Use Of Math Research Articles

Language of Physics, Language of Math: Disciplinary Culture and Dynamic Epistemology

Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we suggest that a fundamental issue has received insufficient exploration: the fact that in science, we don’t just use math, we make meaning with it in a different way than mathematicians do. In this reflective essay, we explore math as a language and consider the language of math in physics through the lens of cognitive linguistics. We begin by offering a number of examples that show how the use of math in physics differs from the use of math as typically found in math classes. We then explore basic concepts in cognitive semantics to show how humans make meaning with language in general. The critical elements are the roles of embodied cognition and interpretation in context. Then, we show how a theoretical framework commonly used in physics education research, resources, is coherent with and extends the ideas of cognitive semantics by connecting embodiment to phenomenological primitives and contextual interpretation to the dynamics of meaning-making with conceptual resources, epistemological resources, and affect. We present these ideas with illustrative case studies of students working on physics problems with math and demonstrate the dynamical nature of student reasoning with math in physics. We conclude with some thoughts about the implications for instruction.

A delivery model for embedding functional skills on vocational courses in offender learning

Purpose – The purpose of this paper is to develop a delivery model for embedding Functional Skills in a prison environment, i.e. HMP Oakwood, to promote Functional Skills (FS) on vocational courses, i.e. Maths and Plumbing at Level 1, establish a research culture in a brand new organisation and raise standards in teaching, learning and outcomes. Design/methodology/approach – The design/methodology of this research included the implementation of a qualitative approach based on classroom research, a focus group with seven students on the Level 1 Plumbing course, joint Practice Development meetings with FS and vocational staff, the development of key principles for creating an embedded model for vocational courses, the creation of lesson plan/bespoke resource developments, lesson observations of the new model followed by teacher and learner evaluation, a practical task (fitting a bathroom suite) undertaken by learners, initial maths exercises drawn from practical task which were vocationally relevant, associations made with real jobs and work, use of IT/video for added interest, highlighting of transferable skills and users undertook dedicated functional maths exercises. Findings – A delivery model/logical sequence was agreed that worked for the teacher and learners – practical task/contextualised maths/transferable skills focus/situated maths. Targeted questions generated interest – will a litre of bath water hold if you use four in joists? The study allowed learners to reflect on maths elements from the practical task. The delivery model is implemented by vocational, not FS tutors. IT/video was used to introduce further maths for transferability to other related plumbing areas, i.e. fitting an outside garage tap. Constant links with use of maths for real job activity need to be made/reinforce relevance. Good tutor subject knowledge in maths is strongly recommended. Learners are ready to do dedicated/situated maths once they have built up their confidence. Research limitations/implications – This delivery model can be used across all other vocational courses at HMP Oakwood, i.e. bricklaying, multi-skills, painting and decorating, site carpentry, horticulture, industrial cleaning, catering, horticulture, etc. A framework/pedagogical guide can be developed for vocational tutors to implement this delivery model in their own subject areas as a basis for continued research. Bespoke CPD sessions for vocational staff can be run to share good practice in session plans and resources relevant to the delivery model. Peer observations can be arranged across the vocational department and the impact of the model on lesson observation grades and success rates can be analysed. Practical implications – Practical implications can include the development of a two-year Learning and Skills Research Strategy with a focus on embedded pedagogy. A senior team leader in FS can become the research lead for the Education Department, and an extensive embedded learning audit across 35 courses can be undertaken by July 2013. Social implications – Further pedagogical research into embedded learning across the whole department including employability/PSD/IT/business courses can be conducted. Originality/value – This study offers a simple, practical and ready to use delivery model which will help particularly non-specialist FS maths and English tutors working in vocational areas (i.e. construction, catering, etc.) to embed the teaching of maths and English in their subject areas.

Factorial, convergent, and discriminant validity of timss math and science motivation measures: A comparison of Arab and Anglo-Saxon countries.

