Based on data from the Longitudinal Study of American Youth (LSAY), students were classified into high-, middle-, and low-ability students. The effects of early acceleration in mathematics on the most advanced mathematics coursework (precalculus and calculus) in high school were examined in each category. Results showed that although early…
Ma, Xin; Wilkins, Jesse L. M.
Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics…
Fowler, Janis C.
Purpose: The purpose of this study was to examine advanced coursework completion rates, Advanced Placement (AP)/International Baccalaureate (IB) testing rates, AP/IB exam passage rates, and the percentage of AP/IB exam scores at or above the criterion that may exist among Texas public high school students from 2001 to 2012 to ascertain (a) the…
Sadler, Philip M.; Tai, Robert H.
The purpose of the current study is to investigate the feasibility of accounting for student performance in advanced high school coursework through the adjustment of high school grade point average (HSGPA) while separating out variables that are independently considered in the admission process, e.g., SAT/ACT scores, community affluence, type of…
Vijil, Veronica G.
An overall increased awareness of the importance of science, technology, engineering, and mathematics (STEM) has prompted attention toward the continued underrepresentation of Hispanic women in this field. The purpose of this collective case study was to explore the support systems, perceived barriers, and prior experiences influencing high school Hispanic girls' decisions to pursue advanced coursework and related careers through a career pathway in science, technology, engineering, and mathematics (STEM) areas. Specifically, participants were interviewed regarding their mathematics and science experiences in elementary and middle schools, as well as perceived supports and barriers to their choices to pursue STEM careers and advanced coursework. Results indicated that the participants linked their elementary and middle school experiences with their teachers rather than specific activities. Accolades such as certificates and good grades for academic achievement contributed to the girls' strong self-efficacy at an early age. The participants possessed self-discipline and self-confidence, using intrinsic motivation to pursue their goals. Support systems included families and a few teachers. Barriers were revealed in different forms including derogatory comments by boys in class, difficult curricula with limited tutors available for higher level courses, and receipt of financial assistance to attend a university of their choice.
Barber, Carolyn; Wasson, Jillian Woodford
Friendships serve as a source of support and as a context for developing social competence. Although advanced coursework may provide a unique context for the development of friendships, more research is needed to explore exactly what differences exist. Using the National Longitudinal Study of Adolescent Health and the Adolescent Health and…
In 2004, the pattern in academic pathways for high school students in the USA showed that students were completing more demanding mathematics courses. Despite the upward pattern in advanced-level mathematics course-taking, disparities among racial/ethnic groups persisted between 1982 and 2004. Using data from the Education Longitudinal Study of…
Sadler, Philip M.; Sonnert, Gerhard; Hazari, Zahra; Tai, Robert
Several avenues are open to students who wish to study advanced science or mathematics in high school, which include Advanced Placement courses and teacher-designed courses unaffiliated with organized programs. We employ a retrospective cohort study of 4,691 nationally representative college students at 34 randomly selected, colleges and…
Bird, Katherine; Oppland-Cordell, Sarah; Hibdon, Joseph
This paper describes the development, results, and future directions of the mathematics component of the EMERGE Summer Program at Northeastern Illinois University. Initiated summer 2014, EMERGE offered English and mathematics sessions for incoming freshmen. The mathematics session aimed to strengthen participants' mathematical foundations,…
Cavazos, Lionel Javier, Jr.
The purpose of this study was to (a) determine the extent to which Latina/o students' perceptions of support from high school teachers and counselors, as well as acculturation, predict enrollment in AP coursework; (b) examine Latina/o students' perceptions of different forms of support that appear to play a role in academic success…
Bahr, Damon L.; Monroe, Eula Ewing; Eggett, Dennis
This paper describes a study of observed relationships between the design of a preservice elementary mathematics methods course with accompanying field practicum and changes in the extent to which participating prospective teachers identified themselves with the mathematics reform movement after becoming practicing teachers. The curriculum of the…
Jackman, Susan; Goldfinch, Judy; Searl, John
Describes the introduction and evaluation of the effectiveness of a single group project given at a new university, and 10 individual tasks at an ancient university, to devise appropriate and relevant assessments for first-year service mathematics courses for science and engineering. Studies the effects of these tasks on attitudes toward…
de Wolf, Virginia A.
On six mathematical subtests studied, males scored higher plus took significantly more algebra, geometry, advanced mathematics, and physics coursework. Females earned higher overall mathematics grades. After statistically controlling for the amount of coursework taken, sex differences disappeared on two quantitative tests and on spatial ability.…
Minor, Elizabeth Covay
Research on achievement gaps has found that achievement gaps are larger for students who take advanced mathematics courses compared to students who do not. Focusing on the advanced mathematics student achievement gap, this study found that African American advanced mathematics students have significantly lower test scores and are less likely to be…
Kinzer, Cathy J.; Rincón, Mari; Ward, Jana; Rincón, Ricardo; Gomez, Lesli
Four elementary school instructors offer insights into their classrooms, their unique professional roles, and their leadership approaches as they reflect on their journey to advance teacher and student mathematics learning. They note a "teacher leader" serves as an example to other educators and strives to impact student learning;…
Ferrari, Pier Luigi
This paper is concerned with the role of language in mathematics learning at college level. Its main aim is to provide a perspective on mathematical language appropriate to effectively interpret students' linguistic behaviors in mathematics and to suggest new teaching ideas. Examples are given to show that the explanation of students' behaviors…
Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin
Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…
In this paper the notion of "procept" (in the sense of Gray & Tall, 1994) is extended to advanced mathematics by considering mathematical proof as "formal procept". The statement of a theorem as a symbol may theoretically evoke the proof deduction as a process that may contain sequential procedures and require the synthesis of distinct cognitive…
Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy
What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding - in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities. One participant uses gestures to clarify the relationships between a function, its derivative and its antiderivative. We show how these gestures help create a virtual mathematical construct, which in turn leads to a new problem-solving strategy. These results suggest that gestures are a productive, but potentially undertapped resource for generating new insights in advanced levels of mathematics.
Tasks to Advance the Learning of Mathematics (TALMs) were developed to stimulate grades 5-8 students' curiosity about complex mathematical relationships, inspire them to reason abstractly and quantitatively, encourage them to consider and create alternative solution approaches, develop their skills to persuade others about the viability of one…
Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy
What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…
Shifrer, Dara; Callahan, Rebecca
Students identified with learning disabilities experience markedly lower levels of science and mathematics achievement than students who are not identified with a learning disability. Seemingly compounding their disadvantage, students with learning disabilities also complete more credits in non-core coursework--traditionally considered nonacademic…
Rengel, R.; Martin, M. J.; Vasallo, B. G.
This paper presents a series of activities and educational strategies related to the teaching of digital electronics in computer engineering. The main objective of these methodologies was to develop a final tutored coursework to be carried out by the students in small teams. This coursework was conceived as consisting of advanced problems or small…
You, Sukkyung; Sharkey, Jill D.
High school mathematics achievement predicts future success. Potentially different factors that lead to success for boys versus girls, termed equifinality, are not well understood. Such factors are needed to inform interventions to increase numbers of students taking advanced mathematics courses and going on into science and mathematics careers.…
Stanford Univ., CA. School Mathematics Study Group.
This text is the second of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. This volume is devoted to a rigorous development of theorems in plane geometry from 22…
Crowe, Cheryll E.; Ma, Xin
Using data from the 2005 National Assessment of Educational Progress, students' use of calculators in the learning of high school mathematics was profiled based on their family background, curriculum background, and advanced mathematics coursework. A statistical method new to educational research--classification and regression trees--was applied…
This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…
McDonnell, Lorraine M.; Ormseth, Tor
The School Reform Assessment (SRA) project began in 1987 with the objective of developing indicators of student coursework that reliably and validly measure this central feature of schooling, while remaining sensitive to major policy changes and the information needs of policymakers, and efficiently collecting and reporting data. This paper…
Griffiths, Barry J.; Selcuk Haciomeroglu, Erhan
To ensure the competitiveness of the USA in the global economy, and its role as a leader in science and engineering, it is important to cultivate the next generation of home grown mathematicians. However, while universities across the USA offer calculus classes to thousands of undergraduate students each year, very few of them go on to major in mathematics. This paper posits that one of the main reasons is that the mathematical community does not expose calculus students to the beauty and complexity of upper-level mathematics, and that by doing so before they fully commit to their programme of study, the number of students with a qualification in mathematics can be increased. The results show a significant increase in the number of students planning to add a minor in mathematics, and an increased likelihood among freshmen and sophomores to change their major.
Inglis, Matthew; Simpson, Adrian
In this paper, we examine the support given for the "theory of formal discipline" by Inglis and Simpson (Educational Studies Mathematics 67:187-204, "2008"). This theory, which is widely accepted by mathematicians and curriculum bodies, suggests that the study of advanced mathematics develops general thinking skills and, in particular, conditional…
Adkins, Michael; Noyes, Andrew
In the late 1990s, the economic return to Advanced level (A-level) mathematics was examined. The analysis was based upon a series of log-linear models of earnings in the 1958 National Child Development Survey (NCDS) and the National Survey of 1980 Graduates and Diplomates. The core finding was that A-level mathematics had a unique earnings premium…
Achieve, Inc., 2013
This fact sheet explains that to thrive in today's world, all students will need to graduate with very strong math skills. That can only mean one thing: advanced math courses are now essential math courses. Highlights of this paper include: (1) Advanced math equals college success; (2) Advanced math equals career opportunity; and (3) Advanced math…
The adverse attitudes of many students in advanced mathematics courses were explored. Results indicated students felt the gap between regular and advanced courses was too great, and that students pursuing arts or social sciences would benefit from courses with broader application. (SD)
Sangpom, Wasukree; Suthisung, Nisara; Kongthip, Yanin; Inprasitha, Maitree
Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students' inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In…
Shifrer, Dara; Callahan, Rebecca
Students identified with learning disabilities experience markedly lower levels of science and mathematics achievement than students who are not identified with a learning disability. Seemingly compounding their disadvantage, students with learning disabilities also complete more credits in non-core coursework—traditionally considered non-academic coursework—than students who are not identified with a learning disability. The Education Longitudinal Study of 2002, a large national dataset with both regular and special education high school students, is utilized to determine whether credit accumulation in certain types of non-core coursework, such as Technology and Communications courses, is associated with improved science and math course-taking outcomes for students with learning disabilities. Results show that credit accumulation in Technology and Communications coursework uniquely benefits the science course-taking, and comparably benefits the math course-taking, of students identified with learning disabilities in contrast to students who are not identified with a learning disability.
Shifrer, Dara; Callahan, Rebecca
Students identified with learning disabilities experience markedly lower levels of science and mathematics achievement than students who are not identified with a learning disability. Seemingly compounding their disadvantage, students with learning disabilities also complete more credits in non-core coursework—traditionally considered non-academic coursework—than students who are not identified with a learning disability. The Education Longitudinal Study of 2002, a large national dataset with both regular and special education high school students, is utilized to determine whether credit accumulation in certain types of non-core coursework, such as Technology and Communications courses, is associated with improved science and math course-taking outcomes for students with learning disabilities. Results show that credit accumulation in Technology and Communications coursework uniquely benefits the science course-taking, and comparably benefits the math course-taking, of students identified with learning disabilities in contrast to students who are not identified with a learning disability. PMID:27695150
Discussions of race in educational research have focused primarily on performance gaps and differential access to advanced coursework. Thus, very little is known about how race mediates the learning process, particularly with respect to classroom participation and student identity formation. This dissertation examines mathematics learning as a…
Natour, Denise M.
This manual is an instructor's guide for the utilization of the "CCA High School Mathematics Curricula: Advanced Algebra and Calculus" courseware developed by the Computer-based Education Research Laboratory (CERL). The curriculum comprises 34 algebra lessons within 12 units and 15 calculus lessons that are computer-based and require mastery for…
Korpershoek, Hanke; Kuyper, Hans; van der Werf, Greetje; Bosker, Roel
Few students (particularly few girls) currently choose to take their Final School Examination (FSE) in advanced mathematics, chemistry and physics, a combination of subjects that is the best preparation for a science-oriented study in higher education. Are these subjects attainable by more students than is currently the case? This study examined…
This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of three mathematical worlds; relatively advanced problem-solving behaviours are defined in terms of taxonomies of proof schemes and heuristic behaviours. The relationships between mathematical knowledge and problem-solving behaviours are analysed in the contexts of solving an insight geometry problem, posing algebraic problems and calculus exploration. A particularly knowledgeable and skilled university student was involved in all the episodes. The presented examples substantiate the claim that advanced mathematical knowledge and advanced problem-solving behaviours do not always support each other. More advanced behaviours were observed when the student worked within her conceptual-embodied mathematical world, and less advanced ones when she worked within her symbolic and formal-axiomatic worlds. Alternative explanations of the findings are discussed. It seems that the most comprehensive explanation is in terms of the Principle of Intellectual Parsimony. Implications for further research are drawn.
Zazkis, Rina; Leikin, Roza
For the purpose of our research we define Advanced Mathematical Knowledge (AMK) as knowledge of the subject matter acquired during undergraduate studies at colleges or universities. We examine the responses of secondary school teachers about their usage of AMK in teaching. We find that the majority of teachers focus on the purposes and advantages…
This paper collects and extends the lectures I gave at the “XXIV International Fall Workshop on Geometry and Physics” held in Zaragoza (Spain) during September 2015. Within these lectures I review the formulation of Quantum Mechanics, and quantum theories in general, from a mathematically advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions, discussing some fundamental ideas, mathematical tools and theorems also related to the representation of physical symmetries. The final step consists of an elementary introduction the so-called (C∗-) algebraic formulation of quantum theories.
Burbank, Mary D.; Shooter, Wynn; Groth, Cori A
The purpose of this project was to investigate stakeholders' perspectives on coursework and the role of mentors within a unique teacher education program for prospective teachers of mathematics in an alternative-route-to-licensure program. The alternative route reflects a partnership between an institution of higher education, a state office…
Attridge, Nina; Inglis, Matthew
Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general 'thinking skills'. Today, this argument, known as the 'Theory of Formal Discipline' is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought.
Gavin, M. Katherine; Casa, Tutita M.; Adelson, Jill L.; Carroll, Susan R.; Sheffield, Linda Jensen
The primary aim of Project M[superscript 3]: Mentoring Mathematical Minds was to develop and field test advanced units for mathematically promising elementary students based on exemplary practices in gifted and mathematics education. This article describes the development of the units and reports on mathematics achievement results for students in…
Ho, Kai Fai
There are concerns about the trends and patterns in enrolments in senior school mathematics. Shortages of suitably qualified teachers and dwindling students' demand for Advanced Mathematics have led some Western Australian schools to collaborate to provide an otherwise unavailable opportunity for their students to study Advanced Mathematics. It is…
Schreiber, James B.
The student variables associated with scoring above the international mean on the Third International Mathematics and Science Study (TIMSS) were studied in a group of U.S. students who took advanced mathematics or advanced mathematics and physics. The total sample was 2,349, with 1,158 females and 1,191 males. Formal parent education level and…
Chang, C. K.; Chen, G. D.; Li, L. Y.
Students can practice skills and construct knowledge by carrying out coursework. However, every student is assigned the same problem in general hands-on coursework activities, with no consideration for learners' diversity. Hence, some students do not take the task seriously when producing their coursework. Furthermore, what one has learned--that…
Grossman, Amanda M.; Johnson, Leigh R.
The perceptions of faculty members, who design and evaluate online accounting coursework content, are an important consideration in determining the quality inherent in such content. This study reports the results of a survey which examines accounting faculty members' attitudes towards online education (measured as their willingness to accept…
Siegfried, John J.; Walstad, William B.
Survey results from a large sample of economics departments describe offerings for principles courses, coursework requirements for economics majors, and program augmentations such as capstone courses, senior seminars, and honors programs. Findings are reported for all institutions, and institutions are subdivided into six different categories…
Walsh, Shari P.; Tucker, Kelly
Master's degree by coursework students have been identified as a "forgotten" cohort by the Queensland University of Technology (QUT) Careers and Employment service. Traditionally, these students have been included in undergraduate career development activities. Master's degree students are arguably a specialised group due to the advanced learning…
Rasmussen, Chris; Kwon, Oh Nam; Allen, Karen; Marrongelle, Karen; Burtch, Mark
This paper provides an overview of the Inquiry-Oriented Differential Equations (IO-DE) project and reports on the main results of a study that compared students' beliefs, skills, and understandings in IO-DE classes to more conventional approaches. The IO-DE project capitalizes on advances within mathematics and mathematics education, including the…
Stanford Univ., CA. School Mathematics Study Group.
This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…
This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…
Schreiber, James B.
Examined advanced mathematics achievement among high school students using data from the Third International Mathematics and Science Study. Examination of school- and student-level factors indicated that gender and economic disparities existed, even with the most advanced students. This disparity varied by school. Parent education related to…
Eklöf, Hanna; Pavešic, Barbara Japelj; Grønmo, Liv Sissel
The purpose of the study was to measure students' reported test-taking effort and the relationship between reported effort and performance on the Trends in International Mathematics and Science Study (TIMSS) Advanced mathematics test. This was done in three countries participating in TIMSS Advanced 2008 (Sweden, Norway, and Slovenia), and the…
de Wolf, Virginia A.
Freshmen placed into the second or third quarter of the first year calculus sequence at the University of Washington were studied. Two major findings were: freshmen eligible for advanced placement earned mean mathematics Grade Point Averages (GPAs) which were quite high; and advanced placement students earned mean mathematics GPAs substantially…
Glamore, Michael James; West, James L; O'leary, James Patrick
The immense advancement of our understanding of disease processes has not been a uniform progression related to the passage of time. Advances have been made in "lurches" and "catches" since the advent of the written word. There has been a remarkable interdependency between such advances in medicine and advances in mathematics that has proved beneficial to both. This work explores some of these critical relationships and documents how the individuals involved contributed to advances in each.
Advanced Technology, Inc., Indianapolis, IN.
This Workshop Leader's Guide contains step-by-step procedures for preparing, organizing, and presenting 1-hour and 3-hour workshops on estimation in mathematics. It was designed to assist Technical Assistance Center staff members and other inservice providers in conducting successful workshops on estimation in mathematics for administrators,…
Lew, Kristen; Fukawa-Connelly, Timothy Patrick; Mejía-Ramos , Juan Pablo; Weber, Keith
We describe a case study in which we investigate the effectiveness of a lecture in advanced mathematics. We first videorecorded a lecture delivered by an experienced professor who had a reputation for being an outstanding instructor. Using video recall, we then interviewed the professor to determine the ideas that he intended to convey and how he…
McLay, Allan F.
Scholarship parameters, in relation to postgraduate coursework studies, are developed against the expectations of the Boyer classifications of scholarship (Boyer, 1990) with particular emphasis on the role of minor thesis development. An example is presented in which postgraduate coursework students are required to undertake a three semester minor…
This paper examines the King's Oxfordshire Assessment Project, which took place in the UK and explored the use of coursework as a means of terminal assessment. In particular, it considers the findings of the six English teachers who were involved. In a standards-based curriculum all six teachers supported 100% coursework. The paper looks at how,…
We present an overview of the nature of academic dishonesty with respect to computer science coursework. We discuss the efficacy of various policies for collaboration with regard to student education, and we consider a number of strategies for mitigating dishonest behaviour on computer science coursework by addressing some common causes. Computer…
Arroyo, Ivon; Burleson, Winslow; Tai, Minghui; Muldner, Kasia; Woolf, Beverly Park
We provide evidence of persistent gender effects for students using advanced adaptive technology while learning mathematics. This technology improves each gender's learning and affective predispositions toward mathematics, but specific features in the software help either female or male students. Gender differences were seen in the students' style…
Fiero, Diane M.
