“…In secondary mathematics education research, the emphasis has been on translations between particular representation types relevant at those levels of mathematics (Bieda & Nathan, 2009;Mainali, 2021). Whereas the early childhood literature focuses on three representations that differ from that used in secondary (numerals, number words, and pictorial representations; Fuson, 2019;Young-Loveridge, 1999), emphasizes multi-sensory learning experiences (Elliot, 1999), and compares pictorial and tactile number book features (Gaylord et al, 2020;Petersen et al, 2014). Thus, at the broadest level we framed this study in terms of the potential sensory experiences the representations of number in children's books intend, then looked for subcategories and traits.…”
Trade books are a common resource used to teach children mathematical ideas. Yet, detailed analyses of the mathematics content of such books to determine potential impacts on learning are needed. This study investigated how trade books represent whole numbers. A two-pronged approach was used a) one team documented every way 197 books represented numerical ideas and b) another team used standards to identify ideal representations. A third team validated the traits on 67 books. Greater variation than expected was documented (103 traits identified) and organized into a field guide for researchers to consult to design studies about how particular traits influence number learning. Studies could investigate how a particular trait supports learning or experimentally compare a selected combination of the 45 pictorial, 45 written symbol, 10 tactile, 2 kinesthetic, and 1 auditory trait. Implications for practice include recognizing what representations are present or missing from books used in classrooms. The study also serves as an example of how the field of mathematics education would benefit from adopting structures from disciplinary science, such as field guides, to inform how we organize phenomena of mathematics learning.
“…In secondary mathematics education research, the emphasis has been on translations between particular representation types relevant at those levels of mathematics (Bieda & Nathan, 2009;Mainali, 2021). Whereas the early childhood literature focuses on three representations that differ from that used in secondary (numerals, number words, and pictorial representations; Fuson, 2019;Young-Loveridge, 1999), emphasizes multi-sensory learning experiences (Elliot, 1999), and compares pictorial and tactile number book features (Gaylord et al, 2020;Petersen et al, 2014). Thus, at the broadest level we framed this study in terms of the potential sensory experiences the representations of number in children's books intend, then looked for subcategories and traits.…”
Trade books are a common resource used to teach children mathematical ideas. Yet, detailed analyses of the mathematics content of such books to determine potential impacts on learning are needed. This study investigated how trade books represent whole numbers. A two-pronged approach was used a) one team documented every way 197 books represented numerical ideas and b) another team used standards to identify ideal representations. A third team validated the traits on 67 books. Greater variation than expected was documented (103 traits identified) and organized into a field guide for researchers to consult to design studies about how particular traits influence number learning. Studies could investigate how a particular trait supports learning or experimentally compare a selected combination of the 45 pictorial, 45 written symbol, 10 tactile, 2 kinesthetic, and 1 auditory trait. Implications for practice include recognizing what representations are present or missing from books used in classrooms. The study also serves as an example of how the field of mathematics education would benefit from adopting structures from disciplinary science, such as field guides, to inform how we organize phenomena of mathematics learning.
“…Diversos trabajos consultados (Baturo, 2002;Browning y Beauford, 2012;Bruno y Noda, 2014;Horne y Livy, 2006;Thomas y Tagg, 2005;Salazar y Vivas, 2013;Young-Loveridge, 1999) que abordan la enseñanza y el aprendizaje del concepto del valor posicional en la educación básica primaria, nos remitieron al trabajo de Jones, Thornton, Putt, Hill, Mogill, Rich y Van Zoest (1996), quienes observaron que la comprensión del concepto de valor posicional requiere el desarrollo de cuatro habilidades: contar, hacer particiones, agrupar y relacionar números. Dado que nuestro propósito fue favorecer la comprensión del valor posicional, consideramos, analizamos y utilizamos las cuatro habilidades mencionadas, y los niveles que describen su desarrollo, para rastrear, trazar, o evaluar la comprensión del valor posicional a lo largo de la implementación de la unidad didáctica diseñada.…”
Section: Habilidades Asociadas a La Adquisición Y Desarrollo Del Concepto De Valor Posicionalunclassified
Se reporta un estudio en el cual se propone una estrategia de enseñanza para hacer frente y, eventualmente, superar las dificultades que presentan estudiantes de 2º de educación básica primaria (5–7 años) de dos colegios públicos de Bogotá (Colombia), en relación con el concepto de valor posicional. A partir de un análisis del contexto de aula de ambos grupos y de la revisión de literatura relacionada, se diseñó, implementó y evaluó una unidad didáctica bajo el enfoque de la Enseñanza para la Comprensión, con el propósito de que los estudiantes avanzaran en la comprensión del concepto de valor posicional. El estudio se realizó desde un enfoque cualitativo de alcance descriptivo, utilizando el diseño metodológico de investigación–acción. Los hallazgos evidencian que los estudiantes avanzaron en la comprensión del concepto de valor posicional, a través de los desempeños de comprensión propuestos en la unidad didáctica.
“…The development of the number framework drew on literature that presented frameworks detailing the acquisition of number concepts (e.g., Fuson et al, 1997;Jones et al, 1996;Wright, 1998;Young-Loveridge, 1999). Prior to the development of the number framework in 2000 in New Zealand, a centrally funded regional professional development initiative explored an australian project, Count Me In Too (Department of education and Training, New South Wales, 1998), the basis of which is Wright's (1998) framework.…”
The design and implementation of the professional development model of the New Zealand Numeracy Development Project has been successful in improving teacher knowledge and practice as well as raising student outcomes. Since 2000, more than 25,000 teachers in English-medium settings have participated in the project. In New Zealand the terms English-medium and Māori-medium are used to distinguish the language of instruction. settings have participated in the project. A content analysis across a large data set from evaluations conducted during the first four years of the project, identified three pedagogical tools that participants describe as improving their mathematics knowledge and practice: the number framework; the diagnostic interview; and the strategy teaching model. The article argues that the power of the professional development model lies in the integration of the three pedagogical tools ensuring that professional learning focuses on the core ideas of the project within the context of the teacher's classroom. This focus has enabled teachers to deepen their professional knowledge, change their instructional practice and improve their responsiveness to students' diverse learning needs.
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