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1.
Brian Hemmings Peter Grootenboer Russell Kay 《International Journal of Science and Mathematics Education》2011,9(3):691-705
Achievement in mathematics is inextricably linked to future career opportunities, and therefore, understanding those factors
that influence achievement is important. This study sought to examine the relationships among attitude towards mathematics,
ability and mathematical achievement. This examination was also supported by a focus on gender effects. By drawing on a sample
of Australian secondary school students, it was demonstrated through the results of a multivariate analysis of variance that
females were more likely to hold positive attitudes towards mathematics. In addition, the predictive capacity of prior achievement
and attitudes towards mathematics on a nationally recognised secondary school mathematics examination was shown to be large
(R
2 = 0.692). However, when these predictors were controlled, the influence of gender was non-significant. Moreover, a structural
equation model was developed from the same measures and subsequent testing indicated that the model offered a reasonable fit
of the data. The positing and testing of this model signifies growth in the Australian research literature by showing the
contribution that ability (as measured by standardised test results in numeracy and literacy) and attitude towards mathematics
play in explaining mathematical achievement in secondary school. The implications of these results for teachers, parents and
other researchers are then considered. 相似文献
2.
Heinz Steinbring 《Educational Studies in Mathematics》2005,59(1-3):313-324
This is a commentary paper in the volume on “Teachings situations as object of research: empirical studies within theoretical
perspectives”. An essential object of mathematics education research is the analysis of interactive teaching and learning
processes in which mathematical knowledge is mediated and communicated. Such a research perspective on processes of mathematical interaction has to take care of the difficult relationship between mathematics education theory and everyday mathematics teaching practice.
In this regard, the paper tries to relate the development in mathematics education research within the theory of didactical situations to developments in interaction theory and in the epistemological analysis of mathematical communication. 相似文献
3.
Shelly Sheats Harkness Beatriz Dambrosio Anastasia S. Morrone 《Educational Studies in Mathematics》2007,65(2):235-254
In this study, data in the form of (preservice teacher) student voices taken from mathematical autobiographies, written at the beginning of the semester, and end-of-semester reflections, were
analyzed in order to examine why preservice elementary school teachers were highly motivated in a social constructivist mathematics
course in which the teacher emphasized mastery goals. The findings suggest that students entered the course with a wide variety
of feelings about mathematics and their own mathematical ability. At the end of the semester, students wrote about aspects
of the course that “led to their growth as a mathematical thinker and as a mathematics teacher…” Student responses were coded
within themes that emerged from the data: Struggle; Construction of meaning [mathematical language; mathematical understanding];
Grouping [working in groups]; Change [self-efficacy; math self-concept]; and the Teacher’s Role. These themes are described
using student voices and within a motivation goal theory framework. The role of struggle, in relation to motivation, is discussed. 相似文献
4.
Brian Griffiths (1927–2008) was a British mathematician and educator who served as a member of the founding editorial board
of Educational Studies in Mathematics. As a mathematician, Griffiths is remembered through his work on what continue to be known as ‘Griffiths-type’ topological
spaces. As a mathematics educator, his most profound contribution was, with Geoffrey Howson, in offering a conceptualisation
of the relationship between mathematics, society and curricula. 相似文献
5.
In this study we investigate a strategy for engaging high school mathematics teachers in an initial examination of their teaching in a way that is non-threatening and at the same time effectively supports the development
of teachers’ pedagogical content knowledge [Shulman (1986). Educational Researcher, 15(2), 4–14]. Based on the work undertaken by the QUASAR project with middle school mathematics teachers, we engaged a group
of seven high school mathematics teachers in learning about the Levels of Cognitive Demand, a set of criteria that can be
used to examine mathematical tasks critically. Using qualitative methods of data collection and analysis, we sought to understand
how focusing the teachers on critically examining mathematical tasks influenced their thinking about the nature of mathematical
tasks as well as their choice of tasks to use in their classrooms. Our research indicates that the teachers showed growth
in the ways that they consider tasks, and that some of the teachers changed their patterns of task choice. Further, this study
provides a new research instrument for measuring teachers’ growth in pedagogical content knowledge.
An earlier version of this paper was presented at the American Educational Research Association Annual Meeting, New Orleans,
LA, April 2002. 相似文献
6.