Purpose: The purpose of this study was to determine which basic skills program factors were exhibited by successful basic skills programs that helped students advance to transfer-level mathematics. This study specifically examined California community college basic skills programs that assist students who place in mathematics courses 2 levels…
The focus of this paper is a group of rural high school students and the factors that contributed to their participation in mathematics classes beyond those minimally required for high school graduation. The author follows Gutierrez (2002) in referring to participation as course taking, particularly in elective and advanced mathematics classes.…
Nabb, Keith A.
The research literature has made calls for greater coherence and consistency with regard to the meaning and use of the term advanced mathematical thinking (AMT) in mathematics education (Artigue, Batanero, & Kent, 2007; Selden & Selden, 2005). Educators and researchers agree that students should be engaged in AMT but it is unclear…
Amalric, Marie; Dehaene, Stanislas
The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124
Amalric, Marie; Dehaene, Stanislas
The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124
Amalric, Marie; Dehaene, Stanislas
The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.
Bellomo, Carryn; Strapp, Remy
The number of students pursuing undergraduate degrees in mathematics is decreasing. Research reveals students who pursue mathematics majors complained about inadequate high school preparation in terms of disciplinary content or depth, conceptual grasp, or study skills. Unfortunately, the decrease in the number of students studying advanced…
Ganikhodjaev, Nasir; Mukhamedov, Farrukh; Hee, Pah Chin
The 4th International Conference on the Advancement of Science and Technology 2012 (iCAST 2012), with theme 'Contemporary Mathematics, Mathematical Physics and their Applications', took place in Kuantan, Malaysia, from Wednesday 7 to Friday 9 November 2012. The conference was attended by more than 100 participants, and hosted about 160 oral and poster papers by more than 140 pre-registered authors. The key topics of the 4th iCAST 2012 include Pure Mathematics, Applied Mathematics, Theoretical/Mathematical Physics, Dynamical Systems, Statistics and Financial Mathematics. The scientific program was rather full since after the Keynote and Invited Talks in the morning, four parallel sessions ran every day. However, according to all attendees, the program was excellent with a high level of talks and the scientific environment was fruitful; thus all attendees had a creative time. The conference aimed to promote the knowledge and development of high-quality research in mathematical fields concerned with the application of other scientific fields as well as modern technological trends in physics, chemistry, biology, medicine, economics, sociology and environmental sciences. We would like to thank the Keynote and the Invited Speakers for their significant contributions to 4th iCAST 2012. We would also like to thank the members of the International Scientific Committee and the members of the Organizing Committee. We cannot end without expressing our many thanks to International Islamic University Malaysia and our sponsors for their financial support . This volume presents selected papers which have been peer-reviewed. The editors hope that it may be useful and fruitful for scholars, researchers, and advanced technical members of the industrial laboratory facilities for developing new tools and products. Guest Editors Nasir Ganikhodjaev, Farrukh Mukhamedov and Pah Chin Hee The PDF contains the committee lists, board list and biographies of the plenary speakers.
Kirkwood Community Coll., Cedar Rapids, IA.
This document is an instructional module prepared in objective form for use by an instructor familiar with mathematics as applied to water and wastewater treatment plant operation. Included are objectives, instructor guides and student handouts. This is the third level of a three module series and is concerned with statistics, total head, steady…
This case study reflects block scheduling's effects on advanced-placement mathematics courses of one veteran teacher tracking personal progress since 1989. Block scheduling began in 1994, creating problems for the teacher, whose resistance to the reform was based on declining advanced-placement scores. Teacher attitude and insufficient…
Gottfried, Michael A.
Advanced mathematics and science course taking is critical in building the foundation for students to advance through the STEM pathway-from high school to college to career. To invigorate students' persistence in STEM fields, high schools have been introducing applied STEM courses into the curriculum as a way to reinforce concepts learned in…
Jacobson, Michael J., Ed.; Kozma, Robert B., Ed.
This collection of essays consists of current work that addresses the challenge not just to put the newest technologies in schools, but to identify advanced ways to design and use these new technologies to advance learning. These essays are intended for science and mathematics educators, educational and cognitive researchers, instructional…
Johnsen, Susan K., Ed.; Sheffield, Linda J., Ed.
"Using the Common Core State Standards for Mathematics With Gifted and Advanced Learners" provides teachers and administrators examples and strategies to implement the new Common Core State Standards (CCSS) with advanced learners at all stages of development in K-12 schools. The book describes--and demonstrates with specific examples from the…
Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930
Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record PMID:26913930
Scharf, John; And Others
This document is a guide to the advanced placement program in calculus for grade 12 in the city schools in Warren, Ohio. The program covers analytic geometry, differential and integral calculus of algebraic functions, elementary transcendental functions, and applications of differentiation and integration. The philosophy and aims of the program…
Grinstead, Mary L.
This study explores the relationship between specific advanced mathematics courses and college readiness (as determined by ACT score). The ACT organization has found a consistent relationship between taking a minimum core number of mathematics courses and higher ACT scores (mathematics and composite) (ACT, Inc., 2012c). However, the extent to…
Ristvey, J.; Bogner, D.
Mid-continent Research for Education and Learning (McREL) partnered with the Colorado School of Mines (CSM) to offer the ESSEA Earth System Science Online Course for Middle School Teachers during the 2002-2003 school year. During the two semesters that the course was offered, we were able to retain 75% of our enrollees. We found that course facilitation was the key ingredient in retaining this large number of students-who are not only scattered across the U.S., but around the world-in a rigorous online course. In this poster session, we will share what we have learned about online facilitation as part of this course, and how this knowledge might translate into other online coursework. Online facilitation begins as soon as a student enrolls in the course. When a student registers online or at CSM, McREL receives notification and then sends course materials and e-mail and written confirmation to the enrollee within 24 hours. This sets the tone for the type of communications that students can expect during the 16-week course. McREL facilitators know how time consuming monitoring participant progress can be, but feel strongly about its importance when facilitating learners who are working in small groups and are completing independent research. Timely monitoring of discussion spaces and e-mail messages is essential to maintaining a high student-retention rate. Kearsley (2000) confirms this when he states that, "the most important role of the instructor in online classes is to ensure that there is a high degree of interactivity and participation." In the ESSEA courses, the isolation of students working independently on classroom applications and reflection is balanced with group construction of interactions and causal chains. Each step of the way facilitators use guided questioning in group discussion sessions and serve as a mentor when participants develop individualized classroom assignments, giving participants the opportunity to apply what they have learned in a
Advanced Technology, Inc., Indianapolis, IN.
This guide is designed to assist inservice providers in conducting successful workshops for teachers, administrators, and others associated with Chapter 1 mathematics programs. It contains step-by-step procedures for preparing, organizing, and presenting the workshop. Included in this guide are: (1) an advanced planner, which includes a detailed…
This document provides a preliminary report of the study Gateways To Advance Mathematical Thinking (GAMT) run by Educational Development Center, Inc. (EDC). The study was designed to see what types of reasoning students who have recently completed a linear algebra course apply to problems in algebraic thinking. Student interviews were used as the…
Davis, Cinda-Sue; And Others
This volume includes 10 reports that present findings and recommendations for advancing women in science, mathematics and engineering. Critical issues facing women in these disciplines are addressed, including demographic myths and realities at various educational levels; the educational pipeline for girls and women; involvement in education and…
DePountis, Vicki M.; Pogrund, Rona L.; Griffin-Shirley, Nora; Lan, William Y.
This research examined the perspectives of teachers of students with visual impairments (TVIs) regarding the use and effectiveness of electronic assistive technology (EAT) purported to assist students who are blind in advanced mathematics subjects. The data for this study were collected via an online survey distributed to a convenience sample of…
Niess, Margaret; Gillow-Wiles, Henry
This primarily online Master's degree program focused on advancing K-8 teachers' interdisciplinary mathematical and science content knowledge while integrating appropriate digital technologies as learning and teaching tools. The mixed-method, interpretive study examined in-service teachers' technological, pedagogical, and content knowledge (TPACK)…
Crosnoe, Robert; Schneider, Barbara
Analysis of the National Education Longitudinal Study revealed that socioeconomically advantaged students persist in high school math at higher rates than their disadvantaged peers, even when they have the same initial placements and skill levels. These disparities are larger among students with prior records of low academic status because students from more privileged backgrounds persist in math coursework even when their prior performance predicts they will not. Among students with low middle school math performance, those from socioeconomically disadvantaged families appear to benefit from having consultants for coursework decisions, so that they make up ground with their socioeconomically advantaged peers. PMID:21743762
Harwell, Michael; Moreno, Mario; Post, Thomas
This study examined the relationship between the American College Testing (ACT) college mathematics readiness standard and college mathematics achievement using a sample of students who met or exceeded the minimum 3 years high school mathematics coursework recommended by ACT. According to ACT, a student who scores 22 or higher on the ACT…
Richardson, John T. E.
In the UK and other countries, the use of end-of-module assessment by coursework in higher education has increased over the last 40?years. This has been justified by various pedagogical arguments. In addition, students themselves prefer to be assessed either by coursework alone or by a mixture of coursework and examinations than by examinations…
Fisher, P. Brian; McAdams, Erin
Purpose: This paper aims to examine how both the amount and type of coursework impact students' conceptualizations of sustainability. Previous research demonstrates that academic coursework influences students' environmental attitudes, yet few studies have examined the impact of coursework on how students conceptualize "sustainability".…
Smalley, Topsy N.
Discusses how librarians can interact with faculty members to incorporate Internet instruction into college coursework. Active learning and creating Web pages are discussed, and a six-page appendix presents an example of a Web-based exercise for a basic oceanography course. (LRW)
Miller, B. J.; Sundre, Donna L.
Two studies were conducted regarding the achievement goal orientations of college students within two contexts: coursework in all courses and in general education courses. Interactions were detected for achievement goals by class level and context. Findings raise concern about student attitudes toward general education, despite its importance to…
Heineke, Amy J.; Preach, Deborah
In this article, we describe our innovative work as teacher educators to integrate coursework for alternatively certified teachers. Rather than maintain boundaries among individual courses for new elementary teachers, explicit connections support first-year teachers professional learning and aid in the immediate application to classroom practice.…
DeKorver, Brittland K.; Towns, Marcy H.
Little research exists on college students' learning goals in chemistry, let alone specifically pertaining to laboratory coursework. Because students' learning goals are linked to achievement and dependent on context, research on students' goals in the laboratory context may lead to better understanding about the efficacy of lab curricula. This…
Curtis, Kynda; Mahon, Jennifer
This article presents a strategy for incorporating experiential learning into university coursework through the use of Extension fieldwork projects. In this case, undergraduate agribusiness management students construct business plans for primary agricultural industries and proposed new industries, such as food processing. Results of the study…
Today's students prioritize employment; they want to be sure that there will be work for them upon graduation. Film and media students, in particular, need a long list of computer software and film equipment skills on their resumes, especially newer technologies that professionals in the workforce have not yet mastered. Consider, in this regard,…
Peak, David J.
Improving student achievement in mathematics in secondary schools remains a priority for public education in our country. With continued federal and state mandates to improve overall student achievement in mathematics, as well as to close the achievement gap, many school districts have sought programs, such as Advancement Via Individual…
Githua, Bernard N.; Nyabwa, Rachel Angela
Students have continued to perform poorly in KCSE examinations in certain mathematics topics taught in secondary schools in Kenya. One such topic is commercial arithmetic. Successful teaching of mathematics depends partly on correct use of teaching methods in classroom settings. This study sought to examine how the use of advance organisers during…
This report discusses advancing precollege science and mathematics education in San Diego Count. Described in this report are: curriculum and teacher development; pre-tour material; facility tour; student workbook; evaluation and assessment; and internet access.
Luther, Kenneth H.
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Points out the diminishing demand for mathematics undergraduate programs and the strong trend in engineering education to make greater use of computer coursework such as Mathcad, Matlab, and other software systems for the mathematical and statistical components of engineering programs. Describes the changing role of mathematics learning centers…
Esprivalo Harrell, Pamela; Eddy, Colleen McLean
This study examines mathematics teacher content knowledge in terms of state and national policymaker recommendations, college coursework and the Mathematics Texas Examination of Educator Standards (TExES) score. Results indicate differences between state and national policy recommendations and college degrees in mathematics. A statistically…
The issue of global warming and related climatic changes from increasing concentrations of greenhouse gases in the atmosphere has received prominent attention during the past few years. The Computer Hardware, Advanced Mathematics, and Model Physics (CHAMMP) Climate Modeling Program is designed to contribute directly to this rapid improvement. The goal of the CHAMMP Climate Modeling Program is to develop, verify, and apply a new generation of climate models within a coordinated framework that incorporates the best available scientific and numerical approaches to represent physical, biogeochemical, and ecological processes, that fully utilizes the hardware and software capabilities of new computer architectures, that probes the limits of climate predictability, and finally that can be used to address the challenging problem of understanding the greenhouse climate issue through the ability of the models to simulate time-dependent climatic changes over extended times and with regional resolution.
Harrell, Pamela Esprivalo; Eddy, Colleen McLean
This study examined mathematics teacher content knowledge in terms of policy maker recommendations, college coursework and teacher certification mathematics test scores. Transcript analysis indicated poor alignment of national policy maker recommendations for mathematics teachers and college degrees in mathematics. Teacher certification test…
Cruthirds, John E.
A habitat for long duration missions which utilizes Advanced Life Support (ALS), the Bioregenerative Planetary Life Support Systems Test Complex (BIO-Plex), is currently being built at JSC. In this system all consumables will be recycled and reused. In support of this effort, a menu is being planned utilizing ALS crops that will meet nutritional and psychological requirements. The need exists in the food system to identify specific physical quantities that define life support systems from an analysis and modeling perspective. Once these quantities are defined, they need to be fed into a mathematical model that takes into consideration other systems in the BIO-Plex. This model, if successful, will be used to understand the impacts of changes in the food system on the other systems and vice versa. The Equivalent System Mass (ESM) metric has been used to describe systems and subsystems, including the food system options, in terms of the single parameter, mass. There is concern that this approach might not adequately address the important issues of food quality and psychological impact on crew morale of a supply of fiesh food items. In fact, the mass of food can also depend on the quality of the food. This summer faculty fellow project will involve creating an appropriate mathematical model for the food plan developed by the Food Processing System for BIO-Plex. The desired outcome of this work will be a quantitative model that can be applied to the various options of supplying food on long-term space missions.
Crisp, Victoria; Green, Sylvia
When General Certificates of Secondary Education (GCSEs) were introduced in the late 1980s, coursework was included as a requirement in many subjects. Coursework was intended to help best represent students' attainments, but concerns about various issues (e.g., tasks becoming formulaic, authenticity of student work, workload) led to a review…
Drennan, Jonathan; Clarke, Marie
Although the coursework master's degree is becoming the principal conduit for the delivery of continuing education to the professions, it is one of the least understood or researched academic levels in higher education. Furthermore, little is known of coursework master's graduates' experience of research or research supervision following the…
Allgood, Sam; Bosshardt, William; van der Klaauw, Wilbert; Watts, Michael
Studies regularly link levels of educational attainment to civic behavior and attitudes, but only a few investigate the role played by specific coursework. Using data collected from students who attended one of four public universities in our study, we investigate the relationship between economics coursework and civic behavior after graduation.…
Macugay, Eva B.; Bernardo, Allan B. I.
Science coursework is an important element of the pre-service education of science teachers. In this study we test the hypothesis that more science coursework influences pedagogical beliefs of science teachers by studying the pedagogical beliefs of 305 Filipino science teachers. We compared pedagogical beliefs of primary school (less science…
Tansey, Timothy N.; Schopieray, Scott; Boland, Elizabeth; Lane, Frank; Pruett, Steven R.
The use of technology-enhanced coursework by rehabilitation counselor educators has increased dramatically over the last decade. In many cases, educators are using new technologies to support traditional modes of teaching and learning. Research conducted in technology-enhanced coursework has primarily focused on the cognitive and psychomotor…
Li, Liang-Yi; Chen, Gwo-Dong
Students can practice skills and acquire knowledge by doing coursework. However, in conventional coursework activities, each student is assigned the same exercises, without considering learners' diversity. Moreover, students typically have difficulty in receiving assistance for completing their exercises after class. Therefore, some students…
This article describes experiences from a professional development project designed to prepare in-service eighth-grade mathematics teachers to develop, explore, and advance technological pedagogical content knowledge (TPCK) in the teaching and learning of Algebra I. This article describes the process of the participating teachers' mathematical…
DePountis, Vicki M.; Pogrund, Rona L.; Griffin-Shirley, Nora; Lan, William Y.
Introduction: This research examined the perspectives of teachers of students who are visually impaired regarding the use and effectiveness of high-tech assistive technology purported to assist visually impaired students in advanced mathematics. Methods: The data for this study were collected via a mixed-methods online survey distributed through…
Roschelle, Jeremy; Shechtman, Nicole; Tatar, Deborah; Hegedus, Stephen; Hopkins, Bill; Empson, Susan; Knudsen, Jennifer; Gallagher, Lawrence P.
The authors present three studies (two randomized controlled experiments and one embedded quasi-experiment) designed to evaluate the impact of replacement units targeting student learning of advanced middle school mathematics. The studies evaluated the SimCalc approach, which integrates an interactive representational technology, paper curriculum,…
Scarborough, Jule Dee
This document (book) reports on the Strategic Alliance to Advance Technological Education through Enhanced Mathematics, Science, Technology, and English Education at the Secondary Level, funded by National Science Foundation. It was a collaborative partnership involving the Rockford Public Schools, Rock Valley College, and Northern Illinois…
Schmidt, Kathleen M.
Thousands of middle school students participate in science competitions such as science fairs and Science Olympiad yearly, but little is known about the effects of their participation on their attitudes toward science, technology, engineering and mathematics (STEM) coursework and careers. Even less is known about whether they increase students' understanding of the practices of scientific inquiry. In this study, 86 seventh-grade students from eight schools who participated in either science fair or Science Olympiad competitions were assessed regarding their attitudes toward STEM coursework and careers and the extent of their science inquiry skills. Quantitative data were collected through pre- and post- competition written assessments. Qualitative data were collected through post-competition focus groups. Both groups increased their understanding of science inquiry as a result of their participation in science competitions. Student attitudes toward STEM coursework and careers were generally positively influenced by their participation in science competitions. However, there was a subgroup of science fair participants for which the opposite was true. The strengths of Science Olympiad programs were the opportunities to study science topics on a deep level, to work with teammates, and to compete. However, there was little student choice at the schools studied because the coaches chose the teams and generally assigned students to particular Science Olympiad events. The level of science inquiry varied according to event. Strengths of the science fair programs were student choice regarding topics and a focus on science inquiry. However, the level of stress experienced by some students, and the negative attitudes toward science that resulted, called into question the appropriateness of engaging in a project of the length and complexity of a typical science fair project with this age group. Recommendations for Science Olympiad competitions are adding events that allow more
Equal Educational Opportunity and Nondiscrimination for Girls in Advanced Mathematics, Science, and Technology Education: Federal Enforcement of Title IX. Equal Educational Opportunity Project Series, Volume V.
Aneckstein, Laura; Baird, Andrea; Butler, Margaret; Chambers, David; Johnson, Wanda; Kraus, Rebecca; Mann, Eric; Trost, Tami; Zalokar, Nadja; Zieseniss, Mireille
This report focuses on the Office for Civil Rights' (OCR's) activities relating to Title IX and advanced mathematics, science, and technology education for girls. It examines some of the barriers and inequities that undermine girls' opportunities to choose college majors and enter careers in the advanced mathematics, science, and technology…
Jones, Ian S.
