Mathematics professional development for elementary teachers: Building trust within a school-based mathematics education community

Despite increased attention in professional development to building communities of teachers, few studies have investigated the development of trust in these communities. This paper presents issues related to trust in a professional development project at an elementary school. The project aimed for school-based elementary teachers and university-based mathematics educators to work together to improve mathematics instruction at the school by developing a mathematics education community of learners, where learners were conceived of as both the teachers and the mathematics educators. This paper addresses the following question: What factors in the project supported the development of trust among mathematics educators and teachers as the community was formed? More specifically, the paper is about one aspect of trust, namely, building school-based elementary teachers’ trust in the university-based mathematics educators. We point to three factors that helped the development of trust and we use care theory to further understand and discuss these factors in the context of in-service teacher education initiatives.     

数学开放性问题和平行任务的设计:处理数学学习差异的一种途径

普及教育推行以来,处理课堂中学生的学习差异一直是一个世界性的课题。在数学科,按照数学问题或习题的难度进行分层教学是一贯的做法,期望不同能力的学生逐阶而上。然而,激发学生的数学思考,提供不同学生更多的学习机会,是处理差异化教学的关键。在面对混合能力的大班教学中,运用数学开放问题,结合平行练习任务进行分层教学或是一条有效的处理学生数学学习差异的途径。     

Use of learner‐centered instruction in college science and mathematics classrooms

Learner‐centered approaches to science and mathematics instruction assume that only when students are active participants will learning be deep, enduring, and enjoyable, and transfer to contexts beyond the classroom. Although their beneficial effects are well known, the extent to which learner‐centered practices are used in college classrooms may be low. Surveys of undergraduate science and math majors reveal general dissatisfaction with how courses in their majors are taught, and their number is half what it was 2 decades ago. In response, federally funded systemic reform initiatives have targeted increasing the use learner‐centered instruction in science and mathematics courses to improve undergraduate education generally and the training of preservice teachers specifically. Few data exist regarding how effective these initiatives have been or how frequently learned‐centered instruction occurs as assessed from faculty's perspective, which may not corroborate undergraduate perceptions. Accordingly, a survey was developed to assess the use of learner‐centered techniques and was administered to science and math professors of Louisiana over the Internet. The return rate was 28%. Analyses reveal that they are used infrequently, but when used, are applied to all aspects of teaching. Data also suggest that federal funding has been slightly effective in promoting its use. © 2003 Wiley Periodicals, Inc. J Res Sci Teach 40: 566–584, 2003     

Characteristic behaviors of students with LD who have teacher-identified math weaknesses

Mathematics learning disabilities (LD) have gained increased attention over the last decade from both researchers and practitioners. A large percentage of students receiving learning disability services experience difficulties with mathematics, but little research has examined the specific mathematics behaviors of students with LD who have teacher-identified math weaknesses. This study examines the literature on mathematics LD and identifies specific behaviors from that body of research for the purpose of determining the extent to which those behaviors are observed in students with LD. Data are presented from observations of 391 special education professionals on 1724 students with LD, 870 of whom had identified math weaknesses and 854 of whom did not. Our results validate the existing literature and provide implications for teachers, researchers, and others interested in studying mathematics LD.     

Effects of biology teachers’ professional knowledge and cognitive activation on students’ achievement

This study examined the effects of teachers’ biology-specific dimensions of professional knowledge – pedagogical content knowledge (PCK) and content knowledge (CK) – and cognitively activating biology instruction, as a feature of instructional quality, on students’ learning. The sample comprised 39 German secondary school teachers whose lessons on the topic neurobiology were videotaped twice. Teachers’ instruction was coded with regard to cognitive activation using a rating manual. Multilevel path analysis results showed a positive significant effect of cognitive activation on students’ learning and an indirect effect of teachers’ PCK on students’ learning mediated through cognitive activation. These findings highlight the importance of PCK in preservice biology teachers’ education. Items of the rating manual may be used to provide exemplars of concrete teaching situations during university seminars for preservice teacher education or professional development initiatives for in-service teachers.     

