How Has Jo Boaler Been Transforming U.S. K-12 Math ?
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Problematizing the Philosophy of Mathematics in a Time of Curriculum Reform Kimberly White-Fredette
The Mathematics Educator 2009/2010, Vol. 19, No. 2, 21–31 Why Not Philosophy? Problematizing the Philosophy of Mathematics in a Time of Curriculum Reform Kimberly White-Fredette This article argues that, as teachers struggle to implement curriculum reform in mathematics, an explicit discussion of philosophy of mathematics is missing from the conversation. Building on the work of Ernest (1988, 1991, 1994, 1998, 1999, 2004), Lerman (1990, 1998, 1999), the National Council of Teachers of Mathematics (1989, 1991, 2000), Davis and Hersh (1981), Hersh (1997), Lakatos (1945/1976), Kitcher (1984), and others, the author draws parallels between social constructivism and a humanism philosophy of mathematics. While practicing mathematicians may be entrenched in a traditional, Platonic philosophy of mathematics, and mathematics education researchers have embraced the fallibilist, humanist philosophy of mathematics (Sfard, 1998), the teachers of school mathematics are caught somewhere in the middle. Mathematics teachers too often hold true to the traditional view of mathematics as an absolute truth independent of human subjectivity. At the same time, they are pushed to teach mathematics as a social construction, an activity that makes sense only through its usefulness. Given these dichotomous views of mathematics, without an explicit conversation about and exploration of the philosophy of mathematics, reform in the teaching and learning of mathematics may be certain to fail. The teaching and learning of mathematics is without a radical change in instructional practices going through tremendous changes. The National and an equally radical change in teachers’ views of Council of Teachers of Mathematics’ (NCTM, 2000) mathematics teaching and learning, as well as the Principles and Standards for School Mathematics discipline of mathematics itself. -
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. -
An Examination of the Potential of Secondary Mathematics
AN EXAMINATION OF THE POTENTIAL OF SECONDARY MATHEMATICS CURRICULUM MATERIALS TO SUPPORT TEACHER AND STUDENT LEARNING OF PROBABIILITY AND STATISTICS by Joshua E. Williams B. S., Clarion University, 2000 M. S., Salisbury University, 2006 Submitted to the Graduate Faculty of The School of Education in partial fulfillment of the requirements for the degree of Doctor of Education University of Pittsburgh 2016 UNIVERSITY OF PITTSBURGH THE SCHOOL OF EDUCATION This dissertation was presented by Joshua E. Williams It was defended on September 7, 2016 and approved by Dr. Ellen Ansell, Associate Professor, Instruction and Learning Dr. James Greeno, Emeritus Professor, Standford University Dr. Mary Kay Stein, Professor, Learning Science and Policy Dissertation Advisor: Dr. Margaret S. Smith, Emeritus Professor, Instruction and Learning ii Copyright © by Joshua E. Williams 2016 iii AN EXAMINATION OF THE POTENTIAL OF SECONDARY MATHEMATICS CURRICULUM MATERIALS TO SUPPORT TEACHER AND STUDENT LEARNING OF PROBABIILITY AND STATISTICS Joshua E. Williams, EdD University of Pittsburgh, 2016 The Common Core State Standards for Mathematics (CCSSSM) suggest many changes to secondary mathematics education including an increased focus on conceptual understanding and the inclusion of content and processes that are beyond what is currently taught to most high school students. To facilitate these changes, students will need opportunities to engage in tasks that are cognitively demanding in order to develop this conceptual understanding and to engage in such tasks over a breadth of content areas including probability and statistics. However, teachers may have a difficult time facilitating a change from traditional mathematics instruction to instruction that centers around the use of high-level tasks and a focus on conceptual understanding and that include content from the areas of probability and statistics that may go beyond their expertise and experience. -
Book Report Winning the Math Wars
Book Report Winning the Math Wars: No Teacher Left Behind Samantha A Peterson Seattle Pacific University 2 Winning the Math Wars: No Teacher Left Behind, is a book written by four Seattle Pacific University scholars, who present a well-articulated and non-biased assessment of the state of mathematics education in the world, in the United States, and specifically in Washington State. The authors divided the book into four chapters, which address the following four topics respectively; what the world is thinking about math education, the American dilemma about math education, math education in Washington State, and ending with a discussion about the implications and conclusions of the math debate. The focus of the book is to present a broad analysis of the math wars and to come to some conclusion about what’s needed in order to realize effective change in the teaching and learning of mathematics. The underlying theme throughout the discussion of reform mathematics is the lack of attention that has been given to the teacher’s role in education reform; “effective reform requires the coordination among standards, assessment, and instruction,” (pg.123). The authors begin by exploring the historical development of the math wars and comparing the United States educational system to that of other cultures. This comparison is helpful because it addresses some of the cultural implications for differences in performance between American students and students from other countries. For instance, Japanese students typically spend far more time on homework and math study. Japanese and American teachers also differ fundamentally in their approach to math teaching. -
