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
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
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.
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Topics: dag yig, zhal gdams/, ang rtsis/, Mathematics Instruction
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
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
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.
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
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
This article presents a problem set which includes a selection of probability problems. Probability theory started essentially as an empirical science and developed on the mathematical side later. The problems featured in this article demonstrate diversity of ideas and different concepts of probability, in particular, they refer to Laplace and Bernoulli models as well as to geometric probability.
Topics: ERIC Archive, Problem Sets, Probability, Mathematics Instruction, Mathematical Concepts,...
Three examples of how the computer terminal can be used to provide the kind of "pictorial" information that makes graphs such a valuable aid in the teaching of quantitatively oriented subjects are presented. In the first example the graph is part of the "frame" of information presented to a student in a tutorial which reviews trigonometric functions and their graphical descriptions. The second example shows how professionally prepared "packages" can be useful,...
Topics: ERIC Archive, Computer Assisted Instruction, Computer Graphics, Computer Programs, Mathematics...
This article is about a very small subset of the positive integers. The positive integer N is said to be "perfect" if it is the sum of all its divisors, including 1, but less that N itself. For example, N = 6 is perfect, because the (relevant) divisors are 1, 2 and 3, and 6 = 1 + 2 + 3. On the other hand, N = 12 has divisors 1, 2, 3, 4 and 6, but since 1 + 2 + 3 + 4 + 6 = 16, rather than 12, 12 is not a perfect number. Ways and exercises for finding perfect numbers are presented....
Topics: ERIC Archive, Number Concepts, Arithmetic, Equations (Mathematics), Mathematics Instruction, Scott,...
Four trigonometry modules of the Project Solo computer-assisted instruction series are presented. The modules deal with circular functions, trigonometry functions and Tchebychev polynomials, and inverse circular functions. A fourth module, VORTAC, allows students to try a two-aircraft navigation simulation. (JY)
Topics: ERIC Archive, Computer Assisted Instruction, Computer Programs, Mathematics Instruction,...
This paper presents an analysis of the different types of meanings that an individual may assign to a collection of algebraic symbols depending on the mathematical context in which the symbols are presented and the mathematical knowledge possessed by that individual. Four contexts for the Quadratic Theorem are used to illustrate the ways in which generalization and abstraction develop the meaning of algebraic entities by changing the focus from process to structure. (Author)
Topics: ERIC Archive, Algebra, Cognitive Style, Mathematics Instruction, Secondary Education, Symbols...
Investigating the relationship between fractions and their equivalent decimal representations helps clarify to students that both representations stand for a single (rational) number on the number line. Since students are taught to perform computations with fractions and also to compute with decimals, performing these computations side-by-side with consistent results further reinforces this, and pulls these two representations into focus. In a way the mystery of these representations is...
Topics: ERIC Archive, Mathematics Instruction, Mathematics Education, Mathematics, Arithmetic, Computation,...
The experimental project which resulted in this manual utilized an electronic calculator to aid in mathematics instruction in the 11th and 12th grades. The requirements for implementing the program are described and illustrated by the experiences at the pilot school. A curriculum guide is given for the inservice teacher training program. Suggestions for using the calculator in a mathematics program includes a curriculum outline, suggested instructional materials, and a list of instructional...
Topics: ERIC Archive, Computer Assisted Instruction, Educational Media, Electromechanical Aids, Mathematics...
In this article, the author discusses the game of Hex, including its history, strategies and problems. Like all good games, the rules are very simple. Hex is played on a diamond shaped board made up of hexagons. It can be of any size, but an 11x11 board makes for a good game. Two opposite sides of the diamond are labelled "red," the other two sides "blue" (or, often, "black" and "white"). The hexagons at the vertices of the diamond belong to either side....
Topics: ERIC Archive, Games, Geometric Concepts, Puzzles, Mathematics Instruction, History, Scott, Paul
This paper investigates some aspects of number patterns that have been a subject of interest and engaged students of mathematics for many years. It is left for the teacher to select and fashion any aspects they feel suit their own students.
Topics: ERIC Archive, Learning Activities, Class Activities, Mathematics Instruction, Mathematics, Numbers,...
This publication is a transcription of a forum held in Washington, D.C. on May 5, 2005 on K-6 math proficiency. James Hiebert, professor of education at the University of Delware, and Deborah Loewengerg Ball, collegiate professor of mathematics education and teacher education and director of teacher education at the University of Michigan, spoke at the forum giving their opinions on the issues. After the speeches, the participants engaged in a question-answer session. Participants included:...
Topics: ERIC Archive, Teaching Methods, Urban Schools, Mathematics Instruction, Mathematics Education,...
