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This paper examines the existence and impact of theoretical mathematical foundations on the teaching and learning of whole numbers in elementary school in France. It shows that the study of the New Math reform -which was eventually itself replaced in the longer term - provides some keys to understanding the influence of mathematical theories on teaching and learning. The paper studies changes related to place value, a notion that was deeply impacted by the introduction of numeration bases other than ten in 1970, and their subsequent removal in the 1980s. What the author terms 'numeration units' (ones, tens, hundreds, thousands, etc.) and 'powers-often written in figures' (1, 10, 100, 1000, etc.) are key tools for describing and understanding changes. The author identifies two theories that have formed the basis for place value teaching in the twentieth century, and examines some aspects of their influence. The paper also addresses epistemological issues in the relation between academic mathematics and school mathematics, and highlights the role of units in the teaching of basic arithmetic.

Abstrakt: Genetický konštruktivizmus sa v kontexte kurikulárnych reforiem v ČR javí ako marginálna iniciatíva skupinky nadšencov. Cieľom predkladanej state je ukázať, že takýto dojem je skreslený a vzniká v dôsledku historicky vzniknutej obmedzenosti horizontu, na ktorom je genetický konštruktivizmus posudzovaný. Keď sa na reformy kurikula pozrieme v širšom kontexte reforiem vyučovania matematiky v západnej Európe a USA v priebehu posledných päťdesiatich rokov, zistíme, že genetický konštruktivizmus je v súlade s hlavným trendom týchto reforiem a v niektorých oblastiach môže ponúknuť riešenia problémov, s ktorými reformné snahy na západe bezvýsledne zápasia. Podobne, keď genetický konštruktivizmus zasadíme do širšieho teoretického rámca kognitívnych vied, zistíme, že je v súlade s trendmi v tejto oblasti. Cieľom predkladanej state je načrtnúť kontext v rámci ktorého je možné genetický konštruktivizmus vnímať ako štandardnú súčasť hlavného prúdu reformných snažení v oblasti didaktiky matematiky. Veríme, že zasadenie genetického konštruktivizmu do tohto širšieho kontextu pomôže prekonať animozitu, s ktorou je v niektorých kruhoch konfrontovaný.

When public schooling was first introduced in the United States, early proponents emphasized the need for mathematics as critical for an informed citizenry in a democracy. Half a century later, this purpose of mathematics has been almost entirely overshadowed by the push for mathematics to maintain technological and economic advantages. The belief that preparation for technological careers is, and has historically been, the only purpose for school mathematics in the US has become a myth widely believed by the public and policymakers alike. As this myth took hold, mathematics curricula were narrowed, incorporating only the mathematics, and applications of mathematics, that supported this specific purpose. Not only does this narrowing of school mathematics negatively impact the development of informed citizens, but it limits the extent to which mathematics can be studied in ways that engage all learners. The emergence of mathematics for social justice is thus—in part—an attempt to recapture the broader purposes of school mathematics.

Besides the birth of new revolutionary concepts and methods, and of new areas of research, mathematicians, logicians, and philosophers have put into question the foundations of the discipline itself and the whole meaning of \"mathematical truth.\" Before then, at the end of the eighteenth century, mathematics was mainly concerned with explaining the \"real world\" and its laws. At the beginning of the \"modern era\" things started to change, sometimes slowly, other times abruptly. Abstract mathematics was no longer intimately related to the real world and its description. This abstract approach, both on research and on mathematical education, generated critical reactions in the mathematical community, and some \"modern\" ideas were rejected or neglected after several decades of experimentation.

