Generalization and Justification: The Challenge of Introducing Algebraic Reasoning Through Patterning Activities

By John Lannin. 2005

230 citations recorded by the source corpus.

Subfields: Education, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6fca2f4ab84f588bbf2d5cf4ac76aeed10266035

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Education

In Statistics and Probability

Citations in the corpus

Visual templates in pattern generalization activity (2010, background): “On the basis of recent findings at the K-9 and preservice elementary undergraduate levels involving generalization in patterning activity, we still need further research in terms of how such coordination could take place more effectively in a systematic manner (Mulligan & Mitchelmore, 2009; Warren &”
Connections Between Generalizing and Justifying: Students' Reasoning with Linear Relationships (2007, background): “…carry the assumption that generalizing patterns will constitute sufficient support for producing appropriate justifications, research demonstrates the widespread phenomenon of students using empirical justification to prove their generalizations (Hoyles, 1997; Knuth & Elliott, 1998; Lannin, 2005).”
The effect of different representations on Years 3 to 5 students’ ability to generalise (2008, background): “(as in Radford, 2003) and that pattern visuals result in better process generalisation (similar to Lannin, 2005 ).”
Middle school children’s cognitive perceptions of constructive and deconstructive generalizations involving linear figural patterns (2008, background): “Justification could mean many things (cf. Lannin, 2005), and considering the cognitive level of middle school students who are still in the beginning phase of learning domain-specific knowledge and practices in algebra, we more or less confined the notion of justification to their capacity to…”
Years 2 to 6 Students’ Ability to Generalise: Models, Representations and Theory for Teaching and Learning (2011, background): “With regard to these forms of generalisation, Lannin (2005) distinguished between generalisation from iconic/visual and numerical representations, arguing that iconic is a better representation to lead to process generalisation.”
A Learning Progression for Elementary Students’ Functional Thinking (2017, background): “…4), (d) express linear correspondence rules in words (e.g., Martinez & Brizuela, 2006, grades 2–5), including those discerned from visual patterns (e.g., Lannin, 2005, grade 6; Moss & McNab, 2011, grade 2;Warren &Cooper, 2008, grade 3); and (e) express linear correspondence rules using literal…”
What Is a Pattern? Criteria Used by Teachers and Young Children (2012, background): “While the literature suggests that most students have no difficulty recognizing a pattern, the route from pattern recognition in the early years to algebraic representations later on remains tenuous (Carraher et al., 2008; Dörfler 2008; Lannin, 2005; Moss & McNab, 2011).”