In light of all the difficulties and challenges facing us today in improving math education, questions arise regarding how to develop students’ mathematical thinking and conception, how to increase ...student motivation to learn math, how to improve achievement in math, and how to maintain an interesting, enjoyable, and successful learning process in math. In this paper we will present one solution to these questions according to the ethnomathematical approach, which combines culture and math instruction: the integration of ethnomathematical folklore games in the instruction of math. On this background, the proposed paper will discuss the following issues: (1) the definition and essence of ethnomathematics; (2) the historical development of the ethnomathematical approach; (3) the political aspect of ethnomathematics; (4) Lev Vigotsky’s constructivist theory and its relation to ethnomathematics; (5) the importance of developing a curriculum that integrates cultural values; (6) the contributions of an ethnomathematical curriculum; (7) various approaches regarding the ethnomathematical curricula; (8) proposals for the development of ethnomathematical curricula; (9) What is a mathematical game; (10) Discussion; (11) Summary and suggestions.
Zusammenfassung
Der folgende Beitrag befasst sich mit dem Mathematiklernen in der frühen Kindheit aus interaktionistischer Perspektive. Mathematiklernen wird hierzu in zwei Aspekte ausdifferenziert: ...den Erwerb mathematischer Begriffe und Prozeduren im Sinne des Lernens von mathematischen Inhalten und die mathematische Denkentwicklung im Sinne des Argumentierenlernens. Der Fokus dieses Beitrags liegt auf dem zweiten Aspekt. Basierend auf interaktionistischen Vorstellungen zum Lernen wird die mathematische Denkentwicklung als zunehmende Partizipation an mathematischen Diskursen beschrieben. Hierdurch rücken mathematische Diskurse als „Ort“ der mathematischen Denkentwicklung ins Zentrum der Betrachtung. Zur näheren Beschreibung dieser Diskurse wird die bis dato gängige Fokussierung interaktionistischer Ansätze des Mathematiklernens auf die Analyse mathematischer Bedeutungsaushandlungen um eine Beschreibung emergierender argumentativer und semantischer Strukturierungen mathematischer Aushandlungsprozesse erweitert. In den empirischen Analysen des Beitrages werden mithilfe dieser theoretischen Erweiterung unterschiedliche Diskursstile rekonstruiert, die wir als narrative, formale und narratorische Diskurse bezeichnen. In künftigen Arbeiten sollen sie als theoretische Grundlage für die longitudinale Rekonstruktion der Partizipation von Lernenden an mathematischen Aushandlungsprozessen zur Beschreibung ihrer mathematischen Denkentwicklung genutzt werden.
This paper deals with one aspect of the endeavor to generate a theory of the development of mathematical thinking of children in the early years ages 3 to 10. By comparing two scenes, one from ...preschool and one from a first grade mathematics class, the relationship between diagrammatic and narrative argumentations among children and teachers is reconstructed and related to possible developmental trajectories of mathematical thinking. Theoretically, I attempt to implement these developmental paths in a concept of an "Interactional Niche in the Development of Mathematical Thinking."
One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. ...Teaching arithmetic involves knowledge about the essence of the concept of “number” and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among pre-service teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners’ level of thinking development might lead to meaningful learning in arithmetic course for PMTs.
, li., div.Abstract {mso-style-name:Abstract; margin-top:0cm; margin-right:1.0cm; margin-bottom:0cm; margin-left:1.0cm; margin-bottom:.0001pt; text-align:justify; line-height:10.0pt; ...punctuation-wrap:simple; text-autospace:none; font-size:9.0pt; font-family:"Arial",sans-serif;} span.apple-style-span {mso-style-name:apple-style-span;} span.hps {mso-style-name:hps;} span.Carcterdenumeracin {mso-style-name:"Carácter de numeración";} span.RTFNum21 {mso-style-name:"RTF_Num 2 1"; font-family:Symbol;} span.RTFNum31 {mso-style-name:"RTF_Num 3 1"; font-family:Symbol;} span.Smbolodenotaalpie {mso-style-name:"Símbolo de nota al pie";} span.Fuentedeprrafopredeter1 {mso-style-name:"Fuente de párrafo predeter\.1";} span.Refdenotaalpie1 {mso-style-name:"Ref\.de nota al pie1";} span.WW8Num3z1 {mso-style-name:WW8Num3z1; font-family:"Courier New";} span.WW8Num3z2 {mso-style-name:WW8Num3z2; font-family:Wingdings;} span.WW8Num3z3 {mso-style-name:WW8Num3z3; font-family:Symbol;} span.Vietas {mso-style-name:Viñetas; font-family:OpenSymbol;} span.WW8Num6z0 {mso-style-name:WW8Num6z0; font-family:Symbol;} span.WW8Num6z1 {mso-style-name:WW8Num6z1; font-family:"Courier