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Articles 61 - 90 of 107
Full-Text Articles in Education
How Do Changes Happen? Transition From Intuitive To Advanced Strategies In Multiplicative Reasoning For Students With Math Disabilities, Dake Zhang, Yan Xin, Ron Tzur, Casey Hord, Luo Si, Suleyman Centintas
How Do Changes Happen? Transition From Intuitive To Advanced Strategies In Multiplicative Reasoning For Students With Math Disabilities, Dake Zhang, Yan Xin, Ron Tzur, Casey Hord, Luo Si, Suleyman Centintas
Ron Tzur
This study investigated how students with mathematics learning disabilities (MD) or at-risk for MD developed their multiplicative reasoning skills from intuitive strategies to advanced strategies through a teaching experiment. The participants consisted of two fifth graders with MD and one at-risk. A micro-genetic approach with a single subject design was used. Investigators coded and analyzed five strategies children used. Results showed that the participants had fewer strategies than normal-achieving students, but they improved their performance throughout the teaching experiment. The participants increased their use of double counting and direct retrieval, and decreased their use of unitary counting during the intervention.
Conceptual And Brain Processing Of Unit Fraction Comparisons: A Cogneuro-Mathed Study, Ron Tzur, Brenden Depue
Conceptual And Brain Processing Of Unit Fraction Comparisons: A Cogneuro-Mathed Study, Ron Tzur, Brenden Depue
Ron Tzur
This mixed-method, qualitative/quantitative study examined (a) how a constructivist- based intervention (CBI) effected adults’ learning of unit fractions and performance on whole-number (WN) or unit fraction (FR) comparisons and (b) brain circuitry implicated (fMRI) when processing these comparisons. The CBI used unit-iteration based activities to foster a shift in participants’ understanding of FR, from the prevalent, limiting “one-out-of-so-many-equal-parts” idea to a multiplicative relation conception and thus inverse magnitude relation among FR (1/n>1/m though m>n). Pre- and two post-intervention tests indicated CBI impact on decreased reaction time in comparing not just FR but also WN and differentiated brain regions …
Intermediate Participatory Stages Of The Concept Of Unit Fraction: Two Students With Learning Disability, Jessica Hunt, Ron Tzur, Arla Westenskow
Intermediate Participatory Stages Of The Concept Of Unit Fraction: Two Students With Learning Disability, Jessica Hunt, Ron Tzur, Arla Westenskow
Ron Tzur
No abstract provided.
Engendering Multiplicative Reasoning In Students With Learning Disabilities In Mathematics: Sam's Computer-Assisted Transition To Anticipatory Unit Differentiation-And-Selection, Evan Mcclintock, Ron Tzur, Yan Xin, Luo Si
Engendering Multiplicative Reasoning In Students With Learning Disabilities In Mathematics: Sam's Computer-Assisted Transition To Anticipatory Unit Differentiation-And-Selection, Evan Mcclintock, Ron Tzur, Yan Xin, Luo Si
Ron Tzur
We examined how a student with learning disabilities (SLD) in mathematics constructed a scheme for differentiating, selecting, and properly operating on/with units that constitute a multiplicative situation, namely, singletons (‘1s’) and composite units (abbreviated UDS). Conducted as part of a larger teaching experiment in a learning environment that synergizes human and computer-assisted teaching, this study included 12 videotaped teaching episodes with a 5th grader (pseudonym-Sam), analyzed qualitatively. Our data provide a window onto the conceptual transformation involved in advancing from absence, through a participatory, to an anticipatory stage of a UDS scheme—a cognitive root for the distributive property. We postulate …
A Comparison Of Instructional Sequence In Intelligent Tutor-Assisted Math Problem-Solving Intervention Program, Joo Park, Yan Xin, Ron Tzur, Luo Si, Casey Hord
A Comparison Of Instructional Sequence In Intelligent Tutor-Assisted Math Problem-Solving Intervention Program, Joo Park, Yan Xin, Ron Tzur, Luo Si, Casey Hord
Ron Tzur
No abstract provided.
