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1.
Gabriel J. Stylianides 《International Journal of Science and Mathematics Education》2008,6(1):191-215
Despite widespread agreement that proof should be central to all students’ mathematical experiences, many students demonstrate poor ability with it. The curriculum
can play an important role in enhancing students’ proof capabilities: teachers’ decisions about what to implement in their
classrooms, and how to implement it, are mediated through the curriculum materials they use. Yet, little research has focused
on how proof is promoted in mathematics curriculum materials and, more specifically, on the guidance that curriculum materials
offer to teachers to enact the proof opportunities designed in the curriculum. This paper presents an analytic approach that
can be used in the examination of the guidance curriculum materials offer to teachers to implement in their classrooms the
proof opportunities designed in the curriculum. Also, it presents findings obtained from application of this approach to an
analysis of a popular US reform-based mathematics curriculum. Implications for curriculum design and research are discussed. 相似文献
2.
This study aims to investigate a construct of reading comprehension of geometry proof (RCGP). The research aims to investigate
(a) the facets composing RCGP, and (b) the structure of these facets. Firstly, we conceptualize this construct with relevant
literature and on the basis of the discrimination between the logical and the epistemic meanings of an argument, then assemble
the content of RCGP from literature and propose a hypothetical model of RCGP. Secondly, mathematicians and mathematics teachers
are interviewed for their ideas on reading mathematical proof in order to enrich the content of RCGP. Adapting the phases
of reading comprehension in language, the content of RCGP is classified into six facets. Lastly, these facets are structured
using the hypothetical model and then justified by students’ performance in the facets of RCGP using the multidimensional
scaling method. The results sustain that the structure of facets can be characterized by this conceptualized model. 相似文献
3.
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: |
4.
Korean elementary school students’ English learning demotivation: a comparative survey study 总被引：1，自引：0，他引：1
Tae-Young Kim 《Asia Pacific Education Review》2011,12(1):1-11
This study explores Korean elementary school students’ decreased motivation for English learning by analyzing the questionnaire
data obtained from 6,301 students in a large city in South Korea. The students’ school grades and their prior experience in
private institutes were considered as the major factors behind the decrease in their motivation. There was a statistically
significant and consistent decrease in the students’ satisfaction with their English learning experience; expectation of ultimate
success in English; and intrinsic/extrinsic motivation and integrative/instrumental motivation. Prior experience in attending
private institutes had a substantial impact on the students’ motivation. Those who attended private institutes (hakwons) exhibited higher levels of instrumental and intrinsic motivation. However, in terms of other motivational constructs of
integrative and extrinsic (parental, academic) motivation, private instruction had a negligible or negative impact. By comparing
the results with those of Lamb (2007), the present study proposes that Korean students should be made to internalize the beneficial role played by English so
that their English learning motivation can be maintained. 相似文献
5.
The relations among students’ motivational beliefs, cognitive processes, and academic achievement were investigated. A 51-item
questionnaire together with a mathematics achievement test was administered to 459 fifth graders in Korean elementary school
mathematics classrooms. Results indicated that, in general, students’ cognitive processes related closely to competence beliefs,
task values, and achievement goals, and more importantly their success or failure in mathematics achievement was closely linked
to competence beliefs, performance-avoidance goals, and persistence strategies. Positive evidence of performance-approach
goals was observed in math learning relative to task goals. As expected, performance-avoidance goals turned out to be detrimental
to students’ math learning. These findings are generally congruent with the motivational theories and support the position
that students should be encouraged to adopt task goals and actively involve themselves in math class activities. However,
it also behooves us to recognize the potential benefits of performance-approach goals in different cultural contexts, such
as the Korean elementary school math classrooms. 相似文献
6.
7.
