Assessment in the service of learning: challenges and opportunities or Plus ça Change, Plus c’est la même Chose

This paper begins with a brief overview of literature indicating that, although there have been significant advances in the field’s capacity to conduct both formative and summative assessments over the past decades, those advances have not been matched by comparable impact. The bulk of the paper is devoted to a series of examples from the Mathematics Assessment Project that illustrate issues of methods, and the unrealized potential for advances

Mathematical practices and mathematical modes of enquiry: Same or different?

Background: In this paper, I share a case study of a teacher’s work on mathematics tasks in the context of a ‘mathematics for teaching’ course aiming to develop mathematical content understandings and mathematical practices among primary teachers in one South African province. The course was developed in a national context of concerns about the nature and levels of primary teachers’ mathematical knowledge. Theories viewing mathematical practices as fundamental, contrasted with those that view mathematical practices and mathematical content in more separate and ‘to be integrated’ ways, are used to frame the analysis and ritically reflect on the findings. Results: Data from this teacher’s pre-test and selected course assessments and interactions suggest that while he was able to develop some aspects of the mathematical practices described in the literature, his overall orientation remained attuned to memorization and recall. Findings also pointed to an ongoing reliance on external validation of the ‘correctness’ of his answers. Conclusions: The data suggest that the presence of elements of mathematical practices cannot be viewed as equivalent to the presence of mathematical modes of enquiry. The analysis presented in this paper suggests that while elements of mathematical practices can be developed, moving towards an encompassing orientation to mathematical modes of enquiry may require more central focus on problem-solving approaches to achieve a change in orientation

Putting it into perspective: Mathematics in the undergraduate science curriculum

Mathematics and science are tightly interwoven, yet they are often treated as distinct disciplines in the educational context. This study details the development, implementation and outcomes of a teaching intervention that highlights the links between mathematics and science, in the form of a first-year interdisciplinary course. A mixed method study using surveys and focus groups was employed to investigate undergraduate science students' perceptions of their experiences. Findings reveal that students bring strong beliefs about the nature of mathematics and science from secondary school, which can impact significanly on the success of interdisciplinary science-mathematics courese at the teritary level. Despite this, a range of beneficial outcomes can arise from such courses when they are delivered within a framework of analysing real-world issues. However, students with weak mathematical skills derived little benefit from an interdisciplinary approach and are likely to disengage from learning, in comparision with students who enter university with a solid foundation in mathematics

The Use of Polls to Enhance Formative Assessment Processes in Mathematics Classroom Discussions

This contribution addresses the theme of technology for formative assessment in the mathematics classroom and in particular the ways connected classroom technology may support formative assessment strategies in whole class activities. Design experiments have been developed through the use of a connected classroom technology by which students may share their productions, opinions, and reflections with their classmates and the teacher during or at the end of a mathematical activity. With this technology the teacher may create polls, submit them to the students, gather their answers and show the results in real time. The paper discusses how polls can be used during classroom activities to foster the activation of formative assessment strategies. As a result of the design-based research, a classification of polls according to their contents and aims is proposed. Different ways of structuring classroom discussions and patterns of formative assessment strategies, which are developed from the different types of polls, are discussed

Affect in mathematics education

There are two different uses for the word “affect” in behavioral sciences. Often it is used as an overarching umbrella concept that covers attitudes, beliefs, motivation, emotions, and all other noncognitive aspects of human mind. In this article, however, the word affect is used in a more narrow sense, referring to emotional states and traits. A more technical definition of emotions, states, and traits will follow later.Peer reviewe

Teacher Questioning in Problem Solving in Community College Algebra Classrooms

In this chapter, we focus on the ways two community college instructors worked with students to demonstrate the solution of contextualized algebra problems in their college algebra lessons. We use two classroom episodes to illustrate how they sought to elicit students' mathematical ideas of algebraic topics, attending primarily to teachers' questioning approaches. We found that the instructors mostly asked questions of lower cognitive demand and used a variety of approaches to elicit the mathematical ideas of the problems, such as using examples relevant to the students and dividing the problems into smaller tasks, that together help identify a solution. We conclude by offering considerations for instruction at community colleges and potential areas for professional development

On the instructional triangle and sources of justification for actions in mathematics teaching

We elaborate on the notion of the instructional triangle, to address the question of how the nature of instructional activity can help justify actions in mathematics teaching. We propose a practical rationality of mathematics teaching composed of norms for the relationships between elements of the instructional system and obligations that a person in the position of the mathematics teacher needs to satisfy. We propose such constructs as articulations of a rationality that can help explain the instructional actions a teacher takes in promoting and recognizing learning, supporting work, and making decisions.The ideas reported in this paper have been developed in part with the support of National Science Foundation grants ESI-0353285 and DRL-0918425 to the authors.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/91281/1/On_the_instructional_triangle_PH&DC_May2012.pdf-

Impact on arsenic exposure of a growing proportion of untested wells in Bangladesh

In many areas of Bangladesh, it has been more than six years since a national campaign to test tubewells for arsenic (As) was conducted. Many households therefore draw their water for drinking and cooking from untested wells. A household drinking water survey of 6646 households was conducted in Singair upazilla of Bangladesh. A subset of 795 untested wells used by 1000 randomly selected households was tested in the field by trained village workers with the Hach EZ kit, using an extended reaction time of 40 min, and in the laboratory by high-resolution inductively-coupled plasma-mass spectrometry (HR ICP-MS). The household survey shows that more than 80% of the wells installed since the national testing campaign in this area were untested. Less than 13% of the households with untested wells knew where a low-As well was located near their home. Village workers using the Hach EZ kit underestimated the As content of only 4 out of 795 wells relative to the Bangladesh standard. However, the As content of 168 wells was overestimated relative to the same threshold. There is a growing need for testing tubewells in areas of Bangladesh where As concentrations in groundwater are elevated. This could be achieved by village workers trained to use a reliable field kit. Such an effort would result in a considerable drop in As exposure as it increases the opportunities for well switching by households

Creating Creative Technologists: playing with(in) education

Since the industrial revolution, the organization of knowledge into distinct scientific, technical or creative categories has resulted in educational systems designed to produce and validate particular occupations. The methods by which students are exposed to different kinds of knowledge are critical in creating and reproducing individual, professional or cultural identities. (“I am an Engineer. You are an Artist”). The emergence of more open, creative and socialised technologies generates challenges for discipline-based education. At the same time, the term “Creative Technologies” also suggests a new occupational category (“I am a Creative Technologist”). This chapter presents a case-study of an evolving ‘anti-disciplinary’ project-based degree that challenges traditional degree structures to stimulate new forms of connective, imaginative and explorative learning, and to equip students to respond to a changing world. Learning is conceived as an emergent process; self-managed by students through critique and open peer review. We focus on ‘playfulness’ as a methodology for achieving multi-modal learning across the boundaries of art, design, computer science, engineering, games and entrepreneurship. In this new cultural moment, playfulness also re-frames the institutional identities of teacher and learner in response to new expectations for learning

Disorders of Transepidermal Elimination

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65203/1/j.1365-4362.1985.tb05799.x.pd