Curricular Change Agenda For Failure-Experienced Mathematics Students: Can Success-Promoting Assessment Make A Difference?, Ron Tzur, Nitsa Movshovitz-Hadar
Curricular Change Agenda For Failure-Experienced Mathematics Students: Can Success-Promoting Assessment Make A Difference?, Ron Tzur, Nitsa Movshovitz-Hadar
Ron Tzur
The study reported in this paper addressed the question: Can a success promoting assessment schema (SPAS) be designed so as to have a positive impact on mathematics learning of failure-experienced students? Addressing the problem of the study is important because assessment of students' mathematics learning greatly impacts the way mathematics is taught and learned in schools (National Council of Teachers of Mathematics, 1995). Learning mathematics is essential for one's functioning in today's society, and it is considered desirable that all students know and use mathematics (For Good Measure, 1992; National Council of Teachers of Mathematics, 1989). However, these goals are …
Explicating The Teacher's Perspective From The Researchers' Perspectives: Generating Accounts Of Mathematics Teachers' Practice, Marty Simon, Ron Tzur
Explicating The Teacher's Perspective From The Researchers' Perspectives: Generating Accounts Of Mathematics Teachers' Practice, Marty Simon, Ron Tzur
Ron Tzur
In this article we articulate a methodology for studying mathematics teacher development in the context of reform. The generation of accounts of teachers'practice, an adaptation of the case study, provides an approach to understanding teachers' current practice and to viewing their current practice in the context of development toward envisioned reforms. The methodology is an alternative both to studies that focus on teachers' deficits and to teachers' own accounts of their practice. Conceptual frameworks developed within the mathematics education research community are applied to the task of investigating the nature of practice developed by teachers in transition. We characterize this …
Characterizing A Perspective Underlying The Practice Of Mathematics Teachers In Transition, Marty Simon, Ron Tzur, Karen Heinz, Margaret Kinzel, Margaret Smith
Characterizing A Perspective Underlying The Practice Of Mathematics Teachers In Transition, Marty Simon, Ron Tzur, Karen Heinz, Margaret Kinzel, Margaret Smith
Ron Tzur
We postulate a construct, perception-based perspective, that we consider to be fundamental to the practices of many teachers currently participating in mathematics education reform in the United States. The postulation of the construct resulted from analyses of data from teaching experiments in teacher education classes with a combined group of prospective and practicing teachers and from case studies with individuals from that group. A perception-based perspective is grounded in a view of mathematics as a connected, logical, and universally accessible part of an ontological reality. From this perspective, learning mathematics with understanding requires learners' direct (firsthand) perception of relevant mathematical …
Moving Students Through Steps Of Mathematical Knowing: An Account Of The Practice Of An Elementary Mathematics Teacher In Transition, Karen Heinz, Margaret Kinzel, Marty Simon, Ron Tzur
Moving Students Through Steps Of Mathematical Knowing: An Account Of The Practice Of An Elementary Mathematics Teacher In Transition, Karen Heinz, Margaret Kinzel, Marty Simon, Ron Tzur
Ron Tzur
We present an account of a sixth-grade teacher's practice as she responds to the challenges of current reform initiatives. We analyzed classroom observations and interviews to understand how the teacher, Ivy, teaches and thinks about teaching mathematics to her students. For Ivy, mathematical meaning is available in particular experiences. She creates these experiences for her students by leading them through a predetermined sequence of steps of mathematical knowing. This account contributed to our postulation of a perspective on mathematics learning that we refer to as perceptionbased, in which the goal of instruction is to create opportunities for students to perceive, …
An Integrated Research On Children's Construction Of Meaningful, Symbolic, Partitioning-Related Conceptions And The Teacher's Role In Fostering That Learning, Ron Tzur
Ron Tzur
A teaching experiment was conducted with two fourth graders to study the co-emergence of teaching and children's construction of fraction knowledge. The children's learning, i.e., modifications in their fraction schemes, was fostered through working on tasks in a computer microworld. The children advanced from thinking about a unit fraction as one of several equal parts in a whole (the equipartitioning scheme) to operating with a unit fraction as a symbolized, iterable part the magnitude of which is based on the numerosity of the partitioned whole (the partitive fraction scheme). The paper interweaves an analysis of children's construction of partitioning-related symbolic …