Joanna O. Masingila Samson M. Muthwii Patrick M. Kimani 《International Journal of Science and Mathematics Education》2011,9(1):89-108
This study examined standard 6 and 8 (Standards 6 and 8 are the sixth and eighth years, respectively, of primary level schooling
in Kenya.) students’ perceptions of how they use mathematics and science outside the classroom in an attempt to learn more
about students’ everyday mathematics and science practice. The knowledge of students’ everyday mathematics and science practice
may assist teachers in helping students be more powerful mathematically and scientifically both in doing mathematics and science
in school and out of school. Thirty-six students at an urban school and a rural school in Kenya were interviewed before and
after keeping a log for a week where they recorded their everyday mathematics and science usage. Through the interviews and
log sheets, we found that the mathematics that these students perceived they used outside the classroom could be classified
as 1 of the 6 activities that Bishop (Educ Stud Math 19:179–191, 1988) has called the 6 fundamental mathematical activities and was also connected to their perception of whether they learned
mathematics outside school. Five categories of students’ perceptions of their out-of-school science usage emerged from the
data, and we found that 4 of our codes coincided with 2 activities identified by Lederman & Lederman (Sci Child 43(2):53,
2005) as part of the nature of science and 2 of Bishop’s categories. We found that the science these students perceived that they
used was connected to their views of what science is. 相似文献
8.
There is a documented need for more opportunities for teachers to learn about students’ mathematical reasoning. This article
reports on the experiences of a group of elementary and middle school mathematics teachers who participated as interns in
an after-school, classroom-based research project on the development of mathematical ideas involving middle-grade students
from an urban, low-income, minority community in the United States. For 1 year, the teachers observed the students working
on well-defined mathematical investigations that provided a context for the students’ formation of particular mathematical
ideas and different forms of reasoning in several mathematical content strands. The article describes insights into students’
mathematical reasoning that the teachers were able to gain from their observations of the students’ mathematical activity.
The purpose is to show that teachers’ observations of students’ mathematical activity in research sessions on students’ development
of mathematical ideas can provide opportunities for teachers to learn about students’ mathematical reasoning. 相似文献
9.
Anderson Hassell Norton Andrea McCloskey 《Journal of Mathematics Teacher Education》2008,11(4):285-305
The challenge that we address concerns teachers’ shifts toward student-centered instruction. We report on a yearlong professional
development study in which two United States elementary school teachers engaged in a teaching experiment, as described by
Steffe and Thompson (in: Lesh and Kelly (eds) Research on design in mathematics and science education, 2000). The teaching
experiment involved close mathematical interactions with a pair of students after school, in the context of solving fractions
tasks. By conducting a teaching experiment, we anticipated that each teacher would have more opportunity to develop insight
into students’ mathematics. We also anticipated that these insights would influence the teachers’ classroom practice, even
without explicit support for such a shift. Indeed, the teachers found that they began asking more probing questions of their
students and spending more time listening to students’ explanations, but shifts to classroom practice were limited by constraining
factors such an inflexible curriculum. 相似文献
10.
In this paper, we argue that history might have a profound role to play for learning mathematics by providing a self-evident
(if not indispensable) strategy for revealing meta-discursive rules in mathematics and turning them into explicit objects
of reflection for students. Our argument is based on Sfard’s theory of Thinking as Communicating, combined with ideas from historiography of mathematics regarding a multiple perspective approach to the history of practices
of mathematics. We analyse two project reports from a cohort of history of mathematics projects performed by students at Roskilde
University. These project reports constitute the experiential and empirical basis for our claims. The project reports are
analysed with respect to students’ reflections about meta-discursive rules to illustrate how and in what sense history can
be used in mathematics education to facilitate the development of students’ meta-discursive rules of mathematical discourse. 相似文献
11.
This study is conducted with self-developed questionnaire on 910 middle school students, aimed at describing middle school
students’ academic subjective well-being and exploring its influential factors. Results show that (1) Academic subjective
well-being of middle school students is generally low and there exist differences in different schools and grades. Students
from non-key middle schools have lower academic subjective well-being than those from the key schools. Grade 2 students in
both junior and senior middle schools have the lowest academic subjective well-being. (2) Factors directly affecting middle
school students’ academic subjective well-being are academic experience and the present academic achievements · · with the
former playing a major role. (3) Factors indirectly influencing middle school students’ academic subjective well-being are
social pressure and expected academic achievements, both of which influence students’ academic subjective well-being through
students’ academic experience or their present academic achievements.
