Teaching Multiplication: An Analysis of Elementary School Mathematics Teachers' Manuals from Japan and the United States

Watanabe, Tad

doi:10.1086/499745

Cited by 15 publications

(11 citation statements)

References 18 publications

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“…Repeated addition is a heuristic used by many elementary mathematics textbooks in their initial lessons on multiplication (Watanabe, 2003), and it is seen as a first step to reasoning about multiplication in many educational settings (e.g., Fischbein, Deri, Nello, & Marino, 1985; Greer, 1988). Further, both children and infants are able to add and subtract using only the ANS (Barth et al, 2005, 2006; McCrink & Wynn, 2004, 2009.)…”

Section: Discussionmentioning

confidence: 99%

Core multiplication in childhood

McCrink

Spelke

2010

Cognition

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A dedicated, non-symbolic, system yielding imprecise representations of large quantities (Approximate Number System, or ANS) has been shown to support arithmetic calculations of addition and subtraction. In the present study, 5–7-year-old children without formal schooling in multiplication and division were given a task requiring a scalar transformation of large approximate numerosities, presented as arrays of objects. In different conditions, the required calculation was doubling, quadrupling, or increasing by a fractional factor (2.5). In all conditions, participants were able to represent the outcome of the transformation at above-chance levels, even on the earliest training trials. Their performance could not be explained by processes of repeated addition, and it showed the critical ratio signature of the ANS. These findings provide evidence for an untrained, intuitive process of calculating multiplicative numerical relationships, providing a further foundation for formal arithmetic instruction.

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Section: Discussionmentioning

confidence: 99%

Core multiplication in childhood

McCrink

Spelke

2010

Cognition

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“…The Tokyo Shoseki series (2006a, b, c) is widely used in Japan. It represents about 35% of the market share (Watanabe, 2003). It is also available in English.…”

Section: Textbook Samplingmentioning

confidence: 99%

How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait

Alajmi

2011

Educ Stud Math

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Textbooks play an important part in the design of instruction. This study analyzed the presentation of fractions in textbooks designed for the elementary grades in Kuwait, Japan, and the USA. The analysis focused on the physical characteristics of the books, the structure of the lessons, and the nature of the mathematical problems presented. Findings showed USA and Kuwaiti mathematics textbooks are larger than Japanese textbooks; this larger size is consistent with a great deal of repetition. The Japanese texts do not address fractions until the third grade; they use linear models and connect fractions with measurement. In the USA and Kuwait, fractions are introduced in the first grade. The Harcourt text uses concrete material to help students learn fraction procedures. For the Kuwaiti series, the lessons depend on using some pictorial representation of the area model to illustrate fraction ideas. All these textbooks focus on standard algorithms as the main computational methods.

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“…Thus far, comparative textbook analyses have addressed a fairly narrow range of mathematics content areas: addition and subtraction of whole numbers (Fuson et al, 1988), multiplication and division of whole numbers (Watanabe, 2003), decimals (Nicely, Fiber & Bobango, 1986), addition and subtraction of integers (Li, 2002), functions (Mesa, 2004), and complex numbers (Nicely, 1985). Wu (2005) claims that the study of fractions represents a student's first serious excursion into abstract mathematics.…”

Section: Rationale For the Studymentioning

confidence: 99%

“…While many early studies mainly focused on quantifiable characteristics of content analysis, such as whether or not a content topic was covered and page space devoted to each topic, more recent studies have begun to examine qualitative characteristics of content presentation such as development of mathematics content. For example, Watanabe (2003) analyzed the number of lessons dedicated to whole number multiplication, the grade levels where particular ideas are introduced and developed, and suggested pacing in textbooks from Japan and the USA. He also examined three qualitative characteristics of content presentation:…”

Section: Related Researchmentioning

confidence: 99%

How reform curricula in the USA and Korea present multiplication and division of fractions

Son

Senk

2010

Educ Stud Math

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In order to give insights into cross-national differences in schooling, this study analyzed the development of multiplication and division of fractions in two curricula: Everyday Mathematics (EM) from the USA and the 7th Korean mathematics curriculum (KM). Analyses of both the content and problems in the textbooks indicate that multiplication of fractions is developed in KM one semester earlier than in EM. However, the number of lessons devoted to the topic is similar in the two curricula. In contrast, division of fractions is developed at about the same time in both curricula, but due to different beliefs about the importance of the topic, KM contains five times as many lessons and about eight times as many problems about division of fractions as EM. Both curricula provide opportunities to develop conceptual understanding and procedural fluency. However, in EM, conceptual understanding is developed first followed by procedural fluency, whereas in KM, they are developed simultaneously. The majority of fraction multiplication and division problems in both curricula requires only procedural knowledge. However, multistep computational problems are more common in KM than in EM, and the response types are also more varied in KM.

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Teaching Multiplication: An Analysis of Elementary School Mathematics Teachers' Manuals from Japan and the United States

Cited by 15 publications

References 18 publications

Core multiplication in childhood

Core multiplication in childhood

How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait

How reform curricula in the USA and Korea present multiplication and division of fractions

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