Pnina S. Klein Esther Adi-Japha Simcha Hakak-Benizri 《Educational Studies in Mathematics》2010,73(3):233-246
The objective of this study was to examine gender differences in the relations between verbal, spatial, mathematics, and teacher–child
mathematics interaction variables. Kindergarten children (N = 80) were videotaped playing games that require mathematical reasoning in the presence of their teachers. The children’s
mathematics, spatial, and verbal skills and the teachers’ mathematical communication were assessed. No gender differences
were found between the mathematical achievements of the boys and girls, or between their verbal and spatial skills. However,
mathematics performance was related to boys’ spatial reasoning and to girls’ verbal skills, suggesting that they use different
processes for solving mathematical problems. Furthermore, the boys’ levels of spatial and verbal skills were not found to
be related, whereas they were significantly related for girls. The mathematical communication level provided in teacher–child
interactions was found to be related to girls’ but not to boys’ mathematics performance, suggesting that boys may need other
forms of mathematics communication and teaching. 相似文献
7.
In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics.
In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research
on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate
the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests
that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms
where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional
approaches that support the learning of mathematics through the process of guided reinvention. 相似文献
8.
Reuven Babai Tali Brecher Ruth Stavy Dina Tirosh 《International Journal of Science and Mathematics Education》2006,4(4):627-639
One theoretical framework which addresses students’ conceptions and reasoning processes in mathematics and science education is the intuitive rules theory. According to this theory, students’ reasoning is affected by intuitive rules when they solve a wide variety of conceptually non-related mathematical and scientific tasks that share some common external features. In this paper, we explore the cognitive processes related to the intuitive rule more A–more B and discuss issues related to overcoming its interference. We focused on the context of probability using a computerized “Probability Reasoning – Reaction Time Test.” We compared the accuracy and reaction times of responses that are in line with this intuitive rule to those that are counter-intuitive among high-school students. We also studied the effect of the level of mathematics instruction on participants’ responses. The results indicate that correct responses in line with the intuitive rule are more accurate and shorter than correct, counter-intuitive ones. Regarding the level of mathematics instruction, the only significant difference was in the percentage of correct responses to the counter-intuitive condition. Students with a high level of mathematics instruction had significantly more correct responses. These findings could contribute to designing innovative ways of assisting students in overcoming the interference of the intuitive rules. 相似文献
9.
andreas j. stylianides 《Educational Studies in Mathematics》2007,65(1):1-20
Despite increased appreciation of the role of proof in students’ mathematical experiences across all grades, little research has focused on the issue of understanding and characterizing the notion of proof at the elementary
school level. This paper takes a step toward addressing this limitation, by examining the characteristics of four major features
of any given argument – foundation, formulation, representation, and social dimension – so that the argument could count as
proof at the elementary school level. My examination is situated in an episode from a third-grade class, which presents a
student’s argument that could potentially count as proof. In order to examine the extent to which this argument could count
as proof (given its four major elements), I develop and use a theoretical framework that is comprised of two principles for
conceptualizing the notion of proof in school mathematics: (1) The intellectual-honesty principle, which states that the notion of proof in school mathematics should be conceptualized so that it is, at once, honest to mathematics
as a discipline and honoring of students as mathematical learners; and (2) The continuum principle, which states that there should be continuity in how the notion of proof is conceptualized in different grade levels so that
students’ experiences with proof in school have coherence. The two principles offer the basis for certain judgments about
whether the particular argument in the episode could count as proof. Also, they support more broadly ideas for a possible
conceptualization of the notion of proof in the elementary grades. 相似文献
10.
In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article
is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's
own representations (in particular ‘diagrams') of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic
framework to answer the question of how students develop a notion of ‘distribution' in a statistics course by ‘diagrammatic
reasoning' and by forming ‘hypostatic abstractions', that is by forming new mathematical objects which can be used as means
for communication and further reasoning. Peirce's semiotic terminology is used as an alternative to concepts such as modeling,
symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning
and communicating in mathematics classrooms. 相似文献
11.
Pessia Tsamir 《Educational Studies in Mathematics》2007,65(3):255-279
This paper indicates that prospective teachers’ familiarity with theoretical models of students’ ways of thinking may contribute
to their mathematical subject matter knowledge. This study introduces the intuitive rules theory to address the intuitive,
same sides-same angles solutions that prospective teachers of secondary school mathematics come up with, and the proficiency they acquired during
the course “Psychological aspects of mathematics education”. The paper illustrates how drawing participants’ attention to
their own erroneous applications of same sides-same angles ideas to hexagons, challenged and developed their mathematical knowledge. 相似文献
12.
