Primary mathematics: towards 2000: 1986 Presidential address

Shuard, Hilary

doi:10.2307/3615672

Cited by 3 publications

(5 citation statements)

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“…To conclude, it is now widely recognised that most adults and children spontaneously invent their own, reliable mathematical procedures, and they rarely use the standard written methods outside school (Fitzgerald, 1985;Shuard, 1986b). These findings are not altogether surprising.…”

Section: ; Reed and Lave 1981)mentioning

confidence: 70%

“…For instance, many educators now believe that a combination of calculator work and a varied repertoire of reliable mental methods of computation is sufficient for most practical purposes and that there is little future for the traditional written methods (e.g. Shuard, 1986b). The use of out-of-school mathematics in school is generally no longer viewed as the intrusion of inappropriate and primitive strategies that need to be replaced by formal mathematics.…”

Section: The Role Of Prior Knowledgementioning

confidence: 97%

“…Hobbs, 1989;PrIME, 1990;Resnick et al, 1987;Shuard, 1986a;Stacey, 1991), and the National Curriculum recognises the limitations of the highly complex conventional written algorithms (NCC, 1989b). Nevertheless, the learning and practice of those algorithms remains a dominant activity in primary classsrooms (in 1986 it took up 80% of the total time spent on number: Shuard, 1986a). The reports by Sewell (1982) and ALBSU (1983) indicated that one consequence of this outdated approach is an exorbitant rate of adult innumeracy in the U.K., leading to unexpected difficulties affecting home life and employment prospects.…”

Section: The Role Of Prior Knowledgementioning

confidence: 98%

“…Significant progress has accordingly been made in developing mathematical curricula which build on children's existing knowledge and foster a flexible problem-solving approach (e.g. Hobbs, 1989;PrIME, 1990;Resnick et al, 1987;Shuard, 1986a;Stacey, 1991), and the National Curriculum recognises the limitations of the highly complex conventional written algorithms (NCC, 1989b). Nevertheless, the learning and practice of those algorithms remains a dominant activity in primary classsrooms (in 1986 it took up 80% of the total time spent on number: Shuard, 1986a).…”

Section: The Role Of Prior Knowledgementioning

confidence: 99%

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Situated Cognition and Cognitive Apprenticeship: Implications for Classroom Learning

Hennessy

1993

Studies in Science Education

217

105

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INTRODUCTIONThis paper reviews recent research in the area of situated cognition, focusing on the domains of mathematics, science and technology. The key issue addressed here is the disjunction between classroom learning and cognition in practice. The notion of apprenticeship inside and outside the classroom, the potential scaffolding function of computer-based learning environments, the role of prior knowledge in learning, and the notion of a general thinking and problem-solving capability are also explored, and implications for pedagogy are considered.The first important implication for our understanding of knowledge construction and problem-solving processes comes from the previously established literature which characterises cognitive differences between novices and experts. This work indicates that predominantly through an interactive process of cognitive apprenticeship, experts spend years acquiring intuitive specialist knowledge and sophisticated mental models of their domain (e.g. Collins and Gentner, 1987). These models are influenced by the social and cultural context in which solving a problem takes place, including the physical structure, the purpose of the activity, the existence of collaborating partners and the social mileu in which the problem is embedded (Furnham, 1992). Rather than being an individual, purely experiential process, then, cultural transmission plays a major role in the construction of domain expertise. However, practical applications of expert/novice comparisons are somewhat limited. Since experts and novices do not normally share similar goals or constraints nor wish to carry out similar tasks, teaching novices what experts are assumed to know is not Downloaded by [University of Montana] at 19:15 03 April 2015 2 Sara Hennessy necessarily an optimal strategy. Direct comparison between expert problem solving and that of young novices in the form of schoolchildren is therefore unlikely to be illuminating. The previous tendencies of cognitive psychologists to characterise various forms of everyday knowledge as deficient by comparison with expert knowledge lack credibility in the light of recent research concerning the construction of informal knowledge. The latter is successfully used in a range of domains -by children and adults -to meet the demands of everyday problemsolving situations, without recourse to school-taught strategies. Expert problem solving is similar to this 'knowledge in action' in that practitioners rarely find it useful to draw upon knowledge or skills attained during schooling. This is because schooling does not really prepare pupils for later life or for problem solving in the workplace; it can be viewed as a unique culture, a specialised practice with its own conventions, organisations and concerns, which are in fact of little value to society outside. The consequent gap between schooling, and everyday practice by children, adult expert practitioners and 'just plain folks' (Lave, 1988), is now well-documented and is explored below. SITUATED COGNITION Learning a...

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Section: ; Reed and Lave 1981)mentioning

confidence: 70%

Section: The Role Of Prior Knowledgementioning

confidence: 97%

Section: The Role Of Prior Knowledgementioning

confidence: 98%

Section: The Role Of Prior Knowledgementioning

confidence: 99%

See 2 more Smart Citations

Situated Cognition and Cognitive Apprenticeship: Implications for Classroom Learning

Hennessy

1993

Studies in Science Education

217

105

View full text Add to dashboard Cite

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“…The same idea was conveyed by Brodie (2010), stating the key in teaching mathematical reasoning is the type of assignment given to students, the way students are involved with the task, and the interaction between assignments, students, and teachers (connections). The statement was also supported by Barmby, Bilsbourough, Harries, & Higgins (2009), confirming "reasoning is the process by which the learner articulates and demonstrates connections between representations." Based on these statements, it can be concluded that the main aspects of mathematical reasoning are communication and connection skills.…”

Section: Figure 1 the Relation Of Reasoning Communication And Connmentioning

confidence: 85%

Improving elementary students' mathematical reasoning abilities through sociohumanistic-based learning

Hidayat¹,

Wahyudin²,

Jailani³

et al. 2020

Journal for the Education of Gifted Young Scientists

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This study aimed to determine the improvement of students' mathematical reasoning abilities through sociohumanistic-based learning. This research was a quasi-experimental study with a non-equivalent control group design. The population in this study were all class IV in one elementary school in Salatiga. The sample consisted of two classes, namely classes and selected by purposive sampling. The instrument used was a mathematical reasoning ability test. Data analysis used t-test (Independent Sample t-Test) and Mann Whitney. The analysis results show that: (1) based on the results on a limited, medium, and wide-scale try-out, the developed model is easy-practical-effective in its implementation; (2) the improvement in mathematical reasoning skill of the students taught using the model is higher than that of taught using direct instructions; and (3) Sociohumanistic-based learning has several advantages especially can generate endorphins (hormone of happiness) to make the students love math, can foster self-reliance of learners, able to activate the storage capabilities of the human brain into long-term memory. Based on the results of this research and development, it can be concluded that the developed model is easy, practical, and effective to improve the mathematical reasoning skill of elementary school students.

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