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Preparing prospective secondary teachers to teach mathematical reasoning and proof: the case of the role of examples in proving
Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and...
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Extrema points: concept images, mis-in and mis-out examples
This paper reports on students’ conceptions of minima points. Written assignments and individual interviews uncovered salient, concept images, as...
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Educating for adaptive expertise: case examples along the medical education continuum
Adaptive expertise represents the combination of both efficient problem-solving for clinical encounters with known solutions, as well as the ability...
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Classifying Examples is More Effective for Learning Relational Categories Than Reading or Generating Examples
Successful teaching requires that student teachers acquire a conceptual understanding of teaching practices. A promising way to promote such a...
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What Are and What Are Not Extrema Points? Examining Definitions and Examples
This paper reports on five secondary school mathematics prospective teachers’ conceptions of extreme point . The analysis of the data addressed...
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A Meta-analysis of the Worked Examples Effect on Mathematics Performance
The current meta-analysis quantifies the average effect of worked examples on mathematics performance from elementary grades to postsecondary...
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Conceptions of span in linear algebra: from textbook examples to student responses
Using Balacheff’s (2013) model of conceptions, we inferred potential conceptions in three examples presented in the spanning sets section of an...
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Learning from erroneous examples in the mathematics classroom: do students with different naïve ideas benefit equally?
Research suggests that troubleshooting activities that require students to reflect on teacher-crafted erroneous examples; i.e., erroneous solutions...
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Impact of an instructional guide and examples on the quality of feedback: insights from a randomised controlled study
While the provision of peer feedback has been widely recommended to enhance learning, many students are inexperienced in this area and would benefit...
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Expert example but not negative example standards help learners accurately evaluate the quality of self-generated examples
In acquiring new conceptual knowledge, learners often engage in the generation of examples that illustrate the to-be-learned principles and concepts....
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Better self-explaining backwards or forwards? Prompting self-explanation in video-based modelling examples for learning a diagnostic strategy
Self-explanation prompts in example-based learning are usually directed backwards: Learners are required to self-explain problem-solving steps just...
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Using Incorrect Worked Examples to Investigate the Consistency of First and Third Graders’ Measurement Conceptions
Elementary students demonstrate conflicts when measuring with rulers as well as measuring with discrete units. Their conflicts often lie in their...
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Online processing while monitoring worked-out examples with embedded errors: defining university student profiles
This study explores the process itself of comprehension monitoring of worked-out examples in mathematics. A ‘reversal error’ was embedded in a...
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The effect of emotive case construction on knowledge acquisition and ethical sense-making
The use of ill-structured case examples as an instructional strategy to teach ethical lessons is well-supported in the literature, however, case...
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Providing Support and Examples for Teaching Linear Equations in Secondary School: the Role of Knowledge of Mathematics Teaching
We present evidence of a secondary school teacher’s Knowledge of Mathematics Teaching when she teaches linear equations in a word problem setting. We...
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Expert example standards but not idea unit standards help learners accurately evaluate the quality of self-generated examples
Generating own examples for previously encountered new concepts is a common and highly effective learning activity, at least when the examples are of...
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Enhancing students’ critical thinking skills: is comparing correct and erroneous examples beneficial?
There is a need for effective methods to teach critical thinking (CT). One instructional method that seems promising is comparing correct and...
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Using heuristic worked examples to promote solving of reality-based tasks in mathematics in lower secondary school
This study examined whether learning with heuristic worked examples can improve students’ competency in solving reality-based tasks in mathematics...
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Analyzing the Structure of the Non-examples in the Instructional Example Space for Function in Abstract Algebra
The concept of function is critical in mathematics in general and abstract algebra in particular. We observe, however, that much of the research on...
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Theoretical Foundation and Examples of Collateral Creativity
This Chapter includes educational and psychological theories explaining the mechanism of collateral creativity in mathematics. It is shown that all...