Introductory Mathematics for Quantum Chemistry

An elementary discussion of some of the mathematics employed in studying Quantum Chemistry in a style appropriate for persons who have not taken advanced mathematical instruction.

Supporting Whole-Class Collaborative Inquiry in a Secondary Mathematics Classroom

Recent mathematics education reform efforts call for the instantiation of mathematics classroom environments where students have opportunities to reason and construct their understandings as part of a community of learners. Despite some successes, traditional models of instruction still dominate the educational landscape. This limited success can be attributed, in part, to an underdeveloped understanding of the roles teachers must enact to successfully organize and participate in collaborative classroom practices. Towards this end, an in-depth longitudinal case study of a collaborative high school mathematics classroom was undertaken guided by the following two questions: What roles do these collaborative practices require of teacher and students? How does the community’s capacity to engage in collaborative practices develop over time? The analyses produced two conceptual models: one of the teacher’s role, along with specific instructional strategies the teacher used to organize a collaborative learning environment, and the second of the process by which the class’s capacity to participate in collaborative inquiry practices developed over time.

A case study of teachers' mathematics content knowledge and attitudes toward mathematics and teaching

This study intended to measure teacher mathematical content knowledge both before and after the first year of teaching and taking graduate teacher education courses in the Teach for America (TFA) program, as well as measure attitudes toward mathematics and teaching both before and after TFA teachers’ first year. There was a significant increase in both mathematical content knowledge and attitudes toward mathematics over the TFA teachers’ first year teaching. Additionally, several significant correlations were found between attitudes toward mathematics and content knowledge. Finally, after a year of teaching, TFA teachers had significantly better attitudes toward mathematics and teaching than neutral.

The Effect of Direct Instruction versus Discovery Learning on the Understanding of Science Lessons by Second Grade Students

This study examined the effectiveness of discovery learning and direct instruction in a diverse second grade classroom. An assessment test and transfer task were given to students to examine which method of instruction enabled the students to grasp the content of a science lesson to a greater extent. Results demonstrated that students in the direct instruction group scored higher on the assessment test and completed the transfer task at a faster pace; however, this was not statistically significant. Results also suggest that a mixture of instructional styles would serve to effectively disseminate information, as well as motivate students to learn.

Symposium on mathematics for engineering students being the proceedings of the joint sessions of the Chicago section of the American mathematical society and Section A, Mathematics, and Section D, Mechanical science and engineering of the American Association for the Advancement of Science held at the University of Chicago December 30 and 31, 1907.

Caption title: The American Association for the Advancement of Science. Section D--Mechanical science and engineering. Engineering Mathematics symposium.

Mathematical instruction in France.

Appendices C and D "for later publication."

Mathematics assessment report, Spring 1977 /

WI docs. no.: Ed.3/2:9320

Guidelines to mathematics, K-8 /

WI docs. no.: Ed.3/2:2126

Mathesis : recueil mathm̌atique, a l'usage des čoles spčiales et des ťablissements d'instruction moyenne /

Suspended 1916-1920.

Instruction to support mental computation development in young children of diverse ability

Fostering young children's mental computation capacity is essential to support their numeracy development. Debate continues as to whether young children should be explicitly taught strategies for mental computation, or be afforded the freedom to develop their own. This paper reports on teaching experiments with two groups of students in their first year of schooling: those considered 'at-risk', and those deemed mathematically advanced. Both groups made considerable learning gains as a result of instruction. Importantly, the gains of the at-risk group are likely to renew both their own, and their teacher's confidence in their ability to learn. In this paper, the instructional programs are documented, highlighting the influence of instruction upon the children's development.

Online Education: What Works in Mathematics

Florida State University and University of Helsinki Information technology has the potential to deliver education to everybody by high quality online courses and associated services, and to enhance traditional face-to-face instruction by, e.g., web services offering virtually unlimited practice and step-bystep solutions to practice problems. Regardless of this, tools of information technology have not yet penetrated mathematics education in any meaningful way. This is mostly due to the inertia of academia: instructors are slow to change their working habits. This paper reports on an experiment where all the instructors (seven instructors and six teaching assistants) of a large calculus course were required to base their instruction on online content. The paper will analyze the effectiveness of various solutions used, and finishes with recommendations regarding best practices.

Matematikaoktatás a bolognai típusú gazdasági képzésekben (Maths instruction in Bologna-type economics tuition)