The assessment of degree level engineering mathematics students using the computer-aided assessment package MapleTA is discussed. Experience of academic and practical issues for both online coursework and examination assessments is presented, hopefully benefiting other academics in this novel area of activity. (Contains 6 figures and 1 table.)
Fukawa-Connelly, Timothy Patrick; Newton, Charlene
Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in "Educational Studies in Mathematics" 69:77-79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the…
Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi
Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…
Graham, Suzanne E.
This Carsey brief reveals that students in rural areas and small towns have less access to higher-level mathematics courses than students in urban settings, which results in serious educational consequences, including lower scores on assessment tests and fewer qualified students entering science, technology, engineering, and mathematics (STEM) job…
This article examines mathematical activity with digital technology by tracing it from its development through its use in classrooms. Drawing on material-semiotic approaches from the field of Science and Technology Studies, it examines the visions of mathematical activity that developers had for an advanced graphing calculator. It then follows the…
Wood, William B.
A recently released National Research Council (NRC) report, "Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools", evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study,…
Montiel, Mariana; Bhatti, Uzma
This article presents an overview of some issues that were confronted when delivering an online second Linear Algebra course (assuming a previous Introductory Linear Algebra course) to graduate students enrolled in a Secondary Mathematics Education program. The focus is on performance in one particular aspect of the course: "change of basis" and…
Lockard, Shannon R.; Metcalf, Rebecca C.
Clickers and classroom voting are used across a number of disciplines in a variety of institutions. There are several papers that describe the use of clickers in mathematics classrooms such as precalculus, calculus, statistics, and even differential equations. This paper describes a method of incorporating clickers and classroom voting in a…
Ortiz-Robinson, Norma L.; Ellington, Aimee J.
A number of learner-centered strategies were implemented during a two-semester course in real analysis that is traditionally taught in lecture format. We seek to understand the role that these strategies can have in this proof-intensive theoretical mathematics classroom and the perceived benefits by the students. Although learner-centered…
Leddy, Mark H.
Americans with disabilities are underemployed in science, technology, engineering and mathematics (STEM) at higher rates than their nondisabled peers. This article provides an overview of the National science Foundation's Research in Disabilities Education (RDE) program, of technology use by students with disabilities (SWD) in STEM, and of…
Hagedorn, Linda Serra; Siadat, M. Vali; Fogel, Shereen F.; Pascarella, Ernest T.; Nora, Amaury
A study using a path-analytic model compared first-year college students enrolled in remedial-type mathematics courses with counterparts enrolled in nonremedial coursework. Results revealed that students enrolled in nonremedial courses entered the institution with many advantages over those enrolled in remedial mathematics. Background variables…
Coombs-Richardson, Rita; Al-Juraid, Sarah E.; Stuker, Jodi D.
This paper describes a state-funded project at Southeastern Louisiana University that offered coursework and direct classroom assistance to general educators attempting to include students with disabilities for mathematics and science instruction. Thirty-five general educators in five parish school systems participated. A sequence of three credit…
Perdigão, Rui A. P.
The fundamental stochastic-dynamic coevolution laws governing complex coevolutionary systems are introduced in a mathematical physics framework formally unifying nonlinear stochastic physics with fundamental deterministic interaction laws among spatiotemporally distributed processes. The methodological developments are then used to shed light onto fundamental interactions underlying complex spatiotemporal behaviour and emergence in multiscale hydroclimate dynamics. For this purpose, a mathematical physics framework is presented predicting evolving distributions of hydrologic quantities under nonlinearly coevolving geophysical processes. The functional formulation is grounded on first principles regulating the dynamics of each system constituent and their interactions, therefore its applicability is general and data-independent, not requiring local calibrations. Moreover, it enables the dynamical estimation of hydroclimatic variations in space and time from knowledge at different spatiotemporal conditions, along with the associated uncertainties. This paves the way for a robust physically based prediction of hydroclimatic changes in unsupervised areas (e.g. ungauged basins). Validation is achieved by producing, with the mathematical physics framework, a comprehensive spatiotemporal legacy consistent with the observed distributions along with their statistic-dynamic relations. The similarity between simulated and observed distributions is further assessed with novel robust nonlinear information-theoretic diagnostics. The present study brings to light emerging signatures of structural change in hydroclimate dynamics arising from nonlinear synergies across multiple spatiotemporal scales, and contributes to a better dynamical understanding and prediction of spatiotemporal regimes, transitions, structural changes and extremes in complex coevolutionary systems. This study further sheds light onto a diversity of emerging properties from harmonic to hyper-chaotic in general
Jung, Eunjoo; Jin, Bora
Research on the role of play coursework in future professionals' integration of play in education is essential in the colleges where future professionals are trained. However, the literature on this topic is very thin. It remains unclear whether college coursework on children's play is related to students' intentions to integrate play in early…
Neuman, Susan B.; Wright, Tanya S.
This study examines the impact of 2 forms of professional development on prekindergarten teachers' early language and literacy practice: coursework and coaching. Participating teachers (N = 148) from 6 urban cities were randomly assigned to Group 1 (coursework), Group 2 (on-site coaching), or Group 3 (control group). Pre- and postassessments…
Jones, Christine S.; Timpson, William M., Comps.
Abstracts of 25 articles and documents provide examples of the delivery of science, math, and vocational education via such media as interactive television, communications satellites, videodiscs, and electronic mail. Studies of instructional effectiveness and design issues are also represented. (SK)
Bozick, Robert; Dalton, Benjamin
Federal legislation has attempted to move career and technical education (CTE) from a segregated component of the high school curriculum to an integrated element that jointly improves both academic and career readiness. However, concerns remain about the ability of CTE to improve academic learning. Using a nationally representative sample of high…
Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby
Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge-in particular in mathematics domains-influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women's perceptions of
Nix, Samantha; Perez-Felkner, Lara; Thomas, Kirby
Students' perceptions of their mathematics ability vary by gender and seem to influence science, technology, engineering, and mathematics (STEM) degree choice. Related, students' perceptions during academic difficulty are increasingly studied in educational psychology, suggesting a link between such perceptions and task persistence. Despite interest in examining the gender disparities in STEM, these concepts have not been considered in tandem. In this manuscript, we investigate how perceived ability under challenge—in particular in mathematics domains—influences entry into the most sex-segregated and mathematics-intensive undergraduate degrees: physics, engineering, mathematics, and computer science (PEMC). Using nationally representative Education Longitudinal Study of 2002 (ELS) data, we estimate the influence of perceived ability under challenging conditions on advanced high school science course taking, selection of an intended STEM major, and specific major type 2 years after high school. Demonstrating the importance of specificity when discussing how gender influences STEM career pathways, the intersecting effects of gender and perceived ability under mathematics challenge were distinct for each scientific major category. Perceived ability under challenge in secondary school varied by gender, and was highly predictive of selecting PEMC and health sciences majors. Notably, women's 12th grade perceptions of their ability under mathematics challenge increased their probability of selecting PEMC majors over and above biology. In addition, gender moderated the effect of growth mindset on students' selection of health science majors. Perceptions of ability under challenge in general and verbal domains also influenced retention in and declaration of certain STEM majors. The implications of these results are discussed, with particular attention to access to advanced scientific coursework in high school and interventions aimed at enhancing young women
Greenfield, Renée A.
This study followed a mixed-methods sequential explanatory design. Phase I involved the collection of quantitative data to examine inservice teachers' (N = 69) attitudes about language and linguistic diversity as well as their teacher education coursework. All participants were graduates from the same teacher education program. Phase II included…
Boyd, Pete; Bloxham, Sue
In the continuing concern about academic standards in the higher education sector a great deal of emphasis has been placed on quality assurance procedures rather than on considering how university tutors learn to grade the quality of work produced by students. As part of a larger research project focused on how tutors grade student coursework,…
Purvis, Caralyn J.; McNeill, Brigid C.; Everatt, John
Low metalinguistic knowledge of pre-service and in-service teachers is likely to restrict the provision of evidence-based literacy instruction in the classroom. Despite such concerns, relatively few studies have examined the effects of teacher preparation coursework in building pre-service teachers' language structure knowledge. This study…
Forsyth, H.; Laxton, R.; Moran, C.; van der werf, J.; Banks, R.; Taylor, R.
Coursework masters degrees in Australia have experienced rapid, decentralised growth since deregulation at the end of the 1980s. The result is an extraordinarily high level of diversity and some confusion as to standards, strategic positioning, purpose and educational approaches. Throughout this period of growth, a sense that large-scale (often…
Wolfe, Randi B.
If preservice teachers are to be capably prepared to meet the challenges of classroom and community diversity, teacher educators have a responsibility to address the full range of diversity issues in teacher preparation coursework, despite controversial or political overtones that may exist. Among these issues is that of considering and responding…
Allgood, Sam; Bosshardt, William; van der Klaauw, Wilbert; Watts, Michael
Using data collected from graduates who attended four large public universities in 1976, 1986, or 1996, the authors investigate the relationship between studying economics and civic behaviors. They compare students who majored in economics, business, or other majors, and by the number of undergraduate economics courses completed. Coursework is…
Moraes, Caroline; Michaelidou, Nina; Canning, Louise
This paper addresses a knowledge gap by presenting an empirical investigation of a group coursework protocol and peer assessment system (GCP&PAS) used in a UK university to support postgraduate marketing students in their assessed group activities. The aim of the research was to examine students' understanding of the GCP&PAS and their…
Gleason, James P.; Violette, Jayne L.
Drawing on a theoretical framework based on "use-inspired" applied research and service learning practice (Honnet-Porter & Poulsen, 1989), this paper argues the relationship between a service-learning approach and Public Relations coursework is a natural and highly desirable fit. Through examination of the goals of both service-learning and public…
O'Neill, Sue; Stephenson, Jennifer
There has been conjecture that completing focused coursework units on classroom management during pre-service teacher preparation might lead to increased feelings of preparedness and confidence. This study reports the preparedness in managing specific problem behaviours, familiarity, and confidence in using management strategies and models of…
Bright, Alan D.; Tarrant, Michael A.
Examines college students' attitudes and complexity of thinking about the Endangered Species Act (ESA) and the effects of environment-based coursework on their attitudes and thinking. Investigates attitudes in terms of their direction, extremity, ambivalence, and importance and measures complexity of thinking as integrative complexity. (Contains…
Kiley, Margaret; Cumming, Jim
The focus of this paper is on student learning pathways--with particular reference to the factors motivating coursework master's students to seek entry to a doctoral programme--along with the implications for higher education policy and practice. It is argued nationally and internationally that although a number of challenges continue to…
Educators and marketing professionals agree that course-work must address interpersonal communication skills and ethical decision making in addition to traditional business functions and skills. This article describes an innovative approach to teaching the professional selling course in which students enhance their competency in these areas…
Moan, Eugene R.; Dereshiwsky, Mary I.
Discussion of student engagement in Web instruction focuses on which facets of online learning, as measured by the Western Governors University Distance Education Self-Test, predict levels and types of student engagement in Web coursework. Highlights include learning styles; time management skills; and the lack of a need for face-to-face…
Cavazos, Alyssa G.
Academia often devalues diverse identities, cultures, and languages through emphasis placed on academic values. To ascertain how established and new Latina/o academics achieved success in academia, the author conducted interviews with ten Latina/o academics; they noted mentoring and multiethnic coursework as influential in their success as…
Foothill-De Anza Community Coll. District, Cupertino, CA. Occupational Training Inst.
The Student's Ultimate Career Coursework, Employment and Student Services (SUCCESS) Handbook project was undertaken to identify student support services available through the California Community Colleges (CCC), increase student retention among special needs vocational education students, and identify common barriers to employment. The project…
This qualitative research study examined how student teachers and novice history teachers learn to teach adolescent bilingual learners (BLs) from coursework to the classroom. The purpose of the study was to investigate to what extent five participants drew upon social justice-oriented pre-service preparation when they taught history to bilingual…
The laboratory notebooks of physics undergraduates taking two second-year practical courses were audited to discover whether they had used feedback comments in their subsequent coursework. Ninety-five per cent of the 37 students on the first course and 100% of the 14 students on the second course whose work was audited had used feedback. The…
Schellhase, Kristen C.
Context: Emphasis is placed on athletic training educators' content area expertise and not on their formal training in educational concepts. Objective: The purposes of this study were to identify the amount of educational coursework completed by ATEP faculty and investigate the relationship between ATEP instructors' student evaluation of…
Campbell, D. Michael
The lack of preparation, participation, and equal access of students in mathematics and the science education continues to afflict America's high school system (Ratliff, 2001). Additionally, gender and ethnic status have become significant factors as females and minority subgroups such as African Americans and Hispanics continue to be underrepresented in these two subject fields. Recognizing and understanding these trends is extremely important for the future of this country. As fewer minorities and females become involved in advanced mathematics and science curriculum there will be a continued lack of minorities and females in mathematics and science careers. Additionally, this insufficient representation leads to fewer numbers of females and minorities in industry and educational leadership positions in mathematics and science to promote participation and equality in these fields. According to Brainard and Carlin (2003) as trends currently stand, these two groups will be under-represented in the fields of math and science and will continue to be denied economic and social power. Thus, a better understanding of these trends in participation in mathematics and science among these groups of students is warranted. This study is intended to accomplish four objectives. The first objective is to identify the extent to which opportunities are increasing or decreasing for students in high schools taking mathematics and science Advanced Placement exams by examining six years of student testing data from the College Board. A second objective is to identify features of high schools that relate to greater expansion in Advanced Placement test taking for females and minority groups in the areas of both math and science. A third objective is to explore whether, and to what extent, any social or educational features such as economic status, regional school and living locations, and ethnic backgrounds have enhanced or reduced Advanced Placement testing in these schools. Lastly
Reports from 13 Further Mathematics Knowledge Networks supported by the National Centre for Excellence in the Teaching of Mathematics [NCETM] are analysed. After summarizing basic characteristics of the networks regarding leadership, composition and pattern of activity, each of the following aspects is examined in greater depth: Developmental aims…
Houben, R M G J; Dowdy, D W; Vassall, A; Cohen, T; Nicol, M P; Granich, R M; Shea, J E; Eckhoff, P; Dye, C; Kimerling, M E; White, R G
Existing approaches to tuberculosis (TB) control have been no more than partially successful in areas with high human immunodeficiency virus (HIV) prevalence. In the context of increasingly constrained resources, mathematical modelling can augment understanding and support policy for implementing those strategies that are most likely to bring public health and economic benefits. In this paper, we present an overview of past and recent contributions of TB modelling in this key area, and suggest a way forward through a modelling research agenda that supports a more effective response to the TB-HIV epidemic, based on expert discussions at a meeting convened by the TB Modelling and Analysis Consortium. The research agenda identified high-priority areas for future modelling efforts, including 1) the difficult diagnosis and high mortality of TB-HIV; 2) the high risk of disease progression; 3) TB health systems in high HIV prevalence settings; 4) uncertainty in the natural progression of TB-HIV; and 5) combined interventions for TB-HIV. Efficient and rapid progress towards completion of this modelling agenda will require co-ordination between the modelling community and key stakeholders, including advocates, health policy makers, donors and national or regional finance officials. A continuing dialogue will ensure that new results are effectively communicated and new policy-relevant questions are addressed swiftly. PMID:24903784
Ayers, Don; And Others
This study conducted a statistical analysis to look at the participation and achievement of Black, Hispanic, and female secondary education students in mathematics, science, and advanced technology programs in schools in Virginia, compared to those of White students and male students. In particular, the study applied descriptive and inferential…
Kavlock, R J
During the last several years, significant changes in the risk assessment process for developmental toxicity of environmental contaminants have begun to emerge. The first of these changes is the development and beginning use of statistically based dose-response models [the benchmark dose (BMD) approach] that better utilize data derived from existing testing approaches. Accompanying this change is the greater emphasis placed on understanding and using mechanistic information to yield more accurate, reliable, and less uncertain risk assessments. The next stage in the evolution of risk assessment will be the use of biologically based dose-response (BBDR) models that begin to build into the statistically based models factors related to the underlying kinetic, biochemical, and/or physiologic processes perturbed by a toxicant. Such models are now emerging from several research laboratories. The introduction of quantitative models and the incorporation of biologic information into them has pointed to the need for even more sophisticated modifications for which we offer the term embryologically based dose-response (EBDR) models. Because these models would be based upon the understanding of normal morphogenesis, they represent a quantum leap in our thinking, but their complexity presents daunting challenges both to the developmental biologist and the developmental toxicologist. Implementation of these models will require extensive communication between developmental toxicologists, molecular embryologists, and biomathematicians. The remarkable progress in the understanding of mammalian embryonic development at the molecular level that has occurred over the last decade combined with advances in computing power and computational models should eventually enable these as yet hypothetical models to be brought into use.
Sevecke, Jessica R; Rhymer, Katrina N; Almazan, Elbert P; Jacob, Susan
College experiences can expand knowledge, decrease negative stereotypes, and increase acceptance toward diversity, especially regarding gay and lesbian issues. This study found that the more interaction undergraduate students have with gay and lesbian people on campus, the more accepting their attitudes are regarding (1) same-sex, consensual sex, (2) same-sex relations between adults is not unnatural, (3) vote for a gay presidential candidate, (4) friends with a feminine man, (5) friends with a masculine woman, (6) knowledge of GL issues important for future career, and (7) comfortable with GL roommate. Furthermore, the more undergraduate students are exposed to coursework addressing gay and lesbian issues, the more positive their attitudes are regarding the importance of knowledge of gay/lesbian issues for future career and comfort with a gay/lesbian roommate. Discussion explores possible long-term implications of systematic interaction experiences and coursework at all levels within the educational system to prevent negative attitude formation.
Purvis, Caralyn J; McNeill, Brigid C; Everatt, John
Low metalinguistic knowledge of pre-service and in-service teachers is likely to restrict the provision of evidence-based literacy instruction in the classroom. Despite such concerns, relatively few studies have examined the effects of teacher preparation coursework in building pre-service teachers' language structure knowledge. This study examined the effects of 7 h of language structure coursework, delivered over 7 weeks, on 121 New Zealand pre-service teachers in their initial year of study. Changes in participants' phonological awareness, morphological awareness, and orthographic knowledge were tracked across the teaching period. The impact of the coursework for participants who presented with strong spelling (n = 24) and poor spelling (n = 24) ability was also compared. The cohort demonstrated significant gains across all measures. Strong spellers responded more favourably to the teaching than poor spellers, even when accounting for initial levels of meta-linguistic knowledge. Implications for the development of teacher preparation programmes that enhance the provision of effective literacy instruction are discussed. PMID:26271915
Jones, Steven Robert
A perception exists that physics and engineering students experience difficulty in applying mathematics to physics and engineering coursework. While some curricular projects aim to improve calculus instruction for these students, it is important to specify where calculus curriculum and instructional practice could be enhanced by examining the…
Fouad, Nadya A.; Hackett, Gail; Smith, Philip L.; Kantamneni, Neeta; Fitzpatrick, Mary; Haag, Susan; Spencer, Dee
This article presents three studies that provide an in-depth examination of STEM-related supports and barriers. These studies constructed an instrument to identify male and female perceptions of the barriers and supports for pursuing coursework and/or careers in mathematics and sciences domains; to pilot test and refine that instrument; and then…
Crawford, Caroline M.; Brown, Evelyn; Chilelli, Chris
Mathematics methods coursework can be an innovative environment through which to emphasize the integration of real-world data structures and opportunities. These opportunities can create instructionally informative opportunities for learners, as well as inform teacher candidates of innovative teaching tools at their fingertips. NASA offers…
Peterson, Wayne, Ed.
