Preservice Teachers’ Understandings of the Relation Between a Fraction or Integer and Its Decimal Expansion: Strength and Stability of Belief

Weller, Kirk; Arnon, Ilana; Dubinsky, Ed

doi:10.1080/14926156.2011.570612

Cited by 24 publications

(10 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The class discussions and in-class work give students an opportunity to reflect on their work, particularly the activities done in the lab. As the instructor guides the discussion, he or she may provide definitions, offer explanations, and/or present an overview to tie together what the students have been thinking about and working on (Weller et al, 2009(Weller et al, , 2011.…”

Section: Ace Cyclementioning

confidence: 99%

Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

Borji

Ahadi

Radmehr

2018

EURASIA J MATH SCI T

View full text Add to dashboard Cite

APOS-ACE (Action, Process, Object, and Schema-Activities, Classroom discussion, and Exercises) is applied in this article to explore the teaching and learning of derivative by giving emphasis on its graphical understanding. For this purpose, a Genetic Decomposition is developed based on the outcomes of previous studies and on our personal teaching experiences. An ACE cycle is designed with the help of the Maple software and implemented on a group of freshmen Iranian students (experimental group). The outcomes of this implementation are evaluated by comparing the performance of the experimental group to the performance of another equivalent student group (control group), to which the same subject was taught in the traditional, lecture-based way. Our findings demonstrated students' who were in the experimental group shown a better understanding of the derivate compared to the control group. Therefore, such ACE cycle with Maple could be used more frequently for teaching calculus, especially derivative.

show abstract

Section: Ace Cyclementioning

confidence: 99%

Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

Borji

Ahadi

Radmehr

2018

EURASIA J MATH SCI T

View full text Add to dashboard Cite

show abstract

“…Novillis (1976) found that part/whole representation is a prerequisite for a number-line representation. A number-line representation has been found to be useful for the development of number sense and magnitude sense of whole numbers (Booth & Siegler, 2008; R. S. Siegler & Booth, 2004) as well as rational numbers (Schneider, Grabner, & Paetsch, 2009;Sprute & Temple, 2011;Weller, Arnon, & Dubinsky, 2009).…”

Section: Rational Number In the Common Corementioning

confidence: 99%

Expanding the CBAL™ Mathematics Assessments to Elementary Grades: The Development of a Competency Model and a Rational Number Learning Progression

Arieli‐Attali

Cayton-Hodges

2014

ETS Research Report Series

View full text Add to dashboard Cite

Prior work on the CBAL™ mathematics competency model resulted in an initial competency model for middle school grades with several learning progressions (LPs) that elaborate central ideas in the competency model and provide a basis for connecting summative and formative assessment. In the current project, we created a competency model for Grades 3–5 that is based on both the middle school competency model and the Common Core State Standards (CCSS). We also developed an LP for rational numbers based on an extensive literature review, consultations with members of the CBAL mathematics team and other related research staff at Educational Testing Service, input from an advisory panel of external experts in mathematics education and cognitive psychology, and the use of small‐scale cognitive interviews with students and teachers. Elementary mathematical understanding, specifically that of rational numbers, is viewed as fundamental and critical to developing future knowledge and skill in middle and high school mathematics and therefore essential for success in the 21st century world. The competency model and the rational number LP serve as the conceptual basis for developing and connecting summative and formative assessment as well as professional support materials for Grades 3–5. We report here on the development process of these models and future implications for task development.

show abstract

“…Several studies have attempted to reveal students' thinking in learning mathematics at college (Dreyfus, 2002;Tall, 2008;Weller, Arnon, & Dubinsky, 2011;Syamsuri, Purwanto, Subanji, & Irawati, 2016;Syamsuri & Santosa, 2017). Tall (2008) expressed the idea of a transition process leading to advanced mathematical thinking.…”

Section: Introductionmentioning

confidence: 99%

“…This APOS theory has been widely used in analyzing the formation of mathematical concepts in universities (Asiala, Cottrill, Dubinsky, & Schwingendorf, 1997;Dubinsky & McDonald, 2001;Weller et al, 2011;Syamsuri, Purwanto, Subanji, & Irawati, 2017) as well as in mathematics learning (Weller et al, 2003;Salgado & Trigueros, 2015;García-Martínez & Parraguez, 2017). In the construction of concepts, this theory describes the paths that students pass through in constructing a mathematical concept.…”

Section: Introductionmentioning

confidence: 99%

APOS analysis on cognitive process in mathematical proving activities

Syamsuri

Marethi

2018

IJTLM

View full text Add to dashboard Cite

Thinking is very necessary in learning mathematics, both at school and college level. Several studies have attempted to reveal students' thinking in learning mathematics at college. This article aims to describe the mental structure that occurs when constructing mathematical proofs in terms of APOS theory. The APOS theory has been widely used in analyzing the formation of mathematical concepts in universities. This research explores a thinking process in proof constructing. It uses a qualitative approach. The research was conducted on 26 students majored in mathematics education in public university at Banten, Indonesia. The consideration of that was because the students were able to think a formal proof in mathematics. Results show that there are two types of thinking process in mathematical proving activities, namely: the deductive-holistic and the inductive-partial type of thinking process. Based on the results, some suitable learning activities should be designed to support the construction of these mental categories.

show abstract

Preservice Teachers’ Understandings of the Relation Between a Fraction or Integer and Its Decimal Expansion: Strength and Stability of Belief

Cited by 24 publications

References 14 publications

Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

Application of the APOS-ACE Theory to improve Students’ Graphical Understanding of Derivative

Expanding the CBAL™ Mathematics Assessments to Elementary Grades: The Development of a Competency Model and a Rational Number Learning Progression

APOS analysis on cognitive process in mathematical proving activities

Contact Info

Product

Resources

About