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A longstanding debate concerns the use of concrete versus abstract instructional materials, particularly in domains such as mathematics and science. Although decades of research have focused on the advantages and disadvantages of concrete and abstract materials considered independently, we argue for an approach that moves beyond this dichotomy and combines… (More)

- Nicole McNeil, Emily Fyfe
- 2012

Recent studies have suggested that educators should avoid concrete instantiations when the goal is to promote transfer. However, concrete instantiations may benefit transfer in the long run, particularly if they are “faded” into more abstract instantiations. Undergraduates were randomly assigned to learn a mathematical concept in one of three conditions:… (More)

Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical… (More)

- Nicole McNeil, Emily Fyfe, Lori Petersen, April E Dunwiddie, Heather Brletic-Shipley
- Child development
- 2011

This study examined whether practice with arithmetic problems presented in a nontraditional problem format improves understanding of mathematical equivalence. Children (M age = 8;0; N = 90) were randomly assigned to practice addition in one of three conditions: (a) traditional, in which problems were presented in the traditional "operations on left side"… (More)

ion Translates patterns into new patterns with same structural rule. ‘‘I made a pattern with these blocks. Please make the same kind of pattern here, using these cubes’’ (using new colors and shapes).

- Emily Fyfe, Marci DeCaro, Bethany Rittle-Johnson
- The British journal of educational psychology
- 2014

BACKGROUND
The sequencing of learning materials greatly influences the knowledge that learners construct. Recently, learning theorists have focused on the sequencing of instruction in relation to solving related problems. The general consensus suggests explicit instruction should be provided; however, when to provide instruction remains unclear.
AIMS
We… (More)

- Emily Fyfe, Nicole McNeil, Bethany Rittle-Johnson
- Child development
- 2015

The labels used to describe patterns and relations can influence children's relational reasoning. In this study, 62 preschoolers (Mage = 4.4 years) solved and described eight pattern abstraction problems (i.e., recreated the relation in a model pattern using novel materials). Some children were exposed to concrete labels (e.g., blue-red-blue-red) and… (More)

- Bethany Rittle-Johnson, Emily Fyfe, Abbey Marie Loehr
- The British journal of educational psychology
- 2016

BACKGROUND
Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding.
AIMS
This study evaluated the effect of instruction on a math concept and… (More)

- Bethany Rittle-Johnson, Emily Fyfe, Kerry Hofer, Dale Farran
- Child development
- 2017

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from ages 4 to 11. This model includes a broad range of math topics, as… (More)