Articles

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The role of prediction in the teaching and learning of mathematics (with Gabriela Buendía, Ok-kyeong Kim, Francisco Cordero, and Lisa Kasmer), International Journal of Mathematical Education in Science and (2010)

The prevalence of prediction in grade-level expectations in mathematics curriculum standards signifies the importance of...

 

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Provoking Intellectual Need, Matematics Teaching in the Middle School (2009)

According to Harel's Necessity Principle (1998) “students are most likely to learn when they see...

 

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Burning the candle at just one end: Using nonproportional examples helps students determine when proportional strategies apply, Mathematics Teaching in the Middle School (2009)

In learning proportions students must understand what makes a situation proportional. If all the missing-value...

 

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通过数学任务提高美国职前教师的数学成熟性 (Advancing pre-service teachers’ mathematical sophistication via mathematical tasks) (with 庞雅丽 and 赵锐), Journal of Mathematics Education (in Chinese) (2009)

2008年5月22日，香港数学教育学会在香港浸会大学举行了研讨会。本文以该研讨会上的发言为蓝本，区分了以下四种差异：（1）约定俗成的数学与学校数学之间的差异；（2）理解方式与思维方式之间的差异；（3）成熟的学习者与被动的学习者之间的差异；（4）知识传授与知识参与这两种教学模式之间的差异。文章还讨论了Harel提出的教学原则以及数学任务的设计与它们在课堂中的使用，并呈现了具体的案例来说明如何设计数学任务以实现特定的学习与教学目标，如激发学生学习某一特定概念的需要，促进理想的思维方式，阻止不合适的思维方式以及评估学生的概念性理解。

 

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Advancing pre-service teachers’ mathematical sophistication via mathematical tasks, EduMath (2008)

This article is based on the seminar that the author presented for the Hong Kong...

 

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Developing Mathematical Habits of Mind (with Selden Annie), MAA Focus (2008)

A Project NeXT panel on “Helping Students Develop Mathematical Habits of Mind without Compromising Key...

 

Dissertation

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Students’ Mental Acts of Anticipating in Solving Problems involving Algebraic Inequalities and Equations, The Selected Works of Kien Lim (2006)


Anticipating is the mental act of conceiving a certain expectation without performing a sequence of...

 

Conference Proceedings

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Planting the seeds of computational thinking: An introduction to programminsuitable for inclusion in STEM curriculag (with Eric A. Freudenthal, Art Duval, Sarah Hug, Alexandria N. Ogrey, Catherine Tabor, Rebeca Q. Gonzalez, and Alan Siegel), Proceedings of the 118th American Society for Engineering Education Annual Conference & Exposition (2011)

Inadequate math preparation discourages many capable students – especially those from traditionally underrepresented groups –...

 

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Impulsive-Analytic Disposition: Instrument Pilot Testing (with Osvaldo F. Morera), Proceedings of the Thirty-third Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (2011)

The likelihood-to-act (LtA) survey measures impulsive and analytic dispositions in solving mathematics problems. The current...

 

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Addressing Impulsive Disposition: Using Non-proportional Problems to Overcome Overgeneralization of Proportionality (with Osvaldo Morera), Proceedings of the 13th Annual Conference on Research in Undergraduate Mathematics Education (2010)

Impulsive disposition is an undesirable way of thinking where one spontaneously applies the first idea...

 

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Continuing Discussion of Mathematical Habits of Mind (with Annie Selden), Proceedings of the Thirty-second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (2010)

The idea of “mathematical habits of mind” has been introduced to emphasize the need to...

 

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Inferring Impulsive-analytic Disposition from Written Responses (with Miguel Mendoza), Proceedings of the Thirty-second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (2010)

Impulsive disposition refers to one’s proclivity to spontaneously proceed with an action that comes to...

 

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Mathematical Habits of Mind (with Annie Selden) (2009)

The idea of “mathematical habits of mind” has been introduced to emphasize the need to...

 

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Assessing Problem-Solving Dispositions: Likelihood-To-Act Survey (with Osvaldo Morera and Mourat Tchoshanov), Proceedings of the Thirty-first Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (2009)

This paper reports an ongoing study that is aimed at developing an instrument for measuring...

 

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Mathematical Knowledge for Pre-service Teachers, Proceedings of the US-Sino Workshop on Mathematics and Science Education: Common Priorities that Promote Collaborative Research (2008)

This presentation highlights Harel's notion of ways of thinking and its importance to learning mathematics....

 

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Improving Students’ Algebraic Thinking: The Case of Talia, Proceedings of the Thirty-first Conference of the International Group for the Psychology of Mathematics Education (2007)

This paper presents the case of an 11th grader, Talia, who demonstrated improvement in her...

 

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Characterizing Students’ Thinking: Algebraic Inequalities and Equations, Proceedings of the Twenty-eight Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (2006)

This paper presents the findings of a study that explores the viability of using students’...

 

Others

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A Collection of Lists of Mathematical Habits of Mind (2010)

Mathematical habits of mind and general habits of mind have been identified in the field...

 

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Mathematical Habits of Mind: A Working Group at the 2009 PME-NA Conference (with Annie Selden) (2009)

The objectives of this working group are: (a) to discuss various views and aspects of...

 

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Helping Students Develop Mathematical Habits of Mind: A Joint Panel Session at the 2009 JMM Conference (with Kristin Camenga), Joint Mathematics Meeting (2009)

Cuoco, Goldenberg, and Mark advocate habits of mind as an organizing principle for a mathematics...