Math education in the United States remains resistant to systemic change, and our country pays the price. Stemhagen's article "Democracy and School Math" further confirms this trend. Despite repeated calls for reform, decades of research on how people learn, millions of dollars invested in teacher professional development, and years of politicized debate, the math wars rage on—between those who believe students have the capacity to construct their own mathematical ideas and others who insist mastery of the traditional canon must come first. Meanwhile, algebra failure among secondary students remains rampant and elementary education majors report the greatest rates of math anxiety of any college major. Adults and children alike joke about being terrible at math, seemingly unaware of the extent to which this innumeracy serves as a barrier to full participation in democracy as well as to the realization of their individual goals, hopes, and dreams. In the math education community itself, there is little discussion of the unique role mathematics can play in preparing students for democracy. In this short paper, I offer a more detailed conceptualization of democratic mathematics education and discuss the role of constructivism in bringing these ideas to fruition. I suggest that a shift in the power dynamic that characterizes most mathematics classrooms will be a key component in moving beyond the gridlock.
Using dialogues with our informants, as well as with each other, we explore how the men and women in our research make it through their mathematics coursework and, in turn, pursue their intended majors. Our research focuses on how students navigate what we call the gendered math path and how that path conforms to and diverges from traditional gender norms. Common themes of women's lower than men's self-perception of their ability to do mathematics, along with the divergent processes of doing gender that emerged in men's and women's discussions of their application of mathematics, reminded us of the continued struggles that women have to succeed in male-dominated academic disciplines. Although self-perception helps us understand why there are fewer women in STEM fields, it is important to understand how different forms of application of ideas might add to the diversity of what it means to do good science.
We consider the nonlinear cubic Wave, the Hartree and the nonlinear cubic Beam equations on T2 and we prove the existence of different types of solutions which exchange energy between Fourier modes in certain time scales. This exchange can be considered "chaotic-like" since either the choice of activated modes or the time spent in each transfer can be chosen randomly. The key point of the construction of those orbits is the existence of heteroclinic connections between invariant objects and the construction of symbolic dynamics (a Smale horseshoe) for the Birkhoff Normal Form truncation of those equations. ; This project has received funding from the European Research Council (ERC) under the EuropeanUnion's Horizon 2020 research and innovation programme (Grant Agreement No 757802). P.M. has beenpartially funded by the Spanish Government MINECO-FEDER Grant PGC2018-100928-B-I00. M. G andS. P. have been also partially supported by the Spanish MINECO-FEDER Grant PGC2018-098676-B-100(AEI/FEDER/UE) and by the Catalan Institution for Research and Advanced Studies via an ICREA AcademiaPrize 2019. F.G., M. G., P. M. and S.P. have been also partially supported by the Catalan Grant 2017SGR1049.S.P. acknowledges financial support from the Spanish "Ministerio de Ciencia, Innovación y Universidades",through the María de Maeztu Programme for Units of Excellence (2015–2019) and the Barcelona GraduateSchool of Mathematics ; Peer Reviewed ; Postprint (published version)
Mathematics anxiety has been associated to performance in school mathematics. The association between math anxiety and psychosocial competencies as well as their specific contribution to explain school mathematics performance are still unclear. In the present study, the impact of sociodemographic factors, psychosocial competencies, and math anxiety on mathematics and spelling performance was examined in school children with and without mathematics difficulties. The specific contributions of psychosocial competencies (i.e., general anxiety and attentional deficits with hyperactivity) and math anxiety (i.e., self-assessment in mathematics) to school mathematics performance were found to be statistically independent from each other. Moreover, psychosocial competencies—but not math anxiety—were related also to spelling performance. These results suggest that psychosocial competencies are more related to general mechanisms of emotional regulation and emotional response towards academic performance, while mathematics anxiety is related to the specific cognitive aspect of self-assessment in mathematics.
