Mathematics as a Constructive Activity: Learners Generating Examples

By A. Watson, John Mason. 2005

379 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/8031907ec3aa1bbd90596b0550db44de1cc6b505

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Citations in the corpus

What makes a counterexample exemplary? (2008, methodology): “Though attention to examples is a recurrent theme in mathematics education research, there appears to be a renewed interest in the use of examples in learning mathematics; both in examples generated upon invitation by learners (Watson and Mason 2005) and examples used by teachers in an instructional”
Exemplifying definitions: a case of a square (2008, background): “Within a variety of educational uses of examples in mathematics, we view examples as “illustrations of concepts and principles” (Watson and Mason 2005, p. 3).”
Using learner generated examples to introduce new concepts (2008, methodology): “spaces' of numbers and actions relevant to this task (Watson and Mason 2005)) but also exploring and extending their experience of multiplicative relationships and getting a wider sense of what happens when two of these 'new' kinds of number are related by multiplication.”
Intuitive nonexamples: the case of triangles (2008, background): “In line with Watson and Mason (2005), who coined the term “personal example space” and observed that very often learners have a very limited collection of examples in mind, we argue that a significant aim of learning mathematics is extending and enriching the space of examples to which one has…”
Solution Spaces of Multiple-Solution Connecting Tasks as a Mirror of the Development of Mathematics Teachers’ Knowledge (2008, methodology): “We used the notion of CT solution spaces to design research tools and analyze the data (inspired by the notion of example spaces introduced by Watson & Mason, 2005 ; see also Leikin, 2007 ).”
Seeing an Exercise as a Single Mathematical Object: Using Variation to Structure Sense-Making (2006, background): “With too many things varying, individual variation is obscured and learners may form an impression of jumping about randomly if they are aware at all of a potential example space (Watson & Mason, 2005) from which the tasks are drawn.”
Exploring mathematics teacher knowledge to explain the gap between theory-based recommendations and school practice in the use of connecting tasks (2007, result): “This finding is consistent with earlier arguments that examples are an effective didactic tool (Watson and Mason 2005) and an integral part of the teachers’ instructional explanations (Leinhardt 1993).”
Facilitating the Transition from Empirical Arguments to Proof. (2009, background): “Condition 1 extended the work of Zazkis and Chernoff (2008) and concerned Watson and Mason's (2005) notion of example spaces, that is, collections of examples that fulfill a particular function.”
Proof constructions and evaluations (2009, methodology): “…we (1) used counterexamples that were in accord with prospective teachers’ “example spaces for validation” at a given time (building on the work of Watson & Mason, 2005; Zazkis & Chernoff, 2008), and (2) incorporated activities in the instructional sequences that helped prospective teachers…”
Doctoral students’ use of examples in evaluating and proving conjectures (2008, methodology): “We do not know to what extent Chris’ response is typical among expert mathematicians, but this does suggest that activities based on exploring example spaces (e.g. Watson and Mason, 2005) might develop skills that are routinely used by some successful mathematical thinkers.”
“Variation problems” and their roles in the topic of fraction division in Chinese mathematics textbook examples (2011, background): “In mathematics education, Watson and Mason (2005) further expanded these notions and emphasized that simply providing examples is rarely sufficient for most learners to detect essential aspects.”
A Comparative Analysis of the Addition and Subtraction of Fractions in Textbooks from Three Countries (2010, methodology): “Drawing from Watson and Mason (2005 ), we considered worked examples as those portions of the textbook “that demonstrate the use of specific techniques” (p.”
Sameness and Difference in Transfer (2006, methodology): “It resembles quite closely another, independently developed framework by Mason and Watson (see, for instance, Mason, 2001; Watson & Mason, 2005). actually made finer discriminations in pair-wise comparisons of singular tones.”
Shedding light on and with example spaces (2008, background): “Watson & Mason (2005) use the term dimensions of possible variation to refer to the features of an example that learners recognize as eligible for change, without losing examplehood.”
The purpose, design and use of examples in the teaching of elementary mathematics (2008, background): “Watson and Mason (2005) develop this notion in terms of learners’ (and teachers’) awareness of dimensions of possible variation, and permissible change within each dimension, within the limits of the concept under consideration.”
Transitions and Proof and Proving at Tertiary Level (2011, neutral): “When Watson and Mason (2002) asked U.”