Secondary Mathematics Curriculum Research Articles

Comparative Study of Secondary Mathematics Curriculum between Malaysia and Singapore

This preliminary study attempts to compare the Malaysian Secondary Mathematics (MSM) curriculum published in 2003 with the Singapore Secondary Mathematics (SSM) implemented in 2007. The study aims to examine the math content and the level at which the content is introduced between the two countries. The results from the study indicated that there is a need for Malaysia Mathematics Curriculum to be revised in order to enable students to have literacy in mathematics and the ability to apply mathematics into other disciplines at higher level.

From ‘proofs without words’ to ‘proofs that explain’ in secondary mathematics

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Building Your Own Regression Model

Regression has rightfully assumed an important role in the secondary mathematics curriculum. Graphing calculators can perform many types of regression quickly and easily, and students can learn a great deal in analyzing the results.

Projects: Historical Modules Project

The Historical Modules Project, a part of the Institute in the History of Mathematics and Its Use in Teaching (IHMT), is sponsored by the Mathematical Association of America (MAA) and supported by the National Science Foundation. In the project, eighteen high school teachers and six college teachers with experience in the history of mathematics have been working in six teams to develop modules for various topics in the secondary mathematics curriculum. These modules are intended to show teachers how to use the history of mathematics in teaching mathematics.

Sharing Teaching Ideas: Making Connections between Sequences and Mathematical Models

Almost all secondary mathematics curricula include linear and exponential models. More and more programs also include arithmetic and geometric sequences, as well. These topics are linked, but students often do not make the connections.

A Critical Examination of Three Factors in the Decline of Proof

Proof seems to have been losing ground in the secondary mathematics curriculum despite its importance in mathematical theory and practice. The present paper critically examines three specific factors that have lent impetus to the decline of proof in the curriculum: a) The idea that proof need be taught only to those students who intend to pursue post-secondary education, b) the view that deductive proof need no longer be taught because heuristic techniques are more useful than proof in developing skills in reasoning and justification, c) the idea that deductive proof might profitably be abandoned in the classroom in favour of a dynamic visual approach to mathematical justification. The paper concludes that proof should be an essential component in mathematics education at all levels and compatible with both heuristic techniques and dynamic visual approaches.

The Ongoing Value of Proof

Over the past thirty years, many mathematics educators in North America have suggested that proof be relegated to a lesser role in the secondary mathematics curriculum. This view has been shaped in large part by developments in mathematics itself, by the thinking of Lakatos and by changing social values. This paper argues that none of these factors justifies such a move, and that proof continues to have value in the classroom, both as a reflection of its central role in mathematical practice and as an important tool for the promotion of understanding.

Technology Tips: Visualizing Least-Square Lines of Best Fit

Statistics and data-analysis topics are becoming an integral part of nearly every secondary mathematics curriculum. Instead of being relegated to the last, unreachable chapter, these topics are now covered early—sometimes first—in the curriculum and are used throughout to complement the study of many mathematical concepts and principles and to form the basis for a vast supply of realistic problems. Other reasons behind this signi ficant change in the focus of the secondary curriculum include the recommendations in the NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) for increased attention to these topics for grades K-12 and, maybe the most important reason of all, the availability of powerful technological tools that place these Computationally intense topics within the reach of all students.

Projects

ln this National Science Foundation (NFS) Teacher Enhancement Project, fifty Minnesota middle school and high school mathematics teachers are collaborating with three Saint Olaf CoUege mathematics professors to integrate inquiry-based geometry and visualization across their secondary mathematics curricula.

Activities: Iterating Linear Functions—An Introduction to Dynamical Systems

The arrival of computers has caused some major changes in both mathematics and mathematics education. One of the biggest shifts has been from an emphasis on symbolic methods to one on numerical methods. One field of mathematics, dynamical systems, requires considerable number crunching and is just coming into its own because we currently have the ability to perform extensive calculations easily. This article introduces students to this new field. The study of sequences created by using numerical iteration provides interesting new ways to approach many of the concepts central to the secondary mathematics curriculum, such as functions in general and linear and exponential functions in particular.

Implementing the Assessment Standards for School Mathematics: Assessing Students' Ability to Analyze Data: Reaching beyond Computation

Quantitative literacy, which includes the ability to read, interpret, and analyze statistical data in visual displays, is an essential skill needed for living and functioning in our highly technological society. In light of this need, recommendations have been made that statistics be included in the secondary mathematics curriculum (NCTM 1989). To help students value the mathematics they are learning, further recommendations suggest that statistical problems involve real data that students will find interesting and informative. As indcated in the Assessment Standards for School Mathematics (NCTM 1995), assessment tasks and instruments communicate to students which activities and learning outcomes are valued. It is therefore essential that assessment tasks engage students in data interpretation and analysis that lead to interesting and meaningful discoveries about real-life data (Burrill et al. 1992).