An Integrated Study Of Children's Construction Of Improper Fractions And The Teacher's Role In Promoting That Learning, Ron Tzur
Ron Tzur
In this constructivist teaching experiment with 2 fourth graders I studied the coemergence of teaching and children's construction of a specific conception that supports the generation of improper fractions. The children's posing and solving tasks in a computer microworld promoted a modification in their fraction schemes. They advanced from thinking about a unit fraction as a part of a whole to thinking about it as standing in a multiplicative relationship with a reference whole (the iterative fraction scheme). In this article I report an intertwined analysis of the children's construction of this multiplicative relationship and an examination of the teacher's …
Developing New Understandings Of Pds Work: Better Problems, Better Questions, Nancy Dana, Diane Silva, Belinda Gimbert, Jim Nolan, Carla Zembal-Saul, Ron Tzur, Lucy Mule, Lynne Sanders
Developing New Understandings Of Pds Work: Better Problems, Better Questions, Nancy Dana, Diane Silva, Belinda Gimbert, Jim Nolan, Carla Zembal-Saul, Ron Tzur, Lucy Mule, Lynne Sanders
Ron Tzur
Through sharing examples, the authors demonstrate how the analysis of long-term Professional Development School (PDS) problems and their evolution can serve as one indicator of growth in the PDS. Three persistent problem areas are identified: (a) building trust and relationships between university and school personnel, (b) reconceptualizing existing coursework to fit in the PDS context, and (3) making inquiry a central feature of the PDS. The historical evolution of these problem areas is traced through three phases of PDS development over a six-year period, including PDS Planning, PDS Pilot Year, and PDS Institutionalization. The authors conclude that, through careful analysis, …
Riding The Mathematical Merry-Go-Round To Foster Conceptual Understanding Of Angle, Ron Tzur, Matthew Clark
Riding The Mathematical Merry-Go-Round To Foster Conceptual Understanding Of Angle, Ron Tzur, Matthew Clark
Ron Tzur
This article presents playful activities for fostering students' conceptual understanding of angle--a root concept in mathematics--that revolve around the Mathematical Merry-Go-Round game. The authors focus on activities for two reasons. On one hand, NCTM's Principles and Standards for School Mathematics (2000) stresses the central role of student activity in coming to understand mathematics. This emphasis is consistent with a constructivist stance (Piaget 1971) about learning as an active process. On the other hand, typical activities used for teaching angle, in which an introduction of the definition is followed by operations on angles, such as measuring, adding, comparing, and classifying, seem …
Is Teaching Parallel Algorithmic Thinking To High School Students Possible? One Teacher’S Experience, Shane Torbert, Uzi Vishkin, Ron Tzur, David Ellison
Is Teaching Parallel Algorithmic Thinking To High School Students Possible? One Teacher’S Experience, Shane Torbert, Uzi Vishkin, Ron Tzur, David Ellison
Ron Tzur
All students at our high school are required to take at least one course in Computer Science prior to their junior year. They are also required to complete a year-long senior project associated with a specific in-house laboratory, one of which is the Computer Systems Lab. To prepare students for this experience the lab offers elective courses at the post-AP Computer Science level. Since the early 1990s one of these electives has focused on parallel computing. The course enrolls approximately 40 students each year for two semesters of instruction. The lead programming language is C and topics include a wide …
Teacher And Students' Joint Production Of A Reversible Fraction Conception, Ron Tzur
Teacher And Students' Joint Production Of A Reversible Fraction Conception, Ron Tzur
Ron Tzur
Within a constructivist perspective, I conducted a teaching experiment with two fourth graders to study how a teacher and students can jointly produce the reversible fraction conception. Ongoing and retrospective analysis of the data revealed the non-trivial process by which students can abstract multiplicative reasoning about fractions. The study articulates a conception in a developmental sequence of iteration-based fraction conceptions and the teacher’s role in fostering such a conception in students.
