Why Are School Districts Abandoning the Core-Plus Mathematics Curriculum?
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Standards-Based Curriculum Summaries
CURRICULUM SUMMARIES Eighth edition September 2005 About This Publication Curriculum Summaries compiles information about 12 comprehensive mathematics curriculum programs that were developed specifically to address the recommendations of the National Council of Teachers of Mathematics’ Curriculum and Evaluation Standards for School Mathematics (1989) and that are well-aligned with the Principles and Standards for School Mathematics (2000). Three of the programs described here are elementary programs, four are for middle school, and five are for high school. All of these programs were developed with support from the National Science Foundation. They are all available as complete and published curricula. Part of our mission at the K–12 Mathematics Curriculum Center (K–12 MCC), and the intention of this document, is to support teachers, schools, and districts in learning about these programs and in considering their use. This publication is intended to be a source of basic information about the mathematics programs it describes. We have included information that we think will help the reader understand the basic tenets of each of the programs, what distinguishes them from traditional curricula, and what distinguishes them from one another. We have also incorporated information that we hope will help you learn more about these programs, through contact with the publishers, developers, or implementation centers, through print materials, or through websites. We have tried to describe the programs as the developers and publishers would represent them. The information about each of the curriculum programs was obtained from the materials themselves and was checked by representatives of each of the programs for accuracy. Curriculum Summaries is not, therefore, a source of evaluative data or critical analyses of these programs. -
Chapter 13 National Science Foundation Systemic Initiatives
Chapter 13 National Science Foundation Systemic Initiatives: How a small amount of federal money promotes ill-designed mathematics and science programs in K-12 and undermines local control of education Michael McKeown Mathematically Correct David Klein California State University, Los Angeles Chris Patterson Education Connection of Texas Since its inception in 1950, the National Science Foundation (NSF) has played a strong, positive role in making American scientific research and technological application the best in the world. Through its funding of peer-reviewed, investigator-initiated research proposals, it has supported basic research in a wide variety of scientific disciplines, such as mathematics, biology, physics, chemistry, geology, astronomy, and psychology. American science owes much to the support it has received, and continues to receive, from NSF. This chapter deals with a program in the Education and Human Resources Division called the NSF Systemic Initiatives Program, not with NSF programs related directly to the support of basic research. We are highly critical of this particular NSF program. Not only do the Systemic Initiatives undermine local control of education, but, as our analysis in this chapter suggests, they also seem to lower academic standards for mathematics education and weaken the educational base for American science. This chapter is composed of three sections. The first section, an overview of NSF Systemic Initiatives, was written by Michael McKeown. The second section, an analysis of the development and 288 Standards Wars features of the Los Angeles Systemic Initiative, was written by David Klein. The third section, an analysis of the development and features of the Texas Statewide Systemic Initiative, was written by Chris Patterson. -
Mathematics in African History and Cultures
