Curiosity as a personality variable influencing learning in a learner controlled lesson with and without advisement

This study investigated the effect of curiosity on learning art education facts and concepts by first- and second-graders in computer-based interactive learner control environments with and without advisement. High-curious subjects, who generally prefer a higher degree of unfamiliarity and uncertainty, were predicted to perform better in either learner control environment than low-curious children. All children regardless of curiosity level were expected to perform better in the advisement condition than in the no-advisement condition. As predicted, a significant difference in achievement scores favored the high-curious children in both conditions. Although there was no main treatment effect, exploratory analyses revealed an unpredicted significant interaction between grade level and treatment. First-graders performed significantly better with advisement than without advisement while second-graders performed better without. Examination of treatment usage data indicated that first-graders followed advisement more than did second-graders.     

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.     

Text density level as a design variable in instructional displays

Presenting narrative text in computer-based instruction (CBI) is more difficult than in print lessons due to limited screen resolution and display area. The present research aimed at achieving a more compatible match between lesson content and the attributes of the presentation media. Subjects received either a print or CBI statistics lesson containing low-density (concise) narrative text, high-density (conventional) text, or the density type they preferred (learner-control). Results showed the low-density lesson to reduce completion time relative to the high-density version, while yielding equivalent achievement. Subjects receiving the lesson in the print mode had shorter completion times and higher achievement than their CBI counterparts. Attitude results showed that CBI was favorably regarded, but perceived as longer and slow-moving than print. Implications of results for designing instructional material in accord with CBI attributes and learner characteristics are discussed.     

Research on mathematics teachers as partners in task design

Mathematical tasks and tools, including tasks in the form of digital tools, are key resources in mathematics teaching and in mathematics teacher education. Even so, the ‘design’ of mathematical tasks is perceived in different ways: sometimes seen as something distinct from the teaching and learning process, and sometimes as integral to it. Whilst task design has often been carried out by designers or mathematicians (perhaps as textbook authors), the focus for this review article is research that has involved mathematics teachers as partners in the design of tasks. The article provides a state-of-the-art review of relevant literature and is presented under three headings that consider, in turn, the role of mathematical ‘tasks’; the nature of ‘task design’; and the notion of ‘partnerships for task design’ in mathematics education. Subsequently, we present current research that is providing new insights into tasks, task design, and task design partnership. Based on this, we argue that ‘task design’ needs to pay particular attention to what to design, which tools are necessary or beneficial, and under what conditions; digital tools and task resources offer particular affordances that traditional resources cannot provide; and not only do teachers benefit from being partners in task design (in terms of their professional learning) but without their involvement some aspects of task design would most likely be neglected.     

Professional development for practicing mathematics teachers: a critical connection to English language learner students in mainstream USA classrooms

This article examines the effects of changing teacher self-efficacy on student achievement. Results from a quantitative study of mathematics teachers in a USA mid-Atlantic state showed that teachers experienced reduced self-efficacy when working with English language learner students (ELLs) relative to non-ELLs. Further, the article explores professional development opportunities for strengthening teachers’ effectiveness with ELLs. The study utilized a four-part survey instrument based on the Teacher Sense of Efficacy Scale (TSES). All participants (n = 181) were mathematics educators from the highlighted state, and 94 % of them were preK-12 public school practicing classroom teachers. Study results indicate that teachers’ participation in professional development on ELL instruction is positively correlated to their heightened sense of self-efficacy. This finding points to continuing education as a potentially viable approach to reducing academic challenges for ELL students in mainstream mathematics classrooms by developing ever more effective practicing teachers.     

Learner agency in language learning: the story of a distance learner of EFL in China

Learner agency plays a key role in self-regulated learning. Yet, there is a paucity of research into its role in the distance learning context. Using reflective narratives written by a distance learner of English in China, this longitudinal case study aims to investigate the ways in which learner agency mediates the language learning in the distance mode. Findings from the study suggest that agency has a major impact on learners’ self-efficacy, identity, motivation, and metacognition—four constructs which are instrumental in determining language learning success, in particular in the distance learning context. Analysis of the data indicates that positive changes in these four constructs, in turn, lead to further agentic engagement, hence forming a virtuous circle of mutual enhancement. Implications are discussed in relation to fostering distance learners’ goal awareness, enhancing their self-efficacy, maintaining their motivation, and encouraging metacognitive efforts.     

Using what matters to students in bilingual mathematics problems

In this study, the author represented what matters to bilingual students in their everyday lives—namely bilingualism and everyday experiences—in school-based mathematical problems. Solving problems in pairs, students demonstrated different patterns of organizing and coordinating talk across problem contexts and across languages. Because these patterns bear consequences for how bilinguals experience mathematics learning, the author takes these patterns as the basis to argue that mathematics education for bilingual students should capitalize on bilingualism and experiences as cognitive resources.     

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.     

Structural exclusion through school mathematics: using Bourdieu to understand mathematics as a social practice

Research on learner errors in mathematics education is beginning to focus on how teachers can learn to identify and engage with the reasoning behind these errors. Research on professional learning communities is beginning to show that they present powerful opportunities for on-going teacher collaboration and learning. In this paper, I bring the two areas of research together. Drawing on data from one professional learning community in the Data Informed Practice Improvement Project, I show how teachers in this community came to understand key concepts about learner errors and shifted their ways of talking about learner errors. I identify three important shifts that the teachers made in their learning about learner errors: from identifying to interpreting errors; from interpreting to engaging errors; and from focusing on learner errors to focusing on their own knowledge. I argue that these three shifts suggest a deepening of teachers’ thinking in relation to learner errors.     

Girls and mathematics —A “hopeless” issue? A control-value approach to gender differences in emotions towards mathematics

This study analyzed gender differences in achievement emotions in the domain of mathematics. Based on Pekrun’s (2000, 2006) controlvalue theory of achievement emotions, we hypothesized that there are gender differences in mathematics emotions due to the students’ different levels of control and value beliefs in mathematics, even when controlling for prior achievement. The structural relationships between prior achievement, control and value beliefs, and emotions were assumed to be invariant across girls and boys in spite of hypothesized mean level differences of beliefs and emotions across genders. The emotions and beliefs of 1,036 male and 1,017 female 5th grade students were assessed by self-report measures, and their prior mathematics achievement was assessed by academic grades. Even though girls and boys had received similar grades in mathematics, girls reported significantly less enjoyment and pride than boys, but more anxiety, hopelessness and shame. Findings suggested that the female emotional pattern was due to the girls’ low competence beliefs and domain value of mathematics, combined with their high subjective values of achievement in mathematics. Multiple-group comparisons confirmed that the structural relationships between variables were largely invariant across the genders.     

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.     

Prior knowledge in mathematics and study success in engineering: informational value of learner data collected from a web-based pre-course

The article describes the development and evaluation of a web-based pre-course in mathematics, delivered to four cohorts of engineering students at a German university. Based on demographic, personal, and learning-related data relationships between students’ preconditions, their learning gains in the pre-course, and study success in the degree programme were analysed. The results support the existing literature in that domain-related prior knowledge and secondary school achievement play a dominant role regarding study success in engineering. The analyses also showed that the influence of cognitive predictors could only be compensated for by a strong learner engagement. At-risk students with high pre-course learning gains showed significantly better first-year performance. The number of self-tests a student attempted was positively related to pre-course learning gains and even to first-year performance, suggesting that this variable is a good indicator of student engagement.     

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 -