Alan Henry Schoenfeld (born July 9, 1947) is an American mathematics education researcher and designer. He is the Elizabeth and Edward Conner Professor of Education and Affiliated Professor of Mathematics at the University of California, Berkeley. [1]
Schoenfeld was raised in New York City, studying at Queens College (BA 1968) before moving to Stanford University to study pure mathematics (MS 1969, PhD 1973 on topology and measure theory). During his graduate studies he became increasingly interested in the teaching and learning of mathematics, particularly of problem solving beyond routine exercises.
He taught at the University of California, Davis (1973–1975), the University of California, Berkeley (1975–1978), Hamilton College (1978–81), and the University of Rochester (1981–1985) before moving back to the University of California, Berkeley where he was a Distinguished Professor in the School of Education with an affiliated appointment in the Mathematics Department, retiring in 2023. [1] [2] [3]
Schoenfeld's work ranges widely across thinking, teaching, and learning in mathematics and beyond, with particular interest in methodological issues aimed at improving the effectiveness of educational research. He has written, edited, or co-edited twenty-two books and more than two hundred articles on thinking and learning. He has focused successively on three major areas:
On problem solving. [4] He made an empirical study of how far mathematics undergraduates tackling non-routine problems can use the strategies set out in George Pólya's work How to Solve It The strategies were based on Pólya's reflections on how he solved problems. Schoenfeld's study found that the strategies alone are weak, and need to be strengthened by complementary domain-specific tactics. He also showed the importance of students' monitoring their work on a problem and adjusting their tactical and technical moves accordingly. This work was published as Mathematical Problem Solving (1985). [5]
On models of teaching. Understanding the decisions that teachers make in real time in the classroom then became a focus. From the analysis in great detail of videos of mathematics lessons, he and his collaborators developed a model of teaching emphasising three key dimensions – the teacher's knowledge, goals and the beliefs about mathematics. He later generalized the work to real time decision making by professionals, published as the book How we think (2010). [6]
On improving classrooms. Since the 1990s Schoenfeld has become increasingly focused on the challenges of translating research insights into tools and processes that improve teaching and learning in real world classrooms. Working with the design team at the Shell Centre for Mathematical Education. [7] in Nottingham, he has led projects to develop tools for teaching and assessment, culminating in the Mathematics Assessment Project. [8] Complementing this he developed a theoretical framework, Teaching for Robust Understanding (TRU), [9] a model of classrooms in which productive learning is likely to occur. This identifies five key dimensions: the Mathematics; Cognitive demand; Access; Agency, authority and identity; Formative assessment.
These include:
Honorary Professor, University of Nottingham, 1994 – present.
President of the American Educational Research Association (AERA) 1998–2000
Vice President of the National Academy of Education, 2001–2005
Lead author for grades 9–12 of the National Council of Teachers of Mathematics' Principles and Standards for School Mathematics, 2000
Senior advisor to the Educational Human Resources Directorate of the National Science Foundation, 2001–2003
Senior content advisor to the U.S. Department of Education's 'What Works Clearinghouse', 2001–2003
A lead author of the mathematics content specifications for the Smarter Balanced Assessment Consortium, 2010–2012
Founding Executive member of the International Society for Design and Development in Education.
Principal investigator of grants from the US National Science Foundation, Bill and Melinda Gates Foundation, the Spencer Foundation, the Sloan foundation, Heising–Simons Foundation and others, totalling more than $45,000,000.
US National Academy of Education, 1994
Fellow, American Association for the Advancement of Science, 2001
Laureate, Kappa Delta Pi, 2006
Inaugural Fellow, American Educational Research Association, 2007
Klein Medal for lifetime achievement in research, from the International Commission on Mathematical Instruction, 2011
Distinguished Contributions to Research in Education Award, AERA, 2013
AERA Division G Henry T. Trueba Award for Research Leading to the Transformation of the Social Contexts of Education to The Center for Diversity in Mathematics Education (DiME), for which Schoenfeld was a PI, 2013
Mary P. Dolciani Award, Mathematical Association of America, 2014
Walter Denham Memorial award, California Mathematics Council, 2014
Doctor of Science Honoris Causa, Queens College of the City University of New York, 2018
International Academy of Education, 2021
George Pólya was a Hungarian-American mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamental contributions to combinatorics, number theory, numerical analysis and probability theory. He is also noted for his work in heuristics and mathematics education. He has been described as one of The Martians, an informal category which included one of his most famous students at ETH Zurich, John von Neumann.
A teaching method is a set of principles and methods used by teachers to enable student learning. These strategies are determined partly by the subject matter to be taught, partly by the relative expertise of the learners, and partly by constraints caused by the learning environment. For a particular teaching method to be appropriate and efficient it has to take into account the learner, the nature of the subject matter, and the type of learning it is supposed to bring about.
How to Solve It (1945) is a small volume by mathematician George Pólya, describingmethods of problem solving.
In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge.
Principles and Standards for School Mathematics (PSSM) are guidelines produced by the National Council of Teachers of Mathematics (NCTM) in 2000, setting forth recommendations for mathematics educators. They form a national vision for preschool through twelfth grade mathematics education in the US and Canada. It is the primary model for standards-based mathematics.
Lee S. Shulman is an American educational psychologist and reformer. He has made notable contributions to the study of teaching; assessment of teaching; education in the fields of medicine, science, and mathematics; and the scholarship of teaching and learning.
