Concept–procedure interactions in children’s addition and subtraction

Canobi, Katherine H.

doi:10.1016/j.jecp.2008.07.008

Cited by 104 publications

(84 citation statements)

References 46 publications

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“…Another alternative to prompted self-explanation is solving additional non-routine problems, which can also promote comprehension and transfer (Canobi, 2009). Again, findings are mixed.…”

Section: Constraint On Effectiveness Relative To Alternative Instructmentioning

confidence: 99%

“…Both self-explanation prompts and solving unfamiliar problems can provide opportunities for thinking about correct procedures, including when each is most appropriate, and noticing patterns across problems. This is especially true when problem-solving exercises are designed with problems sequenced to support noticing of underlying concepts (Canobi, 2009;McNeil et al, 2012).…”

Section: Constraint On Effectiveness Relative To Alternative Instructmentioning

confidence: 99%

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Eliciting explanations: Constraints on when self-explanation aids learning

Rittle‐Johnson

Loehr

2016

Psychon Bull Rev

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Generating explanations for oneself in an attempt to make sense of new information (i.e., self-explanation) is often a powerful learning technique. Despite its general effectiveness, in a growing number of studies, prompting for selfexplanation improved some aspects of learning, but reduced learning of other aspects. Drawing on this recent research, as well as on research comparing self-explanation under different conditions, we propose four constraints on the effectiveness of self-explanation. First, self-explanation promotes attention to particular types of information, so it is better suited to promote particular learning outcomes in particular types of domains, such as transfer in domains guided by general principles or heuristics. Second, self-explaining a variety of types of information can improve learning, but explaining one's own solution methods or choices may reduce learning under certain conditions. Third, explanation prompts focus effort on particular aspects of the to-be-learned material, potentially drawing effort away from other important information. Explanation prompts must be carefully designed to align with target learning outcomes. Fourth, prompted self-explanation often promotes learning better than unguided studying, but alternative instructional techniques may be more effective under some conditions. Attention to these constraints should optimize the effectiveness of self-explanation as an instructional technique in future research and practice.

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“…Another alternative to prompted self-explanation is solving additional non-routine problems, which can also promote comprehension and transfer (Canobi, 2009). Again, findings are mixed.…”

Section: Constraint On Effectiveness Relative To Alternative Instructmentioning

confidence: 99%

Section: Constraint On Effectiveness Relative To Alternative Instructmentioning

confidence: 99%

Eliciting explanations: Constraints on when self-explanation aids learning

Rittle‐Johnson

Loehr

2016

Psychon Bull Rev

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show abstract

“…Previous research has shown that well-organized arithmetic facts practice can facilitate understanding that extends beyond simple retrieval of those facts. For example, Canobi (2009) found that organizing arithmetic practice in conceptual sequences, such as pairs of commuted addition problems, increased second graders' use of more sophisticated solution strategies, such as decomposition and retrieval (cf Steinberg, 1985). Additionally, McNeil et al (2011) found that children who received arithmetic practice with problems presented in a nontraditional format (e.g., 17 = 9 + 8) constructed a better understanding of math equivalence than children who received arithmetic practice with problems presented in the traditional format (e.g., 9 + 8 = 17).…”

mentioning

confidence: 99%

It pays to be organized: Organizing arithmetic practice around equivalent values facilitates understanding of math equivalence.

McNeil¹,

Chesney²,

Matthews³

et al. 2012

Journal of Educational Psychology

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This experiment tested the hypothesis that organizing arithmetic fact practice by equivalent values facilitates children's understanding of math equivalence. Children {M age = 8 years 6 months, N = 104) were randomly assigned to 1 of 3 practice conditions: (a) equivalent values, in which problems were grouped by equivalent sums (e.g., 3+4 = 7, 2-1-5 = 7, etc.), (b) iterative, in which problems were grouped iteratively by shared addend (e.g., 3-1-1=4, 3 + 2 = 5, etc.), or (c) no extra practice, in which children did not receive any practice over and above what they ordinarily receive at school and home. Children then completed measures to assess their understanding of math equivalence. Children who practiced facts organized by equivalent values demonstrated a better understanding of math equivalence than children in the other 2 conditions. Results suggest that organizing arithmetic facts into conceptually related groupings may help children improve their understanding of math equivalence.

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“…For example, Canobi and colleagues found that children with advanced conceptual knowledge of arithmetic principles were faster and more accurate at solving addition problems, and used more sophisticated problem-solving procedures than other children (Canobi, 2004(Canobi, , 2005Canobi et al, 1998Canobi et al, , 2003Farrington-Flint et al, 2007). Indeed, a recent study of schoolchildren undertaking addition and subtraction practice revealed that a conceptual sequencing of practice items led to procedural advances, well-structured procedural practice led to conceptual learning and that conceptual learning was predicted by children's initial procedural skills (Canobi, 2009). However, little is known about conceptprocedure links in preschoolers' arithmetic.…”

Section: Profiles Of Conceptual Understanding and Concept-procedures Rmentioning

confidence: 99%

The role of number words in preschoolers’ addition concepts and problem‐solving procedures

Patel

Canobi

2010

Educational Psychology

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Preschoolers' conceptual understanding and procedural skills were examined so as to explore the role of number-words and concept-procedure interactions in their additional knowledge. Eighteen three-to four-year-olds and 24 four-to five-yearolds judged commutativity and associativity principles and solved two-term problems involving number words and unknown numbers. The older preschoolers outperformed younger preschoolers in judging concepts involving unknown numbers and children made more accurate commutativity than associativity judgements. Children with conceptual profiles indicating a strong understanding of concepts applied to unknown numbers were more accurate at solving numberword problems than those with a poor conceptual understanding. The findings suggest that an important mathematical development during the preschool years may be learning to appreciate addition concepts as general principles that apply when exact numbers are unknown.

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Concept–procedure interactions in children’s addition and subtraction

Cited by 104 publications

References 46 publications

Eliciting explanations: Constraints on when self-explanation aids learning

Eliciting explanations: Constraints on when self-explanation aids learning

It pays to be organized: Organizing arithmetic practice around equivalent values facilitates understanding of math equivalence.

The role of number words in preschoolers’ addition concepts and problem‐solving procedures

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