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Two groups of mathematics faculty, one from a four-year college and one from a two-year college, redesigned their respective introductory college mathematics courses following presentation of observational data regarding how faculty had been teaching the courses. This presentation emphasised how infrequently faculty teaching introductory college mathematics employed recommended pedagogical practices. This work was part of a multi-year federal grant project designed to increase the numbers of underrepresented students majoring in STEM disciplines. While the two teams developed very different redesigned course activities, in both instances the primary motivation for initiating the work was the information provided to faculty in a professional development workshop regarding how they had previously been observed teaching the mathematics content and how infrequently they utilised the pedagogical practices recommended by STEM education experts. The paper also highlights faculty resistance to curricular reform and enumerates some ways of addressing this resistance. The paper also discusses why faculty from two-year and four-year institutions resisted working together on course redesign and provides recommendations for future efforts addressing course redesign. [ABSTRACT FROM AUTHOR]

A steward of the discipline was originally defined as an individual to whom "we can entrust the vigor, quality, and integrity of the field", and more specifically, as "someone who will creatively generate new knowledge, critically conserve valuable and useful ideas, and responsibly transform those understandings through writing, teaching, and application" [8]. Originally articulated for doctoral education, in 2019 the construct of stewardship was expanded so that it can also be applied to non-academic practitioners in any field, and can be initiated earlier than doctoral education [18]. In this paper we apply this construct to the context of mathematics and argue that even for those early in their training in mathematics, stewardly practice of mathematics can be introduced and practiced. Postsecondary and tertiary education in mathematics -- for future mathematicians as well as those who will use math at work -- can include curriculum-spanning training, and documented achievement in stewardship. Even before a formal ethical practice standard for mathematics is developed and deployed to help inculcate math students with a "tacit responsibility for the quality and integrity of their own work", higher education can begin to shape student attitudes towards stewardly professional identities. Learning objectives to accomplish this are described, to assist math instructors in facilitating the recognition and acceptance of responsibility for the quality and integrity of their own work and that of colleagues in the practice of mathematics. [ABSTRACT FROM AUTHOR]

Purpose: This study examines the content and efficacy of instructional leaders’ expectations and feedback (press) in relation to the improvement of middle school mathematics teachers’ instruction in the context of coherent systems of supports. Research Method/Approach: This mixed methods study is a part of a larger, 8-year longitudinal study in four large urban school districts across the United States. We used transcripts of interview data, surveys, and video recordings of instruction of 271 cases, over 4 years, to determine the content of administrator press, as reported by teachers, and the relationship between the content and change (if any) in instruction. To do so we used qualitative coding of interview transcripts, and ran a series of statistical models to examine the nature of the variance in and impact of administrative press. Findings: Most of the administrators’ press, as reported by teachers, was not targeted toward specific teachers’ mathematics instruction in ways that would likely lead toward improvement in those practices. Rather, the press focused on content-neutral instructional practices or classroom management and organization. Implications for Research and Practice: The instructional leadership practice of administrator observation and feedback is widespread, yet understudied as it relates to changes in teacher practice. Our findings indicate that current policies that mandate principals to spend substantial time in classrooms are unlikely to result in significant improvements in the quality of instruction unless meaningful resources are invested to support administrator learning. [ABSTRACT FROM AUTHOR]

The purpose of this paper was to examine current mathematics interventions designed for students in kindergarten through eighth grade to determine how often they incorporated the five strands of mathematical proficiency identified by the National Research Council (2001). The five strands are conceptual understanding, procedural knowledge, strategic competence, adaptive reasoning, and productive disposition. A systematic review of the literature resulted in 13 meta‐analyses of that studied a total of 19 unique interventions. The five strands of mathematical proficiency were then compared to each intervention to determine with which strand(s) the intervention aligned. None of the 19 interventions contained all five strands, but interventions could be combined to enhance math proficiency. The strands of mathematics proficiency could provide a framework with which to meaningfully combine intervention components. HIGHLIGHTS: A review of 19 math interventions found that none of them addressed all five strands of proficiency, and it would require combinations of them to do so. The strands of math proficiency could provide a framework for intervention decisions in math. [ABSTRACT FROM AUTHOR]

This paper reports changes of the quality of instruction and students' attitudes towards mathematics at one high school during 3 years while teachers participated in a teacher community. The setting for this research was a small-sized high school in South Korea with 154 students and three mathematics teachers. I analyzed the teachers' mathematics classes based on types of interaction, types of questions, and mathematical quality in instruction. Their students' responses for the National Assessment of Educational Achievement study about attitudes towards mathematics were also analyzed. The findings show that this school, over all, improved the mathematical quality and changed the types of questions and the types of interactions towards students' participation in discussing, exploring, and probing mathematical meanings. The students' attitudes towards mathematics became more positive throughout the 3-year period. However, the changes in each teacher's mathematics instruction were different. This study discusses the challenges of having an effective teacher community and researching teachers as learners. [ABSTRACT FROM AUTHOR]