Three sequences of coursework are detailed in the curriculum development guidelines provided in this document. The 4-year sequence, structured around problem-solving, applications, and the acquisition of theory, is designed for the college-bound student who plans to enter a mathematics-based field of study. The 3-year sequence is designed for…
Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…
Tuna, Tayfun; Subhlok, Jaspal; Barker, Lecia; Shah, Shishir; Johnson, Olin; Hovey, Christopher
Videos of classroom lectures have proven to be a popular and versatile learning resource. A key shortcoming of the lecture video format is accessing the content of interest hidden in a video. This work meets this challenge with an advanced video framework featuring topical indexing, search, and captioning (ICS videos). Standard optical character recognition (OCR) technology was enhanced with image transformations for extraction of text from video frames to support indexing and search. The images and text on video frames is analyzed to divide lecture videos into topical segments. The ICS video player integrates indexing, search, and captioning in video playback providing instant access to the content of interest. This video framework has been used by more than 70 courses in a variety of STEM disciplines and assessed by more than 4000 students. Results presented from the surveys demonstrate the value of the videos as a learning resource and the role played by videos in a students learning process. Survey results also establish the value of indexing and search features in a video platform for education. This paper reports on the development and evaluation of ICS videos framework and over 5 years of usage experience in several STEM courses.
Shores, Melanie L.; Shannon, David M.; Smith, Tommy G.
A total of 761 students (58.1% female) from selected fifth- and sixth-grade mathematics classrooms in Alabama were examined to investigate the relationships between individual learner variables (gender, ethnicity, socioeconomic status [SES]) and mathematics performance. Specifically, this portion of the study examined individual learner variables…
Banville, Dominique; White, C. Stephen; Fox, Rebecca K.
Research related to professional development opportunities available to physical education teachers is scarce; what is known shows that career-long professional development opportunities are often limited in scope and are sometimes ineffective or inappropriate (Armour, 2010). Meaningful professional development is critical for teachers if they are…
Barton, Susan O'brien
During the high school years, when many students first have some choice in course selection, research indicates that girls choose to enroll in more math and science courses, take more advanced placement courses, and take more honors courses in English, biology, chemistry, mathematics, and foreign languages than ever before. Yet, not only are boys more likely to take all of the three core science courses (biology, chemistry, and physics), boys enroll in advanced placement physics approximately three times as often as do girls. This study examines the perceptions, attitudes, and aspirations of thirty high school girls enrolled in senior-level science electives in an attempt to understand their high school science course choices, and what factors were influencing them. This is a qualitative investigation employing constructivist grounded theory methods. There are two main contributions of this study. First, it presents a new conceptual and analytical framework to investigate the problem of why some high school girls do not enroll in physics coursework. This framework is grounded in the data and is comprised of three existing feminist perspectives along the liberal/radical continuum of feminist thought. Second, this study illuminates a complex set of reasons why participants avoided high school physics (particularly advanced placement physics) coursework. These reasons emerged as three broad categories related to: (a) a lack of connectedness with physics curriculum and instruction; (b) prior negative experiences with physics and math classroom climates; and (c) future academic goals and career aspirations. Taken together, the findings of this study indicate that the problem of high school girls and physics enrollment---particularly advanced placement physics enrollment---is a problem that cannot be evaluated or considered from one perspective.
Advanced high school biology in an era of rapid change: a summary of the biology panel report from the NRC Committee on Programs for Advanced Study of Mathematics and Science in American High Schools.
Wood, William B
A recently released National Research Council (NRC) report, Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools, evaluated and recommended changes in the Advanced Placement (AP), International Baccalaureate (IB), and other advanced secondary school science programs. As part of this study, discipline-specific panels were formed to evaluate advanced programs in biology, chemistry, physics, and mathematics. Among the conclusions of the Content Panel for Biology were that AP courses in particular suffer from inadequate quality control as well as excessive pressure to fulfill their advanced placement function, which encourages teachers to attempt coverage of all areas of biology and emphasize memorization of facts rather than in-depth understanding. In this essay, the Panel's principal findings are discussed, with an emphasis on its recommendation that colleges and universities should be strongly discouraged from using performance on either the AP examination or the IB examination as the sole basis for automatic placement out of required introductory courses for biology majors and distribution requirements for nonmajors.
Advanced Placement (AP), launched in 1955 by the College Board as a program to offer gifted high school students the opportunity to complete entry-level college coursework, has since expanded to encourage a broader array of students to tackle challenging content. This Education Commission of the State's Policy Analysis identifies key components of…
Education for the Talented in Mathematics and Science. A Report of a Joint Conference of the Cooperative Committee on the Teaching of Science and Mathematics of the American Association for the Advancement of Science and the United States Office of Education. Bulletin, 1952, No. 15
Brown, Kenneth E.; Johnson, Philip G.
The Cooperative Committee on the Teaching of Science and Mathematics of the American Association for the Advancement of Science that participated in planning for and publishing this bulletin is composed of representatives of seventeen national scientific and mathematical societies including representatives from the associated teaching…
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem  and of the Poincare Conjecture  have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
Cunningham, R. S.; Smith, David A.
Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
Gavin, M. Katherine; Casa, Tutita M.; Firmender, Janine M.; Carroll, Susan R.
The goal of Project M2 was to develop and field-test challenging geometry and measurement units for K-2 students. The units were developed using recommendations from gifted, mathematics, and early childhood education. This article reports on achievement results for students in Grade 1 at 12 diverse sites in four states using the Iowa Tests of…
Rumsey, Chepina Witkowski
The goals for this study were to investigate how fourth-grade students developed an understanding of the arithmetic properties when instruction promoted mathematical argumentation and to identify the characteristics of students' arguments. Using the emergent perspective as an overarching theoretical perspective helped distinguish between two…
Desoer, C. A.; Polak, E.; Zadeh, L. A.
A series of research projects is briefly summarized which includes investigations in the following areas: (1) mathematical programming problems for large system and infinite-dimensional spaces, (2) bounded-input bounded-output stability, (3) non-parametric approximations, and (4) differential games. A list of reports and papers which were published over the ten year period of research is included.
Eklund, Julie Ann
This multi-faceted study of dual credit programs in Texas was motivated by perceived discrepancies in dual credit data reporting and a lack of comprehensive, state-level information about dual credit student populations and coursework patterns. Using a P-16 framework, the author explored alignment issues that influence the delivery of dual credit…
Forester, Joseph P; McWhorter, David L; Cole, Maria S
Many premedical students enroll in courses whose content will be encountered again during their medical education. Presumably, students believe this practice will lead to improved academic performance in corresponding medical school courses. Therefore, this study was undertaken to determine whether a premedical gross anatomy and/or histology course resulted in increased performance in corresponding medical school courses. A second aim of the study was to examine whether the type of premedical gross anatomy and/or histology course differentially affected medical school performance. A survey that assessed premedical gross anatomy and histology coursework was administered to 440 first-year medical students. The results from this survey showed that students with premedical gross anatomy (n = 236) and/or histology (n = 109) earned significantly more points in the corresponding medical school course than students without the premedical coursework (P < 0.05). Analysis of premedical course types revealed that students who took a gross anatomy course with prosected specimens (n = 35) earned significantly more points that those students without premedical gross anatomy coursework (P < 0.05). The results from this study suggest: 1) premedical gross anatomy and/or histology coursework improves academic performance in corresponding medical school courses, and 2) a premedical gross anatomy course with prosected specimens, a specific type of undergraduate course, significantly improves academic performance in medical gross anatomy.
Ratcliff, James L.; And Others
This paper reports on a study which used a new model, the Cluster Analytic Model (CAM), to determine the relationship between college coursework and general learning, as determined by the nine item types of the General Test of the Graduate Record Examination (GRE) and a faculty survey of perceptions of general learned abilities in relation to…
Dunlap, Karen; Anderson, Gina B.; Rademacher, Joyce; McMenamy, Nancy
Many universities positively impact student retention rates by aligning state competencies and undergraduate coursework with specific learning outcomes known to contribute to success. Faculty from teaching and nursing conducted interdisciplinary focus group research to gather student perceptions concerning whether skills obtained through core…
Rice, Diana C.; Kaya, Sibel
This study investigated the relations among preservice elementary teachers' ideas about evolution, their understanding of basic science concepts and college science coursework. Forty-two percent of 240 participants did not accept the theory of human evolution, but held inconsistent ideas about related topics, such as co-existence of humans and…
Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
The adoption and implementation of the Common Core State Standards and Smarter Balanced assessments in mathematics are intended to provide all students in California with the knowledge and skills required to transition from high school to college-level coursework. This implementation will take time. Concurrent with these efforts, policymakers and…
Swanson, Julie Dingle; Nagy, Steven
The focus of this study was the first year of implementation of the Advanced Placement Academy (APA), a program within a high school providing honors and Advanced Placement coursework for high-ability African American students with previously limited access to rigorous courses. The qualitative investigation explores practical solutions from…
Lee, Stephen R
Los Alamos National Laboratory will review its Computational Physics and Applied Mathematics (CPAM) capabilities in 2010. The goals of capability reviews are to assess the quality of science, technology, and engineering (STE) performed by the capability, evaluate the integration of this capability across the Laboratory and within the scientific community, examine the relevance of this capability to the Laboratory's programs, and provide advice on the current and future directions of this capability. This is the first such review for CPAM, which has a long and unique history at the laboratory, starting from the inception of the Laboratory in 1943. The CPAM capability covers an extremely broad technical area at Los Alamos, encompassing a wide array of disciplines, research topics, and organizations. A vast array of technical disciplines and activities are included in this capability, from general numerical modeling, to coupled mUlti-physics simulations, to detailed domain science activities in mathematics, methods, and algorithms. The CPAM capability involves over 12 different technical divisions and a majority of our programmatic and scientific activities. To make this large scope tractable, the CPAM capability is broken into the following six technical 'themes.' These themes represent technical slices through the CP AM capability and collect critical core competencies of the Laboratory, each of which contributes to the capability (and each of which is divided into multiple additional elements in the detailed descriptions of the themes in subsequent sections): (1) Computational Fluid Dynamics - This theme speaks to the vast array of scientific capabilities for the simulation of fluids under shocks, low-speed flow, and turbulent conditions - which are key, historical, and fundamental strengths of the laboratory; (2) Partial Differential Equations - The technical scope of this theme is the applied mathematics and numerical solution of partial differential equations
Hirsch, Christian R., Ed.; McDuffie, Amy Roth, Ed.
Mathematical modeling plays an increasingly important role both in real-life applications--in engineering, business, the social sciences, climate study, advanced design, and more--and within mathematics education itself. This 2016 volume of "Annual Perspectives in Mathematics Education" ("APME") focuses on this key topic from a…
Nic Chormaic, S.
The Okinawa Institute of Science and Technology Graduate University, established in November 2011, provides a 5- year interdisciplinary PhD program, through English, within Japan. International and Japanese students entering the program undertake coursework and laboratory rotations across a range of topics, including neuroscience, molecular science, physics, chemistry, marine science and mathematics, regardless of previous educational background. To facilitate interdisciplinarity, the university has no departments, ensuring seamless interactions between researchers from all sectors. As part of the PhD program a course in Advanced Optics has been developed to provide PhD students with the practical and theoretical skills to enable them to use optics tools in any research environment. The theoretical aspect of the course introduces students to procedures for complex beam generation (e.g. Laguerre-Gaussian), optical trapping, beam analysis and photon optics, and is supported through a practical program covering introductory interference/diffraction experiments through to more applied fiber optics. It is hoped that, through early exposure to optics handling and measurement techniques, students will be able to develop and utilize optics tools regardless of research field. In addition to the formal course in Advanced Optics, a selection of students also undertakes 13 week laboratory rotations in the Light-Matter Interactions research laboratory, where they work side-by-side with physicists in developing optics tools for laser cooling, photonics or bio-applications. While currently in the first year, conclusive results about the success of such an interdisciplinary PhD training are speculative. However, initial observations indicate a rich cross-fertilization of ideas stemming from the diverse backgrounds of all participants.
Permuth, Steve; Dalzell, Nicole
The advancement of modern societies is fueled by mathematics, and mathematics education provides the foundation upon which future scientists and engineers will build. Society dictates how mathematics will be taught through the development and implementation of mathematics standards. When examining the progression of these standards, it is…
Reys, Robert; Reys, Rustin
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
Shuster, R. D.; Grandgenett, N.
The University of Nebraska at Omaha has been a state leader in helping Nebraska teachers embrace earth systems science education, with a special emphasis in online coursework. UNO was one of the initial members in the Earth Systems Science Education Alliance (ESSEA) and has offered three different ESSEA courses, with a total of 167 students having taken ESSEA courses at UNO for graduate credit. UNO is currently involved in expanding its earth system science courses, modules, and educational research. We are also integrating these courses into several degree programs, including a Masters of Science in Education, a new Middle School Endorsement, a Certificate in Urban Education, and the Graduate Program for the Department of Geography/Geology. UNO is beginning to examine teacher content learning and science reasoning within its coursework. Feedback surveys from earlier ESSEA offerings already indicate a strongly positive perception of the courses by the teachers enrolled in the coursework. Project impact has been documented in teacher projects, quotes, and lessons associated with the coursework activities. We will describe the UNO earth system science efforts (emphasizing ESSEA coursework), and describe past efforts and teacher perceptions, as well as new strategies being undertaken to more closely examine content learning and science reasoning impact with course participants. We will also describe online course modules being developed within the UNO online course efforts, including one on the global amphibian crisis, and also the impact of urbanization on a local native prairie environment.
Greive, Donald E., Ed.
This handbook is designed to help part-time and adjunct faculty who need professional enhancement but do not have the time for formal coursework. The focus is on the modern student, who differs in many ways from the traditional college student. The book provides more advanced strategies that those presented in the earlier "Handbook for…
Missett, Tracy C.; Reed, Christine B.; Scot, Tammy P.; Callahan, Carolyn M.; Slade, Mary
Researchers increasingly embrace online courses to compensate for lack of access to educational opportunities otherwise available in traditional school settings. Researchers also recommend alternatives to traditional AP coursework to better meet the diverse learning styles and needs of advanced learners. These recommendations have particular…
One method of delivering college-level coursework to high school students is through the Advanced Placement (AP) program. Many colleges and universities provide credit to students who earn a qualifying score on any of the 34 available AP exams offered by the College Board. All qualified comprehensive high schools in the Wake County Public School…
Garden, Robert A.; Lie, Svein; Robitaille, David F.; Angell, Carl; Martin, Michael O.; Mullis, Ina V.S.; Foy, Pierre; Arora, Alka
Developing the Trends in International Mathematics and Science Study (TIMSS) Advanced 2008 Assessment Frameworks was a collaborative venture involving mathematics and physics experts from around the world. The document contains two frameworks for implementing TIMSS Advanced 2008--one for advanced mathematics and one for physics. It also contains…
Jones, Thomas A.
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
Sherman, Brian F.; Wither (Post.), David P.
This paper is a distillation of the major result from the 1998 Ph.D. thesis of the late David Wither. It details a longitudinal study over five years of the relationship between mathematics anxiety and mathematics achievement. It starts from the already well documented negative correlation between the two, and seeks to establish one of the three hypotheses—that mathematics anxiety causes an impairment of mathematics achievement; that lack of mathematics achievement causes mathematics anxiety; or that there is a third underlying cause of the two.
Explains the use of the Web as an advanced calculator using numeric, graphic, and symbolic mathematics interactively with the development of XML-standard MathML. Suggests that the problem of decreasing achievement in mathematics courses can be solved using interactive and personalized documents on the Web and improve the understanding of…
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Davis, Pamela; Davis, Michael P.; Mobley, Jerry A.
This study describes the collaboration among a school counselor, a school counselor intern, an Advanced Placement Psychology teacher, and a counselor educator to improve African-American access to Advanced Placement (AP) coursework and increase success on the AP Psychology national examination. The team initiated a process that recruited African…
Musoba, Glenda Droogsma; Krichevskiy, Dmitriy
Utilizing survival analysis, we examined two key first year courses, mathematics and English, and tested whether they were predictive for long-term student success as measured by persistence to graduation at a Hispanic-serving research university. While first math and first English courses were significant, SAT score was not for Hispanic and Black…
Raab, Joseph A.
This pamphlet lists five thousand current, readily available audiovisual materials in mathematics. These are grouped under eighteen subject areas: Advanced Calculus, Algebra, Arithmetic, Business, Calculus, Charts, Computers, Geometry, Limits, Logarithms, Logic, Number Theory, Probability, Soild Geometry, Slide Rule, Statistics, Topology, and…
An understanding of past technological advancements can help educators understand the influence of new technologies in education. Inventions such as the abacus, logarithms, the slide rule, the calculating machine, computers, and electronic calculators have all found their place in mathematics education. While new technologies can be very useful,…
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Kiley, Margaret; Cumming, Jim
The objective of this paper is to identify the impact of current national policies and emerging curricular practices on master's by coursework students in Australia. It is argued that the rate of top-down policy change, together with bottom-up innovation, is resulting in a high level of complexity that is challenging providers, staff and…
O'Neill, Sue C.; Stephenson, Jennifer
Beginning teachers often report feeling less than adequately prepared by their teacher education programs in the area of classroom and behaviour management (CBM). This article reports the prevalence of evidence-based practices in the coursework content on offer in Australian undergraduate primary teacher education programs. First a set of CBM…
Dunst, Carl J.; Raab, Melinda; Hamby, Deborah W.; Long, Anna Lauren
The results from a content analysis of coursework required and offered at the 58 North Carolina Community Colleges to obtain an Associate in Applied Sciences Degree in early childhood education are described. The analyses were conducted to determine the likelihood that the courses could include content knowledge or practice on 12 infant and child…
Putnam, Ralph T.
Two important aspects of transfer in mathematics learning are the application of mathematical knowledge (MK) to problem solving and the acquisition of more advanced concepts. General assumptions and themes of current cognitive research on mathematics learning in schoolchildren are discussed, focusing on issues facilitating the transfer of MK. (TJH)
Hunting, Robert P.; Doig, Brian A.
Discusses a professional development program called Clinical Approaches to Mathematics Assessment. Argues for the advanced training of mathematics teachers who understand knowledge construction processes of students; can use clinical tools for evaluating a student's unique mathematical "fingerprint"; and can create or adapt problems, tasks, or…
Liekar, Christine Y.
Since the time of Sputnik, American educators and policymakers have recognized the need to raise expectations by increasing rigor in high schools across the United States. Copious studies attest to the fact that students who take Advanced Placement coursework experience success in college (Adelman, 1999; Camara, 2003; College Board, 2005;…
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
Dalton, Ben; Ingels, Steven J.; Downing, Jane; Bozick, Robert
While increased academic requirements for high school graduation have long been advocated, current research shows a mixed record in mathematics and science achievement among American middle and high school students relative to some of their international peers. In response to these concerns and other calls for reform, states have increased the…
Fry, Dale Eugene
College students' performance in their first two calculus-level mathematics courses was studied by comparing students skipping, on any basis, one or more courses in the regular calculus sequence and students reaching these same courses through the regular sequence. Those skipping via CEEB AP and those skipping for any other reason were also…
McCammon, Richard B.