Formative assessment, formative evaluation, formative feedback, or assessment for learning, including diagnostic testing, is a range of formal and informal assessment procedures conducted by teachers during the learning process in order to modify teaching and learning activities to improve student attainment. The goal of a formative assessment is to monitor student learning to provide ongoing feedback that can help students identify their strengths and weaknesses and target areas that need work. It also helps faculty recognize where students are struggling and address problems immediately. It typically involves qualitative feedback for both student and teacher that focuses on the details of content and performance. It is commonly contrasted with summative assessment, which seeks to monitor educational outcomes, often for purposes of external accountability.
Linda Darling-Hammond is an American academic who is the Charles E. Ducommun Professor of Education Emeritus at the Stanford Graduate School of Education. She was also the President and CEO of the Learning Policy Institute. She is author or editor of more than 25 books and more than 500 articles on education policy and practice. Her work focuses on school restructuring, teacher education, and educational equity. She was education advisor to Barack Obama's 2008 presidential campaign and was reportedly among candidates for United States Secretary of Education in the Obama administration.
Penelope L. Peterson is an American educational psychologist and academic administrator. Peterson was named Dean of Northwestern University School of Education and Social Policy in September 1997 and previously served as University Distinguished Professor of Education at Michigan State University and Sears-Bascom Professor of Education at University of Wisconsin–Madison. She also served as president of the American Education Research Association (1996–1997).
David Klahr is an American psychologist whose research ranges across the fields of cognitive development, psychology of science, and educational psychology and has been a professor at Carnegie Mellon University since 1969. He is the Walter van Dyke Bingham Professor of Cognitive Development and Education Sciences at Carnegie Mellon University and a member of the National Academy of Education, a Fellow of the American Psychological Association, a Charter Fellow of the Association for Psychological Science, on the Governing Board of the Cognitive Development Society, a member of the Society for Research in Child Development, and the Cognitive Science Society. He was an associate editor of Developmental Psychology and has served on the editorial boards of several cognitive science journals, as well as on the National Science Foundation's subcommittee on Memory and Cognitive Processes, and the National Institutes of Health's Human Development and Aging Study Section.
Professor Tom Lowrie was appointed a Centenary Professor at the University of Canberra, Australia, in 2014. He has an established international research profile in the discipline area of STEM education and mathematics education.
In U.S. education, deeper learning is a set of student educational outcomes including acquisition of robust core academic content, higher-order thinking skills, and learning dispositions. Deeper learning is based on the premise that the nature of work, civic, and everyday life is changing and therefore increasingly requires that formal education provides young people with mastery of skills like analytic reasoning, complex problem solving, and teamwork.
James G. Greeno was an American experimental psychologist and learning scientist whose research focused on learning and problem solving with conceptual understanding, using scientific concepts and methods of association theory, computational cognitive modeling, and discourse analysis.
Michael J. Hannafin was professor of instructional technology and director of Learning and Performance Support Laboratory at the University of Georgia. He obtained a Ph.D. in educational technology from the Arizona State University. Along with Kyle Peck, he developed the field of computer-aided instruction as distinguished from computer-based instruction. He received the AERA SIG- IT Best Paper Award in 2007.
Cathy Kessel is a U.S. researcher in mathematics education and consultant, past-president of Association for Women in Mathematics, winner of the Association for Women in Mathematics Louise Hay Award, and a blogger on Mathematics and Education. She served as an editor for Illustrative Mathematics from the end of 2015 through July 15, 2017.
PR1ME Mathematics teaching programme (PR1ME) is created for the primary or elementary grades and was first introduced in 2014 by Scholastic. It is adopted by schools in multiple countries such as Philippines, Australia, New Zealand and Mexico. PR1ME is a programme based on the Mathematics teaching and learning practices of Singapore, Hong Kong and Republic of Korea, which have consistently performed strongly in international mathematics studies such as the Trends in International Mathematics and Science Study (TIMSS) and Organisation for Economic Co-operation and Development's Programme for International Student Assessment (PISA). This programme was developed in collaboration with the Ministry of Education (MOE), Singapore and is adapted from the Primary Mathematics Project developed by MOE.
Michelene (Micki) T. H. Chi is a cognitive and learning scientist known for her work on the development of expertise, benefits of self-explanations, and active learning in the classroom. Chi is the Regents Professor, Dorothy Bray Endowed Professor of Science and Teaching at Arizona State University, where she directs the Learning and Cognition Lab.
James W. Stigler is an American psychologist, researcher, entrepreneur and author. He is Distinguished Professor in the Department of Psychology at University of California, Los Angeles and a Fellow of the Precision Institute at National University, San Diego.
Laura Mary O'Dwyer is a professor of Measurement, Evaluation, and Statistics at Boston College known for her work on examining the impact of technology in education, especially science education, and for quantifying outcomes for K-12 student success.
Jeremy Kilpatrick was an American mathematics educator. He received the Felix Klein Medal for 2007 from ICMI. He graduated from Chaffey two-year college in California (1954), then he went to the University of California at Berkeley to earn an A.B degree (1956) in mathematics and after an M.A degree (1960) in education. He received his M.S. in mathematics in 1962 and his PhD degree in mathematics education in 1967, both from Stanford University, where he was also a research assistant in the SMSG (1962-1967). His dissertation was supervised by Edward Begle with George Pólya and Lee Conbrach in the doctoral committee, and addressed eight graders’ problem-solving heuristics. From 1967 to 1975 he taught from as an assistant and later as an associate professor at Teachers College, Columbia University, in New York. In 1975, he moved to the University of Georgia, where he was a professor of mathematics education.
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