Math Wars: the Politics of Curriculum
University of Northern Iowa UNI ScholarWorks Presidential Scholars Theses (1990 – 2006) Honors Program 1999 Math wars: The politics of curriculum Raymond Johnson University of Northern Iowa Let us know how access to this document benefits ouy Copyright ©1999 Raymond Johnson Follow this and additional works at: https://scholarworks.uni.edu/pst Part of the Curriculum and Instruction Commons, and the Science and Mathematics Education Commons Recommended Citation Johnson, Raymond, "Math wars: The politics of curriculum" (1999). Presidential Scholars Theses (1990 – 2006). 89. https://scholarworks.uni.edu/pst/89 This Open Access Presidential Scholars Thesis is brought to you for free and open access by the Honors Program at UNI ScholarWorks. It has been accepted for inclusion in Presidential Scholars Theses (1990 – 2006) by an authorized administrator of UNI ScholarWorks. For more information, please contact [email protected]. MATH WARS The Politics of Curriculum Presidential Scholars Senior Thesis by Raymond Johnson Under the advisement of Dr. Edward Rathmell December 9, 1999 Johnson 2 Introduction There is an ongoing battle in mathematics education, a battle sometimes so fierce that some people call it the "math wars". Americans have seen many changes and proposed changes in their educational system in the last fifty years, but few have stirred such debate, publicity, and criticism as have the changes in mathematics education. We will first look at the history of the math wars and take time to examine previous attempts to change mathematics education in America. Second, we will assess the more recent efforts in mathematics education reform . Lastly, we will make some predictions for the future of the math wars and the new directions mathematics education may take. -
What Students Notice As Different Between Reform and Traditional Mathematics Programs
Journal for Research in Mathematics Education 2008, Vol. 39, No. 1, 9–32 What Students Notice as Different Between Reform and Traditional Mathematics Programs Jon R. Star Harvard University John P. Smith III Michigan State University Amanda Jansen University of Delaware Research on the impact of Standards-based mathematics and reform calculus curricula has largely focused on changes in achievement and attitudes, generally ignoring how students experience these new programs. This study was designed to address that deficit. As part of a larger effort to characterize students’ transitions into and out of reform programs, we analyzed how 93 high school and college students perceived Standards-based and reform calculus programs as different from traditional ones. Results show considerable diversity across and even within sites. Nearly all students reported differences, but high-impact differences, like Content, were not always related to curriculum type (reform or traditional). Students’ perceptions aligned moderately well with those of reform curriculum authors, e.g., concerning Typical Problems. These results show that students’ responses to reform programs can be quite diverse and only partially aligned with adults’ views. Key words: College/university; Curriculum; High school (9–12); Integrated curriculum; Learners (characteristics of); Qualitative methods; Reform in mathematics education; Social factors One inevitable outcome of the development of new curricula in any field, but perhaps particularly in mathematics, is to provoke discussion and debate about what content can and should be taught in schools and universities. The recent cycle of The entire Mathematical Transitions Project team played a vital role in the work reported here. In addition to the authors, the other members of this team were, in alphabetical order, Dawn Berk, Carol Burdell, Beth Herbel-Eisenmann, Gary Lewis, and Violeta Rosca-Yurita. -
Reduced Annotated Bibliography