A comparative study of secondary mathematics curricula: Florida, USA and Tamil Nadu, India

A comparative study of current mathematics curricula for grades 6‐12 of Florida (USA) with Tamil Nadu (India) reflects likenesses and differences in the curricula of both states. Likenesses appeared more frequently than were expected; differences were more apparent at the higher levels than at the lower levels. The course outlines/syllabi of each of the grades/standards were analysed in detail and compared for the topics covered in each distinct area. One of the major observations is that mathematics content is treated differently, especially after the eighth grade/standard. In Florida, the subjects are taught in separate units, i.e. algebra, geometry. In Tamil Nadu, the content is taught as strands of knowledge beginning in standard 6 and continuing through standard 12. Further research suggested by this study includes an investigation of the curriculum effectiveness by a survey of selected samples of student population and teachers in both states to determine success rates in the mastery of the mathemat...

Integration of discrete mathematics topics into the secondary mathematics curriculum using Mathematica

Integration of discrete mathematics topics into the secondary mathematics curriculum using Mathematica

Utilization of the microcomputer in the mathematics classroom

This study investigated the utilization of microcomputers in the secondary mathematics curriculum. A sample of 128 mathematics teachers completed a survey describing their use of the microcomputer for instruction. Results from the study suggested the microcomputer was not utilized as often as expected. Findings that describe the computer-using and non-computer-using teachers, the ways computers are used in the mathematics classroom, and the instructional environment where computers are used are reported. Suggestions are provided for improving the integration of the microcomputer into the mathematics classroom.

The 6‐3‐3‐4 education system and tertiary mathematics curriculum—A case for matching the objectives in senior secondary mathematics curriculum with the preparatory stance of the teacher

The National Policy of Education (revised 1981) professes a functional literacy dimension to educational attainments in the Federal Republic of Nigeria. Consequently, obvious and unavoidable steps were adopted by government for the purposes of ensuring the realization of this functional literacy element in the system. One such step bordered on the revision/restructuring of school curricula at the appropriate levels. In this paper, we sought to examine to what extent that teacher preparation at the tertiary levels reflected the attainment of objectives for mathematics education at the senior secondary level. This report centred essentially on the Imo, Bendel and Rivers State School Systems, the result of which guided us to the conclusion that vital elements of teacher preparation seemed lacking in the context of ensuring thorough grounding in mathematics of pupils at the senior secondary level.

Gender differences in the junior secondary (grade 7) mathematics curriculum in Hong Kong

This article seeks to examine gender differences across the mathematics curriculum in the various topic areas and mathematical abilities. It is suggested that a profile of these differences, when compared with students at different grade levels or across curricula, would be more fruitful for classroom teachers and curriculum developers. Breakdown and discriminant function statistics reveal that boys performed better than girls in Geometry and excelled in comprehension, and solving routine and non-routine problems. Girls were better at mathematical manipulation problems.

Difference Equations

Much talk is heard these days about the importance of including topics from discrete mathematics in our secondary mathematics curriculum. They are characterized by their treatment of discrete quantities rather than continuous quantities and limit processes. The mathematics of continuity and limit processes leading into calculus will continue to be a major part of our mathematics curriculum. At the same time topics from discrete mathematics will take on more importance because of the presence of inexpensive computing power that is fundamentally finite and discrete.

The Impact of Computing Technology on School Mathematics: Report of an NCTM Conference

One of the critical problems facing mathematics education today is the need for curricula and instructional methods to respond to the influence that computing technology is having on mathematics and its teaching. Numerous conferences, reports, and projects have focused on different aspects of the effect of emerging technology on mathematics curricula and instruction. For example, the Conference Board of the Mathematical Sciences produced a set of guidelines that identified fundamental topics in K–12 mathematics (CBMS 1983), and an NSF-sponsored conference at the University of Maryland resulted in a document that provided insight into the effect of the computer on subjects in the traditional secondary mathematics curriculum (Fey 1984).

Teaching Descriptive and Inferential Statistics Using a Classroom Microcomputer

There is no doubt that statistics should be an important part of the secondary mathematics curriculum. A single classroom microcomputer can be valuable for work in both descriptive and inferential statistics. This article presents a framework for integrating a microcomputer into a statistics unit and includes descriptions of some programs suitable for the Apple microcomputer and ideas for lessons.

College Preparatory Mathematics: Preparation for What?

"... The relevance of the secondary school col lege preparatory mathematics curriculum to the lives of the future historian, musician, teacher of English, or articulate layman is doubtful."