The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)
Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)
The use of mathematical tools has long proved to be useful in gaining understanding of complex systems in physics . Recently, many researchers have realized that there is an analogy between emerging phenomena in complex social systems and complex physical or biological systems [4,5,12]. This realization has particularly benefited the modeling and understanding of crime, a ubiquitous phenomena that is far from being understood. In fact, when one is interested in the bulk behavior of patterns that emerge from small and seemingly unrelated interactions as well as decisions that occur at the individual level, the mathematical tools that have been developed in statistical physics, game theory, network theory, dynamical systems, and partial differential equations can be useful in shedding light into the dynamics of these patterns [2-4,6,12].
Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen
Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…
The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed. PMID:23512504
Mullis, Ina V. S., Ed.; Martin, Michael O., Ed.
The "TIMSS Advanced 2015 Assessment Frameworks" provides the foundation for the two international assessments to take place as part of the International Association for the Evaluation of Educational Achievement's TIMSS (Trends in International Mathematics and Science Study) Advanced 2015--Advanced Mathematics and Physics. Chapter 1 (Liv…
This article looks at recent work in cognitive science on mathematical cognition from the perspective of history and philosophy of mathematical practice. The discussion is focused on the work of Lakoff and Núñez, because this is the first comprehensive account of mathematical cognition that also addresses advanced mathematics and its history. Building on a distinction between mathematics as it is presented in textbooks and as it presents itself to the researcher, it is argued that the focus of cognitive analyses of historical developments of mathematics has been primarily on the former, even if they claim to be about the latter.
Austin, S. A.; Zirbel, E. L.; Johnson, L. P.
Scientific computing in the traditional Computer Science curriculum typically involves the application of methods across the disciplines of both Engineering and the Physical Sciences. Typical applications detach methods and computational techniques from the underlying science. As part of a OSS-funded educational initiative for Minority Institutions, we are exploring the integration and applications of Astronomy as part of an experimental project course. The exploratory course integrates fundamental background material in Astronomy together with computational methods used to generate graphical simulations of underlying physical concepts. Students participating in the course are advanced Computer Science majors with Physics minors interested in combining the two areas. The course is led by faculty in Astrophysics and Computer Science. Examples of some of the student' projects will be provided with some discussion of the challenges and opportunities posed by this interdisciplinary approach. [Supported by NASA/OSS
Yarbrough, L. D.; Katzenstein, K.
Exposing students to active and local examples of physical geologic processes is beneficial to the learning process. Students typically respond with interest to examples that use state-of-the-art technologies to investigate local or regional phenomena. For lower cognitive level of learning (e.g. knowledge, comprehension, and application), the use of "close-to-home" examples ensures that students better understand concepts. By providing these examples, the students may already have a familiarity or can easily visit the location. Furthermore, these local and regional examples help students to offer quickly other examples of similar phenomena. Investigation of these examples using normal photographic techniques, as well as a more sophisticated 3-D Light Detection And Ranging (LiDAR) (AKA Terrestrial Laser Scanning or TLS) system, allows students to gain a better understanding of the scale and the mechanics of the geologic processes and hazards. The systems are used for research, teaching and outreach efforts and depending on departmental policies can be accessible to students are various learning levels. TLS systems can yield scans at sub-centimeter resolution and contain surface reflectance of targets. These systems can serve a number of learning goals that are essential for training geoscientists and engineers. While querying the data to answer geotechnical or geomorphologic related questions, students will develop skills using large, spatial databases. The upper cognitive level of learning (e.g. analysis, synthesis, and evaluation) is also promoted by using a subset of the data and correlating the physical geologic process of stream bank erosion and rock slope failures with mathematical and computer models using the scanned data. Students use the examples and laboratory exercises to help build their engineering judgment skills with Earth materials. The students learn not only applications of math and engineering science but also the economic and social implication
Discusses the nature of mathematics, the goals of education, and the political dimension of mathematics. Considers ethnomathematics, the history of mathematics, and advances in ethnomathematics. Proposes a new conception of curriculum. (ASK)
Maltese, Adam V.
While the number of Bachelor's degrees awarded annually has nearly tripled over the past 40 years (NSF, 2008), the same cannot be said for degrees in the STEM (science, technology, engineering and mathematics) fields. The Bureau of Labor Statistics projects that by the year 2014 the combination of new positions and retirements will lead to 2 million job openings in STEM (BLS, 2005). Thus, the research questions I sought to answer with this study were: (1)What are the most common enrollment patterns for students who enter into and exit from the STEM pipeline during high school and college? (2) Controlling for differences in student background and early interest in STEM careers, what are the high school science and mathematics classroom experiences that characterize student completion of a college major in STEM? Using data from NELS:88 I analyzed descriptive statistics and completed logistic regressions to gain an understanding of factors related to student persistence in STEM. Approximately 4700 students with transcript records and who participated in all survey rounds were included in the analyses. The results of the descriptive analysis demonstrated that most students who went on to complete majors in STEM completed at least three or four years of STEM courses during high school, and enrolled in advanced high school mathematics and science courses at higher rates. At almost every pipeline checkpoint indicators of the level of coursework and achievement were significant in predicting student completion of a STEM degree. The results also support previous research that showed demographic variables have little effect on persistence once the sample is limited to those who have the intrinsic ability and desire to complete a college degree. The most significant finding is that measures of student interest and engagement in science and mathematics were significant in predicting completion of a STEM degree, above and beyond the effects of course enrollment and performance
Berryman, Sue E.
This paper describes trends in and causes of minority and female representation among holders of advanced science and math degrees. The minority groups studied are Blacks, Hispanic Americans, American Indians, and Asian Americans, all of whom are compared with Whites. The degrees looked at include those in math, the computer sciences, physical…
Hadlock, Charles R
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
Catterton, Gene; And Others
This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…
J.K. Brimacombe; I.V. Samarasekera; E.B. Hawbolt; T.R. Meadowcroft; M. Militzer; W.J. Pool; D.Q. Jin
This report describes the work of developing an integrated model used to predict the thermal history, deformation, roll forces, microstructural evolution and mechanical properties of steel strip in a hot-strip mill. This achievement results from a joint research effort that is part of the American Iron and Steel Institute's (AIS) Advanced Process Control Program, a collaboration between the U.S. DOE and fifteen North American Steelmakers.
Gary City Public School System, IN.
GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…
Singh, B. P.; Singh, Meena; Roy, Sanjay Kumar
The necessity of modeling lies in the nature of technology and its advancement. The modeling minimizes time and cost of the process involved. The mathematical model provides an insight into the behavior of the physical system that reduces the problem to its essential characteristics. The floating admittance matrix (FAM) approach is an elegant method of mathematical modeling of electronic devices and circuits.
Ozel, Serkan; Yetkiner, Zeynep Ebrar; Capraro, Robert M.
Technology integration in mathematics classrooms is important to the field of education, not only because today's society is becoming more and more advanced and reliant upon technology but also because schools are beginning to embrace technology as an essential part of their curricula. The Principles and Standards for School Mathematics (National…
Hull, Ted H.; Balka, Don S.; Miles, Ruth Harbin
A whirlwind of activity surrounds the topic of teaching and learning mathematics. The driving forces are a combination of changes in assessment and advances in technology that are being spurred on by the introduction of content in the Common Core State Standards for Mathematical Practice. Although the issues are certainly complex, the same forces…
Investigates meaningful assessment to give teachers information on students' understanding of mathematical ideas and how their understanding changes over time. Presents examples collected from a teacher-made quiz, the Advanced Placement calculus test, and the SAT-I Mathematics test. Illustrates both the inherent subjectivity of these methods and…
A brief historical introduction to the development of observational astronomy will be presented. The close historical relationship between the successful application of mathematical concepts and advances in astronomy will be presented. A variety of simple physical demonstrations, hands-on group activities, and puzzles will be used to understand how the properties of light can be used to understand the contents of our universe.
Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain
The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…
Dini, Vesal; Hammer, David
Students' physical intuitions and prior knowledge are critical to making sense of and solving problems in classical mechanics. In quantum mechanics (qm), coordinating concepts connected to such everyday thinking becomes more difficult. How then can students develop coherence in their knowledge of qm? Consider how experts do it: they build meaning in, around, and through the mathematics of the theory. This view on the role of mathematics, which is one of among many possible to take, seems most productive for qm. In our work to characterize student views of knowledge that emerge in the context of qm coursework, we came to analyze one student who mostly adopted such a view until a shift in context moved him to express an alternative. We present his case and discuss important implications for instruction.
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
Edwards, A W F
Ernst Mayr called the first part of the evolutionary synthesis the 'Fisherian synthesis' on account of the dominant role played by R.A. Fisher in forging a mathematical theory of natural selection together with J.B.S. Haldane and Sewall Wright in the decade 1922-1932. It is here argued that Fisher's contribution relied on a close reading of Darwin's work to a much greater extent than did the contributions of Haldane and Wright, that it was synthetic in contrast to their analytic approach and that it was greatly influenced by his friendship with the Darwin family, particularly with Charles's son Leonard. PMID:21423339
Weber, Keith; Mejia-Ramos, Juan Pablo
We argue that mathematics majors learn little from the proofs they read in their advanced mathematics courses because these students and their teachers have different perceptions about students' responsibilities when reading a mathematical proof. We used observations from a qualitative study where 28 undergraduates were observed evaluating…
Chabrán, H. Rafael; Kozek, Mark
We describe our team-taught, interdisciplinary course "Numb3rs in Lett3rs & Fi1ms: Mathematics in Literature and Cinema," which explores mathematics in the context of modern literature and cinema. Our goal with this course is to advance collaborations between mathematics and the written/theatre-based creative arts.
Lehigh County Community Coll., Schnecksville, PA.
In this document, detailed objectives for the following courses are listed: Algebra I, Algebra II, Geometry, Trigonometry, Analytic Geometry, Advanced Mathematics, Personal Business Mathematics, and Business Mathematics. Each objective is keyed to an expected level of achievement: awareness, knowledge, application, mastery, reinforcement, and…
Maggio, M. Raine; Sayler, Micheal
Parents and schools often notice the need for addressing advanced mathematical performance in elementary students. Many gifted programs do not offer differentiated or accelerated mathematics as part of their elementary school options. In this report, the efforts of one school system to identify and serve the needs of highly mathematically able…
LeBeau, Brandon; Harwell, Michael; Monson, Debra; Dupuis, Danielle; Medhanie, Amanuel; Post, Thomas R.
Background: The importance of increasing the number of US college students completing degrees in science, technology, engineering or mathematics (STEM) has prompted calls for research to provide a better understanding of factors related to student participation in these majors, including the impact of a student's high-school mathematics curriculum. Purpose: This study examines the relationship between various student and high-school characteristics and completion of a STEM major in college. Of specific interest is the influence of a student's high-school mathematics curriculum on the completion of a STEM major in college. Sample: The sample consisted of approximately 3500 students from 229 high schools. Students were predominantly Caucasian (80%), with slightly more males than females (52% vs 48%). Design and method: A quasi-experimental design with archival data was used for students who enrolled in, and graduated from, a post-secondary institution in the upper Midwest. To be included in the sample, students needed to have completed at least three years of high-school mathematics. A generalized linear mixed model was used with students nested within high schools. The data were cross-sectional. Results: High-school predictors were not found to have a significant impact on the completion of a STEM major. Significant student-level predictors included ACT mathematics score, gender and high-school mathematics GPA. Conclusions: The results provide evidence that on average students are equally prepared for the rigorous mathematics coursework regardless of the high-school mathematics curriculum they completed.
Carr, Michael; Murphy, Eoin; Bowe, Brian; Ni Fhloinn, Eabhnat
Dublin Institute of Technology offers students a number of different routes into engineering, allowing many non-standard entrants the opportunity to study the discipline provided they fulfil certain criteria. The final aim of many of these students is to achieve an Honours Degree in Engineering, which takes a minimum of 4 years. Apart from the…
Tran, Dung; Dougherty, Barbara J.
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Nomi, Takako; Raudenbush, Stephen W.
Algebra is often considered as a gateway for later achievement. A recent report by the Mathematics Advisory Panel (2008) underscores the importance of improving algebra learning in secondary school. Today, a growing number of states and districts require algebra for all students in ninth grade or earlier. Chicago is at the forefront of this…
Alexander, F.; Anitescu, M.; Bell, J.; Brown, D.; Ferris, M.; Luskin, M.; Mehrotra, S.; Moser, B.; Pinar, A.; Tartakovsky, A.; Willcox, K.; Wright, S.; Zavala, V.
Applied mathematics has an important role to play in developing the tools needed for the analysis, simulation, and optimization of complex problems. These efforts require the development of the mathematical foundations for scientific discovery, engineering design, and risk analysis based on a sound integrated approach for the understanding of complex systems. However, maximizing the impact of applied mathematics on these challenges requires a novel perspective on approaching the mathematical enterprise. Previous reports that have surveyed the DOE's research needs in applied mathematics have played a key role in defining research directions with the community. Although these reports have had significant impact, accurately assessing current research needs requires an evaluation of today's challenges against the backdrop of recent advances in applied mathematics and computing. To address these needs, the DOE Applied Mathematics Program sponsored a Workshop for Mathematics for the Analysis, Simulation and Optimization of Complex Systems on September 13-14, 2011. The workshop had approximately 50 participants from both the national labs and academia. The goal of the workshop was to identify new research areas in applied mathematics that will complement and enhance the existing DOE ASCR Applied Mathematics Program efforts that are needed to address problems associated with complex systems. This report describes recommendations from the workshop and subsequent analysis of the workshop findings by the organizing committee.
Modes of Instruction for K-12 School Leadership Candidate Coursework and Internship Preparation in the ISLLC Standards and Candidate Gender and Candidate Scores of New York State Licensure Assessments
The purpose of this study was to investigate the relationships between K-12 school leadership program graduates' descriptions of their coursework and internship preparedness in the Interstate School Leaders Licensure Consortium (ISLLC) Standards among three modes of instruction (online, hybrid, and face-to-face) and their scores on Parts I…
This paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of "mathematics curriculum as story" and defines and…
Ecological sustainability has not been a major focus of mathematics education research, even though it has attracted considerable attention in other areas of educational research in the past decade. The connections between mathematics education and ecological sustainability are not readily apparent. This paper explores how mathematics educators…
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Rounds, James B., Jr.; Hendel, Darwin D.
Results indicate that the Mathematics Anxiety Rating Scale and the Math Anxiety Scale measure similar components of mathematics-anxiety domain. Mathematics-anxiety scales and Fennema-Sherman scales of Confidence and Effectance Motivation measure similar affective domains and are approximately equal predictors of arithmetic performance. (Author)
Sheryn, Louise; Ell, Fiona
Debates about how undergraduate mathematics should be taught are informed by different views of what it is to learn and to do mathematics. In this qualitative study 10 students enrolled in an advanced undergraduate course in mathematics shared their views about how they best learn mathematics. After participating in a semester-long course in…
Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one…
Clark, Charles W.
Not updated since its 1964 publication, the Handbook of Mathematical Functions (Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables), ed. M. Abramowitz and I. A. Stegun, National Bureau of Standards Applied Mathematics Series v. 55 (U. S. Government Printing Office, Washington DC, 1964) presents the state of applied mathematics 40 years ago, in a form suited for computation in an age of numerical tables and mechanical calculators. Yet it remains a workhorse reference of AMO physics and of other scientific fields, having been cited in archival literature over 26,000 times since 1974 (at a still-increasing rate). To incorporate subsequent advances in basic mathematical knowledge, in computational power and technique, and in dissemination of information, the National Institute of Standards and Technology has begun a project to provide a modern source of evaluated mathematical reference data: the NIST Digital Library of Mathematical Functions. The Digital Library is designed to serve the needs of users of applied mathematics via the World Wide Web. We shall demonstrate the operation of a prototype, and hope to elicit expressed needs of the AMO community.
Jensen, Jennifer L.
If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…
What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? These are just some of the questions addressed in "Transforming Primary Mathematics", a highly timely new resource for teachers which accessibly sets out the key theories and latest research in primary maths today. Under-pinned by findings…
Morsy, Zaghloul, Ed.; Draxler, Alexandra, Ed.
A set of articles with the theme "Mathematics for Real Life" is presented. These article titles are: (1) Teaching Mathematics as a Tool for Problem Solving; (2) New Math or New Education; (3) Hand Calculators and Math in Primary School; (4) Mass Media in the Mathematical Training of Polish Primary Teachers; (5) The Goals of Mathematics Teaching in…
Investigates young people's expression of mathematical ideas with a computer, the nature of mathematical practices, and the problem of mathematical meaning from cognitive and socio-cultural perspectives. Describes a mathematical activity system designed for learning and the role of digital technologies in helping to understand and reshape the…
This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…
Cross, Kath; Hibbs, John
In the Association of Teachers of Mathematics (ATM) Easter conference, 2006, the authors presented a list of important aspects of mathematics lessons, recommended for students to have a positive attitude to mathematics and for teachers to acquire effective teaching. The following are discussed in detail: (1) Mathematics lessons without good…
Griffiths, Barry J.; Haciomeroglu, Erhan Selcuk
To ensure the competitiveness of the USA in the global economy, and its role as a leader in science and engineering, it is important to cultivate the next generation of home grown mathematicians. However, while universities across the USA offer calculus classes to thousands of undergraduate students each year, very few of them go on to major in…
South, J. C., Jr. (Editor); Hussaini, M. Y. (Editor)
This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.
The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students' mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth-grade algebra and geometry course placements are academically selective, but considerable between-school variation exists in students' odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness. PMID:24816044
The proportion of eighth graders in United States public schools enrolled in algebra or a more advanced mathematics course doubled between 1990 and 2011. This article uses Early Childhood Longitudinal Study's Kindergarten Cohort data to consider the selection process into advanced middle school mathematics courses and estimate the effects of advanced courses on students' mathematics achievement (n = 6,425; mean age at eighth grade = 13.7). Eighth-grade algebra and geometry course placements are academically selective, but considerable between-school variation exists in students' odds of taking these advanced courses. While analyses indicate that advanced middle school mathematics courses boost student achievement, these effects are most pronounced in content areas closely related to class content and may be contingent on student academic readiness.
Burghes, D. N.; Borrie, M. S.
Describes the advantages of mathematical modeling approach in teaching applied mathematics and gives many suggestions for suitable material which illustrates the links between real problems and mathematics. (GA)
Konhauser, Joseph D. E.; And Others
This book provides a collection of 191 mathematical problems aimed at the advanced high school student level and above. Problems cover general mathematical areas including plane geometry, three-dimensional geometry, number theory, algebra, combinatorics and graph theory, and a number of miscellaneous questions that combine mathematical…
Mullis, Ina V. S., Ed.; Martin, Michael O., Ed.
It is critical for countries to ensure that capable secondary school students receive further preparation in advanced mathematics and science, so that they are ready to enter challenging university-level studies that prepare them for careers in science, technology, engineering, and mathematics (STEM) fields. This group of students will become the…
Sadovskii, L. E.; Sadovskii, A. L.
This volume contains some examples of mathematical applications in sports. Sports discussed include tennis, figure skating, gymnastics, track and field, soccer, skiing, hockey, and swimming. Problems and situations are posed and answers with thorough explanations are provided. Chapters include: (1) Mathematics and Sports; (2) What Is Applied…
Prochazkova, Lenka Tejkalova
The author discusses the balance and mutual influence of the language of instruction and mathematics in the context of CLIL, Content and Language Integrated Learning. Different aspects of the relationship of language and Mathematics teaching and learning are discussed: the benefits of using a foreign language of instruction, as well as the…
Presents a case study of a first-grade class and their teacher who were observed as they ascribed mathematical meanings of numbers and of numerical operations to empirical phenomena. Differences in ascriptions led to negotiation of meanings. Discusses some indirect relations between social interaction and mathematics learning. (Contains 60…
Sowder, Judith Threadgill
Explores possible reasons for the gender differences in mathematics problem-solving strategies found in primary-grade students in the study by E. Fennema and others and considers implications of the findings for mathematics instruction. (SLD)
Houston, A. Glen
The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.