Paulus Gerdes & Ahmed Djebbar MATHEMATICS IN AFRICAN HISTORY AND CULTURES: AN ANNOTATED BIBLIOGRAPHY African Mathematical Union Commission on the History of Mathematics in Africa (AMUCHMA) Mathematics in African History and Cultures Second edition, 2007 First edition: African Mathematical Union, Cape Town, South Africa, 2004 ISBN: 978-1-4303-1537-7 Published by Lulu. Copyright © 2007 by Paulus Gerdes & Ahmed Djebbar Authors Paulus Gerdes Research Centre for Mathematics, Culture and Education, C.P. 915, Maputo, Mozambique E-mail: [email protected] Ahmed Djebbar Département de mathématiques, Bt. M 2, Université de Lille 1, 59655 Villeneuve D’Asq Cedex, France E-mail: [email protected], [email protected] Cover design inspired by a pattern on a mat woven in the 19th century by a Yombe woman from the Lower Congo area (Cf. GER-04b, p. 96). 2 Table of contents page Preface by the President of the African 7 Mathematical Union (Prof. Jan Persens) Introduction 9 Introduction to the new edition 14 Bibliography A 15 B 43 C 65 D 77 E 105 F 115 G 121 H 162 I 173 J 179 K 182 L 194 M 207 N 223 O 228 P 234 R 241 S 252 T 274 U 281 V 283 3 Mathematics in African History and Cultures page W 290 Y 296 Z 298 Appendices 1 On mathematicians of African descent / 307 Diaspora 2 Publications by Africans on the History of 313 Mathematics outside Africa (including reviews of these publications) 3 On Time-reckoning and Astronomy in 317 African History and Cultures 4 String figures in Africa 338 5 Examples of other Mathematical Books and 343 -
An Alternative Route to Teaching Fraction Division: Abstraction of Common Denominator Algorithm
International Electronic Journal of Elementary Education, 2015, 7(3), 399-422. An Alternative Route to Teaching Fraction Division: Abstraction of Common Denominator Algorithm İsmail Özgür ZEMBAT Mevlana (Rumi) University, Turkey Received: February 2015 / Revised: May 2015 / Accepted: May 2015 Abstract From a curricular stand point, the traditional invert and multiply algorithm for division of fractions provides few affordances for linking to a rich understanding of fractions. On the other hand, an alternative algorithm, called common denominator algorithm, has many such affordances. The current study serves as an argument for shifting curriculum for fraction division from use of invert and multiply algorithm as a basis to the use of common denominator algorithm as a basis. This was accomplished with the analysis of learning of two prospective elementary teachers being an illustration of how to realize those conceptual affordances. In doing so, the article proposes an instructional sequence and details it by referring to both the (mathematical and pedagogical) advantages and the disadvantages. As a result, this algorithm has a conceptual basis depending on basic operations of partitioning, unitizing, and counting, which make it accessible to learners. Also, when participants are encouraged to construct this algorithm based on their work with diagrams, common denominator algorithm formalizes the work that they do with diagrams. Keywords: Teaching fraction division, abstracting common denominator algorithm, curriculum development Introduction Arithmetic operations, and teaching and learning of them have always been an interest for mathematics education community. In his historical analysis, Usiskin (2007) pointed out that operations (especially on fractions) still preserve its importance in school mathematics and they should be given enough emphasis. -
AVAILABLE from ABSTRACT DOCUMENT RESUME Exemplary
DOCUMENT RESUME ED 434 033 SE 062 877 TITLE Exemplary and Promising Mathematics Programs. INSTITUTION Department of Education, Washington, DC. PUB DATE 1999-00-00 NOTE 71p.; Prepared by the "Math and Science Education Expert Panel." AVAILABLE FROM ED Pubs, P.O. Box 1389, Jessup, MD. Tel: 877-433-7827 (Toll Free); Web site: <http://www.enc.org>. PUB TYPE Reports Descriptive (141) EDRS PRICE MF01/PC03 Plus Postage. DESCRIPTORS *Academic Standards; Demonstration Programs; Elementary Secondary Education; Mathematics Curriculum; *Mathematics Education; *Program Descriptions; *Program Evaluation ABSTRACT Selecting programs, textbooks, and curriculum materials is one of the most important decisions educators make. An Expert Panel on Mathematics and Science was established by the U.S. Department of Education to develop a high-quality, research-based process for selecting programs and to use that selecting process to identify exemplary and promising programs. This booklet describes eight mathematics programs designated as exemplary or promising. A detailed explanation of the submission and selection process and an explanation of how the programs were separated into exemplary and promising categories is included. The four characteristics used for the selection criteria include quality of program, usefulness to others, educational significance, and evidence of effectiveness and success. Each characteristic has multiple criteria with specific indicators of achievement. Each program is described in terms of the four selection characteristics and professional -
