The Effects of Premature Drill in Third-Grade Arithmetic

Brownell, William A.; Chazal, Charlotte B.

doi:10.1080/00220671.1935.10880546

Cited by 42 publications

(18 citation statements)

References 13 publications

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“…Several previous investigators have argued that backup strategies, such as counting fingers, counting from the minimum addend, and repeated addition, make arithmetic a meaningful activity (Brownell & Chazal, 1935; Cowan, 2003; Cowan, Dowker, Christakis, & Bailey, 1996; Cowan & Renton, 1996). The present findings add evidence that linear representations of numerical magnitudes make arithmetic meaningful even when children learn answers via retrieval.…”

Section: Discussionmentioning

confidence: 99%

Numerical Magnitude Representations Influence Arithmetic Learning

2008

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This study examined whether the quality of first graders' (mean age = 7.2 years) numerical magnitude representations is correlated with, predictive of, and causally related to their arithmetic learning. The children's pretest numerical magnitude representations were found to be correlated with their pretest arithmetic knowledge and to be predictive of their learning of answers to unfamiliar arithmetic problems. The relation to learning of unfamiliar problems remained after controlling for prior arithmetic knowledge, short-term memory for numbers, and math achievement test scores. Moreover, presenting randomly chosen children with accurate visual representations of the magnitudes of addends and sums improved their learning of the answers to the problems. Thus, representations of numerical magnitude are both correlationally and causally related to arithmetic learning.

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Section: Discussionmentioning

confidence: 99%

Numerical Magnitude Representations Influence Arithmetic Learning

2008

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“…Brownell and Chazal (1935) showed that two months of daily drill on addition facts increased speed of direct recall, but the effect soon faded. Questions remain concerning the effects of the degree of variety in the set of tasks; some of these are implicit in the foregoing discussion.…”

Section: Intensitymentioning

confidence: 99%

Principles for the design of teaching

Bell

1993

Educ Stud Math

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In this introductory article, after some initial discussion of an appropriate approach to mathexnatics as a curriculura subject, we sketch a theory for designing teaching, based on mathematical activity, situations, tasks, and interventions, exposing and resolving cognitive conflicts, changes of structure and context, feedback, reflection and review. We next review the main psychological principles underlying this theory, then consider some examples of teaching designs in the light of the theory. Thus we open the discussion of the theme of this issue, which continues with the fuller discussion of other examples in the remaining articles.Other authors have offered more controversial descriptions, which emphasize the logical aspects. One may recall Russell's "the subject in which we never know what we are talking about, nor whether what we say is true". For the purposes of guiding curriculum construction, we find the positive descriptions more helpful.Education is normally seen as a forward-looking, purposeful activity, the aim of which is to develop pupils' capacities and knowledge so as to equip them

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“…This notion encompasses what Baroody (2006) describes as three phases for basic fact mastering which are: counting strategies-using object counting for example blocks, fingers or verbal counting to determine the answer; reasoning strategies-using known information to logically determine an unknown combination as well as mastery-efficient (fast and accurate) production of answers (p. 22). In addition, other researchers (Baroody, 2006;Brownell & Chazal, 1935;Carpenter & Moser, 1984;Fuson, 1992;Henry & Brown, 2008 as cited by Van de Walle et al, 2010) found that basic fact mastering is dependent on the development of reasoning strategies. This mastery is essential if learners are to become proficient at solving basic mathematics problems.…”

Section: Literature Reviewmentioning

confidence: 96%

“…However, the reality is that the majority of fourth or fifth grade learners have not mastered addition and subtraction facts, and that learners at upper primary and beyond do not know their multiplication facts. This method does not work well (Brownell & Chazal, 1935 as cited in Van de Walle et al, 2012). Brownell and Chazal (1935, p. 17) concluded that children develop a variety of different thought processes or strategies for basic facts in spite of the amount of isolated drill that they experience.…”

Section: ) Memorising Factsmentioning

confidence: 99%

Strategies Used by Grade 6 Learners in the Multiplication of Whole Numbers in Five Selected Primary Schools in the Kavango East and West Regions

Ilukena¹,

Utete²,

Kasanda³

2020

IES

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This research paper reports strategies used by Grade 6 learners in multiplying whole numbers in five selected primary schools in Kavango East and West regions. A total of 200 learners' mathematics exercise books were analysed in order to identify the commonly used strategies by learners in multiplying whole numbers. A total of ten teachers teaching grade 6 mathematics were also requested to complete a questionnaire which required them to indicate the strategies that they employed in class when teaching multiplication of whole numbers. The teachers indicated that they used a variety of strategies including repeated addition, complete-number (Including doubling), partitioning and compensation to teach multiplication of whole numbers. The results also disclosed that the majority of the learners' mathematics exercise books reflected the use of the traditional method of repeated addition contrary to the teachers' claims. It was also found that a few of the learners used other strategies such as long method, short method and learner "invented" strategies. Additionally, the mathematics curriculum for upper primary learners (Grade 4-7 mathematics syllabus) requires learners to use paper and pencil algorithms to carry out multiplication of whole numbers without calculators (Ministry of Education, Arts & Culture [MoEAC], 2015, p. 2). However, at Grade 6, learners were expected to use paper and pencil algorithms to multiply numbers within the range 0-100000. Analysis of the learners' exercise books indicated that the majority were not able to multiply a two digit by a single digit, a two digit by a two digit and a three digit by a two digit number.

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The Effects of Premature Drill in Third-Grade Arithmetic

Cited by 42 publications

References 13 publications

Numerical Magnitude Representations Influence Arithmetic Learning

Numerical Magnitude Representations Influence Arithmetic Learning

Principles for the design of teaching

Strategies Used by Grade 6 Learners in the Multiplication of Whole Numbers in Five Selected Primary Schools in the Kavango East and West Regions

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