1. Interaction. The interactions learners have with each other build interpersonal skills, such as listening, politely interrupting, expressing ideas, raising questions, disagreeing, paraphrasing, negotiating, and asking for help. 2. Interdependence. Learners must depend on one another to accomplish a common objective. Each group member has specific tasks to complete, and successful completion of each member’s tasks results in attaining the overall group objective.

将“Cooperative Learning”融入课堂——浅谈英语素质教育

The Visual Display of Quantitative Information

Cognition in Practice: Notes

How to Lie with Statistics

The Developmental Psychology of Jean Piaget

As graphics calculators become more available, interest will focus on how to incorporate them appropriately into curriculum structures, and particularly into examinations. We describe and exemplify a typology of use of graphics calculators in mathematics examinations, from the perspective of people designing examinations, together with some principles for the awarding of partial credit to student responses. This typology can be used to help design examinations in which students are permitted to use graphics calculators as well as to interrogate existing examination practice.

Graphics calculator use in examinations: accident or design?

Issues of equity and assessment loom large early in most discussions about the use of graphics calculators in mathematics, often simultaneously. In this paper, the authors identify and discuss some aspects of these issues, locating them in the broader curriculum framework in which they properly belong. The discussion is informed by the authors' recent experiences with using graphics calculators at the early undergraduate level but is not restricted to those experiences. The issues are of direct importance to mathematics education in the early undergraduate years as well as the senior secondary years, and have implications for the nature of mathematics education throughout secondary education. Of course, issues related to graphics calculators, equity and assessment are not only issues for Australia but have also appeared in socio-economically comparable countries. such as the USA and the UK. While there is not space in this paper to discuss the overseas experiences in great depth, it is perhaps worth noting at least that the National Council of Teachers of Mathematics' 'Curriculum and Evaluation Standards' (1989) assumes availability of graphics calculators to all students at all times from the 9th grade onwards, that all the UK examining bodies now allow students to use graphics calculators in external examinations (although they do not all expect them to be used), and that a good deal of curriculum development is taking place in each country to design mathematics curricula accordingly.

Graphics calculators: Equity and assessment

Students at university encounter quantitative information in tables and graphs or through prose in textbooks, journals, electronic sources and in lectures. The degree to which students are able to engage with this kind of information and draw their own conclusions, influences the extent to which they need to rely on the interpretation of others. In particular, students who are studying in non-mathematical disciplines often fail to engage seriously with such material for a number of reasons. These may include a lack of confidence in their ability to do mathematics, a lack of mathematical skills required to understand the data, or a lack of an awareness of the importance of being able to read and interpret the data for themselves. In this thesis, the successful choice and use of skills to interpret quantitative information is referred to as numeracy.

The level of numeracy exhibited by a student can vary depending on the social or cultural context, his/her confidence to engage with the quantitative information, the sophistication of the mathematics required, and his/her ability to evaluate the findings. The first part of the thesis is devoted to the conceptualisation of numeracy and its relationship to mathematics.
 
The empirical study that follows this is focused on an aspect of numeracy of importance to university students: the reading and interpreting of tables of data in a range of non-mathematical contexts. The students who participated in this study were enrolled in degree programs in the social sciences. The study was designed to measure the effectiveness of a one-hour intervention workshop aimed at improving the levels of the students? numeracy. The short length of the intervention was dictated by practical and organisational constraints. This workshop involved reading and interpreting a table of data using strategies based on the SOLO taxonomy (Biggs and Collis, 1982).
 
The SOLO taxonomy was developed mainly as a means of classifying the quality of responses across both arts and science disciplines. The categorisation uses five levels: prestructural, unistructural, multistructural, relational and extended abstract. It can be used as a diagnostic tool at all levels of education as it can be seen as a spiral learning structure repeating itself with increasing levels of abstraction. It can also be used as a teaching tool in feedback to students.
 
A measuring instrument, also based on the SOLO taxonomy, was designed to gauge the levels of the students' responses to these tasks. Each response was allocated a level that was subsequently coded as a number from zero to seven. Because the responses were in distinct ordered categories, it was possible to analyse the scores using the Rasch Model (Rasch 1960/80) for polytomous responses, placing both the difficulty of the tasks and the ability of the students on an equal interval scale. The Rasch Model was also used to evaluate the measuring instrument itself. Some adjustments were made to the instrument in the light of this analysis. It was found that it is possible to construct an instrument to distinguish between levels of students' written responses for each of the chosen table interpretation tasks.
 
The workshop was evaluated through a comparison of the levels achieved by individual students before and after the workshop. T-tests for dependent samples indicated a significant improvement (p < 0.01) in student performance.

/pdf/developing-critical-numeracy-at-the-tertiary-level-14xm8vqt3q.pdf

Developing critical numeracy at the tertiary level

High school, college, and university students as well as citizens encounter quantitative information in a wide variety of media and contexts, such as in books, journals, newspapers, magazines, advertising, the workplace and on the Internet. While it is often assumed that people are able interpret published data in context, this assumption is open to question. In this paper, a Five Step Framework to help both teachers and students to interpret data in the form of tables or graphs is described and exemplified. Development of the Framework by Kemp was based on the SOLO taxonomy devised by Biggs and Collis. The Framework offers a progression from simple numerical reading of a table, to more complex interpretations of tables and graphs needed for a better understanding of data in their context. The Framework has been used successfully in primary, secondary and tertiary mathematics education to support both students and their teachers.

/pdf/a-five-step-framework-for-interpreting-tables-and-graphs-in-4jybuykhnb.pdf

A five step framework for interpreting tables and graphs in their contexts

The methods by which the graphical and numerical functions of a modern graphics calculator can be used to improve calculus teaching and learning are discussed. The possibilities it affords for conceptual understanding are illustrated through examples.

/pdf/some-calculus-affordances-of-a-graphics-calculator-1lqa85rfy6.pdf

M. Kemp

Papers

Graphics calculator use in examinations: accident or design?

Graphics calculators: Equity and assessment

Developing critical numeracy at the tertiary level

A five step framework for interpreting tables and graphs in their contexts

Some Calculus Affordances of a Graphics Calculator