May 2001 What Are the Children Learning and Who Decides
May 2001 THE TEXTBOOK CONUNDRUM What are the Children Learning and Who Decides? Introduction With the quality of education in the United States now the biggest domestic concern, demands for accountability are in vogue. The drive for better schools however, is usually limited to issues of standards, testing, choice and teachers. Missing from most discussions is the role that textbooks play in the achievement of children. A few facts to consider: • In more than twenty states, the state (state board of education, department of education, secretary or commissioner of education, or another specially designated state textbook committee) picks the textbooks for every classroom in the state – either through outright text selection, or recommendations from a short list. To control curriculum, they tie funding to compliance with the states’ textbook adoption policy. • Textbooks supplied to three states, California, Texas and Florida – all of which give significant influence to state agencies for textbook selection – account for 30 percent of the more than $3.3 billion K-12 textbook market in 1998, the most recent year for which statistics are available.i • Four publishers (McGraw-Hill, Houghton Mifflin, Harcourt, and Pearson) control 70 percent of the industry. Size means money means influence in the textbook world. They are a strong, quiet interest group that works behind the scenes and through major education groups to ensure that the process favoring them stays exactly the way it is. The process for putting books in front of children then, looks something like this: The “big three” states draw up textbook adoption policies to which the “big four” publishers try to align their textbook content. -
The Impact of Information and Communication Technology on Our Understanding of the Nature of Mathematics
FLM 26(1) 2/2/06 12:33 PM Page 29 THE IMPACT OF INFORMATION AND COMMUNICATION TECHNOLOGY ON OUR UNDERSTANDING OF THE NATURE OF MATHEMATICS FREDERICK K. S. LEUNG The incorporation of information and communication tech- scientific calculator) and it can also be used as a transforma- nology (ICT) into mathematics education constitutes one of tional tool, a data collection and analysis tool, a visualizing the most important themes in contemporary mathematics tool and/or a checking tool. Doerr and Zangor (2000) sum- education. For example, one of the six principles of school marized the different roles the graphing calculator plays and mathematics as espoused by the National Council of Teach- the corresponding student actions as follows: ers of Mathematics (NCTM, 2000) is that Role of the Description of Student Actions Technology is essential in teaching and learning math- Graphing Calculator ematics; it influences the mathematics that is taught and enhances students’ learning. (p. 24, emphasis added). Computational Tool Evaluating numerical expressions, esti- mating and rounding The purpose of this article is to review research findings on the effectiveness of the use of some selected ICT tools in Transformational Tool Changing the nature of the task mathematics teaching and learning. [1] This review is then Data Collection and Gathering data, controlling phenomena, set against a summary of the actual use of ICT tools in real Analysis Tool fiding patterns classrooms. Various issues related to the incorporation of Visualizing Tool Finding symbolic functions, displaying ICT into mathematics education arise, including: data, interpreting data, solving equations • the reasons for the discrepancy between the poten- Checking Tool Confirming conjectures, understanding tial and actual use of ICT multiple symbolic forms Figure 1: Table showing the patterns and modes of use of a • the impact of ICT on our understanding of the graphing calculator (p. -
Traditional Mathematics Teaching Is Still the Norm in Our Nation's Schools