THINKING SCHOOLS,LEARNING NATION: A VISION FOR MATHEMATICS EDUCATION AT SINGAPORE POLYTECHNIC

Singapore Polytechnic offers a tertiary education to O and A level school-leavers leading to more than 20 full-time and part-time diplomas in business, computing, engineering, maritime studies, multimedia, optometry, and technology. The mathematics and science department at Singapore Polytechnic supports the need for a sound foundation in mathematics by offering modules in engineering mathematics for students of the engineering courses. The mathematics modules range from a one-year to a two-and-a-half-year module depending on students entry abilities and the extent of mathematics knowledge needed in the respective courses. This article describes some of the initiatives taken in conjunction with the national objective of having 60% of the population achieve a tertiary qualification to support the knowledge-based economy. These initiatives include programs designed for the varying abilities of students and the incorporation of appropriate use of information technology to make students learning experiences more varied and interesting. These initiatives have brought faculty to the realization that they too are involved in a process of lifelong learning.     

The pedagogical agent enhances mathematics learning in ADHD students

Gaining the attention is the first key step to enhance learning. In Attention-Deficit/Hyperactivity Disorder (ADHD) as the most prevalent deficit in school age, the learners face some impairment in attention that requires appropriate intervention. An environment that embedded Pedagogical Agent in computer-assisted instruction (CAI) has been designed to support learning through gaining and guiding attention to relevant information for these students. This study investigated how much the presence of pedagogical agent can improve learning in ADHD students. The learning environment was integrated with a pedagogical agent, named Koosha, as a tutor and motivator. This study employed a pretest and posttest experimental design with a control group. The statistical population was 30 boy students with ADHD in primary school from the North of Iran. The participants were randomly assigned to work with either an agent presenting a multimedia program or without an agent in mathematics. The results (Analysis of covariance -ANCOVA) suggested that experimental and control groups show a significant difference in mathematics achievement. According to this research, using the pedagogical agent can enhance the learning of ADHD students; so it can be considered as a valid school-base intervention for these students.     

A preliminary discourse analysis of constructivist-oriented mathematics instruction for a student with learning disabilities

Reform efforts in mathematics education arose, in part, in response to constructivist works on conceptual learning. However, little research has examined how students with learning disabilities (LD) respond to constructivist-oriented instruction in mathematics, particularly in moment-to-moment interactions. To understand the nature of constructivist-oriented mathematics instruction involving students with LD, the authors conducted a case study to analyze teacher–student interactions during constructivist-oriented small group instruction involving a student with LD. The student demonstrated, to a certain degree, the ability to reason mathematically when provided with appropriate opportunities and prompting. However, given the limited intervention time, his reasoning and problem solving did not seem to go beyond the semiconcrete level of operation, which may have inhibited his solving of complex word problems with large numbers. Findings indicate that more efforts are needed to support students, those with LD in particular, in their transitions from concrete or semiconcrete to abstract conceptual understanding and problem solving.     

Constructivist mathematics education for students with mild mental retardation

This study examined the effects of a constructivist mathematics intervention for students with mild mental retardation, as compared to direct instruction, which is often recommended for these children. A total of 69 students from elementary schools for special education participated in the study, which focused on multiplication learning. They received one of two kinds of mathematics intervention, guided or directed instruction. Multiplication automaticity and ability tests were administered before and after the four-month training period. The results show that students in both conditions improved significantly during the training period. However, students who received directed instruction showed greater improvement than students who had received guided instruction. These results show that students with MMR can profit from constructivist instruction, although direct instruction seems more effective.     

Effects of Tier 2 and Tier 3 Mathematics Interventions for Second Graders with Mathematics Difficulties

Two studies were conducted to examine the effects of Tier 2 and Tier 3 mathematics interventions on students with mathematics learning difficulties. In the first study, the work of Bryant et al. was replicated and expanded upon by documenting the sustained effects of a Tier 2 mathematics intervention on mathematics performance by second graders. In the second study, the Tier 2 intervention was intensified to a Tier 3 intervention through increases in two instructional features: group size and dosage. The results of the first study showed that the Tier 2 intervention improved mathematics performance for the majority of student participated in the study, and the effect of the intervention was sustained for the majority of students who responded to the Tier 2 intervention. The results of the second study showed that intensified Tier 3 intervention that involved one‐on‐one instruction and extended time for daily lessons may benefit students who have persistent difficulties with learning mathematics.     