Resumo O presente artigo tem como objetivo apresentar, na perspectiva da professora Célia Maria Carolino Pires, alguns elementos que possibilitaram a construção de propostas curriculares de Matemática e seus documentos de implementação, no Estado de São Paulo, na década de 1980. A abordagem ao tema é realizada a partir de trechos de entrevista concedida pela professora que participou ativamente dos processos de elaboração, discussão e implementação das reformas associadas à disciplina de Matemática. Para a construção da narrativa fez-se uso de procedimentos metodológicos da história oral temática, recorrendo-se também à fontes escritas para detalhar as referências mencionadas pela professora, as quais estão evidenciadas nas notas de rodapé. O artigo aborda cinco momentos específicos: Geometria Experimental; Movimento Matemática Moderna; Coordenadoria de Estudos e Normas Pedagógicas; Guias Curriculares dos anos 1970/Propostas Curriculares dos anos 1980 e, finalmente, a Implementação das Propostas Curriculares. O artigo mostra a importância dos trabalhos com a História Oral na Educação Matemática e acrescenta o ponto de vista de uma importante pesquisadora no campo da Educação Matemática acerca de temas fundamentais para os estudos dos currículos de Matemática e sua história no Brasil. Abstract This article aims to present, from teacher Célia Maria Carolino Pires perspective, some elements that made the formulation of mathematics curriculum proposals possible, as well as their implementation documents in the Brazilian state of São Paulo in the 1980s. The approach to the theme is based on excerpts from an interview given by the teacher, who actively participated in the processes to devise, discuss and implement mathematics education reforms. To construct the narrative, we used methodological procedures of thematic oral history and written sources to detail the references mentioned by the teacher, which are made explicit in footnotes. The article covers five specific moments: Experimental Geometry, the New Math Movement, the Coordinating Committee on Teaching Norms and Studies, the 1970s Curriculum Guidelines/the 1980s Curriculum Proposals, and the Implementation of Curriculum Proposals. The article shows the importance of Oral History production in Mathematics Education and adds the viewpoints of an important researcher in Mathematics Education about essential themes in studies on mathematics curricula and their history in Brazil.

Is there an achievement gap for online reading ability based on income inequality that is separate from the achievement gap in traditional, offline reading? This possibility was examined between students in two pseudonymous school districts: West Town (economically advantaged) and East Town (economically challenged; N = 256). Performance-based assessments were used within a simulation of the Internet developed as part of a larger project. Seventh graders completed two online research and comprehension assessments, which evaluated four skill areas (locate, evaluate, synthesize, and communicate) and two knowledge domains in science. Students also completed an assessment of prior domain knowledge and a short Internet use questionnaire. Standardized state reading and writing test scores served as measures of offline literacy skills. Results indicated that there was a significant achievement gap favoring West Town students in offline reading scores, offline writing scores, and online research and comprehension scores. A significant gap persisted for online research and comprehension after we conditioned on pretest differences in offline reading, offline writing, and prior knowledge scores. The results of the questionnaire indicated that West Town students had greater access to the Internet at home and were required to use the Internet more in school. These results suggest that a separate and independent achievement gap existed for online reading, based on income inequality. Current estimates of this gap, which rely solely on measures of offline reading, may underrepresent the true nature of the U. S. reading achievement gap in an online age. Policy implications are explored.

This work presents an efficient and original high-order shear and normal deformation theory for the static and free vibration analysis of functionally graded plates. The Hamilton’s principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. The present plate theory approach accounts for both transverse shear and normal deformations and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

Landslide susceptibility assessment is highly valuable for disaster prevention and mitigation. This study utilized the aspects of data and content to comprehensively examine the research status of landslide susceptibility. First, we used CiteSpace to visually analyze papers with “landslide susceptibility” as their theme word in the Web of Science database from 1991 to 2020. Next, we summarized the characteristics of quantitative trends, journals, authors, organization types, and keywords, and created a map of authors, institutions, and keywords. Then we presented the common methods and their advantages and disadvantages of landslide inventory, evaluation index, evaluation unit, evaluation model and verification method, combs the shortcomings of each part at the present stage, and looks forward to the possible research direction in the future. Finally, the research difficulties of landslide susceptibility in spatial scale, qualitative and quantitative problems, and spatial representation of landslide information are discussed. We find that the development of 3S and new technology in computer field promotes the development of landslide susceptibility research, makes landslide inventory more efficient and accurate, makes the assessment factor system considering factor contribution more reasonable, and makes more intelligent models applied to landslide susceptibility research. The results are beneficial for researchers to understand the current landslide susceptibility condition and can provide a reference for subsequent landslide susceptibility studies.