A Thesis Submitted in Partial Fulfillment of Requirements of the CSU Honors Program for Honors in the degree of Bachelor of Science in Education in Special Education College of Health & Education Professions Columbus State University Columbus, Georgia

Topic: Mathematics instruction, iPads, Technology, Disabilities

This study explored how the teaching of probability under the framework of Ference Marton’s Variation Theory affected the learning outcomes of secondary 5 students. After eight probability lessons, the experimental group of 25 secondary 5 students significantly improved their posttest mean score on the overall probabilistic skills by 24% from the pretest mean score under the 90% significance. In contrast, the control group of similar ability (n = 30) unfortunately showed no remarkable...

Topics: Variation Theory, Probability, Mathematics Instruction & Transfer Performance

Secondary math students are often heard to ask these two timeless questions: ?When are we ever going to use this?? and ?Why do we need to know this?? We must be able to provide satisfactory answers to these questions, because students who fail to realize the relevance of content covered in class are often less successful than those who do see the immediate value of the knowledge.

Topics: ERIC Archive, Mathematics Instruction, Bryan, Joel A.

Each year, students in my seventh- and eighth-grade math classes plan and organize a schoolwide popcorn sale. This activity brings to life mathematical concepts learned in the classroom. By transferring textbook mathematics to a real-world situation, my students learn to value the mathematics being studied and are able to understand how it can affect them in the future. To conduct this lesson, we use several technologies, including the TI-83 Plus to find the best selling price for the popcorn...

Topics: ERIC Archive, Mathematics Instruction, Levert, Brenda

In an attempt to identify effective instructional approaches, teachers were videotaped while teaching remedial mathematics. Teacher behaviors were coded and student achievement scores analyzed. Eight categories were found which distinguished between effective and ineffective teachers, including: instruction for the whole class simultaneously rather than individualized or small group work; review of seatwork with immediate feedback; use of questions rather than statements; use of questions that...

Topics: ERIC Archive, Mathematics Instruction, Slow Learners, Teacher Effectiveness, Teaching Methods

This paper reports on the experiences of students who were learning mathematics with CAS for a second consecutive school year. Evidence presented shows that nearly all students managed the challenging task of mastering the technical aspects of using CAS well. It also shows that the level of technical difficulty and the degree to which it presents an obstacle to mathematical learning is not predictable from conventional mathematical ability. There is a complex interaction between cognitive and...

Topics: ERIC Archive, Mathematics Instruction, Calculators, Pierce, Robyn, Stacey, Kaye

Graphing calculator use is often thought of in terms of pre-calculus or continuous topics in mathematics. This paper contains examples and activities that demonstrate useful, interesting, and easy ways to use a graphing calculator with discrete topics. Examples are given for each of the following topics: functions, mathematical induction and recursion, graph theory and matrices, and combinatorics and the Binomial Theorem. A list of discrete topics that do not require the programming of the...

Topics: ERIC Archive, Graphing Calculators, Higher Education, Mathematics Instruction, Secondary Education

Prime numbers play an extremely important role in modern mathematics. Apart from still being the object of intense research activity, their applications in banking and security underline a key phenomenon: in the modern world, useful applications of mathematics often come from very "pure" abstract theories. Curiously, despite their undeniable importance, prime numbers are largely absent from school curricula. Prime numbers are typically encountered in Year 7. There one looks at the...

Topics: ERIC Archive, Numbers, Modern Mathematics, Mathematics Instruction, Cairns, Grant

If you are considering using handhelds in your classroom, you have a number of things to consider: (1) equipment management; (2) student contracts for out of class use;(3) tutorials;(4) curriculum integration, (4)success stories; and (5) current research on handheld effectiveness. To help teachers learn more about classroom use of handhelds, the Organization for Educational Technology and Curriculum (OETC, formerly known as Oregon Educational Technology Consortium) has worked in conjunction...

Topics: ERIC Archive, Career Exploration, Mathematics Instruction, Internet, Lary, Lynn M.

It is always interesting to challenge more capable students with things that they have tended to take for granted. One area in particular that students often tend to overlook in their senior years concerns the important understandings associated with domains and ranges of functions. In this article, the author shares a few favourite questions that he has collected and used many times over the years, and which always result in valuable discussion, frequent bursts of insight, and more than the...