Assuming the role of storyteller, the author uses her experiences as a graduate student and beginning teacher to reflect critically on issues related to mathematics, mathematics education, gender, and diversity.
The author suggests that the efficient use of mathematics in everyday life means translating situations into mathematical contexts, using a calculator and mental methods of calculation. Suggestions for teaching these concepts are included. (PK)
Clary, Joseph R.; Nery, Karen P.
This set of 20 modules was designed for use primarily to help teach and reinforce the basic mathematics skills in electronics classes. The modules are based on electronics competencies that require mathematics skills, as determined by a panel of high school electronics and mathematics teachers. Each module consists of one or two pages of basic…
Mathematics is often portrayed as an "abstract" cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced much like everyday phenomena. This lecture examines how careful design can "phenomenalise" mathematics and support not only engagement but…
Applebaum, Mark; Leikin, Roza
The translation principle allows students to solve problems in different branches of mathematics and thus to develop connectedness in their mathematical knowledge. Successful application of the translation principle depends on the classroom mathematical norms for the development of discussions and the comparison of different solutions to one…
This article revisits methods and debates about teaching mathematics that were common in the 1980s and early 1990s, and then moves up to date with the findings from three mathematics departments that set out to make a difference for their lowest attaining students. The methods they used were distinctly focused on core mathematical ideas, and how…
Kenschaft, Patricia Clark, Ed.; Keith, Sandra Zaroodny, Ed.
Mathematics is an auspicious discipline for young people of both sexes and all ethnic groups. This booklet aims to help members of the Mathematical Association of America (MAA) and others to increase future participation of women in mathematics, to better understand their present roles, and to develop a vision of a world with greater equal…
Martin, Tami S.; Speer, William R.
This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…
Swan, Paul; Marshall, Linda
It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics manipulative…
Rural Mathematics Educator, 2002
This document contains the two issues of "Rural Mathematics Educator" published in 2002. This newsletter of the Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics (ACCLAIM) includes articles on rural mathematics education, as well as information and descriptions of professional development opportunities for…
Schwartz, Richard H.
This resource was written to provide students with an awareness of critical issues facing the world today. In courses for college students, it can motivate their study of mathematics, teach them how to solve mathematical problems related to current global issues, provide coherence to mathematical studies through a focus on issues of human…
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
Examines three strands of elementary mathematics--numerals and counting, recording and calculating, and mathematics exploration and play--and provides ways to integrate culture and mathematics experiences in each area. Specific topics include Egyptian methods for multiplication, the abacus, and the words for the numbers 1-10 in seven different…
In this paper, I draw together a corpus of findings derived from two sources: studies of students using computers to learn mathematics, and research into the use of mathematics in professional practice. Using this as a basis, I map some elements of a theoretical framework for understanding the nature of mathematical knowledge in use, and how it is…
This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…
Gallian, Joseph A., Ed.
"Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…
Early in my career someone else reported that the best indicator of success in calculus-based physics (CBP) at our school was whether students had taken mathematics in a certain region of New Brunswick. I sat down with a very longtime mathematics teacher and asked him what he thought students should know in mathematics after high school to succeed…
Posey, Johnsie Jo, Ed.; And Others
This manual is a collection of materials and teaching strategies to motivate the development of mathematical ideas in secondary school mathematics programs or in beginning college mathematics programs. The unit is written for the instructor with step-by-step procedures including lists of needed materials. The exercises in this unit also appear in…
The wide range of Mathematical Apps targeting different mathematical concepts and the various types of mobile devices available present a demanding and challenging problem to the teaching and learning in the field of mathematics. In an attempt to address this issue, a few Apps were selected, implemented and tested in this work. [For complete…
An historical perspective reveals that sophisticated mathematical activity has been going on in the Latino culture for thousands of years. This paper provides a general definition of the area of mathematics education that deals with issues of culture and mathematics (ethnomathematics) and defines what is meant by the term Latino in this essay.…
Falba, Christy J.; Weiss, Maria J.
Presented is an activity which shows how mathematics is used in real life and helps to establish a need for mathematics in students' futures. Adapted from a scavenger-hunt idea, this activity helps students to discover that almost every career makes use of mathematics. (KR)
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2001 conference: "Secondary Mathematics Methods Course with Technology Units: Encouraging Pre-Service Teachers To Use Technology" (Rajee Amarasinghe); "Competency Exams in College Mathematics" (Kathy R. Autrey and Leigh…
This article provides insights into the "Applying Mathematical Processes" resources, developed by the Nuffield Foundation. It features Nuffield AMP activities--and related ones from Bowland Maths--that were designed to support the teaching and assessment of key processes in mathematics--representing a situation mathematically, analysing,…
Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination.
A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…
Mejia-Ramos, Juan Pablo; Fuller, Evan; Weber, Keith; Rhoads, Kathryn; Samkoff, Aron
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…
Stewart, Sepideh; Thomas, Michael O. J.
Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…
Paul, Cynthia S.; Vaidya, Sheila R.
What does it take to change a school's mathematics achievement profile from low to one that is proficient and advanced? Is this transformed achievement profile sustainable? Such is the story presented here, in this three-phase case study of a K-8 urban charter school's mathematics program. The first phase discusses the school's…
Berkman, Robert M.
This article describes connections between chess and mathematics, including examples of activities that connect chess with set theory, patterns, algebra, geometry, combinatorics, and Pascal's triangle. The author observes that competitive games play a dual purpose in advancing the work of mathematics educators: to reinforce a specific skill and to…
Research documenting teachers' fragile understanding of proof and how it is advanced suggests that enhancing the role of proof in school mathematics will demand substantial teacher learning. To date, there is little research detailing what mathematical knowledge might support the teaching of proof or how professional development (PD) might afford…
Engel, Mimi; Claessens, Amy; Watts, Tyler; Farkas, George
Analyzing data from two nationally representative kindergarten cohorts, we examine the mathematics content teachers cover in kindergarten. We expand upon prior research, finding that kindergarten teachers report emphasizing basic mathematics content. Although teachers reported increased coverage of advanced content between the 1998-1999 and…
Chin, Cynthia E.
The history of Fermat's Last Theorem, recounted in the theatrical piece "Fermat's Last Tango," is a useful vehicle for introducing students to the variety of personalities, processes, and products involved in advanced mathematical investigation. The musical's accessible, informative, and positive portrayal of mathematicians and their work is…
Burris, Carol Corbett; Heubert, Jay P.; Levin, Henry M.
This longitudinal study examined the effects of providing an accelerated mathematics curriculum in heterogeneously grouped middle school classes in a diverse suburban school district. A quasi-experimental cohort design was used to evaluate subsequent completion of advanced high school math courses as well as academic achievement. Results showed…
Speer, Natasha M.; Smith, John P., III; Horvath, Aladar
Though written accounts of collegiate mathematics teaching exist (e.g., mathematicians' reflections and analyses of learning and teaching in innovative courses), research on collegiate teachers' actual classroom teaching practice is virtually non-existent. We advance this claim based on a thorough review of peer-reviewed journals where scholarship…
Answers to questions which were asked after the author's various lectures in Australia are gathered here. Topics touched upon include "new" mathematics, unknown constants and free variables, propositional functions, linear algebra, arithmetic and geometry, and student assessment. (MN)
Clements, Douglas H; Sarama, Julie
Preschool and primary grade children have the capacity to learn substantial mathematics, but many children lack opportunities to do so. Too many children not only start behind their more advantaged peers, but also begin a negative trajectory in mathematics. Interventions designed to facilitate their mathematical learning during ages 3 to 5 years have a strong positive effect on these children's lives for many years thereafter.
Chen, W.Y.C.; Louck, J.D.
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). Combinatorics and geometry have been among the most active areas of mathematics over the past few years because of newly discovered inter-relations between them and their potential for applications. In this project, the authors set out to identify problems in physics, chemistry, and biology where these methods could impact significantly. In particular, the experience suggested that the areas of unitary symmetry and discrete dynamical systems could be brought more strongly under the purview of combinatorial methods. Unitary symmetry deals with the detailed description of the quantum mechanics of many-particle systems, and discrete dynamical systems with chaotic systems. The depth and complexity of the mathematics in these physical areas of research suggested that not only could significant advances be made in these areas, but also that here would be a fertile feedback of concept and structure to enrich combinatorics itself by setting new directions. During the three years of this project, the goals have been realized beyond expectation, and in this report the authors set forth these advancements and justify their optimism.
Dawkins, Paul Christian
This study builds upon the framework of classroom norms (Cobb, Wood, & Yackel, 1993) and socio-mathematical norms (Cobb & Yackel, 1996) to understand how non-traditional socio-mathematical norms influence student reasoning and transitions to advanced mathematical thinking in undergraduate real analysis. The research involves a qualitative…
What Works Clearinghouse, 2011
The "University of Chicago School Mathematics Project ("UCSMP") 6-12 Curriculum" is a series of yearlong courses--(1) Transition Mathematics; (2) Algebra; (3) Geometry; (4) Advanced Algebra; (5) Functions, Statistics, and Trigonometry; and (6) Precalculus and Discrete Mathematics--emphasizing problem solving, real-world applications, and the use…
The outcome of American students' performances during international comparisons consistently scoring inadequately in mathematics exposes the crisis of deficient mathematics achievement thus causing deep concerns. Learners who acquire a strong theoretical foundation in mathematics at the primary level thrived later in more advanced level…
Use of technology in the mathematics classroom has the potential to advance children's learning of mathematics and enhance their attitudes about mathematics. When used in conjunction with purposeful planning, teachers can use technological tools to reinforce their pedagogical intentions and to facilitate relevant learning activities for students.…
Bartlo, Joanna Rachel
Although proof has long been viewed as a cornerstone of mathematical activity, incorporating the mathematical practice of proving into classrooms is not a simple matter. In this dissertation I aim to advance research on proof by addressing this issue. In particular, I explore the role proof might play in promoting the learning of mathematics in…
Richard, Jean W.
This paper examines the mathematical and teaching practices of the renowned self-taught Chinese mathematician Hua Loo-keng in the movement of popularizing mathematics in the People's Republic of China. In this movement, Hua Loo-keng taught industrial workers and peasants with a low level of education how to use fairly advanced mathematical methods…
van Ingen, Sarah; Eskelson, Samuel L.; Allsopp, David
The mathematics consultation represents a powerful opportunity for mathematics teachers to leverage the knowledge base of special education professionals to advance equity for students with special education needs. Yet, most teacher preparation programs do not specifically prepare prospective teachers to engage in mathematics-specific…
Fredua-Kwarteng, Eric; Ahia, Francis
Facilitating effective mathematics learning and higher mathematics achievement have long been recognized as a key to the scientific and technological advancement of the African continent. While the central role that language proficiency plays in mathematics teaching and learning has received an overwhelming research attention in the literature…
House, Peggy A.
Describes some mathematical investigations of the necktie which includes applications of geometry, statistics, data analysis, sampling, probability, symmetry, proportion, problem solving, and business. (MKR)
Stylianides, Gabriel J.; Stylianides, Andreas J.
In this article we elaborate a conceptualisation of "mathematics for teaching" as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design…
Jett, Christopher C.
Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
Ma, Xin; McIntyre, Laureen J.
Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…
In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…
Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa
This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…
Koopman, Lodewijk; Brouwer, Natasa; Heck, Andre; Buma, Wybren Jan
Proper mathematical skills are important for every science course and mathematics-intensive chemistry courses rely on a sound mathematical pre-knowledge. In the first-year quantum chemistry course at this university, it was noticed that many students lack basic mathematical knowledge. To tackle the mathematics problem, a remedial mathematics…
Luz, Paul L.
Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.
In this article, the author states that there are selected issues in mathematics instruction that educators should be well aware of when planning lessons and units of study. These issues provide a basis for thought and discussion when assisting pupils to attain more optimally. Purposeful studying of issues guides mathematics teachers in…
Hoffert, Sharon B.
Mathematics is considered the universal language, but students who speak languages other than English have difficulty doing mathematics in English. For instance, because of a lack of familiarity with the problem's context, many have trouble understanding exactly what operations to perform. In the United States, approximately one in seven students…
Articles on theoretical and applied mathematics are introduced. The articles cover information that might be of interest to workers in statistics and information theory, computational aids that could be used by scientists and engineers, and mathematical techniques for design and control.
As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…
This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…
Sheffield, Linda Jensen, Ed.
This book, written on the recommendation of the Task Force on Mathematically Promising Students, investigates issues involving the development of promising mathematics students. Recommendations are made concerning topics such as the definition of promising students; the identification of such students; appropriate curriculum, instruction, and…
Trombley, Carl; And Others
This mathematics curriculum is designed to be taught by the technology education teacher during the power technology class over a period of 2 years. It is intended to be elective in nature; upon successful completion of both years, one-half credit in mathematics is to be awarded. A list of the academic competencies contained in the curriculum…
Sanft, Rebecca; Walter, Anne
St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The lab classes required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs…
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
Louisiana State Dept. of Education, Baton Rouge.
This guide for high school consumer mathematics (one in a set of curriculum guides developed by Louisiana statewide mathematics curriculum committees) contains a course outline, performance objectives, and coordinated activities designed to teach skills that students will need as citizens and consumers. Background on the development,…
EASTCONN Regional Educational Services Center, North Windham, CT.
This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…
Ros, Rosa M.
There are many European countries where Astronomy does not appear as a specific course on the secondary school. In these cases Astronomy content can be introduced by means of other subjects. There are some astronomical topics within the subject of Physics but this talk concerns introducing Astronomy in Mathematics classes. Teaching Astronomy through Mathematics would result in more exposure than through Physics as Mathematics is more prevalent in the curriculum. Generally it is not easy to motivate students in Mathematics but they are motivated to find out more about the universe and Astronomy current events than appears in the media. This situation can be an excellent introduction to several mathematics topics. The teachers in secondary and high school can use this idea in order to present more attractive mathematics courses. In particular some different examples will be offered regarding * Angles and spherical coordinates considering star traces * Logarithms and visual magnitudes * Plane trigonometry related orbital movements * Spherical trigonometry in connection with ecliptic obliquity * Conic curves related to sundial at several latitudes Some students do not enjoy studying Mathematics but they can be attracted by practical situations using Applied Mathematics: Astronomy is always very attractive to teenagers.
The best teaching possible needs to accrue in the mathematics curriculum. Pupils also need to become proficient in using mathematics in every day situations in life. Individuals buy goods and services. They pay for these in different ways, including cash. Here, persons need to be able to compute the total cost of items purchased and then pay for…
Martin, Danny Bernard
While research by scholars has contributed greatly to an emerging knowledge base on Black children and mathematics, there continues to be a dire need for insightful research that de-centers longstanding accounts that have contributed to the construction of Black children as mathematically illiterate and as less than ideal learners relative to…
Stanford Univ., CA. School Mathematics Study Group.
This SMSG study guide is intended to provide teachers who use "Intermediate Mathematics," as a textbook with references to materials which will help them to gain a better understanding of the mathematics contained in the text. For each chapter of the text a brief resume of its content is followed by a list of annotated references which are…
Presents ideas for creating mathematical classroom activities associated with the history of mathematics: calculating sums and products the way ancient Greeks did it, using an abacus or moving stones on a sanded floor, and engaging elementary students through role playing specific mathematicians. Suggests that through such techniques, mathematics…
Teaching mathematics in today's world requires practices and procedures integrated with performance tasks that actively involve students. In this second edition of Designing Rubrics for Mathematics, Eileen Depka clarifies the purpose of rubrics in math instruction and illustrates the relationship between assessment, rubrics, and the National…
As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2002 conference: (1) "Teachers' Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship" (Mara Alagic); (2) "A Fractal Is a Pattern in Your Neighborhood" (Craig N. Bach); (3)…
Stallings, L. Lynn
This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…
The material in this reprint, with minor editorial changes, is from the chapter "Doing the Impossible" in MONKEY BUSINESS by Irving Adler. This 25-page booklet contains brief accounts of historical attempts to prove impossible problems in mathematics. The mathematical recreations in this booklet of geometric constructions include the trisection…
Wohlhuter, Kay A.; Breyfogle, M. Lynn; McDuffie, Amy Roth
Developing deep knowledge and understanding of mathematics is a lifelong process, and building the foundation for teachers' development must begin in preservice preparation and continue throughout one's professional life. While teaching mathematics content courses and methods courses, the authors have found that preservice elementary school…
The debate has gone on for some time in terms of which is more salient for the teacher to be well versed in, mathematical content versus methods and approaches in teaching. Both are salient. They cannot be separated from each other. The mathematics teacher must indeed have broad, in-depth knowledge of subject matter as well as in teaching and…
Varsavsky, Cristina; Anaya, Marta
This article gives an overview of the state of mathematics education in Argentina across all levels, in the regional and world contexts. Statistics are drawn from Mercosur and UNESCO data bases, World Education Indicators and various national time-series government reports. Mathematics results in national testing programmes, Programme for…
Connell, Michael L., Ed.
This document contains the following papers on issues related to mathematics in technology and teacher education: "A Case for Strong Conceptualization in Technology Enhanced Mathematics Instruction" (Michael L. Connell and Delwyn L. Harnisch); "Faculty/Student Collaboration in Education and Math--Using the Web To Improve Student Learning and…
Grassl, Richard M.; Mingus, Tabitha T. Y.
Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)
Fennema, Elizabeth, Ed.; Leder, Gilah C., Ed.
This book reports on various studies that have increased our understanding of why females and males learn different kinds and amounts of mathematics. In particular, this book explicates the Autonomous Learning Behavior model, proposed by Fennema and Peterson, which is a possible explanation of the development of gender differences in mathematics.…
Research indicates that U. S. teachers' mathematical knowledge continues to be weak, and there is an inherent difference between the mathematical knowledge needed to be an effective teacher and that needed by a mathematician. In this article, the author discusses pedagogical content knowledge. According to Schulman (1987), pedagogical content…
Iben, Miriam F.
Examines seventh and eighth grade students in Australia, Japan, and the United States for attitudes related to mathematics, and the relationship these attitudes have to students' development of abstract mathematical thought and spatial relations. Study uses the Iowa Algebra Aptitude Test, Differential Aptitude Test-Spatial Relations, and the…
Monroe, Eula Ewing; Orme, Michelle P.
This article discusses the importance of mathematical vocabulary, difficulties students encounter in learning this vocabulary, and some instructional strategies. Two general methods for teaching vocabulary are discussed: context and explicit vocabulary instruction. The methods are summarized as they apply to mathematical vocabulary instruction and…
This relationship is omnipresent to those who appreciate the shared attributes of these two areas of creativity. The dynamic nature of media, and further study, enable mathematicians and artists to present new and exciting manifestations of the "mathematics in art", and the "art in mathematics". The illustrative images of the relationship--that…
Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.
Nuschler, Alexandra; And Others
The curriculum guide correlates concepts in business mathematics with career-oriented concepts and activities. The curriculum outline format gives the concepts to be taught, matched with related career-oriented performance objectives, concepts, and suggested instructional activities in facing page layouts. The outline is divided into the major…
Flannery, Carol A.
Designed to accompany a series of videotapes, this textbook provides information, examples, problems, and solutions relating to mathematics and its applications in technical fields. Chapter I deals with basic arithmetic, providing information on fractions, decimals, ratios, proportions, percentages, and order of operations. Chapter II focuses on…
Hebert, Michael A.; Powell, Sarah R.