Mathematics Teachers’ Approaches to Computer‐based Instruction

Schon (1987) has criticized the normative curriculum of professional schools including technical colleges: at first basic science (mathematics, physics, etc.), then applied science, and finally technical skills of day‐to‐day practice. In Schön's opinion, the tradition of professional education is an obstacle to changing teaching methods from drill and practice to open‐learning environments. Solomon (1986) presents the different approaches which teachers take in computer‐based instruction in stages from drill and practice to open‐learning environments. This paper reports a six‐year case study, inspired by the work of Schön and Solomon, on the impact of, and the teachers’ role in, the use of computers and Mathcad in the mathematics instruction of technical colleges. The teaching experiment was started with 51 first‐year students during the academic year 1988‐1989 at the Technical Institute of Jyvaskyld. The class of mechanical engineering had 162 and the class of electrical engineering 206 lessons of mathematics during the first experimental year. Two senior lecturers of mathematics taught the classes. Before the experiment, computers had never been used in mathematics instruction at the institute. The various ways of using Mathcad were classified on the basis of the forms filled and files saved by the teachers, as well as on the notes made by the researcher. The teachers’ ways of using computers in our experiment during the years 1988‐1995 clearly showed the existence of stages. Some of the stages were the same for both teachers, but there were also some differences. Both teachers started by fitting an open computer‐based environment into the traditional instruction.     

转化农村学校数学学困生的方法摭探

农村学校的学困生转化工作应得到重视,否则学困生与学优生的差距越来越大。目前数学学困生的转化工作还存在教学方法单一、教师重视不够、学困生基础薄弱且缺乏家长管理等问题。教师要从关注学困生本身和教学方法两个方面积极开展农村数学学困生的转化工作,让每个学生都不掉队。     

Research‐capacity building,professional learning and the social practices of educational research

There have been numerous attempts in the past few years within education research—and social science research more generally—to alter the character of research practice(s). In particular, there has been a systematic effort to address perceived shortcomings in research practice through a series of ‘research‐capacity building’ initiatives, aimed at the restructuring of professional learning. In this article the authors explore empirically the ways in which different modes of professional learning are implicated in the social practices of education research. These considerations lead to the conclusion that the currently dominant approaches to research‐capacity building are based on an underestimation of the difficulties in influencing the professional learning of educational researchers significantly and, thereby, changing the practices of educational research. More realistic expectations of these forms of research‐capacity building, in turn, suggest the need to develop alternative approaches that acknowledge the exigencies of the current social organisation of educational research more fully.     

Tablet-based AR technology: Impacts on students’ conceptions and approaches to learning mathematics according to their self-efficacy

Most studies of Augmented Reality (AR) in education have considered students’ learning outcomes and motivation. Previous studies have revealed that AR has the potential to help students learn abstract conceptions in mathematics. In this paper, a series of statistics and probability lessons using AR installed on tablets was designed and developed to examine the effect of the AR technology by comparing the conceptions and learning approaches of junior high school students with different levels of self-efficacy. A total of 101 students were divided into two groups based on their mathematics learning self-efficacy. The analysis of the results shows that AR applications in mathematics courses can help students with higher self-efficacy to pay closer attention to higher level conceptions. It can also help higher self-efficacy students to apply more advanced strategies when learning mathematics.     

高等数学学困生的成因与对策

高等数学学困生是当前我校数学教育对象中的主要群体.文章通过对我校学生学习情况的问卷调查,分析了学困生的形成原因,并提出了数学学困生的教学策略.     