__________
Translated from Educational Research and Experiment, 2004:4 相似文献
12.
Joshua Gisemba Bagaka��s 《International Journal of Science and Mathematics Education》2011,9(4):817-842
The study identified two dimensions of teacher self-efficacy and practices and five dimensions of students’ mathematics self-efficacy
and sought to determine the extent to which teacher characteristics and practices can enhance secondary school students’ self-efficacy.
Data were collected from 13,173 students in 193 teachers’ classrooms from 141 schools in the 10 districts of Lake Victoria
Region of Kenya. Two-level hierarchical linear model revealed that teachers’ frequent use of mathematics homework, their level
of interest and enjoyment of mathematics, as well as their ability and competence in teaching mathematics were found to play
a key role in promoting students’ mathematics self-efficacy. Teachers’ ability and competence in teaching were also found
to be effective in narrowing the gender gap in students’ self-confidence and competence in mathematics. The study recommends
that teacher training colleges emphasize such teacher practices and values in order to enhance students’ mathematics self-efficacy,
reduce their level of anxiety and fear of mathematics, and consequently, enhance their achievement in mathematics. Professional
development opportunities should also be made available to in-service teachers to continually update their knowledge and skills
and develop new strategies for teacher effectiveness. 相似文献
13.
Dacheng Zhao Michael Singh 《International Journal of Science and Mathematics Education》2011,9(1):69-87
International comparative studies and cross-cultural studies of mathematics achievement indicate that Chinese students (whether
living in or outside China) consistently outperform their Western counterparts. This study shows that the gap between Chinese-Australian
and other Australian students is best explained by differences in motivation to achieve, attributing success to effort, the
influence of parental help and the use of extra mathematics curricula. The argument explored is, in order to promote students’
mathematics achievement, we must improve the pedagogical knowledge of classroom teachers of mathematics, as well as to encourage
parents’ involvement in the mathematics education of their children and to promote students’ motivation to learn mathematics. 相似文献
14.
Inequalities are one of the foundational subjects in high school math curricula, but there is a lack of academic research into how students learn certain types of inequalities. This article fills part of the research gap by presenting the findings of a study that examined high school students’ methods of approaching absolute value inequalities, their common mistakes, misconceptions, and the possible sources of these mistakes and misconceptions. The research study used two tools—a questionnaire and personal interviews. The questionnaire was given to 481 students in the 10th and 11th grades in Israel who studied mathematics at intermediate and advanced levels. It was administered after the students had studied inequalities. Thirty-two students were interviewed in order to find their ways of thinking and the sources of their errors. The main types of mistakes that students consistently made when solving absolute value inequalities were found. Based on the study’s findings, teachers can understand students’ thought processes and use this understanding to conduct remediation and enhance mathematics instruction. 相似文献
15.
This study was designed to compare the effects of Team Assisted Individualization (TAI) and Student Teams-Achievement Divisions
(STAD) on fourth grade students’ academic achievement in and attitudes towards mathematics. Seven classes of a school were
randomly selected for this experimental study. Two of these were given instruction through TAI; two through STAD, and the
remaining three were treated as a control group. For the purpose of the data analysis regarding academic achievement, the
3 X 1 covariance analysis was used to compare the groups. As a result of this comparison, both the TAI and STAD methods were
found to have positive effects (d = 1.003 for TAI and d = 0.40 for STAD) on students’ academic achievement in mathematics. The pairwise comparisons showed that the TAI method had
a more significant effect than the STAD method. The scores for the attitude towards mathematics were analyzed by using non-parametric
statistics. As a result of this analysis, no significant difference was observed regarding students’ attitudes towards mathematics. 相似文献
16.
Margarida César Isolina Oliveira 《European Journal of Psychology of Education - EJPE》2005,20(1):29-43
Portuguese schools in urban areas became multicultural during the 90s. Some students are quite distanced from the school culture.
Many repeat grades. The curriculum emerges as a means of (re)organizing school practice, so that it is designed to foster
inclusion. It is a tool for social mediation between the culture and knowledge of teenagers, and academic ones. It shapes
the interactions between participants, cultural tools and knowledge. The principles of inclusive schooling promote the respect
for diversity, underlining the need to listen to all voices of a learning community. According to the sociocultural approach
appropriating knowledge and developing competencies is a complex process. Interactive practices shape students’ academic performances.