Topics: ERIC Archive, Mathematics, Mathematics Instruction, High Schools, Arnold, Stephen

Programable desk calculators can provide students with personal experience in the use of numerical methods. Courses at California Polytechnic State University at San Luis Obispo use the Compucorp Model 025 Educator Experiences with it as a teaching device for solving non-linear equations and differential equations show that students can by-pass tedious hand calculations and elminate time-consuming program writing which other modes require; it also allows students to perform mathematical...

Topics: ERIC Archive, College Mathematics, Computation, Electromechanical Aids, Higher Education,...

This paper describes a project one teacher assigns to Calculus I students at the Department of Mathematical Sciences at Loyola College in Baltimore, Maryland. The project is introduced to the students early in the semester and requires the use of technology, team work, and the completion of an extensive writing component. The goal of the project is to lead the students to the formula for the derivative of an exponential function. The teacher assigns the project after the class has studied the...

Topics: ERIC Archive, Calculus, Higher Education, Mathematics Activities, Mathematics Instruction,...

A teaching intervention study was conducted with sixth grade students to explore the interconnections between students' growing understanding of arithmetic expressions and beginning algebra. Three groups of students were chosen, with two groups receiving instruction in arithmetic and algebra, and one group in algebra without arithmetic. Students of the groups that learnt arithmetic developed a strong understanding of the concept of term and applied it to reason about equal expressions. They...

Topics: ERIC Archive, Grade 6, Arithmetic, Concept Formation, Algebra, Mathematics Instruction, Teaching...

This report describes a research project that investigated how to design instruction to help children take the step to generalizing and formalizing their knowledge into powerful abstract systems for representing and operating mathematical ideas. The studies build on existing research on cognitively guided instruction (CGI). The goal of this paper is to begin to understand how to provide support for children to reflect on their procedures in order to form generalizations from them and construct...

Topics: ERIC Archive, Algebra, Elementary Education, Mathematics Curriculum, Mathematics Instruction,...

The main objective of this study is to investigate the role of four different modes of representation in mathematical problem solving (MPS), and more specifically to develop a model, which provides information about the effects of these representations in the solution procedures of one-step problems of additive structures. Data were collected from 1447 pupils in Grades 1, 2 and 3 of elementary school in Cyprus. Confirmatory factor analyses (CFA) affirmed the existence of four first-order...

Topics: ERIC Archive, Mathematics Instruction, Problem Solving, Factor Structure, Foreign Countries,...

A study examining the effects of systematized feedback on mathematics performance was conducted in natural classroom settings to extend the external validity of previous feedback studies. A posttest-only, internal-external control group design was used with three sixth grade classes serving as subjects. All classes utilized a "step" approach to math instruction, where students advanced through a pre-determined sequence of math skills at individual rates. Two classes, each taught by...

Topics: ERIC Archive, Elementary Education, Elementary School Mathematics, Feedback, Grade 6, Mathematics...

This study investigated children's knowledge of division and its relationship to their teacher's conceptual understanding of division following Professional Development. A paper and pencil test was administered to 47 year 7 students and 2 teachers over 2 phases. Following the testing, six students and the teacher from each phase were interviewed. Results from this study indicate that most Phase 1 students rely on following a procedure with limited understanding. Their teacher displayed some...

Topics: ERIC Archive, Concept Formation, Arithmetic, Grade 7, Mathematics Instruction, Misconceptions,...

This document presents a South Carolina statewide consensus of what children are expected to know and be able to do in mathematics and the changes necessary in the education system to support what teachers and students do every day in the classroom. Chapter titles are: (1) "A Vision for Change"; (2) "Learning and Teaching Mathematics"; (3) "K-12 Mathematics Curriculum"; (4) "Instructional Materials"; (5) "Assessment"; (6) "Professional...

Topics: ERIC Archive, Community Support, Elementary Secondary Education, Instructional Materials,...

There are selected philosophies in the teaching of mathematics that can provide guidance to the teacher in developing the curriculum. This paper discusses four philosophies of teaching mathematics. (1) Idealism stresses that the pupil lives in an idea-centered mathematical world, but not an objective real world. Abstract content is prized more highly than concrete and semi-concrete representations. (2) Realism emphasizes that a person can know the real world in whole or in part as it really is....

Topics: ERIC Archive, Educational Philosophy, Elementary Secondary Education, Existentialism, Mathematics...

When students encounter a set of concepts (or terms or principles) that are similar in some way, they often confuse one with another. For instance, they might mistake one word for another word with a similar spelling (e.g., allusion instead of illusion) or choose the wrong strategy for a mathematics problem because it resembles a different kind of problem. By one proposition explored in this review, these kinds of errors occur more frequently when all exposures to one of the concepts are...