For the international Trends in International Mathematics and Science Study (TIMSS2007) math and science motivation scales (self-concept, positive affect, and value), we evaluated the psychometric properties (factor structure, method effects, gender differences, and convergent and discriminant validity) in 4 Arab-speaking countries (Saudi Arabia, Jordan, Oman, and Egypt) and 4 English-speaking Anglo-Saxon countries (United States, England, Australia, and Scotland). In this article, we also highlight methodological weaknesses in the TIMSS approach to these motivation measures. We found reasonable support for within-group invariance across the math and science domains and between-group invariance across countries for full factor loading invariance and partial item intercept invariance. However, the factor structure is complicated by strong negative-item method effects and correlated unique characteristics associated with the use of math and science items with parallel wording. Correlations involving the motivation factors were reasonably similar across countries, supporting both discriminant and convergent validity in relation to achievement, plans to take more coursework in math and science, and long-term educational aspirations. However, gender differences largely favor girls in the Arab countries (with strong single-sex education systems) relative to Anglo countries (and international norms). The juxtapositions of latent mean differences in achievement and motivation factors are perplexing; students from Anglo countries had substantially higher achievement than students from Arab countries but had substantially lower motivation across all 8 math and science factors.

Using Subject Test Scores Efficiently to Predict Teacher Value-Added

This article develops a simple model of teacher value-added to show how efficient use of information across subjects can improve the predictive ability of value-added models. Using matched student–teacher data from North Carolina, we show that the optimal use of math and reading scores improves the fit of prediction models of overall future teacher value-added by up to a third for reading and a tenth for a composite measure (math and reading combined). Efficiency gains are greatest when value-added must be calculated on only 1 or 2 years of data. The methods employed are flexible and can be expanded to incorporate information from other subject or subitem test metrics.

Commentary: Birthweight and childhood cognition: the use of twin studies

Commentary: Birthweight and childhood cognition: the use of twin studies

Eixos convergentes na aprendizagem matemática de alunos com Síndrome de Down DOI: 10.5007/1981-1322.2010v5n1p25

This article presents the results of a qualitative research project that was mediated by learning the software called Intelligent Tutorial System (ITS). This software generates sequences of activities that reinforce the logical-mathematical knowledge of students of the initial grades of elementary school. The research project was conducted with students who have Down syndrome. A comparison was made between two students with Down syndrome, one from the state of Rio Grande do Sul (student A) and one from the state of Bahia (student B). The goal was to identify the convergent axes in the learning of math by students with Down syndrome. The results show that both students have similar difficulties with mathematical logical concepts and need individual assistance outside of the classroom in order to cope better with daily situations that require the use of math. It was also found that the ITS software is an important teaching resource to be used when working with students who have Down syndrome, as it reinforces their learning. The project is a result of the agreement that exists between the GECEM group of ULBRA in Canoas, Brazil, and the group of Educational Technologies of the ULL in Tenerife, Spain. The TEIAS group of the USC in Bahia also participates in that agreement.

Mathematics: The Basis for Quantitative Knowledge

In this editorial, we consider the inference that mathematics has underpinned virtually all of science and engineering in the past and will become increasingly important in future research. Mathematics can be considered the foundation upon which humans can build an immense knowledge set to be used wisely for the good of humanity. In the pioneering days of science and technology, precise physical constants were discovered; explosive gun powder was prepared from the correct proportions of ingredients; temperature scales were designed; lenses for eye glasses, telescopes, and microscopes were precisely constructed; and the shapes and sizes of living organisms, cells, tissues, and organs were determined. Math was used to understand the rates of biochemical reactions, inhibitor effects, and the therapeutic doses of prescription drugs. We know the sizes of the elements in the periodic table and the charges and sizes of elemental particles making up matter. We know the estimated masses of planetary bodies and some galaxies, the speed of light, how to smash particles, and the ages of fossils. We use math and more maths in every aspect of our daily lives. Check, for example, the use of math on a cereal box. The evidence leading up to recognition of DNA as the genetic material of all cells required X-ray diffraction data, a knowledge of the numbers of hydrogen bonds between base pairs, and the math-dependent construction of models to solve DNA structural conformations. These advances, in turn provided an explanation for the precise mechanisms for replication of genetic material and transcription and translation of genes into mRNA and proteins. Math is everywhere. It comprises a language of its own that we have integrated into all our other languages. It allows us to make rational decisions and function on a day-to-day basis. We keep records and accounts to manage our routine and extraordinary activities. We can know what time it is in any time zone on Earth because of math. We can even estimate how much money one can save over a 10-year period by eating as a vegetarian rather than an omnivore, or what each of our contributions to global warming is, depending on our lifestyles. We use math to make predictions about the future. In fact, we have tremendous predictive powers. In recent years, math and mathematical modeling have become important approaches to understanding some of humanity's most pressing problems. In fact, the use of math in predicting human population growth and understanding the crisis of global climate change are literally in the news daily. We can even estimate when the Earth will become too hot for human existence. The use of math via computer systems is now used for making short- and long-term weather predictions, tracking hurricanes and tornadoes, estimating world food reserves and agricultural productivity, the speed of pandemic spread, the percentages of infected individuals, and the numbers of resultant deaths. Mathematics is central to understanding interconnected problems facing all of humanity. These problems, for example, concern the effects of human population growth on resource depletion and subsequent pollution of our biosphere. Without math, relevant calculations would be impossible. We have projections of human population growth, resource depletion, the numbers of humans without the basic necessities of life, and death rates from flooding and extreme weather conditions. We have reasonably reliable methods to calculate rates of polar ice melting, increases in average global temperatures, rates of consumption of our limited energy sources, and consequent rates of build-up of atmospheric greenhouse gases, and the consequences of rising sea levels. We can estimate (with accuracy decreasing with increasing time into the future) the times when coastal cities will be flooded and human populations must migrate. So far, unfortunately, most early estimates have proven to be too conservative, and each revision brings with it recognition that we have less time to act than had previously been claimed. Some of these statistics are not pleasant to think about, and even more difficult to deal with. However, without the use of math, humans would have no way to recognize the correct solutions. There is one interconnected problem that is causative of all the others: human population growth. The math is straightforward. Too many humans producing too much pollution equates to continued disaster. Every human on the planet can understand this essential precept, but too many politicians and corporate executives strive only to make money, even at the expense of humankind. Short-sightedness allows them to do so. We already have too many people and too much total global pollution. The prospect of sustainability may already be past the tipping point.

