Guiding Teachers in the Use of a Standards‐Based Mathematics Curriculum: Teacher Perceptions and Subsequent Instructional Practices After an Intensive Professional Development Program

Reforms in mathematics education call for K‐12 teachers to employ standards‐based pedagogies, which embody the National Council for Teachers of Mathematics' principles and standards. In order to effectively support teachers' implementation of standards‐based curricula, professional development must be provided that meets teachers' needs. The professional development program in this study focused on the implementation of a standards‐based mathematics curriculum entitled Investigations in Number, Data, and Space (Investigations). This study uses Guskey's framework as a guide to examining teachers' perceptions of the impact of the professional development that they received; their perceptions of mathematics teaching and learning; and how elements of the professional development translated into practice. Twenty‐two participants were randomly selected from the 53 professional development participants to be interviewed and observed during their mathematics teaching. Using a constant comparison method, the data sources in this study highlighted themes surrounding teachers' experiences with professional development and the implementation of the curricula. The analysis of the data sources in this study highlighted themes surrounding teachers' experiences with professional development: teachers as learners, teachers as self‐evaluators, shifting paradigms, enactment of professional development content into practice, and the influence of the state standardized mathematics test. The results of this study have several implications for future professional development and also highlight some of the more general issues that teachers face when attempting to enact new knowledge and skills into their practice.     

Evaluating Mathematics Achievement of Middle School Students in a Looping Environment

Looping, a school structure where students remain with one group of teachers for two or more school years, is used by middle schools to meet the diverse needs of young adolescents. However, little research exists on how looping effects the academic performance of students. This study was designed to determine if looping influenced middle school students' mathematical academic achievement. Student scores on the Mississippi Curriculum Test (MCT) were compared between sixth and eighth grade years for 69 students who looped during the seventh and eighth grades with a group of 137 students who did not loop. Looping students achieved statistically significantly greater growth on the MCT than their nonlooping counterparts between sixth and eighth grades. Further, the data were disaggregated by gender, ethnicity, and socioeconomic status. Findings indicate that looping may academically reengage students during the middle school years. Advantages and disadvantages of looping at the middle grades are discussed.     

Gender Differences Regarding Mathematics Achievement: The Case of Turkish Middle School Students

The purpose of this study was to explore gender differences in mathematics achievement as demonstrated by performance on the mathematics subsection of a nationwide high school entrance examination in Turkey. In this study, the cities in Turkey were separated into five groups according to their level of economic development. The analysis was based on 2647 students that were randomly selected from these five different groups of cities. Although results indicated a statistically significant difference in mathematics achievement in favor of cities with the highest economic status, the effect size was quite small, which indicates the difference was not practically significant. Results also showed the effect sizes for gender differences in mathematics achievement were very small in all groups of cities. It was concluded that socio‐economic development of the regions was not a critical factor for gender differences in mathematics achievement.     

高师数学教育的时代要求

21世纪,基础教育的新课程实施与高等教育的大众化是我国教育事业发展的两大主流,教育质量始终是我们事业发展的生命线.本文从基础教育改革和人们对数学素质的需求出发,论述了社会对高师数学教育的基本要求,并探讨了高师数学教育要加强学生的数学教育观念的教育.     

Enhancing Formative Assessment Practice and Encouraging Middle School Mathematics Engagement and Persistence

In the transition to middle school, and during the middle school years, students' motivation for mathematics tends to decline from what it was during elementary school. Formative assessment strategies in mathematics can help support motivation by building confidence for challenging tasks. In this study, the authors developed and piloted a professional development program, Learning to Use Formative Assessment in Mathematics with the Assessment Work Sample Method (AWSM) to build middle school math teachers' understanding of the characteristics of high‐quality formative assessment processes and increases their ability to use them in their classrooms. AWSM proved to be feasible to implement in the middle school setting. It improved teachers' practice of formative assessment, especially in their feedback practices, regardless of their pedagogical content knowledge at entry. Results from focus groups suggested that teachers were better able to implement ungraded practice and student self‐ and peer‐assessment after AWSM, and that students were more willing to engage in complex problem solving.     

由一道高考数学题来看中学数学与大学数学衔接问题

高考是高等学校选拔人才的重要手段．高考命题不仅引导着中学教学的方向,而且对高等教育也具有一定的启示作用．本文通过一道安徽省高考数学试题的解答情况,简要分析了中学当前数学教学中存在的问题,并指出大学数学与之衔接应注意的几个方面,以期为高校培养创新型人才提供一定的思路．     

大学复变函数课程与高中数学的衔接

分析近二十年来高中数学经历的三次重要改革中复数部分教学内容、要求的变化和大学数学与应用数学专业复变函数教材处理复数部分的状况.在此基础上,给出大学复变函数课程关于复数部分的一些教学建议.     