Explicating The Role Of Mathematical Tasks In Conceptual Learning: An Elaboration Of The Hypothetical Learning Trajectory, Marty Simon, Ron Tzur
Explicating The Role Of Mathematical Tasks In Conceptual Learning: An Elaboration Of The Hypothetical Learning Trajectory, Marty Simon, Ron Tzur
Ron Tzur
Simon's (1995) development of the construct of hypothetical learning trajectory (HLT) offered a description of key aspects of planning mathematics lessons. An HLT consists of the goal for the students' learning, the mathematical tasks that will be used to promote student learning, and hypotheses about the process of the students' learning. However, the construct of HLT provided no framework for thinking about the learning process, the selection of mathematical task, or the role of the mathematical tasks in the learning process. Such a framework could contribute significantly to the generation of useful HLTs. In this article we demonstrate how an …
Fine Grain Assessment Of Students' Mathematical Understanding: Participatory And Anticipatory Stages In Learning A New Mathematical Conception, Ron Tzur
Ron Tzur
This study addressed a twofold problem--the soundness of a theoretical stage-distinction regarding the process of constructing a new (to the learner) mathematical conception and how such distinction contributes to fine grain assessment of students' mathematical understandings. As a context for the study served the difficult-to-grasp concept of "inverse" order relationship among unit fractions, that is, the larger the number of parts the smaller the size of each part (e.g., 1/7 greater than 1/10 although 10 greater than 7). I conducted this study as a whole-class teaching experiment in a third grade classroom at a public school in Israel. The qualitative …
Becoming A Mathematics Teacher-Educator: Conceptualizing The Terrain Through Self-Reflective Analysis, Ron Tzur
Ron Tzur
My purpose in this article is to contribute tothe conceptualization of the complex terrainthat often is indiscriminately termedmathematics teacher educator development.Because this terrain is largely unresearched, Iinterweave experience fragments of my owndevelopment as a mathematics teacher educator,and reflective analysis of those fragments, asa tool to abstract notions of generalimplication. In particular, I postulate aframework consisting of four stages ofdevelopment that are distinguished by thedomain of activities one's reflections mayfocus on and the nature of those reflections.Drawing on this framework, I presentimplications for mathematics teacher educatordevelopment and for further research.
Distinguishing Two Stages Of Mathematics Conceptual Learning, Ron Tzur, Marty Simon
Distinguishing Two Stages Of Mathematics Conceptual Learning, Ron Tzur, Marty Simon
Ron Tzur
In this theoretical article, we distinguish two stages of learning a new mathematical concept – participatory and anticipatory. We use a recently developed mechanism for explaining mathematical conceptual learning – reflection on activity-effect relationship – as well as von Glasersfeld’s tripartite model of a scheme, to explain qualitative distinctions between the two stages. We use this distinction to explain why instructional interventions (including inquiry-based approaches) may not bring about the intended instructional goals.
Iteration: Unit Fraction Knowledge And The French Fry Tasks, Ron Tzur, Jessica Hunt
Iteration: Unit Fraction Knowledge And The French Fry Tasks, Ron Tzur, Jessica Hunt
Ron Tzur
Using these tasks can help nurture children’s multiplicative notions of unit fractions beyond part-whole understanding. Often, students who solve fraction tasks respond in ways that indicate inadequate conceptual grounding of unit fractions. Consider, for example, a student, Lia (all names are pseudonyms), who examined a long, rectangular piece of paper she had folded in the middle into two equal parts (halves).
Intermediate Participatory Stages As Zone Of Proximal Development Correlate In Constructing Counting-On: A Plausible Conceptual Source For Children's Transitory "Regress" To Counting-All, Ron Tzur, Matthew Lambert
Intermediate Participatory Stages As Zone Of Proximal Development Correlate In Constructing Counting-On: A Plausible Conceptual Source For Children's Transitory "Regress" To Counting-All, Ron Tzur, Matthew Lambert
Ron Tzur
Quantitative and qualitative analyses of 37 first-graders' solutions to addition problems were conducted to re-examine inconsistencies in children's progress from counting-all to counting-on. The study advances a novel, theoretical coordination among 3 frameworks: constructivist scheme theory with a focus on the notion of prompt, Vygotsky's sociocultural approach, and Siegler's Overlapping Waves Model, and provides a corresponding, threefold stance on mathematical tasks.
