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Science and Mathematics Education Commons™
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Articles 31 - 52 of 52
Full-Text Articles in Science and Mathematics Education
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.
From Theory To Practice: Explaining Successful And Unsuccessful Teaching Activities (Case Of Fractions), Ron Tzur
Ron Tzur
In a teaching experiment, I examined a theoretical model of mathematics teaching and learning in practice. In this paper I focus on how the model can guide the teacher's thinking about students' understandings and the generation of activities that foster intended transformations in those understandings. As a research-teacher I taught, twice a week for four months, basic ideas of fractions to 28 third graders, in a public school in Israel. The analysis of both classroom data and researcher's documented reflections indicates how the model can empower the generation and explanation of successful teaching activities, as well as thinking about and …
Interaction And Fraction Knowledge: Children's Construction Of The Iterative Partitioning Scheme, Ron Tzur
Interaction And Fraction Knowledge: Children's Construction Of The Iterative Partitioning Scheme, Ron Tzur
Ron Tzur
No abstract provided.
How And What Might Teachers Learn Through Teaching Mathematics: Contributions To Closing An Unspoken Gap [Book Chapter], Ron Tzur
Ron Tzur
No abstract provided.
A Perspective On The Use Of Manipulatives: Making Sense Of A Teacher’S Use Of Base-Ten Blocks To Promote Understanding Of The Long-Division Algorithm, Karen Heinz, Marty Simon, Margaret Kinzel, Ron Tzur
A Perspective On The Use Of Manipulatives: Making Sense Of A Teacher’S Use Of Base-Ten Blocks To Promote Understanding Of The Long-Division Algorithm, Karen Heinz, Marty Simon, Margaret Kinzel, Ron Tzur
Ron Tzur
No abstract provided.
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.
Articulating Theoretical Constructs For Mathematics Teaching, Marty Simon, Ron Tzur, Karen Heinz, Margaret Kinzel
Articulating Theoretical Constructs For Mathematics Teaching, Marty Simon, Ron Tzur, Karen Heinz, Margaret Kinzel
Ron Tzur
No abstract provided.
Characterizing A Perspective On Mathematics Learning Of Teachers In Transition, Marty Simon, Ron Tzur, Karen Heinz, Margaret Kinzel, Margaret Smith
Characterizing A Perspective On Mathematics Learning Of Teachers In Transition, Marty Simon, Ron Tzur, Karen Heinz, Margaret Kinzel, Margaret Smith
Ron Tzur
No abstract provided.
A Joint Probabilistic Classification Model Of Relevant And Irrelevant Sentences In Mathematical Word Problems, Suleyman Centintas, Lou Si, Yan Xin, Dake Zhang, Joo Park, Ron Tzur
A Joint Probabilistic Classification Model Of Relevant And Irrelevant Sentences In Mathematical Word Problems, Suleyman Centintas, Lou Si, Yan Xin, Dake Zhang, Joo Park, Ron Tzur
Ron Tzur
Estimating the difficulty level of math word problems is an important task for many educational applications. Identification of relevant and irrelevant sentences in math word problems is an important step for calculating the difficulty levels of such problems. This paper addresses a novel application of text categorization to identify two types of sentences in mathematical word problems, namely relevant and irrelevant sentences. A novel joint probabilistic classification model is proposed to estimate the joint probability of classification decisions for all sentences of a math word problem by utilizing the correlation among all sentences along with the correlation between the question …