Core-Plus Mathematics Project Evaluation and Research Bibliography Peer-Reviewed Journal Publications Chávez, Ó., Tarr, J. E., Grouws, D. A., & Soria, V. M. (2015, March). Third-year high school mathematics curriculum: Effects of content organization and curriculum implementation. International Journal of Science and Mathematics Education. Volume 13, Supplement 1, 97–120. We examined the effect of curriculum organization in US high schools where students could freely choose to study mathematics from textbooks that employed one of two types of content organization, an integrated approach or a (traditional) subject-specific approach. The study involved 2,242 high school students, enrolled in either Course 3 or Algebra 2, in 10 schools in 5 geographically dispersed states. Taking account of curriculum implementation and students' prior mathematics learning, we analyzed two end-of-year outcome measures: a test of common objectives and a standardized achievement test. Our hierarchical linear models with three levels showed that students in the integrated curriculum scored significantly higher than those in the subject-specific curriculum on the common objectives test. In both outcome measures, gender and prior achievement were significant student-level predictors. In the standardized achievement test, ethnicity was a moderating factor. At the teacher-level, in addition to curriculum type, teachers' orientation and free and reduced lunch eligibility were significant moderating factors. Opportunity to learn, implementation fidelity, teacher experience, and professional development were not significant predictors. Hong, D. S., & Choi, K. M. (2014). A comparison of Korean and American secondary school textbooks: The case of quadratic equations. Educational Studies in Mathematics, 85(2), 241–263. This study reports a content analysis of the development of quadratic equations in national Korean and Core-Plus Mathematics textbooks. -
Student Centered Mathematics in an Isolated Skill Environment- Constructivist Methods in Mathematics
Student Centered Mathematics in an Isolated Skill Environment- Constructivist Methods in Mathematics by Amy Katherine Sorensen A Research Paper Submitted to the Faculty of the DEPARTMENT OF MATHEMATICS In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE IN ELEMENTARY AND MIDDLE MATHEMATICS EDUCATION BEMIDJI STATE UNIVERSITY Bemidji, Minnesota, USA April 2013 Constructivist Methods in Mathematics 2 STATEMENT BY AUTHOR Brief quotations from this research paper are allowable without special permission, provided accurate acknowledgement of the source is indicated. Requests for permission to use extended quotations or reproduce the manuscript in whole or in part may be granted by Department of Mathematical Studies, School of Graduate Studies when the proposed purpose is in the interest of scholarship. In all other instances, however, permission must be obtained from the author. Signed: APPROVAL BY RESEARCH PAPER ADVISOR THIS RESEARCH PAPER HAS BEEN APPROVED ON THE DATE SHOWN BELOW: Dr. Glen Richgels Date Committee Chair Professor of Mathematics Dr. Derek Webb Date Professor of Mathematics Dr. Todd Frauenholtz Date Professor of Mathematics Dr. Patricia L. Rogers Dean, School of Graduate Studies Date Constructivist Methods in Mathematics 3 THE IMPORTANCE OF CONSTRUCTIVISM IN A MATHEMATICS CLASSROOM Amy Katherine Sorensen Write a brief statement (not necessary for the proposal) describing what you did and what you found. Consider that some people will read only your abstract so it should represent exactly what your paper is about. One paragraph (perhaps two) is all that should be included here. Approved by Dr. Glen Richgels Date Committee Chair Dr. Derek Webb Date Committee Member Dr. -
Reinvent Mathematics Education and You Change the World
Reinvent Mathematics Education and You Change the World Gary S. Stager, Ph.D. ASB Unplugged Workshop Handouts February 2018 [email protected] @garystager constructingmodernknowledge.com cmkfutures.com/gary cmkpress.com inventtolearn.com APPLYING THE CBM THE MATH SOLUTION HELIX PROCESS OF MATH MATH MODELS QUESTIONS NEW KNOWLEDGE MATH ANSWERS Transform the math models Prepare the questions as math into math answers with the models ready for computing power of computers, or by Did the math answers solve the Think through the scope and the answer. Select from hand-calculating. Identify original problem? Fix mistakes details of the problem; define standard techniques or and resolve operational issues or refine by taking another turn manageable questions to tackle. formulate algorithms. during the computation. around the Solution Helix. DEFINE TRANSLATE COMPUTE INTERPRET QUESTIONS TO MATH ANSWERS RESULT Why Use Math? Computer-Based Math (CBM)… Because it's the most powerful way to get answers to a wide range of real-world questions. Several factors contribute to math’s …is building a completely new math power. One is its ability to describe a large number of apparently diferent situations in precise and standardized ways. Another is curriculum with computer-based because these descriptions come with highly efective methods for working out, or “computing,” answers. Math may look cryptic computation at its heart, while but it’s by this “abstraction” from the problem at hand that the same methods can be reused and refined on so many diferent campaigning at all levels to redefine problems. Math also scales well. Whizz around the CBM Solution Helix in a few seconds for everyday problems like “How fast do I math education away from need to go?”, or apply it over years at the cutting edge of research to solve problems like “How can I make a car go 1000 mph?” historical hand-calculating techniques and toward real-life What Is Computation? problem-solving situations that Clearly defined procedures backed up by proven logic for transforming math questions into math answers. -
