Results 1  10
of
328
Looking toward the 21st century: challenges of educational theory and practice
 Educational Researcher .Vol
, 1999
"... While it may be a truism it is nonetheless true that much of what we do, individually and collectively, is shaped by qu^personal j i is tor ies. For that reason I begin this paper by describing some aspects of n ^ b a c k g r o u n d. Doing so provides a context for what follows, and for understan ..."
Abstract

Cited by 50 (2 self)
 Add to MetaCart
(Show Context)
While it may be a truism it is nonetheless true that much of what we do, individually and collectively, is shaped by qu^personal j i is tor ies. For that reason I begin this paper by describing some aspects of n ^ b a c k g r o u n d. Doing so provides a context for what follows, and for understanding my hopes and aspirations for
Expert blind spot among preservice teachers
 American Educational Research Journal
, 2003
"... This study (N = 48) examined the relationship between preservice secondary teachers ’ subjectmatter expertise in mathematics and their judgments of students ’ algebra problemsolving difficulty. As predicted by the “expert blind spot” hypothesis, participants with more advanced mathematics educati ..."
Abstract

Cited by 32 (6 self)
 Add to MetaCart
This study (N = 48) examined the relationship between preservice secondary teachers ’ subjectmatter expertise in mathematics and their judgments of students ’ algebra problemsolving difficulty. As predicted by the “expert blind spot” hypothesis, participants with more advanced mathematics education, regardless of their program affiliation or teaching plans, were more likely to view symbolic reasoning and mastery of equations as a necessary prerequisite for word equations and story problem solving. This view is in contrast with students’ actual performance patterns. An examination across several subject areas, including mathematics, science, and language arts, suggests a common pattern. This article considers how teachers ’ developmental views may influence classroom practice and professional development, and calls into question policies that seek to streamline the licensure process of new teachers on the basis of their subjectmatter expertise.
Does lesson study have a future in the United States? Retrieved from http://www.sowionlinejournal.de/20041/lesson_lewis.htm
 Educational Leadership
, 2004
"... study, reflective practitioner, professionalization, school reform, teacher, ..."
Abstract

Cited by 22 (1 self)
 Add to MetaCart
study, reflective practitioner, professionalization, school reform, teacher,
Toward evidence for instructional design principles: Examples from Cognitive Tutor Math 6. Invited paper
 in Proceedings of PMENA XXXIII (the North American Chapter of the International Group for the Psychology of Mathematics Education
, 2002
"... There is a significant gap between theories of general psychological functions on one hand (e.g., memory) and theories of mathematical content knowledge on the other (e.g., content of algebra). To better guide the design of ground breaking and demonstrably better mathematics instruction, we need ins ..."
Abstract

Cited by 22 (13 self)
 Add to MetaCart
(Show Context)
There is a significant gap between theories of general psychological functions on one hand (e.g., memory) and theories of mathematical content knowledge on the other (e.g., content of algebra). To better guide the design of ground breaking and demonstrably better mathematics instruction, we need instructional principles and associated design methods to fill this gap in a way that is not only consistent with psychological and content theories but prompts and guides us beyond what those theories can do. Toward this goal, I reflect on lessons from past and current Cognitive Tutor mathematics projects. From this experience, I have abstracted four instructional bridging principles, SituationAbstraction, ActionGeneralization, VisualVerbal, and ConceptualProcedural, and associated methods for applying them. I illustrate these in the context of the design of the successful Cognitive Tutor Algebra course (now in more than 800 schools) and the ongoing research and development of a Cognitive Tutor course for 6 th grade mathematics.
Initiating change in prospective elementary school teachers’ orientations to mathematics teaching by building on beliefs
 Journal of Mathematics Teacher Education
, 2004
"... ABSTRACT. Many mathematics educators have found that prospective elementary school teachers ’ beliefs interfere with their learning of mathematics. Often teacher educators consider these beliefs to be wrong or naïve and seek to challenge them so prospective teachers will reject them for more generat ..."
Abstract

Cited by 22 (0 self)
 Add to MetaCart
(Show Context)
ABSTRACT. Many mathematics educators have found that prospective elementary school teachers ’ beliefs interfere with their learning of mathematics. Often teacher educators consider these beliefs to be wrong or naïve and seek to challenge them so prospective teachers will reject them for more generative beliefs. Because of the resilience of prospective teachers ’ beliefs in response to these challenges, teacher educators could consider alternative ways of thinking about and addressing beliefs, particularly the potential of building on rather than tearing down preexisting beliefs. Data from an earlyfield experience linked to a mathematicsforteachers course provide evidence that when prospective teachers work intimately with children, in this case trying to teach 10yearolds about fractions, the experience has the intensity from which beliefs can grow. Most of the prospective teachers in the study were surprised that mathematics teaching was more difficult than they had anticipated. They began to consider the importance of providing children time to think when solving mathematical problems. The change described in the study is incremental rather than monumental, suggesting that building upon prospective teachers ’ existing beliefs will be a gradual process. KEY WORDS: field experience, mathematics preservice teacher education, prospective teachers ’ beliefs
Chinese children excel on novel mathematics problems even before eleementary school
 Psychological Science
, 2008
"... ABSTRACT—Kindergartners in China showed greater numerical knowledge than their age peers in the United States, not only when tested with arithmetic problems, which Chinese parents present to their children more often than U.S. parents do, but also when tested with numberline estimation problems, w ..."
Abstract

