Abstract/Notes: Manipulatives are ubiquitous in early childhood classrooms; yet, findings regarding their efficacy for learning mathematics concepts are inconsistent. In this article, we present four general principles that have emerged from cognitive science about ways to ensure that manipulatives promote learning when used with young children. We also describe how Montessori instruction offers a concrete example of the application of these principles in practice, which may, in turn, explain the high levels of mathematics achievement among children who attend Montessori programs during early childhood. The general principles and concrete examples presented in this article should help early childhood programs maximize the benefits of using manipulatives for developmentally appropriate mathematics instruction.

Language: English

DOI: 10.1177/2158244015589588

ISSN: 2158-2440

Language: English

ISSN: 0519-0959

Abstract/Notes: Albania comes from a long history of behavioral theories and the error is not yet free from the influence of this theory, even though the curriculum used in pre-university education is based on constructionist approaches. The positive influence of errors in the teaching/learning process has been widely discussed, but in mathematics, there is a lack of real pedagogical plans and differentiated instructional treatment, where there is a tendency to emphasize errors as much as possible. The purpose of this article is to highlight the educational motives of error in the process of enhancing learning in mathematics. Concrete educational planning that makes use of the power of errors is especially important from the perspective of why errors should be studied and what is stimulated by their correct use. The interpretation of mistakes at the metacognitive and non-cognitive levels is of relevance, and we highlight its main parameters, which are self-acceptance, self-control, and self-correction, using a critical and creative approach. The paper provides a solid theoretical framework for the relevance of extensive mistake analysis, where proper interpretation necessitates a variety of pedagogical and didactic treatments that promote learning building. Math instructors and educational institutions at all levels will benefit from this study. / Shqipëria vjen nga një histori e gjatë e teorive bihevioriste ku gabimi ende nuk është i çliruar nga ndikimi i kësaj teorie, edhe pse kurrikula e përdorur në arsimin parauniversitar bazohet në qasje konstruktiviste. Në këtë punim është diskutuar gjerësisht ndikimi pozitiv i gabimeve në procesin e mësimdhënies/të nxënit, por në rastin e matematikës mungojnë plane reale pedagogjike dhe trajtime të diferencuara didaktike, ku gabimet priren të theksohen sa më shumë. Qëllimi i këtij artikulli është të nxjerrë në pah motivet pedagogjike të gabimeve në procesin e përmirësimit të të nxënit në matematikë. Një projektim didaktik konkret që shfrytëzon fuqinë e gabimeve është veçanërisht i rëndësishëm për sa i përket arsyes pse gabimet duhet të studiohen dhe çfarë stimulohet konkretisht nga përdorimi i tyre i saktë. Interpretimi i gabimeve në nivel metakonjitiv dhe jokonjitiv është i rëndësishëm ku veçohen parametrat kryesor, të cilët janë, vetëpranimi, vetëkontrolli dhe vetëkorrigjimi, duke përdorur qasje kritike dhe krijuese. Ky artikull ofron një kornizë solide teorike për rëndësinë e analizës së hollësishme të gabimeve, interpretimi i saktë i tyre kërkon një shumëllojshmëri trajtimesh pedagogjike dhe didaktike që nxisin ndërtimin e të nxënit. Nga ky studim do të përfitojnë mësuesit e matematikës dhe institucionet arsimore të të gjitha niveleve.