Topics: ERIC Archive, Problem Solving, Learning Strategies, Mathematics, Mathematics Instruction,...

Mathematics teachers need to study diverse psychologies of learning so that individual learners may be guided to attain as optimally as possible. This paper discusses meaning theory in mathematics teaching and describes a variety of learning theories such as behaviorism, developmental psychology, and problem solving. (ASK)

Topics: ERIC Archive, Elementary Secondary Education, Learning Theories, Mathematics Instruction, Teaching...

In this article, the author presents his tales of very large numbers. He discusses the concept of infinity and extremely large numbers such as "googol" and "googolplex". "Googol" which could be written as 1, followed by one hundred zeros, was popularized by Edward Kasner and James Newman. Moreover, "googol" was coined by Kasner's nine-year old nephew. Kasner's nephew also coined the term "gogoolplex", which is defined to be a 1 followed by a...

Topics: ERIC Archive, Numbers, Number Concepts, Mathematics Instruction, Elementary School Mathematics,...

This report describes the changes in a freshman-level calculus course that occurred as a consequence of adopting the Harvard Consortium Calculus text. The perspective is that of the lecturer. The course is intended as an introduction to calculus for liberal arts students, that is, students who will not be expected to use calculus as a mathematical tool in their area of major study. The perceptions of the instructor about global changes that occurred in the course include that learning was...

Topics: ERIC Archive, Calculus, College Faculty, Educational Change, Higher Education, Mathematics...

Reported are results of a study of a sample of 259 students at the University of Massachusetts who scored low on a math placement test and later took precalculus math classes. Several possible conclusions are presented to explain the test results. A significantly higher percentage (p

Topics: ERIC Archive, Academic Achievement, College Mathematics, Higher Education, Mathematics Achievement,...

These instructional objectives have been selected from materials submitted to the Curriculum Laboratory of the Graduate School of Education at UCLA. Arranged by major course goals, these objectives are offered simply as samples that may be used where they correspond to the skills, abilities, and attitudes instructors want their students to acquire. These objectives may also serve as models for assisting instructors to translate other instructional units into specific measurable terms. For other...

Topics: ERIC Archive, Behavioral Objectives, College Mathematics, Mathematics, Mathematics Instruction, Two...

This is one of a series that is a collection of translations from the extensive Soviet literature of the past 25 years on research in the psychology of mathematics instruction. It also includes works on methods of teaching mathematics directly influenced by the psychological research. Selected papers and books considered to be of value to the American mathematics educator have been translated from the Russian and appear in this series for the first time in English. The aim of this series is to...

Topics: ERIC Archive, Cognitive Development, Elementary Education, Elementary School Mathematics,...

This paper presents some ideas on how to utilize TI-83 Plus calculators to perform division of one polynomial (the divided) by another polynomial (the divisor) and how that procedure might be incorporated into a college algebra lesson. Four ways to obtain the quotient and remainder when dividing a polynomial by a first-degree polynomial are presented. Each program can be performed interactively using a TI-83 Plus calculator and some insights are provided into the synthetic division procedure as...

Topics: ERIC Archive, Algebra, College Mathematics, Graphing Calculators, Higher Education, Mathematics...

"Mathematics in Context" is a middle school mathematics curriculum for grades 5 through 8. It was developed to align with the 1989 National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards. It is also based on the Dutch Realistic Mathematics Education approach of engaging students in understanding real-life problems and gradually moving to abstract concepts. Rather than focusing on one mathematical domain at a time, "Mathematics in Context"...

Topics: ERIC Archive, Mathematics Curriculum, Middle Schools, Mathematics Instruction, Program...

In this article, the author describes the Lutterloh method of making dress patterns, which was developed in Germany in the 1930s. The underlying principle involves the modification of basic designs and it is claimed that it provides better fits for women of different sizes and shapes than do other commercially available patterns. The method is marketed via classes conducted on a commercial basis and makes use of kits sold at these classes. Each kit comprises a set of basic patterns together...

Topics: ERIC Archive, Patternmaking, Clothing, Mathematics Instruction, Mathematical Concepts, Geometric...

This document represents collaborative efforts to define what is valued and necessary in mathematics education for Pacific region children. Underlying assumptions to these standards include constructivism, communication, problem solving, connections, time for learning, and challenge for all students. The majority of the document contains the standards which are grouped into three grade-level sections, K-4, 5-8, and 9-12, and are based largely on the National Council of Teachers of Mathematics'...