Forum on Public Policy Mathematics and Literature: Educators’ Perspectives on Utilizing a Reformative Approach to Bridge Two Cultures Suzanne J. Nesmith, Associate Dean/Assistant Professor of Education, Wayland Baptist University Abstract The existence of two distinct cultures within our society, the arts and the sciences, was introduced by physicist C. P. Snow in his 1959 Reed Lecture at Cambridge University and was further illuminated by Snow in The Two Cultures, a Second Look (1964). Lamenting the existence of the cultural chasm while also fearing a widening of the schism, Snow opened a dialogue with the hope of reconciliation between the cultures. Fifty years later, although the chasm still exists, numerous entities and individuals within the cultures work to formulate the means by which the cultures may be bridged, and, subsequently, the chasm narrowed and eliminated. The National Council of Teachers of Mathematics (NCTM) is one such entity, and leaders of the group have worked since the council‟s establishment in 1920 to research, promote, and improve the teaching and learning of mathematics through innovative, reformative approaches. Reform-oriented curricula are built upon constructivist perspectives aimed at assisting students in utilizing their own unique backgrounds and experiences to develop a personal understanding of mathematical situations. One means of infusing personal experience into the mathematics curriculum, while also bridging the aforementioned cultures, is through the incorporation of children‟s literature, yet there exists great variance in the type, format, structure, and success of the methodology‟s implementation. Subsequently, while the reformative approach of mathematics literature integration presents as a means of building understanding by bridging the cultures of mathematics and the humanities, it is the educator‟s choices relevant to the approach which have the greatest impact on the outcomes of the approach. -
The Comparison of Physical/Virtual Manipulative on Fifth-Grade Students’ Understanding of Adding Fractions
Running Head: COMPARISON OF PHYSICAL/VIRTUAL MANIPULATIVE The Comparison of Physical/Virtual Manipulative on Fifth-Grade Students’ Understanding of Adding Fractions A dissertation submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Doctor of Education in the Department of Curriculum and Instruction of the College of Education by Sami Alshehri M.A. Umm Al-Qura University July 2008 Committee Chair: M. Sally, Ed.D. COMPARISON OF PHYSICAL/VIRTUAL MANIPULATIVE ABSTRACT The purpose of this quantitative study was to compare two types of manipulatives in order to see their effects upon understanding of adding fractions for three comparable groups of fifth grade students. A total of 163 students who demonstrated low mathematical performance participated in the project in order to learn the addition of fractions by using physical and virtual manipulatives for the experimental groups and the normal mathematic curriculum for the control group. The intervention occurred during a two-week time frame in six public elementary schools in Abha, Saudi Arabia where students used fraction bars for both physical and virtual manipulatives in order to build conceptual understanding of adding fractions properly. Instructions were provided to all the participants directly regarding what the participants were to do each day of the 2-week experiment. Pre-and post-tests, an attitude survey, and a preference survey were the instruments that were used to collect data during the study. A repeated measures design with a cross over treatment was used for comparing the effects of the two modes of treatments, virtual and physical manipulatives, compared to a control group for the understanding of adding fractions for the three groups of students. -
Reforming Mathematics Education Dr. Barry Fagin Professor Of
Reforming K-12 Mathematics Education Dr. Barry Fagin Professor of Computer Science USAFA (opinions are mine, not USAFA’s) What’s the problem? 