New";} span.WW8Num6z2 {mso-style-name:WW8Num6z2; font-family:Wingdings;} span.WW8Num5z0 {mso-style-name:WW8Num5z0; font-family:Symbol;} span.WW8Num5z1 {mso-style-name:WW8Num5z1; font-family:"Courier New";} span.WW8Num5z2 {mso-style-name:WW8Num5z2; font-family:Wingdings;} span.WW8Num4z0 {mso-style-name:WW8Num4z0; font-family:Symbol;} span.WW8Num4z1 {mso-style-name:WW8Num4z1; font-family:"Courier New";} span.WW8Num4z2 {mso-style-name:WW8Num4z2; font-family:Wingdings;} span.Smbolodenotafinal {mso-style-name:"Símbolo de nota final";} span.apple-converted-space {mso-style-name:apple-converted-space;} span.longtext {mso-style-name:long_text;} span.Textoindependiente3Car {mso-style-name:"Texto independiente 3 Car"; mso-style-link:"Texto independiente 3"; font-family:"Times New Roman",serif;} .MsoPapDefault {margin-bottom:10.0pt; line-height:115%;} /* Page Definitions */ @page WordSection1 {size:612.0pt 792.0pt; margin:99.25pt 93.55pt 73.7pt 93.55pt;} div.WordSection1 {page:WordSection1;} /* List Definitions */ ol {margin-bottom:0cm;} ul {margin-bottom:0cm;} --> The development of reflective thought for the training in integral people * El desarrollo del pensamiento reflexivo en la formación de personas integrales * O desenvolvimento do pensamento reflexivo para o treinamento em pessoas integradas* José Joaquín Martínez Lozano** Luisa Stella Paz Montes*** Mawency Vergel Ortega*** Escuela Superior de Administración Pública - Colombia Universidad Francisco de Paula Santander- Colombia Date Received: February 20, 2018 Date Accepted: May 22, 2018 Date of Publication: July 01 of 2018 DOI: http://dx.doi.org/10.22335/rlct.v10i3.622 * Article research result "Onto-historical understanding of financial math in the trajectory of distance education- Universidad Francisco de Paula Santander´s", research group Zulima Science, funded by the FINU-UFPS Research and Extension´s , co-financing 034-2018. ** Bachelor in Biology, specialist in Biomathematics, Master in Educational Management, PhD in Education, Professor-Researcher, member of the Quetelet Research Group of the National Police. Affiliation Professor of the Higher School of Public Administration. E-mail: checo.jf@gmail.com. Orcid: https://orcid.org/0000-0001-6308-1344 ***Business Administrator, Specialist in Educational Management, Master in Business Management, Doctor in Education. Professor-Researcher, Member of the Research Group in Social and Human Sciences, "GICSH" ascribed to the Faculty of Business Sciences of the Universidad Francisco de Paula Santander (Cúcuta, Colombia). Affiliation Professor of the Francisco de Paula Santander University. E-mail: luisastellapm@ufps.edu.co Orcid: https://orcid.org/0000-0002-8887-3441 *** Bachelor of Mathematics and Physics, specialist in applied statistics, Magister in Educational Management, PhD in Education, Post PhD in Imaginary and social representations. Professor-Researcher, Member of the Zulima Science Research Group "ZCD", ascribed to the Faculty of Business Sciences of the Universidad Francisco de Paula Santander (Cúcuta, Colombia). Affiliation Professor of the Francisco de Paula University Santander. . E-mail: mawency@ufps.edu.co Orcid: https://orcid.org/0000-0001-8285-2968 Abstract In this article we present results of research whose objective was to analyze experiences in the growth of plants such as the Duranta and Salvia where the student develops competences in posing and solving problems that allowed him to argue, model, communicate on mathematics in improvement of their academic performance. The methodology followed a quantitative approach, field-type experimental design, applied to a sample of 180 students of engineering programs. Results: 95% of the students remained in the course, 99% scored above the general institutional average in integral calculus. Conclusion: Application in plant growth allowed to develop competences in raising and solving problems, development of mathematical thinking, analyzing variables and changes in a time, modeling situations; argue, represent entities. The use of blogs allowed the generation of new methods of study, and different forms of evaluation and evaluation of learning, both for students and teachers.
By introducing the concept of the “interactional niche in the development of mathematical thinking” (NMT), a new approach, in which the cultural historic and the interactionistic strands of ...socio-constructivist theories merge, will be presented. This concept is to be understood as an attempt to develop a theory about the generation of mathematical thinking of children in the ages between three and ten. Two specific niches will be described that arise under the condition of children’s non-canonical solutions and corresponding improvisation by (nursery) teacher and children.
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