Student learning emotions in middle school mathematics classrooms: investigating associations with dialogic instructional practices

Emotions are central to how students experience mathematics, yet we know little about how specific instructional practices relate to students’ emotions in mathematics learning. We examined how dialogic instruction, a socially dynamic form of instruction, was associated with four learning emotions in mathematics: enjoyment, pride, anger, and boredom. We also examined whether these associations differed by student gender and prior mathematics achievement. The sample consisted of 1307 sixth through eighth grade students (51.6% female, 59.0% White, 30.8% African American, and 10.3% other race; 42.3% receive free/reduced price lunch) from 70 mathematics classrooms. Results indicated that teachers who used more dialogic mathematics instruction had students who reported more enjoyment and pride, and less anger and boredom. Males and low-achieving students reported more positive and fewer negative emotions with greater dialogic instruction compared to their female and high-achieving counterparts.     

高专学生高等数学学习困难原因与对策研究——以山东中医药高等专科学校为例

高等数学是一门注重理论研究的学科,对高专学生来说具有一定的学习困难.从多个角度分析产生学习困难的原因,提出相应的对策.     

Teacher perceptions of the mathematical potential of students in special education in the Netherlands

Research has shown that high expectations of teachers about their students’ academic development have a positive influence on how these students actually develop. Therefore, when aiming to improve students’ learning results it is essential to know how teachers think about their students’ abilities. The present study was meant to investigate what perceptions primary school teachers in special education have of their students’ potential in mathematics and what possibilities they see to reveal this potential. Data were collected through an online questionnaire. Surprisingly, the responses showed that, although the teachers teach students with low achievement scores in mathematics, most of the teachers were positive about the mathematical potential of their students. The teachers often attributed unused potential to causes outside the student and they underpinned this view with observations from school practice. The article concludes with discussing the consequences of these findings for the professional development of teachers.     

Effects of Training in the Use of Social and Cognitive Strategies: An Intervention Study in Secondary Mathematics in Co‐Operative Groups

ABSTRACT

This article reports on an intervention study into the effects of a training in the use of social and cognitive strategies on the learning outcomes of students in secondary mathematics education. Special attention is given to differential effects for high‐ and low‐achieving students. The focus on differential effects is derived from studies into learning in small co‐operative groups, and from the results of meta‐analyses into the effects of training in learning strategies. From these studies it can be concluded that in general such programs contribute to learning. However, it seems that low‐achieving students are unable to benefit from interventions of the kind investigated (i.e., co‐operative learning and training in learning strategies). The main question is whether it is possible to design an instructional program from which all students benefit, and from which the low‐achieving students profit more than their counterparts in the control‐program. In the present study three instructional programs for co‐operative learning were compared: (i) an experimental program with special instruction in the use of social strategies; (ii) an experimental program with special instruction in the use of cognitive strategies; and (iii) a control program without training in either cognitive or social strategies. The programs were identical with respect to mathematical content and general instructional settings (a combination of whole‐class instruction, working in co‐operative groups and individual work). The experiment addressed the following research question: what are the general and differential effects of a training in the use of social and cognitive strategies on the results of learning in secondary mathematics? The research was conducted in two schools for secondary education in a total of 21 classes, involving a total of 511 students. The design was a pretest‐posttest control group design, using two experimental groups and one control group. The data were analysed from a multi‐level perspective. The outcomes of the investigation clearly show the effects of the intervention. Teaching cognitive and social strategies has the expected, positive effects. In addition to this main effect, a compensatory effect for the low‐achieving students was found. The low‐achieving students in the experimental conditions outperformed their counterparts in the control group.

     

Learning by Exploration in Mathematics Courses: a programme for student teachers

In order to adapt teacher education to new demands in mathematics classrooms, it is necessary to change the courses in mathematics at the university. Teachers’ beliefs about mathematics, learning and teaching has great impact on their teaching. At the University of Göteborg, a co‐operative project has been conducted in order to design a programme based on problem solving in courses taken by prospective Comprehensive School teachers (grade 4‐‐9). The main purpose of the project has been to make student teachers more reflective about mathematics as such, about learning and teaching. Another purpose of the project has been to use a teaching method in a university course‐‐a method which could be applied in a school classroom. The student teachers have worked co‐operatively in small groups of 3‐4 students and the educators role has been that of a facilitator. A preliminary evaluation indicates that student teachers have developed an insight into the complexity of learning and teaching, even though there are variations in this respect. However they still have difficulties in applying the method to teaching mathematics at school.