Parts, Wholes, and Place Value: A Developmental View

Ross, Sharon

doi:10.5951/at.36.6.0047

Cited by 64 publications

(49 citation statements)

References 2 publications

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“…Problemsolving, material-based actions, such as grouping or partitioning with base-ten models (e.g., bundles of ten sticks), or pre-grouped base-ten models (plastic cubes, longs, flats, etc.) are common in educational materials (Ross 1989;Fuson and Briars 1990;Fuson et al 1997). However, the introduction of such materials into the classroom-even those with the semiotic potential to demonstrate the idea of the unit-does not guarantee that the student is able to construct the concept (Bartolini Bussi and Mariotti 2002;Fuson et al 1997;Baturo 2000).…”

Section: Quantities As a Support To Give Meaning To Numeration Unitsmentioning

confidence: 99%

“…As Brissiaud (2005) notes, students who associate a representation of a quantity (with some base-ten material) with a written number can give the illusion of understanding; in fact, their reasoning may lack a link with the underlying groupings. Fuson (1990), Ross (1989), Hiebert and Wearne (1992), and Baturo (2000) point out the difficulty of passing from the grouping of objects into tens, to the concept of the group as a unit and, conversely, spotting the group of ten hidden in the notation. Finally, Chandler and Kamii (2009) highlight that the monetary equivalence 1 dime = 10 pennies is obvious to adults, but not so simple for young students.…”

Section: Quantities As a Support To Give Meaning To Numeration Unitsmentioning

confidence: 99%

“…The (symmetrical) relation between ones and tens has been widely studied (e.g., Ross 1989;Fosnot and Dolk 2001;Chandler and Kamii 2009), whether as the organization of a collection, or as an additive or subtractive calculation (mental, online, or in-column). Coordinating these two units (and not just juxtaposing them) influences the understanding of larger numbers (Thomas 2004;Steffe and Cobb 1988).…”

Section: Quantities As a Support To Give Meaning To Numeration Unitsmentioning

confidence: 99%

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Understanding place value with numeration units

Houdement

Tempier

2018

ZDM Mathematics Education

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Numeration units (ones, tens, hundreds, etc.) are an epistemological foundation for place value. Here, we assume that they are a didactic support in countries where spoken numbers are incongruent with written numbers. In France, teaching practices neglect the relations between units, and numeration units are typically used only to designate the positions of digits. Our research, which adopts the didactical engineering framework, aims to develop a set of reference tasks for grades 1 to 5 to support a consistent learning of place value with numeration units. This article reports the theoretical framework on which our research is based, and illustrates it with some examples of tasks designed for grade 3 students and implemented in classrooms.

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Section: Quantities As a Support To Give Meaning To Numeration Unitsmentioning

confidence: 99%

Section: Quantities As a Support To Give Meaning To Numeration Unitsmentioning

confidence: 99%

Section: Quantities As a Support To Give Meaning To Numeration Unitsmentioning

confidence: 99%

See 1 more Smart Citation

Understanding place value with numeration units

Houdement

Tempier

2018

ZDM Mathematics Education

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“…Thus, there were up to six open-ended responses possible for each PSMT. There is some concern about using self-reported data due to a tendency of participants to present favorable images of themselves (Ross, 1989); however, there is little motivation to misreport as confidentiality was preserved (Baldwin, 2000).…”

Section: Methodsmentioning

confidence: 99%

New Standards Require Teaching More Statistics

Lovett

Lee

2017

Journal of Teacher Education

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Mathematics teacher education programs often need to respond to changing expectations and standards for K-12 curriculum and accreditation. New standards for high school mathematics in the United States include a strong emphasis in statistics. This article reports results from a mixed methods cross-institutional study examining the preparedness of preservice secondary mathematics teachers to teach statistics and identifying factors and experiences that influence their preparedness. Our results suggest that the cohort of teachers entering secondary mathematics classrooms in 2015-2016 were not well prepared to teach statistics. Specific suggestions are given for how teacher education programs must rise to the challenge of preparing their graduates to teach statistics.

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“…Give-N10 was designed to assess children's understanding of or sensitivity to the arithmetic operations of the base-10 number system. It should be noted that there is a large literature on children's understanding of the base-10 knowledge using place value in multi-digit Arabic numerals (Kamii, 1986;Miura & Okamoto, 1989;Ross, 1989;Fuson, 1990). While both the place value systems and the cardinal numbers are an external representation of the formal numerical concept, the former is fundamentally different from the latter.…”

Section: General Disscusionmentioning

confidence: 99%

Is thirty-two three tens and two ones? The embedded structure of cardinal numbers

et al. 2020

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The acquisition and representation of natural numbers have been a central topic in cognitive science. However, a key question in this topic about how humans acquire the capacity to understand that numbers make 'infinite use of finite means' (or that numbers are generative) has been left unanswered. Here, we test the hypothesis that children's understanding of the syntactic rules for building complex numerals-or numerical syntax-is a crucial foundation for the acquisition of number concepts. In two independent studies, we assessed children's understanding of numerical syntax by probing their knowledge about the embedded structure of cardinal numbers using a novel task called Give-a-number Base-10 (Give-N10). In Give-N10, children were asked to give a large number of items (e.g., 32 items) from a pool that is organized in sets of ten items. Children's knowledge about the embedded structure of numbers (e.g., knowing that thirty-two items are composed of three tens and two ones) was assessed from their ability to use those sets. Study 1 tested English-speaking 5-to 10-year-olds and revealed that children's understanding of the embedded structure of numbers emerges relatively late in development (several months into kindergarten), beyond when they are capable of making a semantic induction over a local sequence of numbers. Moreover, performance in Give-N10 was predicted by children's counting fluency even when school grade was controlled for, suggesting that children's understanding of the embedded structure of numbers is founded on their earlier knowledge about the syntactic regularities in the counting sequence. In Study 2, this association was tested again in monolingual Korean kindergarteners (5-6 years), as we aimed to test the same effect in a language with a highly regular numeral system. It replicated the association between Give-N10 performance and counting fluency, and it also demonstrated that Koreanspeaking children understand the embedded structure of cardinal numbers earlier in the acquisition path than English-speaking peers, suggesting that the knowledge of numerical syntax governs children's understanding of the generative properties of numbers. Based on these observations and our theoretical analysis of the literature, we propose that the syntax for building complex numerals represents the structure of numerical thinking.

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Parts, Wholes, and Place Value: A Developmental View

Cited by 64 publications

References 2 publications

Understanding place value with numeration units

Understanding place value with numeration units

New Standards Require Teaching More Statistics

Is thirty-two three tens and two ones? The embedded structure of cardinal numbers

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