Participatory and Anticipatory Stages of Mathematical Concept Learning: Further Empirical and Theoretical Development

Simon Martin A.; Placa Nicora; Avitzur Arnon

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Participatory and Anticipatory Stages of Mathematical Concept Learning: Further Empirical and Theoretical Development

机译：数学概念学习的参与阶段和预期阶段：进一步的经验和理论发展

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Tzur and Simon (2004) postulated 2 stages of development in learning a mathematical concept: participatory and anticipatory. In this article, we discuss the affordances for research of this stage distinction related to data analysis, task design, and assessment as demonstrated in a 2-year teaching experiment. We describe our modifications to and further explicate and exemplify the theoretical underpinnings of these stage constructs. We introduce a representation scheme and use it to trace the development of a concept from initial activity, through the participatory stage, and to the anticipatory stage.

机译：Tzur和Simon（2004）提出了学习数学概念的两个发展阶段：参与性和预期性。在本文中，我们讨论了这一阶段与数据分析，任务设计和评估相关的研究的能力，这在两年的教学实验中得到了证明。我们描述了我们的修改，并进一步阐述和举例说明了这些阶段构建的理论基础。我们介绍了一个表示方案，并使用它来跟踪概念的发展，从最初的活动到参与阶段，再到预期阶段。

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《Journal for research in mathematics education》 |2016年第1期|共31页
作者
Simon Martin A.; Placa Nicora; Avitzur Arnon;
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正文语种 eng
中图分类数学;
关键词
Anticipatory; Conceptual learning; Learning stages; Learning theory; Mathematical concept; Participatory; Reflective abstraction;

机译：预期;概念学习;学习阶段;学习理论;数学概念;参与式;反思性抽象;

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1. Participatory and Anticipatory Stages of Mathematical Concept Learning: Further Empirical and Theoretical Development [J] . Simon Martin A., Placa Nicora, Avitzur Arnon Journal for research in mathematics education . 2016,第1期

机译：数学概念学习的参与阶段和预期阶段：进一步的经验和理论发展
2. Development of an Instructional Learning Object Design Model for Tablets Using Game-based Learning with Scaffolding to Enhance Mathematical Concepts for Mathematic Learning Disability Students [J] . Suwit Waiyakoon, Jintavee Khlaisang, Prakob Koraneekij Procedia - Social and Behavioral Sciences . 2015,第2期

机译：平板电脑的教学学习对象设计模型的开发，其中使用基于游戏的支架学习来增强数学学习障碍学生的数学概念
3. Theoretical conception and some practical results of the development of mathematical competences with use of e-learning [J] . Agnieszka Heba, Jana Kapounova, Eugenia Smyrnova-Trybulska International Journal of Continuing Engineering Education and Life-long Learning . 2014,第3a4期

机译：利用电子学习发展数学能力的理论构想和一些实际结果
4. Evaluation Model For Real and Virtual Learning Environments: Theoretical Concept and Empirical Results [C] . Kerstin Fink, Friedrich Roithmayr 2002 Information Resources Management Association International Conference Vol.1; May 19-22, 2002; Seattle, Washington, USA . 2002

机译：真实和虚拟学习环境的评估模型：理论概念和实证结果
5. Factors affecting students' learning of new mathematics concepts in three Nashville area remedial and developmental studies mathematics programs. [D] . Jackson, Jeanetta Williams. 1997

机译：在三个纳什维尔地区补习和发展研究数学课程中，影响学生学习新数学概念的因素。
6. Shape of the self-concept clarity change during group psychotherapy predicts the outcome: an empirical validation of the theoretical model of the self-concept change [O] . Rafał Styła -1

机译：团体心理治疗期间自我概念清晰度改变的形状可预测结果：自我概念改变的理论模型的经验验证
7. Occupational therapy intervention with a child is based upon an understanding and appreciation of normal development. Knowledge of current concepts and theories related to child development is essential when occupational therapist evaluates children. This background information helps therapist to plan intervention for the child. The aim of this study is to make observation video about development of about one year old child. The purpose of my study is to help occupational therapy students learn about child development. My study is practice-based thesis. It includes product, which is the observation video and study rapport. I describe my whole process in my rapport. The process includes different kinds of stages. First, I studied those theories of child development, which are used in the studies of occupational therapy for children. These theories are Moseys Developmental Frame of Reference and the theory of development according to Sensory Integration Theory. These theories are the frames of reference of my study. I organize the child development areas according to child occupations and skills. Then I start to plan, film and edit my video based on the theories of child development and the principles of making a video. In my rapport I describe all the stages of my study and explain the sequence and the content of the stages. I also evaluate the process of my study. In the observation video you can see those stages of development where about one year old child is based on the frames of reference, which I have used in my study. I believe that my observation video can at least be good for inspiring occupational therapy students learning about child development. Keywords child development, learning, observation video [O] . Lehtinen Ann-Mari 2006

机译：对儿童的职业治疗干预基于对正常发育的理解和欣赏。当职业治疗师评估儿童时，与儿童发育相关的当前概念和理论的知识必不可少。这些背景信息可帮助治疗师为孩子计划干预措施。这项研究的目的是制作有关约一岁儿童发育的观察视频。我研究的目的是帮助职业治疗学生学习儿童成长。我的研究是基于实践的论文。它包括产品，这是观察视频和学习融洽的关系。我以融洽的方式描述我的整个过程。该过程包括不同阶段。首先，我研究了有关儿童发育的理论，这些理论被用于儿童的职业治疗研究中。这些理论是Moseys发展参考框架和根据感觉统合理论的发展理论。这些理论是我研究的参考框架。我根据儿童职业和技能组织儿童发展领域。然后，我根据儿童发育理论和视频制作原理开始计划，拍摄和编辑视频。在融洽的关系中，我描述了学习的所有阶段，并解释了这些阶段的顺序和内容。我还评估了我的学习过程。在观察视频中，您可以看到那些发展阶段，其中大约一岁的孩子基于我的研究框架。我相信，我的观察视频至少可以对激发职业治疗的学生学习儿童发育有帮助。关键字儿童发展，学习，观察视频
8. An Analysis of Theoretical and Empirical Advances in Learning Curve Concepts Since 1966. [R] . Orsini, J. A. 1970

机译：1966年以来学习曲线概念的理论与实证研究进展。

Participatory and Anticipatory Stages of Mathematical Concept Learning: Further Empirical and Theoretical Development

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