Exploring mathematics problems prepares children to learn from instruction

DeCaro, Marci S.; Rittle‐Johnson, Bethany

doi:10.1016/j.jecp.2012.06.009

Cited by 123 publications

(109 citation statements)

References 54 publications

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“…Learners sometimes struggle to provide relevant explanations, and, in these cases, self-explanation often does not improve learning (e.g., Broers & Imbos, 2005;DeCaro & Rittle-Johnson, 2012;Matthews & Rittle-Johnson, 2009;Mwangi & Sweller, 1998). In other cases, learners' explanations focus their attention on particular types of information, decreasing their attention to, and learning of, other information (e.g., Berthold et al, 2011;Kuhn & Katz, 2009;.…”

Section: Constraints On When Prompting For Explanation Aids Learningmentioning

confidence: 99%

Eliciting explanations: Constraints on when self-explanation aids learning

Rittle‐Johnson

Loehr

2016

Psychon Bull Rev

Self Cite

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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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Section: Constraints On When Prompting For Explanation Aids Learningmentioning

confidence: 99%

Eliciting explanations: Constraints on when self-explanation aids learning

Rittle‐Johnson

Loehr

2016

Psychon Bull Rev

Self Cite

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“…New technologies can benefit students' learning, but the details of implementing such technologies are crucial to their success, for instance in terms of the social engineering of the learning environment, sequencing of instruction/exploration, activity design, as well as the level of allowed discovery/inquiry. DeCaro and Rittle-Johnson (2012) have shown that when open-ended activities precede formal instruction (such as exploring quantities before receiving explanation about math equivalence), students are more able to solve math problems and achieve deeper conceptual knowledge. This approach was also useful to adults learning college-level content, as is pointed out by Schneider et al (2013).…”

Section: Stem Instructions Creativity and Technologymentioning

confidence: 99%

The Effect of Highly Scaffolded Versus General Instruction on Students’ Exploratory Behavior and Arousal

Blikstein¹,

Gomes

Akiba

et al. 2016

Tech Know Learn

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Technology is changing the way students interact with knowledge, and openended activities are one of the main types of tasks that students engage with in technologyrich environments. However, the amount of guidance needed to promote learning in these environments remains unknown. We explore this issue by focusing on the effects of stepby-step versus generic instructions on student's exploratory behavior and arousal levels. In this experiment, students completed three computer-based activities within a physics simulation software: building a tower, building a bridge and a free task. We did not find any effect of our experimental manipulation on students' task performance. We found, however, that detailed instruction induced higher level of activation followed by a relaxation phase and a recovery of the activation level in the last segment of the task (U-shaped curve). On the other hand, generic instructions seemed to lead students into a continuous relaxation pattern along the task (decreasing slope). Moreover, low and high-aroused students appear to be affected by the instructions differently, with high-aroused students at baseline showing less cognitive flexibility. Finally, we observed carryover effects, where types of instruction kept influencing students' levels of activation in a following openended task. We discuss implications of those results for designing learning activities in constructionist, technology-rich environments.

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“…The mathematical equivalence assessment was adapted from previous research (DeCaro & Rittle-Johnson, 2012;Matthews, Rittle-Johnson, McEldoon, & Taylor, 2012;Rittle-Johnson, Taylor, Matthews, & McEldoon, 2011). The assessment included four subscales (see Table 2): Conceptual Knowledge items evaluated both individuals' understanding of the meaning of the equal sign as a relational symbol and the structure of equations.…”

Section: Mathematical Equivalence Assessmentmentioning

confidence: 99%

“…Two additional Conceptual Knowledge items were included, based on previous research (e.g., DeCaro & Rittle-Johnson, 2012;RittleJohnson & Alibali, 1999). For these two items, students were shown a mathematical equivalence problem for 5 seconds and were asked to write down the problem from memory.…”

Section: Mathematical Equivalence Assessmentmentioning

confidence: 99%

Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics

DeCaro

2016

Mem Cogn

Self Cite

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An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals' ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate (N = 41, Experiment 1) and fifth-and sixthgrade students (N = 87, Experiment 2) solved mathematical equivalence problems in one of two set-inducing conditions. Participants in the complex-first condition solved problems without a repeated addend on both sides of the equal sign (e.g., 7 + 5 + 9 = 3 + _), which required multistep strategies. Then these students solved problems with a repeated addend (e.g., 7 + 5 + 9 = 7 + _), for which a shortcut strategy could be readily used (i.e., adding 5 + 9). Participants in the shortcutfirst condition solved the same problem set but began with the shortcut problems. Consistent with laboratory studies of mental set, participants in the complex-first condition were less likely to use the more efficient shortcut strategy when possible. In addition, these participants were less likely to demonstrate procedural flexibility and conceptual understanding on a subsequent assessment of mathematical equivalence knowledge. These findings suggest that certain problem-solving contexts can help or hinder both flexibility in strategy use and deeper conceptual thinking about the problems.

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Exploring mathematics problems prepares children to learn from instruction

Cited by 123 publications

References 54 publications

Eliciting explanations: Constraints on when self-explanation aids learning

Eliciting explanations: Constraints on when self-explanation aids learning

The Effect of Highly Scaffolded Versus General Instruction on Students’ Exploratory Behavior and Arousal

Inducing mental set constrains procedural flexibility and conceptual understanding in mathematics

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