In this paper, we give possible suggestions for a classroom lesson about an application of probability using basic mathematical notions. We will approach to some combinatoric results without using ‘induction’, ‘polynomial identities’ nor ‘generating functions’, and will give a proof of the ‘Vandermonde Identity’ using elementary notions of probability. [ABSTRACT FROM AUTHOR]

Background: The research on diagrammatic representations highlights their importance for the teaching and learning of mathematics. However, the empirical evidence to support their use in the classroom is mixed and somewhat lacking. Purpose: The aim of this study was to develop the use of diagrammatic representations of mathematical concepts in primary classrooms, through introducing primary teachers to the research literature in this area, and researching the subsequent impact on children and teachers. A professional development programme was designed, involving three one-day training sessions for mathematics co-ordinators. They were asked to implement the ideas from the training back in their schools. Sample: Mathematics co-ordinators from eight primary schools attended the professional development programme. The study focussed on Year 3 pupils (aged seven–eight) and Year 5 pupils (aged nine–10). Design and methods: In this paper, we report the qualitative findings from the larger project looking at the overall impact of the professional development programme. The paper focuses on semi-structured interviews carried out with the mathematics co-ordinators attending the professional development sessions, and the Year 3 and Year 5 class teachers who subsequently worked with the co-ordinators on their use of diagrammatic representations in their teaching of mathematics. Lesson observations involving the class teachers were also carried out in order to explore further the possible impact of the project on classroom practice. Results: The qualitative results identified the impact of the project on mathematics co-ordinators and class teachers’ knowledge and practice. However, the nature of this impact was complex, with a variety of facilitating and hindering factors identified for the transfer of the professional development ideas on the use of diagrammatic representations. In addition, different levels of sophistication of class teachers’ use of diagrammatic representations were identified. Conclusions: Implications for the development of professional development programmes to facilitate the transfer of research into practice were identified. Recommendations for the use of diagrammatic representations are also put forward. [ABSTRACT FROM PUBLISHER]

In this paper we present some operational indicators to assess the theses presented by graduates of the MA in Mathematics Education. The paper presents data from the theses by orientation, by thematic field, and by theoretical framework and methodological tools; and lists the authors most often cited. Using this information, we infer graduates? vision concerning mathematics education; their role as teachers; and the knowledge that various courses have left with them for their professional development. The question this research seeks to answer is: what theoretical framework and methodological tools did students working on their Masters Degree in Mathematics Education use to carry out their proposals for pedagogical intervention in their theses? [ABSTRACT FROM AUTHOR]

It is known that an appropriately developed foundational number sense (FONS), or the ability to operate flexibly with number and quantity, is a powerful predictor of young children's later mathematical achievement. However, until now not only has FONS been definitionally elusive but instruments for identifying opportunities for children to acquire its various components have been missing from the classroom observation tools available. In this paper, drawing on a constant comparison analysis of appropriate literature, we outline the development of an eight dimensional FONS framework. We then show, by applying this framework to three culturally diverse European grade one lessons, one English, one Hungarian and one Swedish, that it is both straightforwardly operationalised and amenable to cross cultural analyses of classroom practice. Some implications are discussed. [ABSTRACT FROM AUTHOR]

This paper summarizes results from a math intervention implemented in a high-poverty urban community. Over 7,300 students from kindergarten to 4th grade in 1 low-socioeconomic-status school district participated in the study. Students from 13 different schools (36 different classroom) participated in the treatment. Comparisons were made to purposely selected control-group schools and all other students in the district. The aim of the intervention was to help early elementary-age students living in poverty learn essential math facts and master basic computational skills as a foundation for improving their math ability. The study used a pre-test/post-test quasi-experimental design with control and treatment groups. Achievement for both groups was compared to that of the school district as a whole, with analysis disaggregated by poverty status. The results found positive gains in the treatment group's math achievement at every grade level, transcending differences in socioeconomic status. [ABSTRACT FROM PUBLISHER]