Cited by 18 (0 self)
 Add to MetaCart
(Show Context)
ABSTRACT—Kindergartners in China showed greater numerical knowledge than their age peers in the United States, not only when tested with arithmetic problems, which Chinese parents present to their children more often than U.S. parents do, but also when tested with numberline estimation problems, which were novel to the children in both countries. The Chinese kindergartners ’ numberline estimates were comparable to those of U.S. children 1 to 2 years more advanced in school. Individual differences in arithmetic and numberlineestimation performance were positively correlated within each country. These results indicate that performance differences between Chinese and U.S. children on both practiced and unpracticed mathematical tasks are substantial even before the children begin elementary school. Children in China, Japan, and other East Asian countries outperform their American age peers on numerous mathematical tasks, including those involving counting, arithmetic, algebra,
Teachers’ content knowledge, teacher education, and their effects on the preparation of elementary teachers
 in the United States. Mathematics Teacher Education and Development
, 2001
"... This paper summarises and critiques research on the role of mathematics content knowledge in the preparation and teaching practice of elementary (K8) teachers in the United States. Research conducted over the last 40 years has given us snapshots of teachers ’ knowledge at particular points in time, ..."
Abstract

Cited by 18 (0 self)
 Add to MetaCart
(Show Context)
This paper summarises and critiques research on the role of mathematics content knowledge in the preparation and teaching practice of elementary (K8) teachers in the United States. Research conducted over the last 40 years has given us snapshots of teachers ’ knowledge at particular points in time, such as during their preservice methods courses. The paper calls for future research to give us longitudinal “videotapes ” of teachers ’ knowledge and how it is developed and used in a variety of contexts. Every study or subject thus has two aspects: one for the scientist as a scientist; the other for the teacher as teacher. These two aspects are in no sense opposed or conflicting. But neither are they immediately identical. (Dewey, 1990, p. 200) In recent years, policymakers in the United States have focused a great deal of time and attention on teacher preparation. In particular, many policy documents are based on the logical assumption that teachers ’ content knowledge has a significant influence on student learning. For example, the American Council on Education (ACE) recently proclaimed that “A thorough grounding in collegelevel subject matter and professional competence in professional practice are necessary for good teaching. The data are unequivocal: students learn more mathematics when their teachers report having taken more mathematics ” (ACE, 1999, p. 6). The ACE report presents data that suggest that earning a college degree in mathematics, being certified in mathematics, and being mathematically skillful “all contribute to effective teaching of mathematics ” (p. 6). Many national policy organisations have created documents specifying the content that teachers should know in order to be effective teachers, (e.g., ACE, 1999; Conference Board of the
The developmental bases for early childhood number and operations standards
 In
, 2004
"... This chapter is based on papers presented at the symposium “Linking Research and the New ..."
Abstract

Cited by 15 (0 self)
 Add to MetaCart
(Show Context)
This chapter is based on papers presented at the symposium “Linking Research and the New
Parental roles in students' learning of mathematics: An exploratory study
 Research in Middle Level Education Quarterly
, 1999
"... This study investigates the roles parents in the United States of America and parents in the People’s Republic of China play in their children’s mathematics learning. It also examines the relationship between parental involvement and students ' mathematical problemsolving performance. In the s ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
(Show Context)
This study investigates the roles parents in the United States of America and parents in the People’s Republic of China play in their children’s mathematics learning. It also examines the relationship between parental involvement and students ' mathematical problemsolving performance. In the study, 232 US sixthgrade students and 310 Chinese sixthgrade students along with their parents were surveyed. The results of this study support the argument, from a broader crossnational perspective, that parental involvement is a statistically significant predictor of their children's mathematics achievement. Crossnationally, Chinese parents seemed to play a more positive role than do the US parents. There is a general consensus that parental involvement, as an enhancing variable, contributes to students ' higher academic achievement, positive behavior, and emotional development (Booth & Dunn, 1996; HooverDempsey & Sandler, 1995; Wang, Haertel, & Walberg, 1993). However, we are still searching for the kinds of parental involvement that have the greatest impact on students ' learning (Cai, Moyer, & Wang, 1999). We are also trying to understand why parental
Mathematics for teaching
 Notices Amer. Math. Soc
"... Reflecting a growing interest in mathematics education at all levels, many in the mathematics community have turned their attention to the mathematical preparation of prospective precollege teachers. Education researchers ([1], [2], for example) have documented striking differences in mathematical s ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
(Show Context)
Reflecting a growing interest in mathematics education at all levels, many in the mathematics community have turned their attention to the mathematical preparation of prospective precollege teachers. Education researchers ([1], [2], for example) have documented striking differences in mathematical sophistication between teachers in the U.S. and teachers from other countries. A decade of thought and effort has produced several sets of specific recommendations for the improvement of the mathematical preparation of teachers [3], [4], [5]. And the NCTM document Principles and Standards for School Mathematics outlines some broad goals: Teachers need several different kinds of mathematical knowledge—knowledge about the whole domain; deep flexible knowledge about curriculum goals and about the important ideas that are central to their grade level; knowledge about how the ideas can be represented to teach them effectively; and knowledge about how students’ Al Cuoco directs the Center for Mathematics Education at Education Development Center. His email address is