The effect of language modification of mathematics story problems on problem-solving in online homework

Instructional Science - Students’ grasp of the non-mathematical language in a mathematics story problem—such as vocabulary and syntax—may have an important effect on their...     

Problem length as a structural variable in verbal arithmetic problems

Of five structural variables that in previous studies accounted for a significant amount of the observed variance in the error rate in verbal arthmetic problems, the length variable (number of words in the problem statement) apparently was more important in the upper grades than in the lower grades. In this study three forms of a verbal problem set in which the number of words in the problem statements were systematically varied were administered to classes of students in Grades 4–9. Using regression analysis, the investigator found that although the length variable did not measure a significant amount of variance between two of the forms, with the third it did.This study was begun while the author was a staff member of the Institute for Mathematical Studies in the Social Sciences at Stanford University. The research was partially supported by National Science Foundation grant G18709.     

Problem length as a structural variable in verbal arithmetic problems

Of five structural variables that in previous studies accounted for a significant amount of the observed variance in the error rate in verbal arthmetic problems, the length variable (number of words in the problem statement) apparently was more important in the upper grades than in the lower grades. In this study three forms of a verbal problem set in which the number of words in the problem statements were systematically varied were administered to classes of students in Grades 4–9. Using regression analysis, the investigator found that although the length variable did not measure a significant amount of variance between two of the forms, with the third it did.     

Problem length as a structural variable in verbal arithmetic problems

Of five structural variables that in previous studies accounted for a significant amount of the observed variance in the error rate in verbal arithmetic problems, the length variable (number of words in the problem statement) apparently was more important in the upper grades than in the lower grades. In this study three forms of a verbal problem set in which the number of words in the problem statements were systematically varied were administered to classes of students in Grades 4–9. Using regression analysis, the investigator found that although the length variable did not measure a significant amount of variance between two of the forms, with the third it did.This study was begun while the author was a staff member of The Institute for Mathematical Studies in the Social Sciences at Stanford University. The research was partially supported by National Science Foundation grant G18709.     

Towards conceptual coherence in the research on mathematics learner identity: a systematic review of the literature

We examine the case of a lesson planning session within the context of professional development for dialogic instruction, and the lesson enacted following this session, which was intended to provide opportunities to 11th and 12th grade algebra students to explore polynomial functions in terms of their roots and linear factors. Our goal was, through the close analysis of the planning and enactment of the lesson, to gain deeper understanding of how the two participants were framing mathematical learning and how such different frames may explain the disparity between the planned lesson and its outcome. The analysis and discussion point to the complexities of supporting teachers in transitioning from a “doing” frame to an “exploring” frame.     

From disturbance to task design,or a story of a rectangular lake

We present a story of a teacher educator’s response to a situation of contingency and describe how her experience enhanced her personal mathematical knowledge and influenced her teaching. In our analysis, we attend to different levels of awareness that support a teacher educator’s work and illuminate the qualities of a teacher educator’s knowledge, in particular, knowledge at the mathematical horizon.     

The computer as a tutor — can it adapt to the individual learner?

Educational literature indicates that computers have not yet completely fulfilled the promise for systematic individualization of instruction. We offer here a partial explanation for this, based on observations of elementary-school children doing computer-managed drill and practice in arithmetic in four different CAI systems. A general model for adaptation of instruction to the learner, using computerized management of practice, is presented. Our data show that the key elements of this process — the software-based students' evaluations and the subsequent decisions — are sometimes inaccurate or even totally wrong and result in presentation of inappropriate material or feedback to the learner. We suggest the incorporation of human teachers into the evaluation and decision-making process.This paper was presented at the annual meeting of the American Educational Research Association, Boston, April, 1990.     

高职高等数学课业评价方案的设计

本文从高等数学课业评价的目的、以能力目标为导向的评价标准、评价原则、综合评价成绩计算公式、构建新的课业评价的考核方法及教师的素质要求等方面研究高职高等数学课程的课业评价方案。     

Book Review: A common ground of mathematics and mathematics education for the classroom and for researchers. Erich Christian Wittmann (2021) Connecting mathematics and mathematics education. Collected papers on mathematics education as a design science

Educational Studies in Mathematics -     

How to write a story in English

<正>When it comes to writing a story,the first thing that strikes me is fear.Where to start?What is the title of the story?What is it going to be about?After struggling with some monstrous idea of using a first person perspective to tell a story of a horrific murder,I give up before starting to write and resort to my pillow and blanket for warmth and comfort."Not everyone gets to be Dan Brown."I     

如何合理设计政治课堂教学中的问题

课堂教学中问题的设置要依据教学内容、目的、要求来进行,是探究式教学中尤为关键的一环。本文意在阐明课堂提问的关键在于要优化设计课堂教学中的问题,良好的、阶梯式的问题呈现,才能激发学生的学习兴趣,使学生的思想情感得到升华,才能将知识应用于实践。     

Latent semantic analysis as a tool for learner positioning in learning networks for lifelong learning

As we move towards distributed, self‐organised learning networks for lifelong learning to which multiple providers contribute content, there is a need to develop new techniques to determine where learners can be positioned in these networks. Positioning requires us to map characteristics of the learner onto characteristics of learning materials and curricula. Considering the nature of the network envisaged, maintaining data on these characteristics and ensuring their integrity are difficult tasks. In this article we review the usability of Latent Semantic Analysis (LSA) to generate a common semantic framework for characteristics of the learner, learning materials and curricula. Although LSA is a promising technique we identify several research topics that must be addressed before it can be used for learner positioning.     

Issues relating to curriculum,policy and gender raised by national and international surveys of achievement in mathematics

Scottish schools have provided performance data for five international surveys of attainment in mathematics since 1990. Performance measured against national targets and progression over time and between age‐stages have been monitored nationally, on a regular basis, for 20 years, within the Assessment of Achievement Programme (AAP) (Scotland). The 1994 AAP mathematics survey findings facilitated interpretation of the age 9 and 13 TIMSS results for Scotland. Both studies were influential in formulation of national policies to improve learning and teaching of mathematics, at ages 5–14. Research available to support policies recommended in 1997 is examined. Concerns about validity and reliability of findings from international studies are discussed in the context of a collaboration undertaken between Scotland and France in 1994. It is concluded that simplistic comparisons ignore important cultural and curricular differences. Outcomes of more recent national and international surveys are reported and performance findings from 1988–2000 that relate to gender are reviewed.     

Video as a tool for fostering productive discussions in mathematics professional development

This article explores the use of classroom video as a tool for fostering productive discussions about teaching and learning. The setting for our research is a 2-year mathematics professional development program, based on the Problem-Solving Cycle model. This model relies on video from the teachers’ own classrooms and emphasizes creating a community in which members feel comfortable learning from video. We describe our experiences carrying out the Problem-Solving Cycle model, focusing on our use of video, our efforts to promote a supportive and analytical environment, and the ways in which teachers’ conversations around video developed over a 2-year period.     

Contributions from sociology of science to mathematics education in Brazil: logic as a system of beliefs

In Brazil, mathematics education was associated with Jean Piaget’s theory. Scholars in the field of education appropriated Piaget’s work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of interlocutions and pose a dialogue between the field of mathematics education in Brazil and the sociology of science proposed by David Bloor. The main point of Bloor’s theory is that logical-mathematical knowledge is far from being true and universal and is socially conditioned. In particular we will be discussing the first principle of the strong program, which deals with conditions that generate beliefs promoted by education policies in Brazil, such as the MEC/USAID treaties. In this case the “naturalization of logic” was stimulated by a widespread diffusion of both Piaget studies and the Modern Mathematics Movement.