Cognitive and metacognitive predictors of mathematics strategy use

Carr, Martha; Jessup, Donna L.

doi:10.1016/1041-6080(95)90012-8

Cited by 35 publications

(27 citation statements)

References 31 publications

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“…Research carried out in the 1990s and after the millennium continued to use these core categories of metacognition to explore the utility of the concept in research with children and adolescents, assessing the predictive potential of metacognitive knowledge and skillfulness in mathematics (e.g., Carr & Jessup, 1995;Lucangeli & Cornoldi, 1997;Desoete & Veenman, 2006a). As can be inferred from the overview presented by Desoete and Veenman (2006b), a large proportion of the relevant studies focused on the importance of metacognitive skills, thus emphasizing the relevance of procedural metacognitive knowledge (e.g., planning, monitoring, self-control) on problem solving in mathematics.…”

Section: More Recent Research On Metacognition and Mathematics Educationmentioning

confidence: 98%

Metacognition and mathematics education

Schneider

Artelt

2010

ZDM Mathematics Education

196

128

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The role of metacognition in mathematics education is analyzed based on theoretical and empirical work from the last four decades. Starting with an overview on different definitions, conceptualizations and models of metacognition in general, the role of metacognition in education, particularly in mathematics education, is discussed. The article emphasizes the importance of metacognition in mathematics education, summarizing empirical evidence on the relationships between various aspects of metacognition and mathematics performance. As a main result of correlational studies, it can be shown that the impact of declarative metacognition on mathematics performance is substantial (sharing about 15-20% of common variance). Moreover, numerous intervention studies have demonstrated that ''normal'' learners as well as those with especially low mathematics performance do benefit substantially from metacognitive instruction procedures.

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Section: More Recent Research On Metacognition and Mathematics Educationmentioning

confidence: 98%

Metacognition and mathematics education

Schneider

Artelt

2010

ZDM Mathematics Education

196

128

View full text Add to dashboard Cite

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“…This result was the first to provide evidence for the use of the min strategy by children. This strategy consists in counting on from the larger of the two operands by the number indicated by the smaller of the operands (Carr & Jessup, 1995;Siegler, 1987;Siegler & Crowley, 1994). Adults also show a significant increase in response latencies as a function of the size of the operands, but this increase is much smaller than that in children.…”

mentioning

confidence: 99%

Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm

2007

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The authors showed that for primary school children, response times (RTs) for simple addition problems (e.g., 4 3) increase linearly with the size of the smaller operand. This result was the first to provide evidence for the use of the min strategy by children. This strategy consists in counting on from the larger of the two operands by the number indicated by the smaller of the operands (Carr & Jessup, 1995;Siegler, 1987;Siegler & Crowley, 1994). Adults also show a significant increase in response latencies as a function of the size of the operands, but this increase is much smaller than that in children. Moreover, unlike in children, adults' RTs form a curvilinear function that is best explained by the square of the sum or the product of the operands than by the size of the operands. These differences between adults and children have been interpreted as evidence that, unlike children, adults use fast and efficient retrieval from memory to solve simple addition problems.However, LeFevre, Sadesky, and Bisanz (1996) stressed that, as has already been mentioned for children (Siegler, 1987(Siegler, , 1989, averaging solution latencies across trials that involve different procedures can result in misleading conclusions about how adults solve problems. These authors note that the researchers who have used the more direct approach of asking participants to report their procedure have challenged the strong assumption that adults always use retrieval for simple addition problems. For example, Svenson (1985) showed that adults were certain that they had used a retrieval strategy on simple addition problems on only 78% of the trials (for similar results, see also Geary, Frensch, & Wiley, 1993;Geary & Wiley, 1991). Then, to address the issue of how the selection of procedures varies across problems and participants, LeFevre et al. collected trial-by-trial reports of procedure, in addition to the classical chronometric data. The authors concluded that the importance of retrieval had been overemphasized in models of adult performance. Indeed, in the case of addition problems, 81% of their participants had used two or more of the counting, retrieval, and decomposition procedures in order to solve simple problems (i.e., both the addend and the augend inferior to 10). In fact, retrieval was the most frequently used procedure for problems with sums lower According to LeFevre, Sadesky, and Bisanz (1996), averaging solution latencies in order to study individuals' arithmetic strategies can result in misleading conclusions. Therefore, in addition to classical chronometric data, they collected verbal reports and challenged the assumption that adults rely systematically on retrieval of arithmetic facts from memory to solve simple addition problems. However, Kirk and Ashcraft (2001) questioned the validity of such a methodology and concluded that a more appropriate method has to be found. Thus, we developed an operand recognition paradigm that does not rely on verbal reports or on solution latencies. In accordance with LeFevre et al.,...

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“…Over the last few decades, several studies have focused on the use of metacognitive skills, in general, while performing different tasks, for instance, reading comprehension (Markman, 1977(Markman, , 1979Pressley & Afflerbach, 1995; or problem solving (Carr & Jessup, 1995;Christoph, 2006;Mevarech & Fridkin, 2006;Schoenfeld, 1992;Veenman & Spaans, 2005;Veenman, Wilhelm, & Beishuizen, 2004). Others focused on one or more separate components of metacognitive skills, such as planning (Shore & Lazar, 1996;Focant et al, 2006) or monitoring skills (Mengelkamp & Bannert, 2008).…”

Section: Metacognitive Skillfulnessmentioning

confidence: 99%

The increasing role of metacognitive skills in math: a cross-sectional study from a developmental perspective

Stel

Veenman

Deelen

et al. 2009

ZDM Mathematics Education

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Both intelligence and metacognitive skillfulness have been regarded as important predictors of math performance. The role that metacognitive skills play in math, however, seems to be subjected to change over the early years of secondary education. Metacognitive skills seem to become more general (i.e., less domain-specific) by nature (Veenman and Spaans in Learn Individ Differ 15: [159][160][161][162][163][164][165][166][167][168][169][170][171][172][173][174][175][176] 2005). Moreover, according to the monotonic development hypothesis (Alexander et al. in Dev Rev 15:1-37, 1995), metacognitive skills increase with age, independent of intellectual development. This hypothesis was tested in a study with 29 second-year students (13-14 years) and 30 third-year students (14-15 years) in secondary education. A standardized intelligence test was administered to all students. Participants solved math word problems with a difficulty level adapted to their age group. Thinking-aloud protocols were collected and analyzed on the frequency and quality of metacognitive activities. Another series of math word problems served as post-test. Results show that the frequency of metacognitive activity, especially those of planning and evaluation, increased with age. Intelligence was a strong predictor of math performance in 13-to 14-year-olds, but it was less prominent in 14-to 15-year-olds. Although the quality of metacognitive skills appeared to predict math performance in both age groups, its predictive power was stronger in 14-to 15-yearolds, even on top of intelligence. It bears relevance to math education, as it shows the increasing relevance of metacognitive skills to math learning with age.

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Cognitive and metacognitive predictors of mathematics strategy use

Cited by 35 publications

References 31 publications

Metacognition and mathematics education

Metacognition and mathematics education

Retrieval or nonretrieval strategies in mental arithmetic? An operand recognition paradigm

The increasing role of metacognitive skills in math: a cross-sectional study from a developmental perspective

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