Professional Development + Coaching = Enhanced Teaching: Increasing Usage of Math Mediated Language in Preschool Classrooms

In an effort to determine the most efficacious manner to deliver professional development training to early childhood educators, this study investigated the effect of a 2-h workshop followed by side-by-side classroom coaching. Twelve early childhood educators with 4-year degrees teaching in a university child development center participated in the study. The twice weekly classroom observations were analyzed for the use of math mediated language. Results indicate a 56% increase of math mediated language following the professional development; however, the greatest increase (39% increase over professional development condition) occurred during the side-by-side coaching phase of the treatment. These results corroborate previous findings that implementation of teaching strategies presented in professional development trainings can be enhanced by coaching teachers on the use of the strategies.

Theory, Data, Interpretations, and More Theory

Even though the paper had been revised and resubmitted for a second round of reviews at JCA, at some level I felt like the authors were perversely begging the editorial referees to recommend rejection of the manuscript. The revision involved an extensive rewriting of some sections, citations were added, the data were subjected to additional new analysis, and the authors provided very detailed supplemental notes to explain the changes to the reviewers. Yet for the directive from the decision on the first version that they provide a stronger conceptual context for study, the authors only noted they considered it unnecessary. To my amazement, they refused to provide a theoretical basis for the research. The omission was explained with the simple assertion that are behaviorists and therefore not concerned with theory, as if that would excuse data collection for its own sake. At the most basic level, they misunderstood that psychologists invented behaviorism itself as a basis for theoretical explanations, prediction and testing. If you will forgive a minor lapse into the pedantic, the original term referenced a direction for research in a social science that would allow control and measurement of all relevant variables by ignoring human thought or cognition. Instead of speculating as to what might transpire in people's minds, only behavior responses would be measured in relation to test stimuli so researchers could conduct experiments that would provide stronger tests of theoretical predictions. In other words, behaviorism was a route to being more scientific in a manner similar to the so-called hard sciences of chemistry or physics. This narrow and more directly measurable focus, in turn, allowed for greater use of statistical analysis of experimental results. The goal was a greater use of methods for stronger theories, or so they hoped. This tendency for stimulus-response experiments and overall preference for some type of mathematical statement has today spread into other social sciences. To critics of these approaches, important research questions are ignored if they do not fit into confines of a quantitative study. The techniques for mathematical data manipulation have become increasingly sophisticated and complex, and governed by strict assumptions, as if the analytical method is an end unto itself. Making more sense might be the preeminent economist and mathematician of the late 19th century Alfred Marshall who is credited with stating a five-step directive for use of math in research: (1) use it as a shorthand language rather than as an engine of inquiry, (2) keep them until you are done, (3) translate into English; (4) illustrate with examples that are important in real life, and (5) bum the mathematics. In the 21st century, people have forgotten this. But my point here is not to condemn any research approach, be it quantitative or qualitative, but to place emphasis on the thought behind the research. Numbers suggest, constrain, and refute; they do not, by themselves, specify the content of (Gould 1981, 106). As the numbers and methods gain greater attention, some might forget or ignore the need for a conceptual foundation that must precede the analysis. The late naturalist Stephen Jay Gould repeatedly explained that often think, naively, that missing data are the primary impediments to intellectual progress--just find the right facts and all problems will dissipate. But barriers are often deeper and more abstract in thought. We must have access to the fight metaphor, not only the requisite information. Revolutionary thinkers are not, primarily, gatherers of facts, but weavers of new intellectual structures (Gould 1985, 151). As one of his many examples, he explained that the original theories of DNA and genetics needed the invention of a computer not to crunch existing data but to provide a conceptual metaphor for how biological binary signals can work. …

