Access the full text.
Sign up today, get DeepDyve free for 14 days.
H. Rogers (1988)Exploring the Episodic Structure of Algebra Story Problem Solving. Revised.
An analysis of the task demands of algebra and the cognitive processes needed to meet them
H. Simon (1970)The Sciences of the Artificial
D. Ball (1988)Unlearning to Teach Mathematics.
for the learning of mathematics, 8
M. Riley (1984)Development of Children's Problem-Solving Ability in Arithmetic.
D. Grouws (1992)Handbook of research on mathematics teaching and learning
Allan Wigfield, Alice Galper, Kristin Denton, C. Seefeldt (1999)Teachers' beliefs about former Head Start and non-Head Start first-grade children's motivation, performance, and future educational prospects.
Journal of Educational Psychology, 91
When Ted got home from his waiter job, he multiplied his hourly wage by the 6 hours he worked that day. Then he added the $66 he made in tips and found he earned $81.90
Starting with some number, if I multiply it by 6 and then add 66
Gail Mccutcheon (1980)How Do Elementary School Teachers Plan? The Nature of Planning and Influences on It
The Elementary School Journal, 81
Mitchell Nathan (1998)Knowledge and Situational Feedback in a Learning Environment for Algebra Story Problem Solving
Interact. Learn. Environ., 5
K. Fuson (1987)Children's Counting and Concepts of Number
J. Richards, C. Lockhart (1994)Reflective Teaching in Second Language Classrooms: Teacher decision making
TEACHERS' BELIEFS OF EARLY ALGEBRA
(1999)Representational difficulty factors in quantitative problem solving
G. Posner, K. Strike, P. Hewson, William Gertzog (1982)Accommodation of a scientific conception: Toward a theory of conceptual change
Science Education, 66
Carolyn Kieran (1992)The learning and teaching of school algebra.
(1996)Mathematics learning and teaching
P. Cobb (1988)The Tension Between Theories of Learning and Instruction in Mathematics Education
Educational Psychologist, 23
Measuring elementary school teachers' beliefs about teaching mathematics: A preliminary report. Paper presented at the annual meeting of Teacher Educators
(1994)The place of practical argument in the education of teachers
H. Ginsburg (1983)The development of mathematical thinking
M. Eisenhart, Judith Shrum, J. Harding, Alexander Cuthbert (1988)Teacher Beliefs
Educational Policy, 2
(1980)Learned helplessness and intellectual achievement
H. Borko, M. Eisenhart, Catherine Brown, R. Underhill, Doug Jones, Patricia Agard (1992)Learning to Teach Hard Mathematics: Do Novice Teachers and Their Instructors Give Up Too Easily?
Journal for Research in Mathematics Education, 23
A. Thompson (1992)Teachers' beliefs and conceptions: A synthesis of the research.
(1988)Two different approaches among algebra learners
(1986)Teachers' thought processes
P. Peterson, E. Fennema, T. Carpenter, M. Loef (1989)Teachers' Pedagogical Content Beliefs in Mathematics
Cognition and Instruction, 6
C. Hirsch (1988)Curriculum and Evaluation Standards for School Mathematics
Angie Su (1932)The National Council of Teachers of Mathematics
The Mathematical Gazette, 16
M. Just, P. Carpenter, T. Keller (1996)The capacity theory of comprehension: new frontiers of evidence and arguments.
Psychological review, 103 4
C. Clark (1978)A New Question for Research on Teaching.
Educational research quarterly, 3
Anne Raymond (1997)Inconsistency between a Beginning Elementary School Teacher's Mathematics Beliefs and Teaching Practice.
Journal for Research in Mathematics Education, 28
(1983)The acquisition of mathematical concepts and processes
(1996)Evaluating models of practice : Reformbased mathematics at the middle school level
S. Goldman (1991)On the Derivation of Instructional Applications From Cognitive Theories: Commentary on Chandler and Sweller
Cognition and Instruction, 8
T. Carpenter, E. Fennema, P. Peterson, C. Chiang, M. Loef (1989)Using Knowledge of Children’s Mathematics Thinking in Classroom Teaching: An Experimental Study