A gazdálkodási és közgazdasági alap- és mesterszakok tanterveiben számos matematikai tárgy szerepel. A kétciklusú bolognai képzésre történő áttérés Európa-szerte igényelte a matematikaoktatás szerkezetének, mennyiségének és mélységének újragondolását a gazdálkodási és közgazdasági képzési területeken. Mivel az átállás országonként és intézményenként párhuzamosan és jelentős mértékben egymástól függetlenül ment végbe, egyetemenként számos eltérő megoldással találkozhatunk. Az egyetemek operatív tanterveit és tantárgyi adatlapjait felhasználva, utólagosan már összehasonlítható az egyes egyetemek matematikaoktatása. A tanulmány a matematika közgazdaságtanban betöltött szerepének áttekintése után a vezető európai egyetemek és négy magyar egyetem gazdálkodási és közgazdasági képzésén folyó matematikaoktatásának összehasonlító elemzése alapján arra az alapvető következtetésre jut, hogy Magyarországon a vizsgált képzési területen a matematikaoktatás mennyiségileg és minőségileg kritikus szintre süllyedt. / === / The basic and master's curricula for business and economics include plenty of mathematics subjects. Business and economics courses had to be rethought when the change was made across Europe to the two-cycle Bologna system. This change took place simultaneously but independently in each country and institution, so that notably different solutions can be found in each university. A retrospective comparison of maths instruction in various universities can be made by examining their operative syllabuses and subject data-sheets. The study reviews the part mathematics plays in economics, then uses comparative analysis of the maths teaching in business and economics courses at leading European and four Hungarian universities to reach a general conclusion: maths teaching in Hungary, in the field examined, has sunk to a critical level, in terms of quality and quantity.

Intuition as it relates to curriculum, instruction, and resulting academic success in elementary school

Regardless of the fact that children learn in significantly different ways, most curriculum and instruction are guided by the idea that sequential organization of the material to be learned is the best and most efficient way of presenting information to children. Children who learn and think intuitively are denied their preference, forced to conform to the sequential nature of the curriculum and instruction. Based on the theory of psychological type, this study sought to identify any relationship between a student's cognitive style of learning, either Sensing or Intuitive, and his/her academic success in elementary school. The Murphy-Meisgeier Type Indicator for Children was used to identify the cognitive style of students in grades two through eight in a small, private, parochial school. Scores on a standardized achievement test and grades were then analyzed to see if there was a relationship of cognitive style to grades and achievement test scores. Also, the researcher investigated whether or not the teacher's cognitive style had any relationship to students' cognitive style and academic achievement. Although none of the results was statistically significant, the achievement test scores indicated that Sensing students score higher in reading, mathematics concepts, and mathematics computation. However, Intuitive students had higher mean grades in reading and language arts, and virtually equal means mathematics concepts and computation. It was also found that all students, both Sensing and Intuitive, had higher mean grades in the classes of Intuitive teachers. ^

The effectiveness of an intelligent tutoring system on the attitude and achievement of developmental mathematics students in a community college

This study examined the effectiveness of intelligent tutoring system instruction, grounded in John Anderson's ACT theory of cognition, on the achievement and attitude of developmental mathematics students in the community college setting. The quasi-experimental research used a pretest-posttest control group design. The dependent variables were problem solving achievement, overall achievement, and attitude towards mathematics. The independent variable was instructional method.^ Four intact classes and two instructors participated in the study for one semester. Two classes (n = 35) served as experimental groups; they received six lessons with real-world problems using intelligent tutoring system instruction. The other two classes (n = 24) served as control groups; they received six lessons with real-world problems using traditional instruction including graphing calculator support. It was hypothesized that students taught problem solving using the intelligent tutoring system would achieve more on the dependent variables than students taught without the intelligent tutoring system.^ Posttest mean scores for one teacher produced a significant difference in overall achievement for the experimental group. The same teacher had higher means, not significantly, for the experimental group in problem solving achievement. The study did not indicate a significant difference in attitude mean scores.^ It was concluded that using an intelligent tutoring system in problem solving instruction may impact student's overall mathematics achievement and problem solving achievement. Other factors must be considered, such as the teacher's classroom experience, the teacher's experience with the intelligent tutoring system, trained technical support, and trained student support; as well as student learning styles, motivation, and overall mathematics ability. ^

A comparison of content-based and context-based teaching on ninth-grade mathematics achievement

The purpose of this study was to determine if an experimental context-based delivery format for mathematics would be more effective than a traditional model for increasing the performance in mathematics of at-risk students in a public high school of choice, as evidenced by significant gains in achievement on the standards-based Mathematics subtest of the FCAT and final academic grades in Algebra I. The guiding rationale for this approach is captured in the Secretary's Commission on Achieving Necessary Skills (SCANS) report of 1992 that resulted in school-to-work initiatives (United States Department of Labor). Also, the charge for educational reform has been codified at the state level as Educational Accountability Act of 1971 (Florida Statutes, 1995) and at the national level as embodied in the No Child Left Behind Act of 2001. A particular focus of educational reform is low performing, at-risk students. ^ This dissertation explored the effects of a context-based curricular reform designed to enhance the content of Algebra I content utilizing a research design consisting of two delivery models: a traditional content-based course; and, a thematically structured, content-based course. In this case, the thematic element was business education as there are many advocates in career education who assert that this format engages students who are often otherwise disinterested in mathematics in a relevant, SCANS skills setting. The subjects in each supplementary course were ninth grade students who were both low performers in eighth grade mathematics and who had not passed the eighth grade administration of the standards-based FCAT Mathematics subtest. The sample size was limited to two groups of 25 students and two teachers. The site for this study was a public charter school. Student-generated performance data were analyzed using descriptive statistics. ^ Results indicated that contrary to the beliefs held by many, contextual presentation of content did not cause significant gains in either academic performance or test performance for those in the experimental treatment group. Further, results indicated that there was no meaningful difference in performance between the two groups. ^