An elementary arithmetic workbook in whole numbers for speakers of Hmong has an introductory section and a variety of exercises in conceptualizing, writing, spelling, and sequencing numbers from 0 to 999. (MSE)
Topics: ERIC Archive, Computation, Elementary Education, Mathematics Instruction, Number Concepts, Whole...
The author of this article, while recently working through some problem sets on determining volumes by triple integrals in cylindrical and spherical coordinate systems, realized that, although the textbook he was using included many interesting problems involving spheres, cylinders and cones and the increasingly complex solids that arose from the intersections of two or more of these, it did not include the common torus. He has written this brief guide for teachers who need some assistance with...
Topics: ERIC Archive, Problem Sets, Textbooks, Mathematics Instruction, Geometry, Teaching Methods, Farmer,...
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Topics: Mathematics -- Instruction and study, Mathématiques -- Étude et enseignement, Mathematics --...
The mysteries of mathematics are not easily revealed. Much of present day school mathematics is the product of years, sometimes centuries, of inquiring, wrestling and discovering by men of the highest intellect. The number "i" (designation for the square root of -1) is no exception. This article presents a lesson on the need for "i".
Topics: ERIC Archive, Number Concepts, Mathematics Instruction, Lesson Plans, Day Schools, Scott, Paul
In the summer of 1975 a program to improve reading and mathematics skills for pregnant school age girls was implemented in New York City. The program was designed to provide continuity of instruction in reading and mathematics from spring to fall for girls who were at least two years behind in reading and mathematics achievement. The summer program was initiated at four schools, one each in the Bronx, Brooklyn, Manhattan, and Queens. Each of the schools provided instruction for pregnant girls...
Topics: ERIC Archive, Corrective Reading, Mathematics Instruction, Pregnant Students, Reading Instruction,...
As time has progressed, the role of applied mathematics has become increasingly important. Indeed there are now more students enrolled in applied mathematics courses in senior high schools and colleges than in pure mathematics. Such courses become more relevant both to the student and to future employers, if the same constants and equations that are used in industry are reflected in the student's texts. The appropriate formulae for these constants and equations are featured in this article.
Topics: ERIC Archive, Mathematics Instruction, Equations (Mathematics), Geometry, Trigonometry, Earth...
This workbook introduces curriculum mapping, a process used by schools and districts to reform and improve curricula. The school's or district's elementary and middle level science curriculum can be mapped out by indicating what topics are taught at what grade levels. This workbook is part of the North Central Regional Educational Laboratory's (NCREL's) ongoing effort to develop accessible and user-friendly, data-driven decision making tools. The workbook allows for the analysis and comparison...
Topics: ERIC Archive, Curriculum Development, Elementary Education, Mathematics Curriculum, Mathematics...
The history of the number zero is an interesting one. In early times, zero was not used as a number at all, but instead was used as a place holder to indicate the position of hundreds and tens. This article briefly discusses the history of zero and challenges the thinking where divisions using zero are used.
Topics: ERIC Archive, Number Concepts, Arithmetic, Mathematics Instruction, Teaching Methods, History,...
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...
There is an old joke that says that given the choice between eternal happiness and a ham sandwich, one should choose the ham sandwich. The proof is quite simple: (1) nothing is better than eternal happiness; (2) a ham sandwich is better than nothing; and therefore, it straightforwardly follows from (1) and (2) that (3) a ham sandwich is better than eternal happiness. So, given the choice, one should choose a ham sandwich. This article takes a slightly more serious view of transitive...
Topics: ERIC Archive, Psychological Patterns, Mathematics Instruction, Games, Teaching Methods, Roberts,...
Despite the assurances of store employees, whenever a deal is on offer it always pays to apply a little logic (and mathematics) to see just how to use it most effectively. In this article, the author displays how to employ this technique by using the example of a shoe store that advertised "second pair half price" (with the fine print stating that the second pair was the pair of lesser value).
Topics: ERIC Archive, Mathematics Instruction, Classroom Techniques, Costs, Mathematical Logic, Croucher,...
Perhaps next time teachers head towards the fundamental theorem of calculus in their classroom, they may wish to consider Fermat's technique of finding expressions for areas under curves, beautifully outlined in Boyer's History of Mathematics. Pierre de Fermat (1601-1665) developed some important results in the journey toward the discovery of the calculus. One of these concerned finding areas under simple polynomial curves. It is an amazing fact that, despite deriving these results, he failed...