Increasingly, students are expected to write about mathematics. Mathematics writing may be informal (e.g., journals, exit slips) or formal (e.g., writing prompts on high-stakes mathematics assessments). In order to develop an effective mathematics-writing intervention, research needs to be conducted on how students organize mathematics writing and…
Spangler, Denise A.
Presents 11 open-ended questions that can be presented to students and teachers at all educational levels in various formats to assess mathematical beliefs. Questions investigate beliefs toward mathematics, the problem-solving process, mathematicians, and mathematical applications. (MDH)
Meza, Juan; Campbell, Scott; Bailey, David
The role of mathematics in a complex system such as the Internet has yet to be deeply explored. In this paper, we summarize some of the important and pressing problems in cyber security from the viewpoint of open science environments. We start by posing the question 'What fundamental problems exist within cyber security research that can be helped by advanced mathematics and statistics'? Our first and most important assumption is that access to real-world data is necessary to understand large and complex systems like the Internet. Our second assumption is that many proposed cyber security solutions could critically damage both the openness and the productivity of scientific research. After examining a range of cyber security problems, we come to the conclusion that the field of cyber security poses a rich set of new and exciting research opportunities for the mathematical and statistical sciences.
Marr, M Jackson
"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. PMID:25595115
Marr, M Jackson
"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk.
Boisvert, Ronald F.; Donahue, Michael J.; Lozier, Daniel W.; McMichael, Robert; Rust, Bert W.
In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST’s current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of mathematics to measurement science, including the solution of ill-posed inverse problems, characterization of the accuracy of software for micromagnetic modeling, and in the development and dissemination of mathematical reference data. Finally, we comment on emerging issues in measurement science to which mathematicians will devote their energies in coming years. PMID:27500024
Bailey, David H.; Borwein, Jonathan M.
What mathematical discovery more than 1500 years ago: (1) Is one of the greatest, if not the greatest, single discovery in the field of mathematics? (2) Involved three subtle ideas that eluded the greatest minds of antiquity, even geniuses such as Archimedes? (3) Was fiercely resisted in Europe for hundreds of years after its discovery? (4) Even today, in historical treatments of mathematics, is often dismissed with scant mention, or else is ascribed to the wrong source? Answer: Our modern system of positional decimal notation with zero, together with the basic arithmetic computational schemes, which were discovered in India about 500 CE.
Brahmia, Suzanne M.
Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in
The cochlea is an intricate organ in the inner ear responsible for our hearing. Besides acting as a transducer to convert mechanical sound vibrations to electrical neural signals, the cochlea also amplifies and separates the sound signal into its spectral components for further processing in the brain. It operates over a broad-band of frequency and a huge dynamic range of input while maintaining a low power consumption. The present research takes the approach of building cochlear models to study and understand the underlying mechanics involved in the functioning of the cochlea. Both physical and mathematical models of the cochlea are constructed. The physical model is a first attempt to build a life- sized replica of the human cochlea using advanced micro- machining techniques. The model takes a modular design, with a removable silicon-wafer based partition membrane encapsulated in a plastic fluid chamber. Preliminary measurements in the model are obtained and they compare roughly with simulation results. Parametric studies on the design parameters of the model leads to an improved design of the model. The studies also revealed that the width and orthotropy of the basilar membrane in the cochlea have significant effects on the sharply tuned responses observed in the biological cochlea. The mathematical model is a physiologically based model that includes three-dimensional viscous fluid flow and a tapered partition with variable properties along its length. A hybrid asymptotic and numerical method provides a uniformly valid and efficient solution to the short and long wave regions in the model. Both linear and non- linear activity are included in the model to simulate the active cochlea. The mathematical model has successfully reproduced many features of the response in the biological cochlea, as observed in experiment measurements performed on animals. These features include sharply tuned frequency responses, significant amplification with inclusion of activity
Garabedian, Paul R.
Theory has contributed significantly to recent advances in magnetic fusion research. New configurations have been found for a stellarator experiment by computational methods. Solutions of a free-boundary problem are applied to study the performance of the plasma and look for islands in the magnetic surfaces. Mathematical analysis and numerical calculations have been used to study equilibrium, stability, and transport of optimized fusion reactors. PMID:14614129
Mahoney, John F.
Benjamin Banneker, a self-taught African American mathematician, kept a journal containing a number of mathematical puzzles. Explores four of these puzzles, 200 years later, with the aid of 21st century technology. (Author/NB)
Barnett, Carne S.
Presents an overview and analysis of the Mathematics Case Methods Project, which uses cases in order to examine and reflect upon teaching. Focuses on a special kind of teacher knowledge, coined pedagogical-content knowledge. (ASK)
This article is based on a lecture given at the 1978 Easter Course at Padgate College of Higher Education. The lecture is an analysis of the complexity of mathematics teaching and the setting of teaching standards. (MN)
This study examined reciprocal relationships between attitude toward mathematics and mathematics achievement. High school seniors from the Dominican Republic completed mathematics achievement tests and a questionnaire on mathematics attitudes. Results indicated that reciprocal relationships existed, suggesting that the reciprocal nature between…
Changes to the mathematics and science curriculums are designed to increase rigour in mathematics, and place greater emphasis on mathematical content in science subjects at key stages 3, 4 and 5 (ages 11-18). One way to meet the growing challenge of providing increased emphasis on mathematics in the science curriculum is greater collaboration…
Austin, Joe Dan, Ed.
This book provides applications for use in the secondary school mathematics curriculum by selecting related articles appearing in the "Mathematics Teacher" during the last 15 years. The articles are grouped into chapters that reflect the main secondary school mathematics courses and categorized by the highest level of mathematics needed for…
Fish, Michael Charles
This study examines how critical mathematical literacy teachers conceptualize their practices and how those practices were demonstrated in the classroom. Practices were considered from an ontology of mathematics education, specific to critical mathematical literacy, in which classroom interactions question what it means to do mathematics as an…
Ipek, A. Sabri; Berigel, Muhammed; Albayrak, Mustafa
Role of technology which is an important tool for new approaches in learning mathematics is rapidly increasing at focus point of learning mathematics with new designs. One of the biggest factors at learning and instructing technology based mathematic education is attitudes of mathematics teachers towards technology. At this study, attitudes of…
Kaya, Defne; Aydin, Hasan
Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Bosshardt, William; Watts, Michael
The National Center for Educational Statistics' Baccalaureate and Beyond study, which had data from its second follow-up released in 1999, drew a nationally representative sample of approximately 11,000 graduates in the 1992-93 academic year. Using transcript data from the study, the authors report what economics courses students in different…
Since 2007 the author has been teaching a hybrid Information Literacy course at Lakeview High School in Battle Creek, Michigan. It combines an online information literacy focus with real-world library work experience in her media center. This blended course has just been revised so that high school graduates will be able to fulfill Michigan's…
Srivastava, H M; Baleanu, Dumitru; Li, Changpin
This Special Focus Issue contains several recent developments and advances on the subject of Fractional Dynamics and its widespread applications in various areas of the mathematical, physical, and engineering sciences. PMID:27586617
Srivastava, H. M.; Baleanu, Dumitru; Li, Changpin
This Special Focus Issue contains several recent developments and advances on the subject of Fractional Dynamics and its widespread applications in various areas of the mathematical, physical, and engineering sciences.
Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis
Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology.
Australian secondary school systems offer three levels of senior (year 12) mathematics studies, none of them compulsory: elementary, intermediate and advanced. The intermediate and advanced studies prepare students for further mathematics studies at university level. In the state of Victoria, there are two versions of intermediate mathematics: one where students learn and are examined with a computer algebra system (CAS) and another where students can only use scientific calculators. This study compares the performance of 1240 students as they transitioned to traditional university-level mathematics and according to whether they learned intermediate mathematics with or without the assistance of a CAS. This study concludes that students without CAS show a slight advantage, but the most important factor affecting student performance is the uptake of advanced-level mathematics studies in secondary school.
Pearson, Jennifer; Crissey, Sarah R.; Riegle-Crumb, Catherine
This study explores the association between sports participation and course taking in high school, specifically comparing subjects with varied gendered legacies—science and foreign language. Analyses of a nationally representative longitudinal sample (N=5,447) of U.S. adolescents from the National Longitudinal Study of Adolescent Health and the linked Adolescent Health and Academic Achievement transcript study show that male and female athletes are more likely than non-athletes to take both advanced foreign language and Physics, largely because of their higher academic orientation. However, the association between sports participation and course taking was strongest for girls’ Physics coursework, suggesting that sports may provide girls with a unique opportunity to develop the skills and confidence to persevere in the masculine domain of science. PMID:20221304
Davies, Robin; Hodge, Terrell; Enyedi, Alexander
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955
Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.
Cuevas, Gilbert, Ed.; Driscoll, Mark, Ed.
The National Council of Teachers of Mathematics'"Curriculum and Evaluation Standards for School Mathematics" and "Professional Standards for Teaching Mathematics" reflect the belief that all students can learn a significant core of high-quality mathematics. Recognizing the magnitude of the task of reaching all students, this book was put together…
In this paper I use situated and socio-cultural perspective (Gee, 1996 & 1999) to examine descriptions of mathematical discourse and an example of student talk in a mathematics classroom. Using this example, I discuss how the distinction between everyday and mathematical discourse can help or hinder us in hearing the mathematical content in…
Kloosterman, Peter; Tassel, Janet; Ponniah, Ann G.; Esses, N. Kathryn
This study examined students' perceptions about gender and the subject of mathematics, as well as gender and mathematics learning. Secondary school students and pre-service elementary teachers were surveyed using the Mathematics as a Gendered Domain and Who and Mathematics instruments developed by Leder and Forgasz (Leder, 2001). The data indicate…
Anhalt, Cynthia Oropesa; Cortez, Ricardo
Mathematical modeling, in which students use mathematics to explain or interpret physical, social, or scientific phenomena, is an essential component of the high school curriculum. The Common Core State Standards for Mathematics (CCSSM) classify modeling as a K-12 standard for mathematical practice and as a conceptual category for high school…
Cohen, Marion D.
Today there are many categories of mathematics literature, including fiction and poetry. Mathematics fiction appears in such anthologies as "Fantasia Mathematica" (Fadiman 1958, 1997) and "The Mathematical Magpie" (Fadiman 1962, 1997). In addition, mathematics fiction is featured at http://kasmana.people.cofc.edu/MATHFICT.…
Lim, Vanessa K.; Wilson, Anna J.; Hamm, Jeff P.; Phillips, Nicola; Iwabuchi, Sarina J.; Corballis, Michael C.; Arzarello, Ferdinando; Thomas, Michael O. J.
Objective: To examine whether or not university mathematics students semantically process gestures depicting mathematical functions (mathematical gestures) similarly to the way they process action gestures and sentences. Semantic processing was indexed by the N400 effect. Results: The N400 effect elicited by words primed with mathematical gestures…
The Summer Institute for Mathematics and Science Teachers (SIMS) was to provide training for science and mathematics educators in strategies and techniques to use for educating and motivating historically under-represented populations. The Institute featured 40 hours of training over five days, July 13-17, 1993 plus half-day follow-up training November 13, 1993 and April 30, 1994. The objective of the training was to include sensitization to cultural and gender issues, and to instruct participants in the utilization of a variety of techniques and activities for encouraging historically under-represented groups to take more advanced science and mathematics courses.
Goodson, Joshua E.
This is a dissertation about the beliefs that mathematics majors have about mathematics and how their beliefs are affected by the introduction of mathematics research. The mathematics research presented to the students dealt with counting regular orbits of an action. Research has shown that the beliefs that teachers hold about mathematics…
Dickerson, David S.; Doerr, Helen M.
Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were…
The relationship of attitudes toward mathematics to mathematics performance, gender, mathematics course-taking plans, and career interests were investigated. Students enrolled in public middle and high school mathematics courses (722 male, 794 female) served as subjects. The Fennema-Sherman Math Attitude scales were used to measure attitudes…
Gaber, David; Schlimm, Dirk
Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. PMID:26263425
Sheryn, Louise; Ell, Fiona
Debates about how undergraduate mathematics should be taught are informed by different views of what it is to learn and to do mathematics. In this qualitative study 10 students enrolled in an advanced undergraduate course in mathematics shared their views about how they best learn mathematics. After participating in a semester-long course in combinatorics, taught using a non-traditional, formal group work approach, the 10 students shared their views about how such an approach fitted in with their experience of learning mathematics. A descriptive thematic analysis of the students' responses revealed that despite being very comfortable with the traditional approach to learning new mathematics, most students were open to a formal group work approach and could see benefits from it after their participation. The students' prior conceptions of the goal of undergraduate mathematics learning and their view of themselves as 'mathematicians' framed their experience of learning mathematics in a non-traditional class.
Dawson, A. J. Sandy
The first goal of this Project is the development of elementary school mathematics curricula sensitive to indigenous mathematical thought and experience. A necessary prerequisite for the achievement of this goal is to recapture and honor the mathematics developed and practiced in the Micronesian communities. This is the Project's second goal. The third goal of the project is to build local capacity by offering advanced degree opportunities to the indigenous mathematics educators who transform what they find in their local cultural practices into grades 1, 4, and 7 mathematics curriculum units.
Mokhtar, Siti Fairus; Ali, Noor Rasidah; Rashid, Nurazlina Abdul
This article described a statistical study of students' perception in mathematics. The objective of this study is to identify factors related to perception about learning mathematics among non mathematics' student. This study also determined the relationship between of these factors among non mathematics' student. 43 items questionnaires were distributed to one hundred students in UiTM Kedah who enrolled in the Business Mathematics course. These items were measured by using a semantic scale with the following anchors: 1 = strongly disagree to 7 = strongly agree. A factor analysis of respondents were identified into five factors that influencing the students' perception in mathematics. In my study, factors identified were attitude, interest, role of the teacher, role of peers and usefulness of mathematics that may relate to the perception about learning mathematics among non mathematics' student.
Astronomy in South Asia's Sanskrit tradition, apparently originating in simple calendric computations regulating the timing of ancient ritual practices, expanded over the course of two or three millennia to include detailed spherical models, an endless variety of astrological systems, and academic mathematics in general. Assimilating various technical models, methods, and genres from the astronomy of neighboring cultures, Indian astronomers created new forms that were in turn borrowed by their foreign counterparts. Always recognizably related to the main themes of Eurasian geocentric mathematical astronomy, Indian astral science nonetheless maintained its culturally distinct character until Keplerian heliocentrism and Newtonian mechanics replaced it in colonial South Asia's academic mainstream.
Castro, Mario; Lythe, Grant; Molina-París, Carmen; Ribeiro, Ruy M.
Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered. PMID:27051512
Castro, Mario; Lythe, Grant; Molina-París, Carmen; Ribeiro, Ruy M
Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling-experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered.
Many of Earth's glaciers are currently shrinking and it is expected that this trend will continue as global warming progresses. To virtually reproduce the evolution of glaciers and finally to predict their future, one needs to couple models of different disciplines and scales. Indeed, the slow motion of ice is described by fluid mechanics equations while the daily snow precipitations and melting are described by hydrological and climatic models. Less visible, applied mathematics are essential to run such a coupling at two different levels: by solving numerically the underlying equations and by seeking parameters using optimisation methods. This talk aims to make visible the role of mathematics in this area. I will first present a short educational film I have made for the "Mathematics of Planet Earth 2013", which is an introduction to the topic. To go further, solving the mechanical model of ice poses several mathematical challenges due to the complexity of the equations and geometries of glaciers. Then, I will describe some strategies to deal with such difficulties and design robust simulation tools. Finally, I will present some simulations of the largest glacier of the European Alps, the Aletsch glacier. As a less unexpected application, I will show how these results allowed us to make a major advance in a police investigation started in 1926.
Rozek, Christopher S.; Hyde, Janet S.; Svoboda, Ryan C.; Hulleman, Chris S.; Harackiewicz, Judith M.
A foundation in science, technology, engineering, and mathematics (STEM) education is critical for students' college and career advancement, but many U.S. students fail to take advanced mathematics and science classes in high school. Research has neglected the potential role of parents in enhancing students' motivation for pursuing STEM courses.…
Wilson, W. Stephen
This article first describes some of the basic skills and knowledge that a solid elementary school mathematics foundation requires. It then elaborates on several points germane to these practices. These are then followed with a discussion and conclude with final comments and suggestions for future research. The article sets out the five…
Jones, Karrie; Jones, Jennifer L.; Vermette, Paul J.
By examining how people learn, the educational theories of Dewey, Piaget, Vygotsky and Bruner can be synthesized to give this set of core Constructivist principles. Principles of effective mathematics teaching: (1) allows learning that is "active" and "reflective". Students are required to transfer key concepts to new situations; (2) allows…
Noblitt, Bethany A.; Buckley, Brooke E.
Teams, pit stops, clues, time limits, fast forwards, challenges, and prizes are all components of the CBS hit show "The Amazing Race." They were also elements of the Amazing Mathematical Race sponsored by the Math and Stats Club at Northern Kentucky University in April 2009. Held in recognition of Math Awareness Month, which is advocated by the…
Lichtenberg, Betty K., Ed.; Troutman, Andria P., Ed.
The 26 activities described in this volume deal with a wide variety of mathematical ideas. Most of the activities are appropriate for grades 6-9; many could be used with older or younger groups as well. All activities are described in detail; some descriptions include sample worksheets, and several provide suggestions for followup activities. The…
Oregon State Univ., Corvallis. Vocational-Technical Education Dept.
This handbook was developed to help the vocational teacher aid students in solving mathematical problems in vocational education classes. Most of the examples in the handbook were derived from metal-working and industrial mechanics classes; however, the procedures explained through them will work in any vocational class. The handbook is divided…
Bureau of Indian Affairs (Dept. of Interior), Window Rock, AZ.
Heavy emphasis is placed on development of understanding of arithmetic in this mathematics curriculum prepared specifically for Navajo children and intended for use in reservation schools. Materials are presented so that only when a given concept is understood are skills associated with it and a written format introduced. Learning activities…
Houssart, Jenny; Roaf, Caroline; Watson, Anne
This book looks at how practitioners have focused on the fully educational application of intellect to the problem of developing mathematical thinking among one's pupils. Each chapter demonstrates reflective minds at work, relying on close observation, willingness to understand the student's thinking processes and patient commitment to students…
Portales Public Schools, NM.
This curriculum guide provides aid in organizing and planning for the mathematical needs of the individual classroom. It is recommended that: (1) each teacher study the entire curriculum to become familiar with the concepts that interlock and blend all the grades together, and (2) all students with average ability master 70% of the skills. The…
Stevenson, Frederick W.
This book attempts to introduce students to the creative aspects of mathematics through exploratory problems. The introduction presents the criteria for the selection of the problems in the book. Criteria indicate that problems should: be immediately attractive, require data to be generated or gathered, appeal to students from junior high school…
Fernandez, Maria L.
Presents examples of students' work when they are engaged in problem solving and reasoning tasks as they determine how to fill bottles with water to create musical notes by blowing across the tops of the bottles, and as they create mathematical models that represent these notes. (ASK)
This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)
Clary, Joseph R.; Nery, Karen P.
This set of three modules was designed for use primarily to help teach and reinforce the basic mathematics skills in drafting classes. The modules are based on the needs of drafting students in beginning courses as determined by a survey of teachers across North Carolina. Each module consists of basic information and examples and problem sheets…
Popelka, Susan R.