This article documents teacher learning through participation in lesson study, a form of professional development that originated in Japan and is currently practiced widely in the US. Specifically, the paper shows how teachers in three different lesson study teams 1) expanded their mathematical content knowledge, 2) grew more skillful at eliciting and analyzing student thinking, 3) became more curious about mathematics and about student thinking, 4) emphasized students' autonomous problem-solving, and 5) increasingly used multiple representations for solving mathematics problems. These outcomes were common across three lesson study teams, despite significant differences among teams composition, and content foci. [ABSTRACT FROM AUTHOR]

This paper investigates the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the mathematical quality of instruction by comparing the enactment of a fractions problem taught by two teachers with differing MKT. It was found that MKT seem to support teachers' precise use of mathematical language and to prevent errors; the curriculum materials provided a rich representational context for mathematical work. However, teachers' orientations toward mathematics and mathematics teaching and their goals for student learning also seemed to contribute to their use of curriculum materials to engage students with rich mathematics and to support students' participation in the development of the mathematics. Although orientations and goals made it more likely for a teacher to use multiple representations and elicit multiple solution methods, MKT was needed to productively use these elements in instruction. Based on this analysis, it is argued that there are aspects of developing orientations and goals that are related to MKT. [ABSTRACT FROM AUTHOR]

This article describes key elements for mathematics teachers, through the faculty development process, to increase student engagement and motivation in learning mathematics. It addresses common barriers facing student motivation and achievement in the field of mathematics and provides potential remedies from a faculty development viewpoint to alleviate these barriers. The paper offers practical examples from the authors' own faculty development programs and experiences in teaching mathematics to both foster and grow the intellectual curiosity of students and offers suggestions for successful faculty development programs. [ABSTRACT FROM AUTHOR]

Past research has demonstrated that males outperform females in mathematics (Hyde, J. S., Fennema, E., & Lamon, S. J., Psychol Bull 107:139–155, ). Research has also shown that encouraging mindful learning–learning information in a conditional rather than an absolute way–can increase mathematics performance in females (Ritchhart, R., & Perkins, D. N., J Social Issues 56:27–47, ). This paper examines the moderating role of mindful learning for gender differences, by manipulating mindful learning for females’ and males’ performance on a novel math task. The results from this study show that males performed better than females when mindful learning was not encouraged (absolute instruction), but males and females performed equally well when mindful learning was encouraged (conditional instruction). Thus we find that mindful learning moderates gender differences in math performance. [ABSTRACT FROM AUTHOR]

Abstract: This paper reports on a small-scale EU-funded study of the teaching of mathematics in the age range 10–14 in Flanders, England, Hungary, and Spain. Drawing on video recordings of sequences of lessons taught on standard topics, and exploiting a coding schedule developed from live observations in each country, the inferable learning objectives of, and the didactic strategies teachers employ during, each of a lesson''s episodes are examined. Two analyses were undertaken. The first, despite some common ground, indicated that teachers in each country behave in ways similar to teachers from the same country that distinguishes them from teachers elsewhere. The second identified typologies of teacher behaviour that were international in their teacher composition and challenged the robustness of the national script. [Copyright &y& Elsevier]

In this paper the author presents the results obtained from an exploratory and comparative study on the application of two different ways of structuring the mathematical content in the B.S. program of Agronomy Engineering at the University of Guantanamo. The compared forms were: one consistent with the formal systematization of the exposition of the knowledge already obtained, and the other one based on problem solving. In the verification of the hypothesis the sign test was used. Preliminary results showed that the variant of systemic structuring of knowledge by means of problems has greater effects in the efficiency of the knowledge acquired by the students than the one gained by means of the logic of the exposition of the obtained knowledge. [ABSTRACT FROM AUTHOR]

• Substantial overlap in content coverage across three "hybrid" frameworks. • Marked differences, however, in conceptualisations of some instructional constructs. • Ratings of three lessons show how instructional quality may be captured differently. • Analysis across frameworks can fostering cross-cultural understandings. • Single frameworks may be more efficient for professional development/accountability. This paper considers various approaches to classroom observation that combine generic and mathematics content-specific dimensions of instructional quality. Using results from previous research in which three research teams each analysed the same three mathematics lessons (from fourth-grade mathematics classrooms in the USA) using different frameworks, we compare features of the frameworks and assess the extent to which these lead to convergent, divergent or complementary assessments of instructional quality. These findings inform reflections on how a synthesis of existing conceptualisations of instructional quality captures shared aspects of different frameworks but may be differentially useful than individual frameworks depending upon the purposes of observations. Specifically, single frameworks may be particularly useful within specific contexts and for professional development and accountability, but a synthesis of frameworks can foster more coherent cross-cultural understandings of instructional quality. We argue that establishing international networks of scholars can facilitate collaborations aiming to investigate and understand instructional quality. [ABSTRACT FROM AUTHOR]