8th grade math scores, IAEEA 2000 Report 700 600 500 400 300 200 100 0 y n a a a A ia n ca re a i ri S n ra ri o p ss ysi a U a rke I f p u la lg u A a Ja a m T g R u o th in M B R u S o S 1. Singapore 2. Korea 3. China 13. Australia 4. Hong Kong 2. Czechoslovakia 5. Japan 3. Finland 1. Moldova 6. Belgium 4. Malaysia 2. Thailand 7. Netherlands 5. Bulgaria 3. Israel 8. Slovak Rep. 6. USA 4. Tunisia 9. Hungary 7. England 5. Macedonia 10.Canada 8. New Zealand 6. Turkey 11.Slovenia 9. Lithuania 7. Jordan 12.Russia 10.Italy 8. Iran 11.Cyprus 9. Indonesia 12.Romania 10.Chile 11.Philippines 12.Morocco 13.South Africa % CSAP Advanced or Proficient (5th grade) 100 90 80 70 60 W 50 H 40 B 30 20 10 0 2001 2002 2003 % CSAP Advanced or Proficient (8th grade) 100 90 80 70 60 W 50 H 40 B 30 20 10 0 2001 2002 2003 % CSAP Advanced or Proficient (10th grade) 100 90 80 70 60 W 50 H 40 B 30 20 10 0 2001 2002 2003 Class of 2005 100 90 80 70 60 W 50 H 40 B 30 20 10 0 8th (2001) 9th (2002) 10th (2003) What’s the cause? Widespread adoption of curricula that: • Emphasize process over content • De-emphasize math facts • Embrace constructivism • Encourage calculator use in early grades • Encourage group work How did this happen? Open letter of protest published in Post, Carter elected DOE forms expert signed by > 200 panel to identify mathematicians and DOE created noteworthy math scientists programs Reagan elected, Secretary -
The Use Or Non-Use of Calculators Affects on Student's Ability to Perform Basic Mathematics Problems
Old Dominion University ODU Digital Commons OTS Master's Level Projects & Papers STEM Education & Professional Studies 2008 The Use or Non-Use of Calculators Affects on Student's Ability to Perform Basic Mathematics Problems Christina Miles Old Dominion University Follow this and additional works at: https://digitalcommons.odu.edu/ots_masters_projects Part of the Education Commons Recommended Citation Miles, Christina, "The Use or Non-Use of Calculators Affects on Student's Ability to Perform Basic Mathematics Problems" (2008). OTS Master's Level Projects & Papers. 89. https://digitalcommons.odu.edu/ots_masters_projects/89 This Master's Project is brought to you for free and open access by the STEM Education & Professional Studies at ODU Digital Commons. It has been accepted for inclusion in OTS Master's Level Projects & Papers by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. THE USE OR NON-USE OF CALCULATORS AFFECTS ON STUDENT’S ABILITY TO PERFORM BASIC MATHEMATICS PROBLEMS A RESEARCH PAPER PRESENTED TO THE GRADUATE FACULTY OF THE DEPARTMENT OF OCCUPATIONAL AND TECHNICAL EDUCATION STUDIES AT OLD DOMINION UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE MASTER OF SCIENCE DEGREE BY CHRISTINA GORDON MILES AUGUST 2008 ii APPROVAL PAGE This research paper was prepared by Christina Gordon Miles under the direction of Dr. John Ritz at Old Dominion University in Norfolk, Virginia. It was submitted to the Graduate Program Director as partial fulfillment of the requirements for the Degree of Master of Science. APPROVAL BY: _____________________________ Date _______________________ Dr. John M. Ritz Advisor and Graduate Program Director iii ACKNOWLEDGEMENTS I would like to especially thank my husband, Captain Paul E. -
3 Reasons Why Singapore Math Is NCTM Recommended
3 Reasons Why Singapore Math Curriculum is Recommended by the NCTM web.archive.org/web/20100211050856/http://www.learningthings.com:80/articles/Singapore-Math-Recommended-by- NCTM.aspx Math education in U.S. schools has been broken for many years but now a fix is available. Students in U.S. high schools have been consistently scoring near the bottom of the list of countries participating in International math tests. Among the 30 nations participating in the 2006 PISA test, only 4 nations had lower test scores. The 2006 results were about the same as the results from the 2003 PISA tests. In other words, U.S. students are near the bottom, barely above developing nations, and showing no signs of moving up. By contrast, these same math tests consistently show Asian nations scoring at the top. In the 2003 Trends in International Mathematics and Science Study (TIMSS), Singapore ranked number 1 followed by South Korea and Hong Kong. In the 2006 PISA tests, Asian countries took 4 of the top 10 spots. In the U.S., math standards are set at the state level and curriculum choices are made by local school districts. States and local districts rely on guidelines provided by the National Council for Teachers of Mathematics (NCTM). Based on the research and theories of education "experts", the NCTM published 1989 guidelines which embraced new 'reform math' curriculums. Rather than helping achieve higher test scores, these programs caused many districts to achieve lower test scores. The following programs are examples: • 'Everyday Mathematics' (Bell, 1988-1996) • 'Connected Mathematics' (Lappan et al, 1991-1997).