Exploring the challenge of developing student teacher data literacy

Abstract

A number of trends are converging to drive the need for more informed teacher data use. These include advocacy for formative assessment and the need for teachers to account for student learning. In this context, assessment literacy and data literacy have emerged as a focus in research and professional development. Problematically, research signals that developing assessment/data literacy is challenging with evidence that teachers may not have mastered relevant aspects of mathematics and statistics. This paper reports lecturer, student teacher and school leader views of the role and requirements of data literacy using data from a larger study into how to foster student teacher mathematical thinking for the breadth of teacher professional work. Data were generated via interviews, surveys and document analysis. Findings suggest a concern and opportunity to develop assessment/data literacy as this calls on mathematical and statistical understanding.     

小学数学核心素养的特质与建构分析

本文针对小学数学核心素养的特质,从数学应用、数学运算、逻辑推理以及几何直观这四个方面进行研究分析;并针对小学数学核心素养的建构策略,从数学活动、逻辑思维、生活实际和知识结构这四个方面展开探究分析,以期能够为有效培养小学生的数学核心素养提供参考性建议。     

FACTORS IMPLICATED IN HIGH MATHEMATICS ACHIEVEMENT

The most recent Program for International Student Assessment (PISA) (2009) mathematical literacy results provide evidence that in Western English-speaking countries, including Australia, the gender gap in achievement appears to be widening in favour of males. In the study reported in this article, the aim was to explore the effects of gender, school type (a measure of socioeconomic background), school learning setting and geographic location on mathematics performance amongst the highest achievers (top 2 %) in the grade 12 Victorian Certificate of Education (VCE) mathematics subjects based on results reported in a metropolitan newspaper. The analyses revealed that over the period 2007–2009, males, students from higher socioeconomic backgrounds and those attending metropolitan schools predominated amongst the highest achievers in all three VCE mathematics subjects. Students in single-sex settings, particularly males, were also over-represented. For each factor, the dominance was more pronounced as the level of difficulty of the mathematics subject increased.     

核心素养视角下的数学教学策略摭探

在小学阶段的数学教学中,教师应结合学情与教学任务,以核心素养为出发点培养学生以数学眼光观察问题、解决问题的意识。教师要以灵活性、操作性强的教学策略调动学生的学习积极性,以图示引导强化运算能力,基于问题研究丰富几何直观,开展游戏实践拓宽逻辑思维,使学生学会借助数学语言精准表达数学问题与结果。     

小学数学教学中培养学生应用能力探析

小学数学教学在小学课程的编排体系当中占据了文化课的半壁江山,是教学中的重中之重,因此上小学数学教学当中,培养学生的数学应用能力是一大教学难点。众所周知,小学生因为年龄小,数学思维能力有限,这就需要教师全力以赴培养学生的数学应用能力,全面提高学生的数学素养。首先要增强学生丰富的基础知识,有了丰富的数学知识,才能在生活当中加以应用,提高自身的数学思维逻辑能力,掌握最基本的解决问题的方法技巧,为今后的学习打下扎实的基础。     

School leaders’ identification of school level and teacher practices that influence school improvement in national numeracy testing outcomes

Since 2008, all Australian students in Years 3, 5, 7 and 9 have been assessed in literacy and numeracy through an annual National Assessment Program—Literacy and Numeracy (NAPLAN) test. In 2015, a team of mathematics education researchers across Australia conducted a nationwide research project to identify school practices and policies that were consistent between schools that showed growth and/or improvement in their NAPLAN numeracy results. This paper reports findings from three case study schools, using a school improvement framework to interpret evidence gathered from the schools’ principals and school leaders. The study has particular implications for policy makers and school leaders who may be seeking ways to improve mathematical practices in their own jurisdictions and schools.     

Big Math for Little Kids

Big Math for Little Kids, a comprehensive program for 4- and 5-year-olds, develops and expands on the mathematics that children know and are capable of doing. The program uses activities and stories to develop ideas about number, shape, pattern, logical reasoning, measurement, operations on numbers, and space. The activities introduce the mathematical ideas in a coherent, carefully sequenced fashion, and are designed to promote curiosity and excitement about learning and doing mathematics. The program produces playful but purposeful learning of deep mathematical ideas, and encourages children to think about and express their mathematical thinking. Throughout the program, great emphasis is placed on the development of mathematical and mathematics-related language. Our observations suggest two broad questions for future research: What kinds of competence can children develop in the context of a rich mathematics environment? In what ways can mathematics learning promote language and literacy?     