Topics: ERIC Archive, Elementary Secondary Education, Learning Activities, Mathematics Curriculum,...

In a multicultural society such as Australia, it can be difficult to acquire a strong mathematics education because of language, locale, or other differences including access to technology. The widespread use of devices such as calculators and computers has changed the nature of work. It has become more important for students to have the confidence to use their mathematical knowledge and be able to apply mathematics throughout their lives. It is in the national interest that schools promote...

Topics: ERIC Archive, Access to Education, Elementary Secondary Education, Foreign Countries, Mathematics...

Math can sometimes seem like a strange language from foreign land--one communicated in symbols, numbers, and geometric figures. When teachers talk about mathematical concepts, even familiar, garden variety words such as "parallel," "power," "even," "odd," "multiply," "difference," "product," "positive," and "negative" take on brand-new meanings. What's the best way for teachers to help students master this...

Topics: ERIC Archive, Geometric Concepts, Vocabulary Development, Teaching Methods, Mathematics...

The impact of written and printed texts on the geometry curriculum has a very long history. Static diagrams, static definitions, and static proofs have dominated the classrooms for centuries. Geometry is about shape and space, and about the relationships between shapes in space. Movement is a key aspect of those relationships, but movement cannot be shown in a printed text book, so it is relegated to a minor role in the primary mathematics curriculum. One area where print has had a particularly...

Topics: ERIC Archive, Mathematics Instruction, Printed Materials, Geometry, Geometric Concepts, Elementary...

This paper describes three fundamental principles, dictated by Wilhelm von Humboldt, that were widely adapted as the basic philosophy of higher education in the United States, and proposes to revise the unfulfilled dream of von Humboldt to make it come true. This paper stresses the achievements of humanity not only in technology, health, or the natural sciences, but also in humanities in general in order for education to make a significant contribution to the future. Mathematics is regarded as...

Topics: ERIC Archive, Concept Formation, Curriculum Development, Higher Education, Interdisciplinary...

This is the third part of a three-part SMSG algebra text for high school students. Chapter titles include: Truth Sets of Open Sentences; Graphs of Open Sentences in Two Variables; Systems of Equations and Inequalities; Quadratic Polynomials; and Functions. (MK)

Topics: ERIC Archive, Algebra, Inequality (Mathematics), Mathematics Curriculum, Mathematics Instruction,...

The 27th Undergraduate Mathematics Teaching Conference took place in September of 2001 at the University of Birmingham. Major topics of the conference included preparing a teaching portfolio, engineering mathematics should be taught by engineers, issues in teaching discrete mathematics, action research, study skills, and issues for web-delivered assessment. Papers and presentations given at the conference include: (1) "Why Do Non-Mathematicians Need More Maths?" (Alison Wolf); (2)...

Topics: ERIC Archive, Higher Education, Mathematics Instruction, Numeracy, Teaching Methods, Undergraduate...

Archimedes, the famous Greek mathematician, lived from 287 BCE until approximately 212 BCE. He thought that the figure of two semi-circles on a straight line enclosed by a larger semi-circle resembled a shoemaker's knife. Archimedes called this figure an "arbelos" since arbelos is the Greek word for a shoemaker's knife. The author describes the properties of the arbelos and how the arbelos continues to fascinate mathematicians.

Topics: ERIC Archive, Mathematics Instruction, Mathematical Concepts, Graphing Calculators, Teaching...

Three Project Solo modules are presented. They are designed to teach the concepts of elementary matrix operation, matrix multiplication, and finite-state automata. Together with the module on communication matrices from Newsletter #17 they form a well motivated but structured path to expertise in this area. (JY)

Topics: ERIC Archive, Computer Assisted Instruction, Computer Programs, Computer Science Education,...

Using mathematical gossip in the classroom allows teachers to expand their students' horizons, and provide pathways to improvement of understanding. The expansion of a simple idea into another mathematical context can enrich a student's learning. In particular it may help to bridge the gap between purely procedural approaches and a conceptual understanding of the underlying mathematics. Having both procedural and conceptual understanding provides a springboard for strategic use of mathematics...

Topics: ERIC Archive, Mathematics Instruction, Teaching Methods, Concept Formation, Mathematics Skills,...

Revised material from earlier Project Solo newsletters is presented here. The revised material updates programs to explain the law of sines and cosines and to apply the idea of rectangular coordinates approach to aircraft navigation systems such as VORTAC. A brief discussion of the value of off-line as opposed to on-line activity is also presented. (JY)

Topics: ERIC Archive, Computer Assisted Instruction, Computer Programs, Computer Science Education,...

