Measure for Measure: What Combining Diverse Measures Reveals About Children's Understanding of the Equal Sign as an Indicator of Mathematical Equality

Matthews, Percival G.; Rittle‐Johnson, Bethany; McEldoon, Katherine L.; Taylor, Roger S.

doi:10.5951/jresematheduc.43.3.0316

Cited by 86 publications

(135 citation statements)

References 47 publications

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“…Next there were four transfer problems, two with equal addends not located in a matching position and two with no equal addends. Finally, there were six conceptual questions, which were true/ false questions about equality, adapted from prior research (Matthews, Rittle-Johnson, McEldoon, & Taylor, 2012). Children's responses and reaction times were recorded for analysis.…”

Section: Methodsmentioning

confidence: 99%

Hand Gesture and Mathematics Learning: Lessons From an Avatar

et al. 2016

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A beneficial effect of gesture on learning has been demonstrated in multiple domains, including mathematics, science, and foreign language vocabulary. However, because gesture is known to co-vary with other non-verbal behaviors, including eye gaze and prosody along with face, lip, and body movements, it is possible the beneficial effect of gesture is instead attributable to these other behaviors. We used a computer-generated animated pedagogical agent to control both verbal and non-verbal behavior. Children viewed lessons on mathematical equivalence in which an avatar either gestured or did not gesture, while eye gaze, head position, and lip movements remained identical across gesture conditions. Children who observed the gesturing avatar learned more, and they solved problems more quickly. Moreover, those children who learned were more likely to transfer and generalize their knowledge. These findings provide converging evidence that gesture facilitates math learning, and they reveal the potential for using technology to study non-verbal behavior in controlled experiments.

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Section: Methodsmentioning

confidence: 99%

Hand Gesture and Mathematics Learning: Lessons From an Avatar

et al. 2016

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“…The math equivalence assessment was adapted from past work (Matthews, Rittle-Johnson, McEldoon, & Taylor, 2012;Rittle-Johnson, Matthews, Taylor, & McEldoon, 2011). Two parallel forms were used: Form 1 at pre-test and Form 2 at post-test and retention test.…”

Section: Measures and Coding Assessmentmentioning

confidence: 99%

An alternative time for telling: When conceptual instruction prior to problem solving improves mathematical knowledge

Fyfe

DeCaro

Rittle‐Johnson

2014

Brit J of Edu Psychol

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“…These measures can be effective at getting an in-depth understanding of a single misconception (Lucariello, Tine, & Ganley, 2014;Matthews, Rittle-Johnson, McEldoon, & Taylor, 2012), or even distinguishing between several misconceptions at a given time point (Booth, Lange, Koedinger, & Newton, 2013;Cangelosi, Madrid, Cooper, Olson, & Hartter, 2013). Instances of these types of assessments may range from 25 minutes to measure the potential misconceptions in a single topic area for an entire class (Booth et al, 2013) to 45 minutes to measure one particular misconception in depth simultaneously for all students in a classroom (Matthews et al, 2012), to 20 minutes to interview each individual student about particular misconceptions (Cangelosi et al, 2013). Thus, for the purpose of comparing many misconceptions over a number of students over a longer period of time these methods are unlikely to be realistic for classroom use.…”

mentioning

confidence: 99%

Persistent and Pernicious Errors in Algebraic Problem Solving

Booth¹,

Barbieri²,

Eyer³

et al. 2014

The Journal of Problem Solving

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Students hold many misconceptions as they transition from arithmetic to algebraic thinking, and these misconceptions can hinder their performance and learning in the subject. To identify the errors in Algebra I which are most persistent and pernicious in terms of predicting student difficulty on standardized test items, the present study assessed algebraic misconceptions using an in-depth error analysis on algebra students' problem solving efforts at different points in the school year. Results indicate that different types of errors become more prominent with different content at different points in the year, and that there are certain types of errors that, when made during different levels of content, are indicative of math achievement difficulties. Recommendations for the necessity and timing of intervention on particular errors are discussed.

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Measure for Measure: What Combining Diverse Measures Reveals About Children's Understanding of the Equal Sign as an Indicator of Mathematical Equality

Cited by 86 publications

References 47 publications

Hand Gesture and Mathematics Learning: Lessons From an Avatar

Hand Gesture and Mathematics Learning: Lessons From an Avatar

An alternative time for telling: When conceptual instruction prior to problem solving improves mathematical knowledge

Persistent and Pernicious Errors in Algebraic Problem Solving

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