Tiny prisms in reflective road signs and safety vests have interesting geometrical properties that can be discussed at any level of high school mathematics. At the beginning of the school year, the author teaches a unit on these reflective materials in her precalculus class so that students can review and strengthen their geometry and trigonometry…
Mireles, Selena Vasquez
The change from students learning all subjects together in a one-room schoolhouse to learning in classes separated by subject and grade resulted in distinct disciplines such as social studies, mathematics, science, and English. What was lost was the unified, holistic curriculum that a one-room setting required. Since students move from…
Lee, Joohi; Autry, Mary Murray; Fox, Jill; Williams, Cynthia
A sample of 244 children (average age: 61 months) and their parents from the Dallas and Fort Worth (DFW) metroplex area in Texas were surveyed to investigate children's mathematics readiness. This study was conducted as part of a project funded by a local child care council, composed of business, civic, and education leaders in the community. The…
Battista, Michael T.
Presents a series of 13 activities to explore the mathematics of baseball. Activities examine the numerical measures of player statistics and team standings and the geometry of baseball. Discusses the use of computer spreadsheets and LOGO computer simulations to study the concepts embodied in the activities. (MDH)
The Williams Review (Dept. for Children, Schools and Families, 2008) is significantly important to all early years and primary educationalists, including those who are involved in teaching mathematics to the next generation of primary school teachers. The report, compiled as a result of this review, sets out the ways that children in primary…
Dreyfus, Tommy; Eisenberg, Theodore
Discusses the creed in symmetry and the omnipresence of symmetrical relationships in mathematics and nature, discusses mathematicians' attraction toward looking for symmetrical relationships as an unstated problem-solving heuristic, and shows how symmetry can be used as a didactical tool. (Author/MKR)
North Carolina State Dept. of Public Instruction, Raleigh.
GRADES OR AGES: Secondary school. SUBJECT MATTER: Consumer mathematics including--money management, transportation, probability, swindles and gyps, insurance, housing, taxes, consumer credit, banks, savings, and investments. ORGANIZATION AND PHYSICAL APPEARANCE: The guide is divided into ten parallel units, one for each of the above areas, which…
Barger, Rita H.; Jarrah, Adeeb M.
March 14 is special because it is Pi Day. Mathematics is celebrated on that day because the date, 3-14, replicates the first three digits of pi. Pi-related songs, websites, trivia facts, and more are at the fingertips of interested teachers and students. Less celebrated, but still fairly well known, is National Metric Day, which falls on October…
Parma City School District, OH.
Five activities are presented in this student workbook designed for exploration of a career in computers, and the mathematics related to that career. Included are activities on basic computer language, flow charts, and basic computer programming. Each activity includes the objective, materials needed, and information for completing the activity.…
Whitin, Phyllis; Whitin, David J.
The habit of looking for patterns, the skills to find them, and the expectation that patterns have explanations is an essential mathematical habit of mind for young children (Goldenberg, Shteingold, & Feurzeig 2003, 23). Work with patterns leads to the ability to form generalizations, the bedrock of algebraic thinking, and teachers must nurture…
This article describes an activity that can be carried out in one of the final classes of Italian secondary schools. The aim of the activity is to stimulate pupil curiosity, demonstrating that Mathematics is not a barren subject and allowing the students, according to an interdisciplinary point of view, to investigate some literary works and the…
The curriculum guide offers a course of training in the fundamentals of mathematics as applied to baking. Problems specifically related to the baking trade are included to maintain a practical orientation. The course is designed to help the student develop proficiency in the basic computation of whole numbers, fractions, decimals, percentage,…
The definition is an important language form in the register of mathematics. Students need to understand the structure of a definition so that they can make sense of the definitions they encounter and so that they can construct their own definitions as part of organising their thoughts about the concepts they have explored. This article suggests…
White, Tobin; Martin, Lee
This paper argues for an approach to mobile learning that leverages students' informal digital practices as resources for designing mathematics classrooms activities. We briefly describe two exploratory designs along these lines, one featuring the use of photos taken by students outside class and the other centered on their recording and…
Bureau of Naval Personnel, Washington, DC.
The second of three volumes of a mathematics training course for Navy personnel, this document contains material primarily found at the college level. Beginning with logarithms and trigonometry, the text moves into vectors and static equilibrium (physics). Coordinate geometry, conic sections, and the tangents, normals, and slopes of curves follow.…
The Nobel prize winning physicist Richard Feynman (2007) famously enthused about "the pleasure of finding things out". In day-to-day classroom life, however, it is easy to lose and undervalue this pleasure in the process, as opposed to products, of mathematics. Finding things out involves a journey and is often where the learning takes place.…
Pratt, Dave; Noss, Richard
Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as "designing for abstraction." In this paper, we draw on detailed design experiments from our research on children's understanding about chance and distribution to re-present this work as a case study in designing…
Reviews CATUSPLOT, a mathematics utility aimed at high school algebra through college-level calculus. Basic program capabilities include plotting, tabulating, integrating, and locating of intersections of functions composed of combinations of polynomial, trigonometric, and exponential functions. Rated excellent on all areas examined…
Yee, Lee Peng
A decade of PMRI saw the changes in the classroom in some of the primary schools in Indonesia. Based on observation, we can say that though the mathematics syllabus in Indonesia did not change, its curriculum has changed under the movement of PMRI. In this article, we put in writing some of the experience gained through the involvement in…
This article presents a way to engage students in mathematics learning by using the innovative instructional method of storigami. The author shares reactions from teachers who have used her storigami techniques in their classes and provides an example of storigami using the Norwegian fable "The Dog and the Mountain." (Contains 6 figures.)
Bruun, Faye; Diaz, Joan M.; Dykes, Valerie J.
Students may excel in computation, but their ability to apply their skills will suffer if they do not understand the math vocabulary used in instructions and story problems. This action research project examines two methods for strengthening students' ability to communicate mathematically: (1) Journal writing and peer discussion; and (2) The…
Describes the most enduring link between Napoleon and mathematics as the geometric result known as Napoleon's Theorem, which states that if equilateral triangles are drawn on the three sides of any triangle, the line segments joining the centers of these equilateral triangles will themselves form an equilateral triangle. (ASK)
When considering the use of games for teaching mathematics, educators should distinguish between an "activity" and a "game". Gough (1999) states that "A 'game' needs to have two or more players, who take turns, each competing to achieve a 'winning' situation of some kind, each able to exercise some choice about how to move…
Thiering, Jeannette; And Others
This Australian document is a guide to teaching mathematics as it relates to specific work situations. After a brief introduction, chapter 1 looks at problem solving, advises teachers to lower the reading level and thus raise the understandability of written math problems, and describes a four-step problem-solving process. Chapter 2 outlines a…
Conradie, Jurie; Frith, John
Presents an alternative way for testing a student's understanding of theory in a tertiary mathematics course. Provides two sample questions and discusses the advantages and disadvantages of the method. Argues that the method is an acceptable and flexible means of testing students and can be adapted to use in other contexts as well. (Author/ASK)
Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…
Leutzinger, Larry, Ed.
This book contains articles that help to further the process of reform in the middle grades, recognizing that the knowledge acquired during these years greatly affects how well the secondary school curriculum will attain its goals. Critical issues facing middle grade classes in particular and all mathematics classrooms in general are discussed.…
Olson, Alton T.
This booklet is a revised edition of Donovan Johnson's "Paper Folding for the Mathematics Class" (ED 077 711). It begins with directions for folding basic constructions such as as a straight line, the line perpendicular to a given line passing through a given point, and the bisector of an angle. Subsequent chapters cover concepts related to…
Zack, Laurie; Fuselier, Jenny; Graham-Squire, Adam; Lamb, Ron; O'Hara, Karen
Our study compared a flipped class with a standard lecture class in four introductory courses: finite mathematics, precalculus, business calculus, and calculus 1. The flipped sections watched video lectures outside of class and spent time in class actively working on problems. The traditional sections had lectures in class and did homework outside…
In this article, the author looks at ways of creating conditions to bring about learning. If one is to "arrange conditions to bring about learning," one needs written guidance and support systems. Two books that discusses how to arrange these conditions are: "Thinking Mathematically" by John Mason with Leone Burton and Kaye Stacey and "Starting…
Mathematics teachers are both more difficult to attract and more difficult to retain than social sciences teachers. This fact is not unique to the United States; it is reported as being a problem in Europe as well (Howson, 2002). In the United States, however, the problem is particularly preoccupying. Because of the chronic teacher shortages and…
COLICCHIO, ANTOINETTE J.
THE NEEDLE TRADES INDUSTRY CONSISTS OF THREE TYPES OF ESTABLISHMENTS -- THE REGULAR MANUFACTURERS, THE APPAREL JOBBERS, AND THE CONTRACTORS. THE FUNCTIONS INCLUDED COVER A WIDE SCOPE FROM BUYING OF RAW MATERIAL TO SELLING OF THE FINISHED APPAREL. THE PURPOSE OF THIS STUDY GUIDE IS TO FURNISH BASIC KNOWLEDGE IN MATHEMATICS AND DEVELOP SKILL IN…
DORNFIELD, BLANCHE E.
THE UNDERSTANDING AND MASTERY OF FUNDAMENTAL MATHEMATICS IS A NECESSARY PART OF COMMERCIAL FOODS WORK. THIS STUDENT HANDBOOK WAS DESIGNED TO ACCOMPANY A COMMERCIAL FOODS COURSE AT THE HIGH SCHOOL LEVEL FOR STUDENTS WITH APPROPRIATE APTITUDES AND COMMERCIAL FOOD SERVICE GOALS. THE MATERIAL, TESTED IN VARIOUS INTERESTED CLASSROOMS, WAS PREPARED BY…
New York City Board of Education, Brooklyn, NY. Div. of Computer Information Services.
This manual provides a resource for mathematics teachers who wish to take advantage of the extensive library of computer software materials available to expand and strengthen classroom instruction. Classroom management procedures, software duplication guidelines, copying procedures of diskettes for MS DOS and Apple II computers, and methods for…
Vaughn, Christy H.
This qualitative study addressed the perceptions toward the study of mathematics by middle school students who had formerly been in a remedial mathematics program. The purpose of the study was to explore the past experiences of nine students in order to determine what is needed for them to feel successful in mathematics. The conceptual framework…
Moreira, Candida Queiroz
Investigated stresses confronted by Portuguese secondary mathematics teachers during the first semester in a master's course, Perspectives on Mathematics Education, noting how they negatively affected teachers' self-confidence and morale and discussing fundamental issues teachers addressed in bridging the academic mathematics and mathematics…
Erdogan, Ahmet; Yazlik, Derya Ozlem; Erdik, Cengiz
The main purpose of this study was to research mathematics teacher candidates' perceptions about the concept of "mathematics" through the use of metaphors. The research is conducted during 2012-2013 academic year, on a group of 111 mathematics teacher candidates at the Education Faculty of a University in Turkey. To collect the research…
Jankvist, Uffe Thomas
This article discusses the integration of history of modern applied mathematics in mathematics education as well as the possible teaching and learning benefits of introducing a newer history of mathematics over an old(er) one--something that seems to be done most often when integrating history. Three cases of the history of modern applied…
This project was concerned with the development of mathematical models of elementary mathematics learning and performance. Probabilistic finite automata and register machines with a finite number of registers were developed as models and extensively tested with data arising from the elementary-mathematics strand curriculum developed by the…
Bautista, Alfredo; Wilkerson-Jerde, Michelle H.; Tobin, Roger G.; Brizuela, Bárbara M.
This paper describes the ideas that mathematics teachers (grades 5-9) have regarding mathematical models of real-world phenomena, and explores how teachers' ideas differ depending on their educational background. Participants were 56 United States in-service mathematics teachers. We analyzed teachers' written responses to three open-ended…
Until recently there have not been many links to students' culture in the mathematics classroom. This may be one of the major barriers to achievement of many groups historically underrepresented in mathematics, for these students may see mathematics as a subject that has very little meaning or value for their current or future lives. This digest…
Harrell, Gregory K.
This article illustrates how to integrate mathematics with social issues. Social issues discussed in the newspaper provide a rich context for connecting mathematical activities to the real world. The sample activities focus on measurement concepts. (Contains 2 figures.)
Kirtland, Joseph; Hoh, Pau-San
Describes the development of an integrated approach for teaching mathematics and writing to freshmen. The goals are to strengthen mathematical skills, develop writing competencies, and foster interdisciplinary awareness. (Author/MM)
Kim, K. H.; And Others
Provides a survey of models that use mathematics in a variety of fields of social science. Discusses specifically mathematical applications in demography, economics, management, political science, psychology, sociology, and other areas. Proposes four unsolved problems. (20 references) (MDH)
Salmon, Robert; And Others
The effect of an advance organizer on post test performance was studied in a 2 X 2 X 2 factorial design with the effects of the organizer, pretest and mathematics learning passage controlled. An advance organizer of approximately 500 words and a learning passage of approximately 1,000 words were developed. A 41-item multiple choice test based on…
Many people believe that mathematics provides a model of what thinking is, or should be. They imagine that mathematical thinking always proceeds in a logically rigorous, step-by-step fashion from one truth to another, like a formal proof or a computer program. In fact, insights in mathematics -- whether they are the scholar's breakthroughs or the…
Rosenstein, Joseph G.; And Others
The New Jersey Mathematics Curriculum Framework is based on the "Mathematics Standards" adopted by the New Jersey State Board of Education on May 1, 1996, and is intended to provide guidance to teachers, administrators, and districts that will help them translate a vision of exemplary mathematics education into reality. It includes information and…
The relationships between mathematics, mathematics education and issues such as social justice and equity have been addressed by the sociopolitical tradition in mathematics education. Others have introduced explicit discussion of ethics, advocating for its centrality. However, this is an area that is still under developed. There is a need for an…
Offers examples of what infants and toddlers might do in early childhood settings, how these behaviors are related to mathematics, and what teachers can do to encourage the natural mathematical interests of this age group. Asserts that teachers' interactions with children are vitally important to children's understanding of early mathematics. (KB)
Hegedus, Stephen John; Moreno-Armella, Luis
We present epistemological ruptures that have occurred in mathematical history and in the transformation of using technology in mathematics education in the twenty-first century. We describe how such changes establish a new form of digital semiotics that challenges learning paradigms and mathematical inquiry for learners today. We focus on drawing…
Lobato, Joanne; Hohensee, Charles; Rhodehamel, Bohdan
Even in simple mathematical situations, there is an array of different mathematical features that students can attend to or notice. What students notice mathematically has consequences for their subsequent reasoning. By adapting work from both cognitive science and applied linguistics anthropology, we present a focusing framework, which treats…
Sriraman, Bharath, Ed.
The interaction of the history of mathematics and mathematics education has long been construed as an esoteric area of inquiry. Much of the research done in this realm has been under the auspices of the history and pedagogy of mathematics group. However there is little systematization or consolidation of the existing literature aimed at…
With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…
Although breaking down a mathematical problem into smaller parts can often be an effective solution strategy, when the same reductionist approach is applied to mathematics pedagogy the effects are far from beneficial for students. Mathematics pedagogy in UK schools is gaining an increasingly reductionist flavour, as seen in an excessive focus on…
Parker, Renee; Breyfogle, M. Lynn
Beginning in third grade, Pennsylvania students are required to take the Pennsylvania State Standardized Assessment (PSSA), which presents multiple-choice mathematics questions and open-ended mathematics problems. Consistent with the Communication Standard of the National Council of Teachers of Mathematics, while solving the open-ended problems,…
This paper outlines problems which are central to the psychological foundations of mathematics. Discussed are the relations that exist between psychological and classical foundations of mathematics. It is shown how the inadequacies of current learning theories which account for complex mathematics learning may be made explicit for appropriate…
Mathematical knowledge has developed from human activities through thousands of years and is bound to the world and cultures that men and women experience. One can say that mathematics is rooted in humans' everyday life, an environment where people reach agreement regarding principles in mathematics. Through interaction with worldly phenomena and…
Copley, Juanita V., Ed.
Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining…
Research suggests that understanding new images of mathematics is very challenging and can contribute to teacher resistance. An explicit exploration of personal views of mathematics may be necessary for pedagogical change. One possible way for exploring these images is through mathematical metaphors. As metaphors focus on similarities, they can be…
Cemen, Pamala Byrd
This paper attempts to generate a comprehensive description of the nature of mathematics anxiety through a synthesis of: (1) the general and test anxiety literatures applied to mathematics anxiety; (2) the mathematics anxiety literature, and (3) case studies developed through in-depth interviews. The indepth interviews were conducted with seven…
Mann, Eric L.
For the gifted mathematics student, early mastery of concepts and skills in the mathematics curriculum usually results in getting more of the same work and/or moving through the curriculum at a faster pace. Testing, grades, and pacing overshadow the essential role of creativity involved in doing mathematics. Talent development requires creative…
Koshy, Valsa, Ed.; Murray, Jean, Ed.
Now in a fully updated second edition, "Unlocking Mathematics Teaching" is a comprehensive guide to teaching mathematics in the primary school. Combining theory and practice, selected experts outline the current context of mathematics education. They suggest strategies, activities and examples to help develop readers understanding and confidence…
Leder, Gilah C., Ed.
This book addresses the link between student learning of mathematics, the teaching method adopted in the mathematics classroom, and the assessment procedures used to determine and measure student knowledge. Fifteen chapters address issues that include a review of different models of mathematics learning and assessment practices, three contrasting…
Wiles, Clyde A., Ed.; Schoon, Kenneth J., Ed.
This booklet contains mathematics unit plans for Algebra 1, Geometry, Math for Technology, Mathematical Problem Solving, and Pre-Algebra developed by PACE (Promoting Academic Excellence In Mathematics, Science & Technology for Workers of the 21st Century). Each unit plan contains suggested timing, objectives, skills to be acquired, workplace…
This essay discusses inservice professional development and suggests that any improvement in mathematics education must begin with teachers already in the classroom. It includes three examples of mathematical presentations in professional development made in Californian schools relating to discrete mathematics, connections, and technology. (MM)
Hefty, Lukas J.
The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…
Identification and development of giftedness is a major task of mathematics teachers worldwide. An early identification of gifted children in mathematics can have a number of benefits, like, providing opportunities for the nourishment of their talent, saving them from burnout, and proper utilisation of mathematical talent in future. As creativity…
Nagle, Courtney R.; Styers, Jodie L.
Although many factors affect students' mathematical activity during a lesson, the teacher's selection and implementation of tasks is arguably the most influential in determining the level of student engagement. Mathematical tasks are intended to focus students' attention on a particular mathematical concept and it is the careful developing and…
Ferri, Rita Borromeo
Teaching and learning of mathematical modelling has become a key competence within school curricula and educational standards in many countries of the world. The term mathematical modelling, its meaning, and how it can be implemented in mathematics lessons have been intensively discussed during several Conferences of the European Society for…
Scillieri, Elissa Mains
International tests indicate that United States students have been outscored by other countries in the area of mathematics. Researchers warn that elementary mathematics curricula and instruction in this country is not designed around helping students achieve mathematics proficiency. Much of this could also be attributed to the weak development and…
History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necessitate ever greater particularity whereas mathematics and…
Matney, Gabriel T.
To develop second-grade students' confidence and ease, this author presents examples of learning tasks (Number of the Day, Word Problem Solving, and Modeling New Mathematical Ideas) that align with Common Core State Standards for Mathematics and that build mathematical fluency to promote students' creative expression of mathematical…
Mathews, Susann M.
This article describes a mathematical model that connects mathematics with social studies. Students use mathematics to model independent versus convoyed ship deployments and sinkings to determine if the British should have convoyed their merchant ships during World War I. During the war, the British admiralty opposed sending merchant ships grouped…