Second-Order Models: A Theoretical Bridge To Practice, A Practical Bridge To Theory, Ron Tzur
Second-Order Models: A Theoretical Bridge To Practice, A Practical Bridge To Theory, Ron Tzur
Ron Tzur
Open peer commentary on the article “Constructivist Model Building: Empirical Examples From Mathematics Education” by Catherine Ulrich, Erik S. Tillema, Amy J. Hackenberg & Anderson Norton. Upshot: I address the value of Ulrich et al.’s distinction between three types of second-order models. I conclude that their work contributes to the theorizing of adaptive teaching on the basis of a constructivist stance on knowing and learning.
Can Dual Processing Theories Of Thinking Inform Conceptual Learning In Mathematics?, Ron Tzur
Can Dual Processing Theories Of Thinking Inform Conceptual Learning In Mathematics?, Ron Tzur
Ron Tzur
Concurring with Uri Leron's (2010) cross-disciplinary approach to two distinct modes of mathematical thinking, intuitive and analytic, I discuss his elaboration and adaptation to mathematics education of the cognitive psychology dual-processing theory (DPT) in terms of (a) the problem significance and (b) features of the theory he adapts. Then, I discuss DPT in light of a constructivist stance on the inseparability between thinking and learning. In particular, I propose a brain-based account of conceptual learning -- the Reflection on Activity-Effect Relationship (Ref*AER) framework--as a plausible alternative to DPT. I discuss advantages of the Ref*AER framework over DPT for mathematics education.
Teachers' Use Of Alternate Assessment Methods, Ron Tzur, Karen Brooks, Mary Enderson, Margaret Morgan, Thomas Cooney
Teachers' Use Of Alternate Assessment Methods, Ron Tzur, Karen Brooks, Mary Enderson, Margaret Morgan, Thomas Cooney
Ron Tzur
No abstract provided.
Technology-Enriched Elementary Mathematics Education, Ron Tzur
Technology-Enriched Elementary Mathematics Education, Ron Tzur
Ron Tzur
No abstract provided.
Why Do We Invert And Multiply: Elementary Teachers’ Struggle To Conceptualize Division Of Fractions, Ron Tzur, Maria Timmerman
Why Do We Invert And Multiply: Elementary Teachers’ Struggle To Conceptualize Division Of Fractions, Ron Tzur, Maria Timmerman
Ron Tzur
No abstract provided.
Profound Awareness Of The Learning Paradox: A Journey Towards Epistemologically Regulated Pedagogy In Mathematics Teaching And Teacher Education [Book Chapter], Ron Tzur
Ron Tzur
No abstract provided.
Relationship Of Affective And Cognitive Aspects Of Learning, Ron Tzur
Relationship Of Affective And Cognitive Aspects Of Learning, Ron Tzur
Ron Tzur
No abstract provided.
Chapter 3: Mathematics Teaching In A Chinese Classroom : A Hybrid-Model Analysis Of Opportunities For Students' Learning, Rongjin Huang, L. Miller, Ron Tzur
Chapter 3: Mathematics Teaching In A Chinese Classroom : A Hybrid-Model Analysis Of Opportunities For Students' Learning, Rongjin Huang, L. Miller, Ron Tzur
Ron Tzur
No abstract provided.
Postulating Relationships Between Levels Of Knowing And Types Of Tasks In Mathematics Teaching: A Constructivist Perspective, Ron Tzur, Marty Simon
Postulating Relationships Between Levels Of Knowing And Types Of Tasks In Mathematics Teaching: A Constructivist Perspective, Ron Tzur, Marty Simon
Ron Tzur
No abstract provided.