Collaborative project work has been used to promote students’ engagement. This action-research project developed an alternative
curriculum in a class (grades 5 and 6) from a poor and multicultural school in Lisbon. A follow-up investigated the impact
of the educational changes on the learners’ participation in school and in social practices, and on their future life. We
aim at analyzing this alternative curriculum process by focussing on students’ narratives. Results highlight improvements
in students’ academic and social competencies. Changing practices during compulsory education facilitated achievement and
resulted in a better socialization. 相似文献
17.
The influence of homework experiences on students’ academic grades was studied with 223 college students. Students’ self-efficacy
for learning and perceived responsibility beliefs were included as mediating variables in this research. The students’ homework
influenced their achievement indirectly via these two self-regulatory beliefs as well as directly. Self-efficacy for learning,
although moderately correlated with perceptions of responsibility, predicted course grades more strongly than the latter variable.
No gender differences were found for any of the variables, a finding that extends prior research based on high school girls.
Educational implications about the importance of students’ homework completion and its relationship to college students’ development
of self-regulation and positive self-efficacy beliefs is discussed from a social cognitive perspective. 相似文献
18.
Anita A. Wager 《Journal of Mathematics Teacher Education》2012,15(1):9-23
Connecting students’ cultural and community mathematical practices to school mathematics is a critical issue in mathematics
education. The goal of the study was to identify how teachers incorporate children’s cultural and out-of-school mathematics
in instruction. Four related practices were identified, and three drew on children’s cultural or out-of-school experiences:
(a) using these experiences as contexts for problems, (b) linking these experiences to school mathematics, and (c) identifying
embedded mathematical practices prominent in these experiences. A fourth category, teacher initiated situated settings, focused
on shared experiences using the classroom as a site of culture. Findings suggest that these practices represent varying levels
of complexity and that use of this framework might support teachers in better relating students’ cultural and out-of-school
experiences to mathematics. 相似文献
19.
The attitude construct is widely used by teachers and researchers in mathematics education. Often, however, teachers’ diagnosis
of ‘negative attitude’ is a causal attribution of students’ failure, perceived as global and uncontrollable, rather than an
accurate interpretation of students’ behaviour, capable of steering future action. In order to make this diagnosis useful
for dealing with students’ difficulties in mathematics, it is necessary to clarify the construct attitude from a theoretical viewpoint, while keeping in touch with the practice that motivates its use. With this aim, we investigated
how students tell their own relationship with mathematics, proposing the essay “Me and maths” to more than 1,600 students
(1st to 13th grade). A multidimensional characterisation of a student’s attitude towards mathematics emerges from this study.
This characterisation and the study of the evolution of attitude have many important consequences for teachers’ practice and
education. For example, the study shows how the relationship with mathematics is rarely told as stable, even by older students:
this result suggests that it is never too late to change students’ attitude towards mathematics. 相似文献
20.
Cristina Frade Oto Borges 《International Journal of Science and Mathematics Education》2006,4(2):293-317
This paper reports on study that investigated the tacit-explicit dimension of the learning of mathematics. The study was carried out in a secondary school and consisted of an episode analysis related to a class discussion about the difference between plane figures and spatial figures. The data analysis was based on integration between some aspects of Polanyi’s theory on tacit knowledge and Ernest’s model of mathematical knowledge, with reference to its mainly explicit and mainly tacit components. This integration has involved not only the types of knowledge – mainly explicit or mainly tacit – the students used in a psychological way to perform a mathematical task involving conversation, but also and particularly how much the projection of those types of knowledge on the task were manifest tacitly or formalized by the students. Among the results of the research, a strong finding was that the lack of correspondence between the students’ utterances and their original understandings is directly related to the manner in which the tacit co-operates with the explicit in the process of articulation.This paper is a development of three short papers presented at ICME-10, Copenhagen, Denmark, 4–11 July 2004, and PME-28, Bergen, Norway, 14–18 July 2004. 相似文献