Angie Su (2000)National Council of Teachers of Mathematics
Starting with 81.9, if I subtract 66 and then divide by 6, I get a number
G. Miller (1956)The magical number seven plus or minus two: some limits on our capacity for processing information.
Psychological review, 63 2
T. Carpenter, E. Fennema, P. Peterson, D. Carey (1988)Teachers' pedagogical content knowledge of students' problem solving in elementary arithmetic
Journal for Research in Mathematics Education, 19
T. Carpenter, J. Moser (1984)The Acquisition of Addition and Subtraction Concepts in Grades One through Three.
Journal for Research in Mathematics Education, 15
Student learning of negative number : A classroom study and difficulty factors assessment
Symbol precedence view (6 items) holds the view commonly expressed
H. Borko, Ralph Putnam (1996)Learning to teach.
R. Glaser (1976)Components of a Psychology of Instruction: Toward a Science of Design
Review of Educational Research, 46
A. Thompson (1984)The relationship of teachers' conceptions of mathematics and mathematics teaching to instructional practice
Educational Studies in Mathematics, 15
Mitchell Nathan, K. Koedinger (2000)Teachers' and Researchers' Beliefs about the Development of Algebraic Reasoning.
Journal for Research in Mathematics Education, 31
(2000)Mathematics textbooks: Are they the seeds of teacher's misconceptions? Paper presented at the
P. Cheng, K. Holyoak, R. Nisbett, L. Oliver (1986)Pragmatic versus syntactic approaches to training deductive reasoning
Cognitive Psychology, 18
Virginia Richardson‐Koehler (1994)Teacher change and the staff development process : a case in reading instruction
A. Sfard (1991)On the dual nature of mathematical conceptions: Reflections on processes and objects as different sides of the same coin
Educational Studies in Mathematics, 22
P. Wason, P. Johnson-Laird (1972)Psychology of Reasoning: Structure and Content
A. Newell (1990)Unified Theories of Cognition
R. Gagne (1968)Presidential address of division 15 learning hierarchies
Educational Psychologist, 6
Gary Fenstermacher (1978)4: A Philosophical Consideration of Recent Research on Teacher Effectiveness
Review of Research in Education, 6
R. Mistretta, J. Porzio (2001)"Principles and Standards for School Mathematics" in the Classroom.
Teaching children mathematics, 7
(1990)Restructuring elementary school mathematics: The 1990 John Wilson memorial address
Thomas Cooney (1985)A Beginning Teacher's View of Problem Solving.
Journal for Research in Mathematics Education, 16
Teachers should encourage invented solution methods (8 items) states that students may possess valid ways of reasoning as they enter the classroom, and may figure out for themselves
D. Kahneman, A. Tversky (1982)Judgment under uncertainty: On the psychology of prediction
A. Schoenfeld (1983)Beyond the Purely Cognitive: Belief Systems, Social Cognitions, and Metacognitions As Driving Forces in Intellectual Performance
Cogn. Sci., 7
A. Tversky, D. Kahneman (1973)Availability: A heuristic for judging frequency and probability
Cognitive Psychology, 5
P. Peterson, T. Carpenter, E. Fennema (1989)Teachers' knowledge of students' knowledge in mathematics problem solving: correlational and case analyses
Journal of Educational Psychology, 81
Self - reflection on teacher goals and actions in the mathematics classroom
(1986)Research on teaching and learning mathematics: Two disciplines of scientific inquiry
B. Lazerick (1997)Third international mathematics and science study
Teaching children mathematics, 4
K. Ericsson, Jacqui Smith (1991)Toward a general theory of expertise : prospects and limits
Martin Simon (1995)Reconstructing Mathematics Pedagogy from a Constructivist Perspective.
Journal for Research in Mathematics Education, 26
(1998)The impact of theories of learning on learning environment design
Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative problem-solving difficulty. Teachers also rated their levels of agreement to a variety of reform-based statements on teaching and learning mathematics. Analyses suggest that teachers hold a symbol-precedence view of student mathematical development, wherein arithmetic reasoning strictly precedes algebraic reasoning, and symbolic problem-solving develops prior to verbal reasoning. High school teachers were most likely to hold the symbol-precedence view and made the poorest predictions of students' performances, whereas middle school teachers' predictions were most accurate. The discord between teachers' reform-based beliefs and their instructional decisions appears to be influenced by textbook organization, which institutionalizes the symbol-precedence view. Because of their extensive content training, high school teachers may be particularly susceptible to an expert blindspot, whereby they overestimate the accessibility of symbol-based representations and procedures for students' learning introductory algebra.
Cognition and Instruction – Taylor & Francis
Published: Jun 1, 2000
Access the full text.
Sign up today, get DeepDyve free for 14 days.