Erin E. Turner Corey Drake Amy Roth McDuffie Julia Aguirre Tonya Gau Bartell Mary Q. Foote 《Journal of Mathematics Teacher Education》2012,15(1):67-82
Research repeatedly documents that teachers are underprepared to teach mathematics effectively in diverse classrooms. A critical
aspect of learning to be an effective mathematics teacher for diverse learners is developing knowledge, dispositions, and
practices that support building on children’s mathematical thinking, as well as their cultural, linguistic, and community-based
knowledge. This article presents a conjectured learning trajectory for prospective teachers’ (PSTs’) development related to
integrating children’s multiple mathematical knowledge bases (i.e., the understandings and experiences that have the potential to shape and support children’s mathematics learning—including
children’s mathematical thinking, and children’s cultural, home, and community-based knowledge), in mathematics instruction.
Data were collected from 200 PSTs enrolled in mathematics methods courses at six United States universities. Data sources
included beginning and end-of-semester surveys, interviews, and PSTs’ written work. Our conjectured learning trajectory can
serve as a tool for mathematics teacher educators and researchers as they focus on PSTs’ development of equitable mathematics
instruction. 相似文献
13.
Luciana Bazzini 《Educational Studies in Mathematics》2001,47(3):259-271
The mutual relationship between real objects and mathematical constructions is at the very base of studies concerned with
making sense in mathematics. In this wider perspective recent research studies have been concerned with the cognitive roots
of mathematical concepts. Human perception and movement and, more generally, interaction with space and time are recognized
as being of crucial importance for knowledge construction. A new approach to the cognitive science of mathematics, based on
the notion of ‘embodied cognition’ assumes that mathematics cannot be considered as mind free. Accordingly, mathematical concepts
derive from the cognitive activities of subjects and are highly influenced by the body structure. This article reports some
examples of teaching experiments based on body-related metaphors. Some of them are carried out by means of technological devices.
A call for legitimacy in school mathematics is made, both for an embodied cognition perspective and for a related use of technology.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
14.
M. Otte 《Educational Studies in Mathematics》2003,53(3):203-228
Niels Bohr's term‘complementarity' has been used by several authors to capture the essential aspects of the cognitive and
epistemological development of scientific and mathematical concepts. In this paper we will conceive of complementarity in
terms of the dual notions of extension and intension of mathematical terms. A complementarist approach is induced by the impossibility
to define mathematical reality independently from cognitive activity itself. R. Thom, in his lecture to the Exeter International
Congress on Mathematics Education in 1972,stated ‘‘the real problem which confronts mathematics teaching is not that of rigor,but
the problem of the development of‘meaning’, of the ‘existence' of mathematical objects'. Student's insistence on absolute
‘meaning questions’, however,becomes highly counter-productive in some cases and leads to the drying up of all creativity.
Mathematics is, first of all,an activity, which, since Cantor and Hilbert, has increasingly liberated itself from metaphysical
and ontological agendas. Perhaps more than any other practice,mathematical practice requires acomplementarist approach, if
its dynamics and meaning are to be properly understood. The paper has four parts. In the first two parts we present some illustrations
of the cognitive implications of complementarity. In the third part, drawing on Boutroux' profound analysis, we try to provide
an historical explanation of complementarity in mathematics. In the final part we show how this phenomenon interferes with
the endeavor to explain the notion of number.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
15.
Learning Mathematics for Teaching Project 《Journal of Mathematics Teacher Education》2011,14(1):25-47
In this article, we describe a framework and instrument for measuring the mathematical quality of mathematics instruction.
In describing this framework, we argue for the separation of the mathematical quality of instruction (MQI), such as the absence of mathematical errors and the presence of sound mathematical reasoning, from pedagogical method.
We argue that conceptualizing this key aspect of mathematics classrooms will enable more clarity in mathematics educators’
research questions and will facilitate study of the mechanisms by which teacher knowledge shapes instruction and subsequent
student learning. The instrument we have developed offers an important first step in demonstrating the viability of the construct. 相似文献
16.