This program, funded under Elementary and Secondary Education Act Title I, for eligible non-public school students in New York City consisted of corrective mathematics services and other supportive services. The supportive services were guidance, homework help and paraprofessional assistance. The program was aimed at first through twelfth graders, who were six months or more deficient in math. Instruction was in small groups with periods of individual instruction where applicable. The program...

Topics: ERIC Archive, Achievement Gains, Elementary Secondary Education, Mathematics, Mathematics...

Between the 17th and 19th centuries, the Japanese government closed its borders to the outside world in an attempt to become more powerful. Foreign books were banned, people could not travel, and foreigners were not allowed to enter the country. One result of this isolation was the flourishing of sangaku--wooden tablets inscribed with intricately decorated geometry problems that were hung beneath the eaves of Shinto shrines and Buddhist temples all over Japan (Fukagawa & Pedoe, 1989). The...

Topics: ERIC Archive, Foreign Countries, Geometric Concepts, Geometry, Mathematics Instruction,...

This paper discusses TI-89 and TI-92 graphing calculators as a tool for teaching mathematics. How this technology is likely to affect the teaching of mathematics and the role of technology in general is described. Discussion begins with a comparison of two areas, mathematics and moving/transportation, from a technological aspect, and focuses on the benefits of teaching with this technology such as trivialization, experimentation, visualization, and concentration. Discussion centers around the...

Topics: ERIC Archive, Educational Technology, Elementary Secondary Education, Graphing Calculators,...

This article illustrates spatial thinking tasks through cube diagrams and drawings. The author talks about the pentacube diagram that is based on the principle that a vertical cube-edge is shown "vertically". The author describes how to extend isometric drawing to include triangular wedges that are made by slicing single cubes, bi-cubes, tri-cubes, and so on.

Topics: ERIC Archive, Cognitive Processes, Spatial Ability, Geometric Concepts, Mathematical Concepts,...

This paper attempts to locate a leitmotif for the mathematics education of adults, and discusses whether there exists a specific problematique for research into this area. The term 'problematique' is described and discussed. A problematique within didactics of mathematics is presented, and a conceptual framework for the construction of a systemically linked problem field is explicated. Contains 10 references. (ASK)

Topics: ERIC Archive, Adult Learning, Educational Research, Foreign Countries, Mathematics Education,...

In this paper we study how a student begins to acquire the concept of the derivative, what kind of representations he acquires and how he connects these representations. A teaching period, in which different perceptual and symbolic representation were emphasized, was carried out and task based interviews conducted to five students. The students used several different kinds of representations to process the derivative. They were all able to consider the derivative as an object by using...

Topics: ERIC Archive, Calculus, Concept Formation, High School Students, Mathematics Instruction,...

The main purpose of this paper is to describe the answers given by adults without primary schooling to different ratio-and rate-comparison tasks. The framework and the analysed data are part of an ongoing research, in which the responses of subjects of different ages and schoolings are studied. The behaviour of quasi-illiterate adults could throw some light on the effect of school on proportional reasoning in normal conditions; evidence will be shown regarding the similarities of their...

Topics: ERIC Archive, Mathematical Concepts, Adult Students, Interviews, Illiteracy, Mathematics...

In this paper I illustrate how kinaesthetic experiences associated with dance might be used in teaching to promote engagement and learning in spatial, rhythmic, structural and symbolic aspects of mathematics.

Topics: ERIC Archive, Mathematics Instruction, Student Attitudes, Dance, Kinesthetic Perception, Spatial...

A good mathematics instructor is a proficient organizer of pupils for instruction in mathematics. There are many specifics involved in organizing for instruction. This paper discusses organizational structures in mathematics instruction such as learning stations. "A Geometry Center" is provided as an example of a learning station. The organization of instruction in unit teaching and the evaluation processes used by pupils are also discussed. (ASK)

Topics: ERIC Archive, Class Organization, Elementary Secondary Education, Geometry, Mathematics...

This article explores the impact of students' thinking centered professional development on mathematics teaching and learning. Purposeful pedagogy and problem posing are examined as mechanisms by which teachers can potentially deepen students' understanding of mathematics. A classroom example comparing student generated strategies versus algorithmic approaches also highlights the benefits of instructional approaches that emphasize students' understanding of mathematics.

Topics: ERIC Archive, Mathematics Instruction, Teaching Methods, Comprehension, State Standards,...