School mathematics in work and life: what we know and how we can learn more

Underlying current K-12 math education reform initiatives are two premises. First, math education is necessary and should aim for success in the adult world of work and everyday life. Second, aligning the methods and content of K-12 math programs with those of real-world adult math use will facilitate learning. The existing research, however, challenges these premises. Studies of the actual demands of everyday adult practices reveal that most occupations involve only a low level of mathematical content and expose the disparate natures of everyday and school mathematics. Several limitations of existing mathematics-in-practice research, however, make it problematic to draw clear implications for school programs. In this article, I summarize the current research and identify some of its shortcomings for guiding educational content and pedagogy, including its focus on occupations and practices known to involve little math, its use of stereotypical conceptions of math, and its reliance on surveys and worker self-report. I propose a conceptual framework for future investigations of math-in-practice that would better inform K-12 education.

NRJ Book: Math Tools for Journalists, Numbers in the Newsroom: Using Math and Statistics in News

Math Tools for Journalists. By Kathleen Woodruff Wickham (Oak Park, Ill.: Marion Street Press, 2002), 159 pages, $16.95. Numbers in the Newsroom: Using Math and Statistics in News. By Sarah Cohen (Columbia, Mo.: Investigative Reporters and Editors, 2001), 108 pages, $25. Reviewed by Scott R. Maier In a focus group on newsroom use of math, a frazzled copy editor pleaded almost tearfully for a reference book she could consult on journalistic use of numbers just as she turns to the AP Stylebook for guidance on language. Fortunately, two excellent handbooks now provide a guide to the math that reporters and editors commonly encounter in their work. Math Tools for Journalists by Kathleen Woodruff Wickham and Numbers in the Newsroom by Sarah Cohen are written on the premise that all journalists, despite their pervasive fear of numbers, need math to describe the complex world that the numbers represent. Both books seek to help take the terror out of reporting numbers by conveying math fundamentals in practical journalistic terms. Both emphasize basic math but are comprehensive in their reach. And both books draw on the authors' extensive experience in the newsroom as well as in the classroom. In spite of their similarities, each differs in its approach to making math accessible to journalists. In Math Tools for Journalists, Wickham notes that journalists should be able to perform basic math before they begin their basic writing courses, but many cannot because these skills were learned long ago and shunted aside. She writes: not that journalists can't do basic math. It's that journalists have forgotten how. To address this deficiency, Wickham starts with the most basic math -- addition and subtraction - and covers increasingly complex topics ranging from percentage change to statistical analysis. For example, Wickham explains and demonstrates standard deviation in terms that journalists can understand. A former reporter who now teaches journalism at the University of Mississippi at Oxford, Wickham has devised skill drills (with answers) that apply to math problems that reporters confront on the job. In addition, each chapter provides Learning Challenges - hands-on activities that take the math lessons out of the classroom and into the real world. Underscoring the point that all journalists need math, Wickham sprinkles capsule accounts of real-life use of numbers in the news throughout her book. These components make Math Tools for Journalists especially useful in the journalism classroom. In Numbers in the Newsroom, Cohen seeks to show that skillful use of numbers requires journalistic sensibility. Selecting the right number for just the right place in a story, Cohen says, depends on the same news judgment you use in selecting just the right quote, anecdote or image. …

Award recognises innovative use of maths and stats

Award recognises innovative use of maths and stats