Figure 7 - available via license: CC BY
Content may be subject to copyright.
Source publication
p align="LEFT">This article presents a number of carefully selected activities for the mathematics classroom in the early grades. The motivation for their selection is the development of concepts rather than the learning of the procedural skills of arithmetic. As the teacher is faced with a great heterogeneity of children starting school, the concr...
Context in source publication
Citations
... Instead, teachers have to navigate this space of demands for inclusive mathematics education. Within mathematics education research, instructional approaches have been developed for addressing different demands at the same time, for example, using the same rich open-ended tasks for all students with "natural differentiation", in other words, tasks allowing students to work on different levels according to their abilities (Lawrence-Brown, 2004;Scherer, 2013), and the approach of "mutual learning" by which heterogeneous small-group communication is initiated on different levels (Höveler, 2019). However, like for many other innovations (Century & Cassata, 2016), the implementation of instructional approaches depends on the teachers' practices and orientations. ...
... Suitable instructional approaches for this integration have been already established in the research community (e.g., open differentiation tasks by Lawrence-Brown 2004, or Scherer 2013 or the approach of "mutual learning" by Höveler 2019). However, their successful enactment in classrooms seems to largely depend on teachers' integration of demands that can be perceived as exclusive. ...
When implementing educational innovations, teachers’ approaches to integrating new teaching demands are a crucial factor in their professional development. This becomes especially important in inclusive mathematics education, where teachers are demanded to integrate two jobs: (a) create joint learning experiences for all students and (b) provide focused learning opportunities for individuals. These jobs and the orientations in which they are pursued are perceived as conflicting demands by some teachers, while others do not. Within the model of content-related teacher expertise, this qualitative study investigates teachers’ practices for integrating these demands by disentangling the interplay between teachers’ self-reported practices and their underlying orientations about inclusive education. The analysis reveals that only some teachers explicate conflicts between inclusive teaching demands. It also shows that teachers command a variety of different practices for dealing with the new teaching demands and that some complex practices can indeed integrate different demands simultaneously. Implications include the insight that professional development programs on inclusive education should pay careful attention to teachers’ articulated jobs and orientations in order to promote the integration of teaching demands. Beyond this specific professional development content, the search for practices for integrating demands arising from an interplay of jobs and orientations might be a promising professional development research approach for increasing the scope of professional development.
... É neste contexto, que o jogo de Tarumbeta, do povo Chaga, da Tanzânia chega na Alemanha e de lá para outras regiões, sofrendo modificações a partir da visão do colonizador, conforme será abordado noutra seção deste estudo. Scherer (2013) em seu trabalho denominado Natural differentiation in theteachingofmathematicstochildrenstartingschool, publicado no South African JournalofChildhoodEducation, retrata o jogo de Tarumbeta e de forma adaptada e sem referência na linguagem numérica utilizada no contexto da Tanzânia, tendo como referência os estudos de Zaslavsky (1991). Tal atitude legitima os processos coloniais do conhecimento ao suprimir os elementos da linguagem de raiz africana que dá sentido e lógica ao jogo.Ademais, conforme indica a sociologia do conhecimento, a linguagem como um elemento importante na produção e reprodução da cultura e estruturação do conhecimento na vida cotidiana, por tanto, de subjetivação e objetivação da realidade (Berger &Luckmann, 2007). ...
... Este jogo no Brasil ainda é pouco difundido, mas aparece em trabalhos acadêmicos e não acadêmicos sobre jogos e brincadeiras africanas, com destaque: Raum (1996), , Scherer (2013) e Cunha (2016). Para conhecer suas potencialidades etnomatemáticas para o cálculo mental é importante conhecer suas regras e possibilidades de uso como dispositivo pedagógico. ...
... Nesta segunda versão o juiz (referee) passa a ser denominado de Chefe (chief), os assistentes (assistants) tornam-se jogadores (players) e o candidato (candidate) ganha o nome de desafiante (Challenger). Esta última versão é a mais comum na literatura Scherer, 2013;Cunha, 2016), todavia os papeis de cada um no jogo continuam os mesmos. É importante destacar que alunos e professores, em sala de aula ou fora dela, podem confeccionar o jogo por meio de desenhos no chão e peças com os materiais disponíveis no ambiente, desde que sejam promocionais às localizações projetadas para o jogo. ...