Math Is Not a Universal Language: Supporting Middle School Students with Learning Disabilities Using Explicit Vocabulary Instruction in Mathematics Classrooms

Middle school students with learning disabilities often struggle with reading and literacy skills, including vocabulary, and require support in content-area classes such as mathematics where weak vocabulary knowledge can negatively affect learning, achievement, and deep understanding. However, in general, middle school mathematics teachers do not receive training in literacy instruction, much less in explicit vocabulary instruction. Additionally, relatively few studies have examined content-area vocabulary instruction at the middle or secondary school level. This study addressed these gaps in the research by examining the effect of a performance feedback and coaching intervention on middle school mathematics teachers’ use of explicit mathematics vocabulary instruction. Results of the study indicate that performance feedback and coaching had moderately positive effects on teachers’ use and quality of explicit mathematics vocabulary instruction.     

Conceptualising Resources as a Theme for Teacher Education

In this report, I examine resources and their use in school mathematics. I do so from the perspective of mathematics teacher education and with a view to the practice of school mathematics. I argue that the effectiveness of resources for mathematical learning lies in their use, that is, in the classroom teaching and learning context. The argument pivots on the concepts of school mathematics as a hybrid practice and on the transparency of resources in use. These concepts are elaborated by examples of resource use within an in-service teacher education research project in South Africa. I propose that mathematics teacher education needs to focus more attention on resources, on what they are and how they work as an extension of the teacher in school mathematics practice. In so doing, the report provides a language with which mathematics teacher educators and mathematics teachers can investigate teachers' use of resources to support mathematical learning in particular and diverse contexts. This revised version was published online in September 2006 with corrections to the Cover Date.     

深度学习导向下小学数学交流策略探究

随着教育的不断深入革新,人们对小学数学教育提出了更高的要求。小学生在学校除了要接受教育,掌握必要的数学知识以外,还要进行深度学习,并在深度学习的过程中进行良好的数学交流,以此让学生掌握更多的数学知识以及与数学有关的学习方法、学习思维,通过这样的方式全方面提高小学生的数学综合素养。     

On mathematics teaching for future engineers—in the digital era

Current changes, especially the wide application of information technology, in all fields of our life, mean that mathematical knowledge becomes necessary in almost every domain. It implies new expectations for mathematical education. An urgent need of a new mathematical literacy for all—also a new mathematical literacy for engineers—is evident. It is necessary to consider a process of mathematics learning at tertiary level from the epistemological perspective and to investigate students’ ways of mathematical thinking. This epistemological knowledge is especially indispensable when students use information technology. In this article current requirements regarding mathematical education are discussed, especially those for future engineers. Analysis of examples of learning elementary statistics, using graphing calculators as supporting tools, leads to the formulation of essential aims for mathematics educators concerning mathematics teaching for future engineers.     

小学数学魔术校本课程的开发和实施

根据学生的身心发展规律,抓住学生的兴趣点实施课程的开发与实施才能真正达到促进学生成长的效果。数学是一门抽象的学科,小学生正处于形象思维阶段,数学学习对于他们确实存在不小的难度。而在数学教学中引入学生喜爱的魔术元素,可以有效激活学生思维,促进学生的主动参与。在魔法教学中加深学生的数学学习体验,更好地掌握数学思想规律,提高其核心素养。     

Writing in Math: A Disciplinary Literacy Approach

Mathematics teachers often resist generic literacy strategies because they do not seem relevant to math learning. Discipline-specific literacy practices that emerge directly from the math content and processes under study are more likely to be embraced by math teachers. Furthermore, national and state-level mathematics standards as well as Common Core standards provide frameworks for situating literacy practices squarely within the disciplines. A disciplinary literacy approach to writing in math requires teachers to develop innovative strategies and practices that link writing to particular mathematical processes and tasks. An example is shared of a math writing approach developed by a middle school teacher used to prompt her students' critical thinking and problem solving processes during the study of algebra. She designed a template that when completed can serve as a reflective tool for her students and provide the teacher useful feedback on their learning. The example of teaching with the template as a guide for working through steps to solve a story problem demonstrates what disciplinary writing can look like in a typical middle school classroom.     

Physics and Mathematics as Interwoven Disciplines in Science Education

The relationship between physics and mathematics is reviewed upgrading the common in physics classes’ perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.     