The project, Bite size maths: Building mathematics low socioeconomic student capability in regional/remote Australia, establishes the foundations for a change in the way that online education is offered to low socioeconomic students in regional/remote Australia. The Bite size maths project is a $140,000 project funded in 2016 through the Department of Education and Training (DET) as part of the Higher Education Participation and Partnerships Programme (HEPPP) 2015 National Priorities Pool. The Bite size maths project has delivered an innovative set of interactive modules (as an online learning system) that can be used singly or linked together in a Massive Open Online Course (MOOC—http://www.bitesizemaths.net). The 20 interactive modules developed within the project provide a foundation for improvements in mathematics education across the higher education sector as well as throughout the school system in regional/remote Australia. The use of self-paced learning in the form of guided instruction and opportunities for practice have the potential to profoundly impact on the learning experiences of undergraduate students who have little or no experience in mathematics. Mathematics forms the core of multiple course structures at universities, and previous research emphasises the importance of engaging undergraduate students in building a strong mathematics foundation. This is particularly the case in regional/remote Australia where universities, like those in the Regional Universities Network (RUN), focus particularly on professional careers, such as education and health care, that require mathematical competencies. Contemporary students need to be both proficient in and comfortable with mathematics, so as to bridge the gap between curriculum and understanding the mathematics that is required in such careers. The Bite size maths project showed, for the first time, that a MOOC can be designed on the basis of studies of human cognitive architecture, in this case the principles and effects of cognitive load theory. Development and trials of five modules demonstrated that the combination of worked examples and practice questions (the worked example effect in cognitive load theory) makes a significant difference to test results of students who have little experience in mathematics. After the initial trials, a MOOC (comprised of 20 interactive modules) was built incorporating a number of improvements and innovations. These included other cognitive load effects, as well as point-of-contact feedback. This is the first time that point-of-contact feedback developed at SCU has been used as part of a MOOC. This feedback serves to let students know about their learning approaches, provides guidance on appropriate learning styles, and allows feedback from the students on how well the MOOC facilitated their learning. The end result is a set of integrated resources that can be embedded in undergraduate mathematics units as interactive modules or as a MOOC. The interactive modules in the MOOC offer course-based resources that are designed to allow students to tackle 'bite-size chunks' of the coursework mathematics in which they must develop expertise. The MOOC offers a self-paced introduction to key features of undergraduate mathematics, and is adaptive in that it also offers continual graded assessment and point-of-contact feedback. The content of the modules is based on the literature, as well as on a dedicat students. Many of these students have had less experience in mathematics than their urban counterparts. Furthermore, there is a broad range of mathematical capabilities within this group. As one of the 21 projects funded under the HEPPP 2015 National Priorities Pool, Bite size maths addresses the HEPPP Priority Funding Area, "More effective programme implementation". The Bite size maths project facilitates more equitable and effective program delivery via a mathematics intervention resource that caters for the wide range of student abilities and economic circumstances evident in the education sector in regional/remote areas. In so doing, the Bite size maths project targets low socioeconomic students who are at particular disadvantage, and provides modules that build student expertise and confidence. Commonwealth and State governments, via the National STEM School Education Strategy (Education Council, 2015) have mandated increased emphasis on science and mathematics in pre-service teaching and increased rigour of pre-service courses. This project will assist not only education students, but also those in other courses that require mathematics skills. It provides higher education teachers, senior managers and policy advisors with a tested approach to support significant long-term improvements in the quality of mathematics learning in universities. Importantly, the Bite size maths project offers: • A new vision of the way that mathematics can be learned in online settings and how this can be integrated in the preparation of graduates with mathematics capabilities suited to their professions, and • A mechanism for university teachers to grow the mathematics capability of their students. Successful take-up of the interactive modules or the MOOC requires: • Leadership, clarity of purpose and influence whereby the Bite size maths partners champion the mathematics MOOC at regional and national levels • Strong collaborative relationships between RUN partners to be nurtured and strengthened • Planning for 2017 trials and subsequent roll-out of the interactive modules or the MOOC • Communication about the resource to mathematics students at risk of failure, university mathematics teachers, staff in other disciplines, senior management teams at tertiary institutions, educational policy makers and other senior government strategists • Review of institutional protocols around enrolment, pre-requisites, course accreditation and assessment in order to successfully embed the interactive modules and the MOOC • Resourcing for trials, development and embedding of the interactive modules in mathematics units • Mentoring mechanisms such as workshops for university educators and a website for feedback/support, and • Promotion of the modules and the MOOC by the Department of Education and Training as a means of improving the mathematical capabilities of low socioeconomic or otherwise disadvantaged students at regional/rural universities. This report presents the four main components of the project: • Reviewing undergraduate mathematics in regional/rural Australia (identification of at- risk students, overview of intervention processes and identification of major issues) • Developing and trialling of five online learning system modules • Developing 20 interactive modules that comprise the MOOC, using feedback from the trial • Reporting on the potential of the MOOC as a resource for use in the university sector.
In this study, 244 children (average age: 61 months) and their parents from the Dallas and Fort Worth metroplex area in Texas were surveyed to investigate children's proficiency in mathematics content on numbering, sizes, comparisons, and shapes. The researchers investigated children's proficiency in mathematics associated with children's gender, ethnic background, and prekindergarten experience. Major findings of this study were as follows: (a) no gender differences were found in mathematics proficiency in all content areas; (b) among four major ethnic groups of children, White children showed higher proficiency in all mathematics content areas than other racial/ethnic groups including African American, Hispanic, and Asian children; (c) children without prekindergarten experiences outperformed children who had prekindergarten experiences in all mathematics content areas except "numbering." No significant mean differences were found in "numbering" between these two groups.
Designed for students, faculty, and professionals, this book describes the role of mathematics in the world of economics and business. Beginning with the fundamental nature of numbers and progressing into more complex realms like hyperreal numbers and the intricacies of set theory, this book constructs a strong foundational understanding of mathematical concepts. The book uses PYTHON code throughout the text to illustrate problems numerically. As readers advance, the text seamlessly integrates essential topics such as linear simultaneous equations, which are pivotal in analyzing market equilibrium, and covers the mechanics of matrices for solving larger equation systems. Furthermore, chapters dedicated to calculus, especially its applications in economics and the innovative use of infinitesimal methods, equip learners with tools to tackle profit maximization challenges, factor optimization, and beyond. Later chapters unfold the world of differential and difference equations, revealing their significance in analyzing dynamic systems. All these concepts are illuminated through practical examples and numerous images from economics and business, ensuring relevance and clarity.