O artigo objetiva demonstrar as potencialidades etnomatemáticas do jogo de Tarumbeta cujas regras orientam formas de pensar e agir baseadas em etnomodelos matemáticos de raiz africana. O estudo dialoga com a perspectiva da Etnomatemática e etnomodelagem como possibilidades de articulação entre conhecimentos êmicos e éticos nas situações do jogo onde está presente os valores da cosmovisão africana, a exemplo da oralidade, ancestralidades, cooperação, dentre outros. Cita-se ainda as contagens e cálculos mentais que, dentro dos limites da regra jogo, remete ao pensamento africano. Aborda-se o jogo como propiciador de circunstâncias para a produção de conhecimento por meio das situações problemas cuja solução exige tomada de decisão e participação ativa dos jogadores. Neste sentido, a questão que move o estudo é saber: Que conhecimentos matemáticos a Tarumbeta é capaz de mobilizar no observador outsider? Para aproximação de uma resposta aponta-se para captura dos etnomodelos êmicos presentes nas regras do jogo cuja interpretação mobiliza etnomodelos éticos do observador outsider gerando conhecimento dialógico que articula diferentes lógicas. Argumenta-se que o jogo de Tarumbeta possui potenciais pedagógicos que dialoga com os objetos do conhecimento previstos no currículo da escola brasileira, a exemplo da contagem, números triangulares, progressão aritmética, triângulo de Tartaglia dentre outros.
... A rich discussion about mathematics can only be initiated by a variety of students' findings. In addition, the interaction and exchange among students not only promote content-related knowledge but also contributes to the development of process-related competencies such as mathematical reasoning; communicating in, with, and about mathematics; or representing mathematics [22]. ...
Life in today’s world is characterized by complexity and rapid change. Twenty-first century skills and especially mathematical understanding are supposed to crucially contribute to meeting the demands of our world since mathematics offers strategies to structure or simplify complex problems. An open question is which teaching practices are appropriate to provide all students with such skills and to broaden the participation of underprivileged students. The present article explores these aspects by focusing on complex tasks, a practice that can be considered highly accepted in the context of mathematics education all over the world. We will concentrate on the perspective of the German mathematics education community as the foundation of our considerations. Based on an analytical investigation of mathematical literacy and twenty-first century skills (such as creativity, critical thinking, or problem-solving), we will address central ideas and characteristics of complex mathematical tasks. To complement the analytical approach, we will illustrate their characteristics as well as possible intersections with twenty-first century skills by presenting an elementary school teaching experiment. Finally, we will critically discuss the potentials and pitfalls of complex mathematical tasks from an abstract perspective and conclude by debating practical consequences for organizing mathematical learning-teaching-processes.
... In one study, expert teacher trainers mostly advocated organizational differentiation (Prast, van de Weijer-Bergsma, Kroesbergen, & van Luit, 2015). Scherer and Krauthausen (2010;Scherer, 2013) suggested addressing the challenge of differentiation with so-called natural differentiation. This includes open-ended math problems -for example, finding tasks with the solution 100 (Scherer et al., 2016) -where the students can choose the level they wish to work at and later discuss the product of their individual work with peers. ...
This paper discusses the aims and challenges of inclusive mathematics instruction and presents data from a video study of 34 inclusive classrooms. Criteria for inclusive mathematics instruction are identified, and a conceptual framework is presented with a particular focus on very heterogeneous groups of learners that include students with intellectual disabilities. Key issues with the inclusive approach are the need to adapt learning goals (differentiation) and to manage joint learning settings. Data from the study show a rather limited use of differentiated learning goals in general and for students with intellectual disabilities in particular during inclusive mathematics instruction. Correlation analyses reveal that, in the classrooms studied, there was either a focus on differentiated learning goals or a focus on joint learning situations. The simultaneous implementation of both differentiated learning goals and joint learning settings seems to be very challenging in inclusive teaching settings. Therefore, teachers must be given specific support aimed at enabling them to meet this challenge.