Topics: ERIC Archive, Calculus, Mathematics Instruction, Teaching Methods, High School Seniors, Staples, Ed
Prediction is a great skill to have in any walk of life: it can, in fact, save lives at times. While the two investigations posed in this column may not be that dramatic, they might just increase one's appreciation of some important connections between grids and rectangles and the divisors of numbers that appear in the dimensions of those rectangles.
Topics: ERIC Archive, Prediction, Investigations, Numbers, Geometry, Problem Solving, Mathematics...
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,...
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 document presents helpful suggestions (tips) for tutors. Introductory material indicates the purposes and commitment involved in tutoring. Suggestions are categorized according to general, first session, later sessions, tutoring reading, and tutoring arithmetic. Several approaches to aid a tutor-study partner relationship are included. (MJM)
Topics: ERIC Archive, Cross Age Teaching, Mathematics Instruction, Reading Instruction, Teaching Methods,...
"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...
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,...
The Expert Mathematician (version 3.0), a middle school math curriculum, was developed from LogoWriter, a computer program that the developer claims is designed to help children learn independently through exploration. According to J. J. Baker, the Expert Mathematician is designed to provide a creative environment that is intended to foster a child?shigher learning skills. It contains 196 lessons. This WWC Study Report reviews a study that compares the effects of The Expert Mathematician with...
Topics: ERIC Archive, Computer Software, Instructional Design, Mathematics Instruction, Grade 8, Middle...
Arguing that college mathematics education must be made more effective, especially for technology, engineering, mathematical sciences, and physical sciences students, this paper presents nine general principles to enhance math instruction for all students. Introductory material argues that changes in perception, attitudes, and role models are needed to realize the goals of integrating knowledge acquisition and knowledge utilization and exploring metacognitive instructional considerations. Next,...
Topics: ERIC Archive, College Mathematics, Instructional Improvement, Learning Strategies, Mathematics...
The preface to this book notes the relationship of its contents to the 1968 conference "to appraise mathematics educators of the present status and future prospects of computer-assisted instruction (CAI) and its implications for the teaching of mathematics." The introduction, "Computers in Mathematics and Other Education," was the keynote address by R. W. Gerard. Part 1 on CAI hardware development contains two papers: "Economically Viable Large-Scale Computer-based...
Topics: ERIC Archive, Computer Assisted Instruction, Mathematics Curriculum, Mathematics Instruction,...
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...
The 26th Undergraduate Mathematics Teaching Conference took place in September of 2000 at Sheffield Hallam University. Major topics of the conference included what use might mathematics education research be to university mathematics teachers?, attracting students to mathematics, use of the internet in teaching mathematics, and supporting the professional development of mathematics lecturers. Papers and presentations given at the conference include: (1) "The Popularization of...
Topics: ERIC Archive, Higher Education, Mathematics Instruction, Numeracy, Teaching Methods, Undergraduate...
This collection of activities is designed to show how graphics display calculators can be used to foster algebraic thinking in middle school students. The collection consists of five activities addressing such topics as functions, estimation and scatterplots, and patterns. Blackline masters for the activities are included. (MM)
Topics: ERIC Archive, Algebra, Graphing Calculators, Mathematics Activities, 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...
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,...
Since Shulman's (1986) seminal work on Pedagogical Content Knowledge (PCK) was released, it has created opportunities for the creation of constructs to scaffold the knowledge and understandings that teachers need in order to be effective. Adapting this work from being a heuristic to an operational structure has seen the development of many models. One such model regarding Mathematical Knowledge for Teaching (MKT) (Hill et al., 2008) has enjoyed a good deal of attention. This paper aims to argue...
Topics: ERIC Archive, Pedagogical Content Knowledge, Mathematics Instruction, Models, Foreign Countries,...
The trouble with mathematics is that it looks a little more logical and consistent than it is. Mathematics has a universally recognised exactitude. It also has an inexactitude that tends to remain concealed. This author contends that the trouble with mathematics is that it is neither structured, nor unstructured. It is nearly structured, but not fully. It is neither tamed nor wild. It is both nearly tamed and forever untameable. The author uses the jazz metaphor as a useful way of understanding...
Topics: ERIC Archive, Figurative Language, Music, Mathematics Instruction, Mathematics Education, Teaching...
Mathematics should not be studied simply because it is useful; mathematics should be also studied because it nurtures both the mind and soul with its beauty. By completing the four activities described in this paper, students will appreciate mathematical ideas both rationally and emotionally. Since students' appreciation of mathematical ideas requires learning by self-discovery, they will be encouraged to see mathematical and real-world connections via mathematical demonstrations. They will...
Topics: ERIC Archive, Mathematics Instruction, Mathematics Curriculum, Graphs, Mathematical Formulas,...