独立学院数学课程体系的探索

为解决独立学院数学教学中能力强的学生"吃不饱",能力欠佳的学生"吃不消"的问题,提出了"基础+提高"统筹优化的数学课程体系."基础"模块的教学坚持为后续专业课服务,并穿插教书中"育人"理念;"提高"模块作为公共选修范畴,具有自主性、多元化特点,并突出人才培养的阶梯式发展.通过近5年的教学改革与实践,新课程体系有效地提高了学生学习数学的兴趣,降低了期末考试的不通过率,并造就一批有创新意识的人才.     

The Effects of Metacognitive Reflective Assessment on Fifth and Sixth Graders' Mathematics Achievement

The purpose of this experimental study was to investigate the effects of metacognitive reflective assessment instruction on student achievement in mathematics. The study compared the performance of 141 students who practiced reflective assessment strategies with students who did not. A posttest‐only control group design was employed, and results were analyzed by conducting one‐way analysis of variance (ANOVA) and nonparametric procedures. On both a posttest and a retention test, students who practiced reflective strategies performed significantly higher than students who did not use the strategies. A within‐subjects ANOVA was also conducted six weeks following the intervention to assess how the factor of time affected retention levels. No significant difference was found between the posttest and retention test results for the experimental groups or the control group.     

Characteristics of Second Graders' Mathematical Writing

This study compared the characteristics of second graders' mathematical writing between an intervention and comparison group. Two six‐week Project M2 units were implemented with students in the intervention group. The units position students to communicate in ways similar to mathematicians, including engaging in verbal discourse where they themselves make sense of the mathematics through discussion and debate, writing about their reasoning on an ongoing basis, and utilizing mathematical vocabulary while communicating in any medium. Students in the comparison group learned from the regular school curriculum. Students in both the intervention and comparison groups conveyed high and low levels of content knowledge as indicated in archived data from an open‐response end‐of‐the‐year assessment. A multivariate analysis of variance indicated several differences favoring the intervention group. Both the high‐ and low‐level intervention subgroups outperformed the comparison group in their ability to (a) provide reasoning, (b) attempt to use formal mathematical vocabulary, and (c) correctly use formal mathematical vocabulary in their writing. The low‐level intervention subgroup also outperformed the respective comparison subgroup in their use of (a) complete sentences and (b) linking words. There were no differences between groups in their attempt at writing and attempts at and usage of informal mathematical vocabulary.     

The Effect of a Horseshoe Crab Citizen Science Program on Middle School Student Science Performance and STEM Career Motivation

The purpose of the present quasi‐experimental study was to examine the impact of a horseshoe crab citizen science program on student achievement and science, technology, engineering, and mathematics (STEM) career motivation with 86 (n = 86) eighth‐grade students. The treatment group conducted fieldwork with naturalists and collected data for a professional biologist studying horseshoe crab speciation and a mock survey. The comparison group studied curriculum related to horseshoe crabs in the science classroom. A series of measures related to self‐efficacy, interest, outcome expectations, choice goals, and content knowledge were given to participants before and after the intervention. It was hypothesized that students would report higher motivational beliefs regarding science and show higher levels of achievement following the intervention than the comparison group. Support was shown for most of the hypotheses. In addition, path analyses indicated that students' motivational beliefs influence content knowledge and outcome expectations, which in turn affect their career goals. These results have implications for incorporating authentic fieldwork within a formal school structure as an effective method for promoting student achievement and STEM career motivation.     

The Effect of Area Measurement Tools on Student Strategies: The Role of a Computer Microworld

This study focuses on the role of tools, provided by a computer microworld (C.AR.ME), on the strategies developed by 14-year-old students for the area measurement of a non-convex polygon. Students' strategies on a transformation and a comparison task were interpreted and classified into categories in terms of the tools used for their development. The analysis of the data shows that an environment providing the students with the opportunity to select various tools and asking them to produce solutions `in any possible way' can stimulate them to construct a plurality of solution strategies. The students selected tools appropriate for their cognitive development and expressed their own individual approaches regarding the concept of area measurement. The nature of tools used affected the nature of solution strategies that the students constructed. Moreover, all students were involved in the tasks and succeeded in completing them with more than one correct solution strategy thereby developing a broader view of the concept, although not all of them realized the same strategies. Three different approaches to area measurement emerged from the strategies which were constructed by the students in this microworld: automatic area measurement, provided by the environment, the operation of area measurement using spatial units and the use of area formulae. Almost all the students experienced qualitative aspects of area measurement through being involved in the process of covering areas using spatial units. Students also managed to use the area formulae meaningfully by studying it in relation to automatic area measurement and to area measurement using spatial units. Through these strategies, the concepts of conservation of area and its measurement as well as area formulae were viewed by the students as interrelated. Finally, some basic difficulties regarding area measurement were overcome in this computer environment.This revised version was published online in September 2005 with corrections to the Cover Date.