... For all students, and especially for children with mathematical learning difficulties, making connections and using relationships could be helpful for developing understanding (see Scherer 1997). As a consequence, for instance, from the very beginning of the first year of schooling the numbers up to 20 should be offered and dealt with instead of introducing the numbers one after the other (cf.Moser Opitz 2000;Scherer 2013). Taking into account some of the research reviewed in Sects. ...
When looking at teaching and learning processes in mathematics education students with mathematical learning difficulties or disabilities are of great interest. To approach the question of how research can support practice to assist these students one has to clarify the group or groups of students that we are talking about. The following contribution firstly concentrates on the problem of labelling the group of students having mathematical difficulties as there does not exist a single definition. This problem might be put down to the different roots of mathematics education on the one hand and special education on the other hand. Research results with respect to concepts and models for instruction are multifaceted based on the specific content and mathematical topics as well as the underlying view of mathematics. Taking into account inclusive education, a closer orientation to mathematical education can be identified and the potential of selected teaching and learning concepts can be illustrated. Beyond this, the role of the teacher, their attitudes and beliefs and the corresponding teacher education programs are discussed.
... Such exercises are called 'productive exercises'. According to Scherer (2013), productive exercises: ...
This paper argues for teaching pre-service teachers about remediation strategies for learners who encounter problems in mathematics in the early grades. The premise is that all teachers should be equipped with theory-based practical knowledge to support learning. A few teaching sessions to develop the concepts that underlie the mathematical operations of addition and subtraction are introduced in this paper. An empirically validated, comprehensive model of cumulative arithmetic competence development from the ages of four to eight years forms the basis for the construction of the suggested teaching unit. The model distinguishes five competence levels of arithmetical conceptual development, and proposes that concepts build on one another hierarchically. A ‘part plus part is equivalent to whole’ model was constructed based on this hierarchical structure and the understanding that the concept of addition is a dynamic process. The teaching examples include exercises for all children, not only ones who struggle. Possibilities for adapting the exercises to the individual development level of slower or faster learners are also included. All exercises are accompanied by a reflection on the procedure and strategies applied in order to support meaningful and sustainable learning and to give student teachers the opportunity to use knowledge of mathematical cognition theory during their pre-service years.
Saber como a Tarumbeta influencia o desenvolvimento do cálculo mental e aprendizagem de objetos de conhecimento matemáticos, em nível fundamental, é a questão central deste estudo. O objetivo geral é demonstrar as implicações desse jogo africano na mobilização de conhecimentos etnomatemáticos relativos ao cálculo mental e reconhecimento dos valores civilizatórios afro-brasileiros. Enquanto os objetivos específicos: sistematizar as bases teóricas da utilização do jogo como material didático; diagnosticar os fatores que dificultam a aprendizagem matemática; perceber os valores de matriz africana e afro-brasileira; classificar conteúdos e habilidades matemáticas; avaliar as vantagens e desvantagens do jogo como material didático. O enfoque da pesquisa é do tipo misto com aplicação de situações-problemas, entrevistas e ficha avaliativa. Os resultados demonstram que: a Etnomatemática e Etnomodelagem são referenciais para a compreensão das estratégias, dos conhecimentos aplicados às situações-problemas e das dificuldades enfrentadas; o jogo contribui para o ensino de conteúdos e habilidades específicas da unidade temática Números; além de acionar funções cognitivas necessária ao cálculo mental; por fim, privilegia a atitude cooperativa.
When looking at teaching and learning processes in mathematics education students with mathematical learning difficulties or disabilities are of great interest. To approach the question of how research can support practice, an important step is to clarify the group or groups of students that we are talking about. The following contribution firstly concentrates on the problem of labelling the group of students having mathematical difficulties as there does not exist a single definition. This problem might be put down to the different roots of mathematics education on the one hand and special education on the other hand. Research results with respect to concepts and models for instruction are multifaceted and related to specific content and mathematical topics as well as underlying views of mathematics. Taking into account inclusive education, a closer orientation to mathematical education can be identified and the potential of selected teaching and learning concepts can be illustrated. Beyond this, the role of the teacher and the corresponding teacher education programs are discussed.
