathematics tasks, knowledge of learners' misconceptions and difficulties, and knowledge of mathematics instructions). We also recommend further studies to determine how high school mathematics teachers' knowledge can impact learners' academic performance in other education regions in Namibia.
Este trabajo tiene un doble objetivo; por un lado, analizar las definiciones que brindan estudiantes universitarios sobre el concepto de límite en un punto de una función y, por otro, tanto diseñar ...como validar un sistema de categorías para llevarlo a cabo. Se estudiaron las definiciones de límite proporcionadas por 38 estudiantes universitarios de Biología e Ingeniería en Química Industrial, matriculados en un curso de Cálculo Diferencial e Integral, durante el primer semestre del 2018, en la Universidad Nacional, Costa Rica. Para ello, se utilizaron categorías a priori y fue necesario complementarlas con otras de naturaleza inductiva, surgidas durante el análisis de contenido de las respuestas. Estas categorías fueron ratificadas mediante un análisis de fiabilidad. Los estudiantes evidenciaron la categoría límite como objeto en la mitad de sus respuestas, aproximadamente, y la categoría límite como proceso en más de tres cuartas partes. Además, constataron las categorías términos de posición relativa y descoordinación general de los procesos, en un estimado de la mitad de sus respuestas. El sistema de categorías creado permitió examinar unidades de información de una manera ordenada, simple y replicable. Finalmente, los estudiantes muestran una concepción dual del límite ya sea como un objeto, noción fija y estática, o como un proceso, noción procesual y dinámica. Asimismo, consideramos que el análisis de contenido descrito en la metodología puede permitir a futuros investigadores crear un sistema de categorías similar o usar este para indagaciones en otros contextos.
The Primary Teacher Education (PrimTEd) project was established in response to concerns about the pre-service preparation of primary teachers in South Africa. In order to inform the development of ...appropriate pre-service mathematics courses, an initial need in the PrimTEd project was to establish the nature of the mathematical knowledge of pre-service teachers both near the start and also near the end of their studies, through an online assessment. This paper describes the design of this PrimTEd online mathematics test and reports on the performance on the test of first-year and fourth-year primary mathematics student teachers, at three different universities. The overall performance of students together with the small differences between first and fourth year student performance indicate a need for student teachers to revisit primary school mathematics in a way that provides a deep understanding of key mathematical concepts in order to be better prepared for future teaching careers.
Research suggests that teachers of mathematics are frequently reluctant to pose challenging tasks to students. Reasons for this reluctance include fears of negative student reactions, time and ...resource constraints, and a lack of relevant teacher content knowledge. The current study involved interviewing three early primary-grade (elementary) teachers to explore their perceptions of teaching with challenging tasks, following their observations of 2 units of mathematical work taught by the first author. Contrary to some other studies where classroom teachers were themselves observed teaching with such tasks and asked to reflect on the experience, we found that teacher-participants perceived that students responded positively to the 2 units of work. Specifically, teacher-participants described their students as autonomous, persistent and highly engaged. These positive student reactions were attributed to a variety of factors, including a classroom culture that embraced struggle, high teacher expectations, and consistent classroom routines. Despite these positive reflections, teacher-participants differed in their views of whether challenging tasks are a suitable means of differentiating instruction, with such evaluations apparently linked to how they defined student success.
La chica del gorro extraño Martínez López, Lucía
Pensamiento matemático,
04/2016, Volume:
6, Issue:
1
Journal Article
Open access
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 second level (students of Secondary).
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 2ª categoría (estudiantes de Enseñanza Secundaria
Obligatoria: ESO).
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