高职数学教学中数学文化的渗透

数学文化对培养学生的创新意识以及提高学习兴趣具有非常重要的作用。然而,我国高职院校的数学课堂中数学文化的渗透做的不到位。为了解决此问题,进行了理论与实践的探索,分析了在高职数学教学中渗透数学文化的意义和途径,结果表明数学文化的渗透能够让学生更愉快地接受数学,提升数学修养,为教学提供了有力的参考价值。     

有关数学证明的一次教师问卷调查

Mathematical proofs are not only the focus of every country’s mathematics curriculum reforms, but also the subject of research on mathematics education. This paper is based on a survey of mathematics teachers, the goal of which was to investigate the understanding of mathematical proofs of secondary school math teachers, their levels of mathematical proofs, and their ability to comprehensively teach mathematical proofs. Preliminary results of the survey provide insight into several characteristic aspects of Chinese secondary school teachers’ literacy of mathematical proofs.     

基于Fuzzy-AHP质疑式数学核心素养评价指标体系的研究

数学核心素养培养是当下基础教育数学课程与教学改革的热点.培养学生的质疑能力和创新精神,建立科学合理的数学核心素养评价指标体系是当下迫切需要解决的问题.质疑式学习包括认知性质疑、迁移性质疑、创造性质疑.质疑式3维空间学习模式搭建了数学核心素养框架与课堂衔接的"立交桥";"634"质疑式学习发展空间模式,实现了数学学习过程的"提档增速".利用AHP软件及模糊综合评价法构建的质疑式数学核心素养评价指标体系,有助于促进学生数学学科的高效学习及核心素养水平的提高.     

Klassenwiederholen in PISA-I-Plus: Was lernen Sitzenbleiber in Mathematik dazu?

This study analyses the effects which repeating a class has on ninth grade students’ development of mathematical competency. The following research questions were addressed: How many students repeat grades in the different types of schools? How do students who repeat a grade differ from those who do not in their performance and background characteristics? How much extra mathematics do students repeating a grade learn in one school year? What are the differences between various types of school? Can students with poor mathematics grades in particular profit from repeating a grade? The sample is a sub-sample of the PISA-I-Plus study and comprises N = 360 ninth grade students. The total sample of PISA-I-Plus is representative for all ninth/tenth grade students from the different school types in Germany. The data survey was carried out in the ninth grade and then repeated after the students had repeated a year. The results document differences in the amount of grade repeat quotas between types of school. Furthermore, compared to students not repeating, those repeating a grade had lower mathematics (d = 1.02) and german (d = 1.14) grades, a lower level of mathematical literacy (d = 0.51), and lower test results with regard to basic cognitive abilities (d = 0.32). In terms of the development of mathematical literacy, the students repeating a grade could improve by an average of 23 points (d = 0.27) on the PISA mathematics scale. However, the results identify 38 percent of students repeating a grade who do not make any significant improvement in mathematics or even get worse. A differentiation according to school types shows that students repeating a grade in integrated comprehensive secondary schools and in schools with several educational levels in particular do not, on average, show any noteworthy improvement in their mathematical literacy. The analysis of the school grades received in mathematics shows that students whose mathematics grades are unsatisfactory do not benefit more from repeating a grade than students whose mathematics performance has been rated as being “satisfactory” or better. The article concludes with a discussion of the possible consequences of changing the way in which repetitions of grades are dealt with.     

The Transition from School to University in Mathematics: Which Influence Do School-Related Variables Have?

Particularly in mathematics, the transition from school to university often appears to be a substantial hurdle in the individual learning biography. Differences between the characters of school mathematics and scientific university mathematics as well as different demands related to the learning cultures in both institutions are discussed as possible reasons for this phenomenon. If these assumptions hold, the transition from school to university could not be considered as a continuous mathematical learning path because it would require a realignment of students’ learning strategies. In particular, students could no longer rely on the effective use of school-related individual resources like knowledge, interest, or self-concept. Accordingly, students would face strong challenges in mathematical learning processes at the beginning of their mathematics study at university. In this contribution, we examine these assumptions by investigating the role of individual mathematical learning prerequisites of 182 first-semester university students majoring in mathematics. In line with the assumptions, our results indicate only a marginal influence of school-related mathematical resources on the study success of the first semester. In contrast, specific precursory knowledge related to scientific mathematics and students’ abilities to develop adequate learning strategies turn out as main factors for a successful transition phase. Implications for the educational practice will be discussed.