Language: English

ISSN: 2305-882X

Abstract/Notes: The goal of the presented work was to determine whether and how individualization, differentiation, and personalization are utilized in the principles of the selected programs and in the teachers’ beliefs and practices in the teaching of mathematics at elementary school. In order to collect data, six teachers in the Czech Republic were selected with three different approaches to teaching– Scheme oriented approach, child–centred educational approach, and an undesignated mainstream approach. The basic concepts and all three selected approaches to teaching were defined in the theoretical part of the work. In the experimental part, episodes from interviews about beliefs and practices identified in teaching were interpreted within the context of characteristics of individualization, differentiation, and personalization. Practices such as the use of textbooks and homework assignments were specifically described. The study shows that teachers of a scheme-oriented approach and a child–centred educational approach use elements of individualization, differentiation, and personalization in their practices. Individualization appears in the teaching of the undesignated mainstream approach, but this approach does not contain aspects of differentiation and personalization. The analysis in all monitored areas of selected teachers indicates which of the characteristics prevail in individual teachers’ work and the approaches. The research confirmed that selected teachers in all three approaches (Hejny method, Montessori method and an undesignated) individualize, differentiate, or personalize to some extent. / Cílem předkládané práce bylo popsat, zda a jak jsou uplatňována individualizace, diferenciace a personalizace ve vybraných programech, jejich principech, učitelských přesvědčeních a praktikách ve výuce matematiky na prvním stupni základní školy. Za účelem sběru dat bylo vybráno šest učitelů se třemi odlišnými přístupy k výuce – výuka orientovaná na budování schémat, pedocentricky orientovaná metoda a nevyhraněný přístup hlavního vzdělávacího proudu v České republice. V teoretické části práce byly definovány základní pojmy a vymezeny všechny tři vybrané přístupy k výuce. V experimentální části byly na pozadí charakteristik individualizace, diferenciace a personalizace interpretovány epizody z rozhovorů o přesvědčeních a praktikách sledovaných při výuce. Z praktik bylo konkrétně popsáno užití učebnic a zadávání domácích úkolů. Ukázalo se, že učitelé ve výuce orientované na budování schémat i učitelé pedocentricky orientované metody využívají při výuce prvky individualizace, diferenciace i personalizace. U učitelů v nevyhraněném přístupu hlavního proudu se objevuje individualizace. Analýza ve všech sledovaných oblastech u vybraných učitelů naznačuje, které z charakteristik převažují u jednotlivých učitelů a přístupů (v Hejného metodě, montessoriovské metodě a nevyhraněném přístupu).

Language: English

Published: Prague, Czechia, 2023

Abstract/Notes: Learning media has an important role in learning mathematics because mathematics is an abstract science and requires a deep understanding of concepts. Students have difficulty in understanding mathematics due to the teacher's monotonous explanation in class without any learning media or epraga tools. Fun learning media is interactive learning media, which allows students to use the media themselves and interact both with other students and with teachers. One example of interactive learning media is Montessori learning media. Based on observations at partner locations, it was found that mathematics teachers in elementary and secondary schools have never used Montessori learning media, therefore training on the use of Montessori-based learning media is needed for elementary and secondary school teachers so that classroom learning runs optimally in accordance with learning objectives. Training on the use of Montessori-based learning media has a positive impact on teachers, it can be seen from the final questionnaire of the training participants provide positive feedback, to this training activity, namely with data interpretation of 96%.

Language: English

DOI: 10.58258/abdi.v5i2.6251

ISSN: 2715-9108

Language: English

ISSN: 0040-7887

Language: German

Published: Innsbruck, Germany: Studien Verlag, 2009

Edition: 1st ed.

ISBN: 978-3-7065-4721-5 3-7065-4721-X

Series: Initiative neues Lernen

Abstract/Notes: Making math instruction accessible to students can be a challenge, particularly when students have limited English proficiency. This paper explores how teachers can best suit the needs of their non-native English speakers when teaching math. Teacher affect, visuals and translanguaging are used in this study in an attempt to boost student confidence and academic progress. These strategies result in an increase in student confidence and engagement, as measured by a math attitude survey as well as observation data. Centered around a Montessori classroom, this paper shows how aspects of the Montessori philosophy cater to English learners and suggests additional supports that may be beneficial.

Language: English

Published: River Falls, Wisconsin, 2023

Abstract/Notes: One of the best-known quotes in pedagogical literature is Maria Montessoris “Help me to do it myself.” This citation can be applied to many open questions. For example, how to help students working autonomously on cognitively demanding tasks is not only an unanswered question in didactical literature, but there has also been relatively little research done in this area.

Language: English

DOI: 10.1007/s11858-005-0015-3

ISSN: 1863-9704

Language: English

Published: Chicago, Illinois: American Montessori Society, 1963