Insights Into the Beliefs and Practices of Preservice Elementary Mathematics Teacher Educators: a Naturalistic Inquiry
University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 12-2013 Insights Into the Beliefs and Practices of Preservice Elementary Mathematics Teacher Educators: A Naturalistic Inquiry Linda Ann Arnold University of Tennessee - Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Science and Mathematics Education Commons Recommended Citation Arnold, Linda Ann, "Insights Into the Beliefs and Practices of Preservice Elementary Mathematics Teacher Educators: A Naturalistic Inquiry. " PhD diss., University of Tennessee, 2013. https://trace.tennessee.edu/utk_graddiss/2551 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Linda Ann Arnold entitled "Insights Into the Beliefs and Practices of Preservice Elementary Mathematics Teacher Educators: A Naturalistic Inquiry." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Doctor of Philosophy, with a major in Education. Vena M. Long, Major Professor We have read this dissertation and recommend -
The Math Wars California Battles It out Over Mathematics Education Reform (Part II)
comm-calif2.qxp 6/12/97 4:27 PM Page 817 The Math Wars California Battles It Out over Mathematics Education Reform (Part II) Note: The first part of this article appeared in the June/July issue of the Notices, pages 695–702. The Numbers Battle examinations but also group assignments, long- “Show us the data, show us that this program term projects, and portfolios of work done over works,” demands Michael McKeown, the head of a period of time. Some also favor the idea of judg- Mathematically Correct, the San Diego-based ing the efficacy of curricular programs by criteria group critical of mathematics education reform. other than standardized tests, such as the num- McKeown makes his living in the data-driven ber and type of mathematics courses students field of biology, as a researcher at the Salk In- subsequently take. stitute and an adjunct faculty member at UC Such are the views in that portion of the math San Diego. One of the things he finds most vex- wars devoted to testing. The scramble to find ing about the reform is that it has been imple- numbers to support certain viewpoints has led mented without having been subject to large- to some questionable uses of data. For example, scale, well-designed studies to show that student the anti-reform group HOLD (Honest Open Log- achievement rises when the reform materials ical Debate on mathematics reform) recently cir- are used. He points out that what convinced culated an e-mail message containing data on the everyone that there is a problem in mathemat- Elementary Level Mathematics Examination, ics education was low scores on tests like the Na- which is administered in the California State tional Assessment of Educational Progress. -
Jo Boaler's Fame, Stanford's Shame
Jo Boaler’s Fame, Stanford’s Shame; Students’ Gloom, America’s Doom Rooted in Profound Anti-intellectualism, Elitism, Racial and Gender Prejudice, the 2021 California Math Framework Threatens to Undermine Math Learning for All Students and Leave Disadvantaged Learners Permanently Behind. June 16, 2021 Index • Introduction • Section A: The Origin and Development of Reform Math in America • Section B: What Is Wrong With American K-12 Math Education? Why Is Reform Math Disastrous? • Section C: Reform Math is Rooted in Profound Anti-intellectualism, Racism, Sexism, and Elitism • Section D:The Incalculable Cost of Calculators • Section E: Knowledge and Skills, Memorization, Critical Thinking, and Conceptual Understanding • Section F: Manipulatives, Visuals, Finger Math, Multiple Representations, and “Brain science” • Section G: Open-ended Questions, Open Tasks, Projects, and Investigations • Section H: “Authentic,” “Real-world,” “Relevant,” “Problem-Solving” • Section I: The Playful, Feel-good Reform Math • Section J: Math Reformers’ Feuding With Algebra • Section K: Cooperative Learning, Group work, Mixed Ability and Heterogeneous Classrooms • Section L: Formative Assessments Redefine Success and Obscure Failure • Section M: Educational Experts’ Research-based Findings: Do They Hold Water? • Section N: Will America Eventually Survive the Tyranny of Reform Math? This presentation is to demonstrate that the 2021 Draft California Mathematics Framework (CMF) is a manifesto of Reform Math/Fuzzy Math. Firmly rooted in profound anti-intellectualism, elitism, racial and gender prejudice, reform math stultifies all students and disproportionally hurts the disadvantaged learners, worsening the academic achievement gaps and threatening the future of America. Keynotes of the CMF 2021: • A fundamental aim of this framework is to respond issues of inequity in math learning.