Andrew Noyes Geoff Wake Pat Drake 《International Journal of Science and Mathematics Education》2011,9(2):483-501
This paper explores the potential impact of a national pilot initiative in England aimed at increasing and widening participation
in advanced mathematical study through the creation of a new qualification for 16- to 18-year-olds. This proposed qualification
pathway—Use of Mathematics—sits in parallel with long-established, traditional advanced level qualifications, what we call ‘traditional Mathematics’ herein. Traditional Mathematics is typically required for entry to mathematically demanding undergraduate programmes. The structure, pedagogy and assessment
of Use of Mathematics is designed to better prepare students in the application of mathematics, and its development has surfaced some of the tensions
between academic/pure and vocational/applied mathematics. Here, we explore what Use of Mathematics offers, but we also consider some of the objections to its introduction in order to explore aspects of the knowledge politics
of mathematics education. Our evaluation of this curriculum innovation raises important issues for the mathematics education
community as countries seek to increase the numbers of people that are well prepared to apply mathematics in science and technology-based
higher education courses and work places. 相似文献
17.
Gabriel J. Stylianides Andreas J. Stylianides George N. Philippou 《Journal of Mathematics Teacher Education》2007,10(3):145-166
There is a growing effort to make proof central to all students’ mathematical experiences across all grades. Success in this goal depends highly on teachers’ knowledge
of proof, but limited research has examined this knowledge. This paper contributes to this domain of research by investigating
preservice elementary and secondary school mathematics teachers’ knowledge of proof by mathematical induction. This research
can inform the knowledge about preservice teachers that mathematics teacher educators need in order to effectively teach proof to preservice teachers. Our analysis is based
on written responses of 95 participants to specially developed tasks and on semi-structured interviews with 11 of them. The
findings show that preservice teachers from both groups have difficulties that center around: (1) the essence of the base
step of the induction method; (2) the meaning associated with the inductive step in proving the implication P(k) ⇒ P(k + 1) for an arbitrary k in the domain of discourse of P(n); and (3) the possibility of the truth set of a sentence in a statement proved by mathematical induction to include values
outside its domain of discourse. The difficulties about the base and inductive steps are more salient among preservice elementary
than secondary school teachers, but the difficulties about whether proofs by induction should be as encompassing as they could
be are equally important for both groups. Implications for mathematics teacher education and future research are discussed
in light of these findings.
相似文献
George N. PhilippouEmail: |
18.
Lora B. Bailey 《Early Childhood Education Journal》2010,38(2):123-132
This 3 year longitudinal study reports the feasibility of an Improving Teacher Quality: No Child Left Behind project for impacting teachers’ content and pedagogical knowledge in mathematics in nine Title I elementary schools in the
southeastern United States. Data were collected for 3 years to determine the impact of standards and research-based teacher
training on these aspects of teacher quality. Content knowledge for the scope of this research study refers to the knowledge
that teachers have about subject matter. Teacher quality is directly related to teachers’ “highly qualified” status, as defined
by the No Child Left Behind mandate. According to this mandate, every classroom should have a teacher qualified to teach in
his subject area and be able to “raise the percentage of students who are proficient in reading and math, and in narrowing
the test-score gap between advantaged and disadvantaged students.” Participants were six second grade and seven third grade
teachers of mathematics from nine schools within one failing school district. The implementation of standards-based methods
in the nine Title I Schools increased teacher quality in elementary school mathematics. In fact, qualitative and quantitative
data revealed significant gains in teachers’ mathematics content and pedagogical knowledge at both grade levels. 相似文献
19.
Shulman (1986, 1987) coined the term pedagogical content knowledge (PCK) to address what at that time had become increasingly evident—that content knowledge itself was not sufficient for teachers
to be successful. Throughout the past two decades, researchers within the field of mathematics teacher education have been
expanding the notion of PCK and developing more fine-grained conceptualizations of this knowledge for teaching mathematics.
One such conceptualization that shows promise is mathematical knowledge for teaching—mathematical knowledge that is specifically useful in teaching mathematics. While mathematical knowledge for teaching has
started to gain attention as an important concept in the mathematics teacher education research community, there is limited
understanding of what it is, how one might recognize it, and how it might develop in the minds of teachers. In this article,
we propose a framework for studying the development of mathematical knowledge for teaching that is grounded in research in
both mathematics education and the learning sciences.
相似文献
Jason SilvermanEmail: |