Case Study 3 – Researching the Unknown: Developing an Understanding of Children's Informal Mathematical Activity

2022 ◽  
pp. 39-48
Author(s):  
Tim Jay ◽  
Jo Rose
Keyword(s):  
Mathematical Activity

scholarly journals Pre–service and In-service primary teachers’ generic and subject-specific skills On Geometric understanding of symmetry: A case study

2021 ◽  
Author(s):  
Shiva Mafakheri
Keyword(s):  
Symmetry Axis ◽  
Primary Teachers ◽  
Primary Teacher ◽  
Elementary Level ◽  
Mathematical Activity ◽  
Math Teachers ◽  
Teacher Needs ◽  
Service Training ◽  
Prospective Primary Teachers

Abstract According to the curricula all over the world symmetry plays an important role in the teaching geometry at primary levels. Geometry is one of topics that have the most problematic content knowledge for the prospective primary teachers. This paper studies the understanding of the symmetry of shapes among pre-service and in-service teachers to find out their visual perception of the geometric shapes symmetry and the symmetry axis. The aim is to create a symmetrical pattern with symmetry axis of the shapes. Evidence that only content-oriented professional development coursework taken by primary school math teachers appears effective, suggests that relatively more resources ought to be put into content focused training for teachers and that changes are warranted at the elementary level and in pedagogical in-service training generally. The primary teacher needs to be able to modify some proposed problems in order to get a richer mathematical activity, being aware of their mathematical benefits. It should be part of growing the capacity of analyzing didactically the mathematics activity.

scholarly journals Mathematical Mystery in a Cultural Game

2020 ◽  
Vol 10 (6) ◽  
pp. 64
Author(s):  
Mustafa Gök
Keyword(s):  
Descriptive Analysis ◽  
Structured Interview ◽  
Research Data ◽  
Mathematical Activity ◽  
Recording Device ◽  
Eastern Anatolia ◽  
Mathematical Relationship ◽  
Learning Mathematics ◽  
Mathematical Experience

This study described the mathematical depth in a mathematical activity carried out in a village in Turkey’s Eastern Anatolia Region. This activity presented in the context of the game reflects a cultural situation of doing mathematics over time. In this context, it can identify as a study of ethnomathematics. Therefore, the cultural game was introduced first, and then the mathematical depth behind this game was uncovered in all its aspects. Finally, the mathematical relationship behind the game was analysed in terms of mathematics education. The case study, as one of the qualitative research methods, was used in the study. The participants of the study consist of 1 person who knows, transmits, and teaches the cultural game. The game process and semi-structured interview that constituted the research data were recorded with a camera and a voice recording device. Descriptive analysis was used in the analysis of the interview. Findings of the study suggest that the cultural game is played without considering its mathematical depth, but that there is a rich mathematical depth behind it. The results also indicate that such games offer an effective way for adults learning mathematics. On the other hand, the study revealed that there could be different ways of thinking between school mathematics and ethnomathematics. It is thought that synthesizing mathematics with games that include ethnomathematics has the potential to provide students at diverse levels with an excellent mathematical experience.

scholarly journals Application of Luria’s Theoretical-Methodological Principles for Evaluation in Infants with School Difficulties in Math: a Case Study of Epilepsy

2017 ◽  
Vol 10 (2) ◽  
pp. 72
Author(s):  
Izabel Hazin ◽  
Daniele Caroline Leôncio ◽  
Laura Aragão
Keyword(s):  
Cognitive Functions ◽  
Qualitative Evaluation ◽  
Educational Assessment ◽  
Rehabilitation Program ◽  
Idiopathic Epilepsy ◽  
Mathematical Activity ◽  
Neuropsychological Evaluation ◽  
History Of ◽  
Methodological Principles

The objective of the present study was to discuss the theoretical and methodological principles recommended by Alexsander Romanovich Luria and their application to neuropsychological and educational assessment in infants. We present a case study of a male child, 11 years of age, diagnosed with generalized idiopathic epilepsy absence with a history of school in mathematics. The neuropsychological evaluation followed four steps proposed by Luria: (1) qualitative analysis of the symptoms, (2) quantitative evaluation of activity, (3) qualitative evaluation of activity, and (4) the proposition of a rehabilitation program. These steps were contemplated based on a neuropsychological protocol composed of nomothetic and idiographic tasks. We found deficits in manipulation activities, especially ones that demand visuospatial and visuoconstructive skills, associated with school difficulties in mathematics. The Lurian method allowed us to identify preserved and compromised cognitive functions, allowing interventions that minimized the identified deficits. Keywords: Neuropsychological Assessment. Mathematical Activity. Luria. Epilepsy Absence. Childhood.ResumoO objetivo do presente estudo foi discutir acerca dos princípios teórico-metodológicos recomendados por Alexsander Luria e sua aplicação para a avaliação neuropsicológica e educacional infantil. Apresenta-se um estudo de caso de uma criança do sexo masculino, 11 anos de idade, diagnosticado com epilepsia idiopática generalizada do tipo ausência com histórico de dificuldades escolares em matemática. A avaliação neuropsicológica realizada seguiu os quatro passos propostos por Luria: (1) análise qualitativa do sintoma, (2) avaliação quantitativa da atividade, (3) avaliação qualitativa da atividade, e (4) a proposição de um programa de reabilitação. As etapas aludidas foram realizadas a partir da utilização de protocolo composto por tarefas nomotéticas e idiográficas. Foram identificados déficits em atividades manipulativas, notadamente aqueles que demandaram habilidades visoespaciais e visoconstrutivas, associadas com dificuldades em matemática. O modelo luriano possibilitou a identificação de funções cognitivas deficitárias e preservadas, além de proposição de intervenções que minimizaram os déficits identificados.Palavras-chave: Avaliação Neuropsicológica. Atividade Matemática. Luria. Epilepsia de Ausência. Infância.

scholarly journals Activity with Signs and Speaking About It: Exploring Students’ Mathematical Lines of Thought Regarding the Derivative

2019 ◽  
Vol 18 (8) ◽  
pp. 1587-1611
Author(s):  
Annika M. Wille
Keyword(s):  
The Other ◽  
Mathematical Activity ◽  
Student Needs ◽  
Other Hand ◽  
The One ◽  
Grade 11

AbstractIn order to participate proficiently in mathematical activity, a student needs to become fluent in both mathematical sign activity and speaking about the activity with signs. From the theoretical viewpoint of the philosophers Wittgenstein and Peirce, on the one hand, mathematics is seen as a sign game, while on the other hand experiments with signs allow for observable, communicable and describable reasoning. In this article, the focus is on the student’s sign activity and his or her speaking about it and the question of how they are intertwined. To that end, a method is presented to display the interplay of student’s activity with signs and speaking about it, and in particular, to reconstruct the student’s line of argumentation. This is applied to a case study where imaginary dialogues written by a class of grade 11 students on the topic “derivative” were analyzed.

scholarly journals The Didactic Notion of “Mathematical Activity” in Japanese Teachers’ Professional Scholarship: A Case Study of an Open Lesson

2021 ◽  
Vol 10 (1) ◽  
pp. 88
Author(s):  
Yukiko Asami-Johansson
Keyword(s):  
Mathematics Education ◽  
Mathematics Teachers ◽  
Teaching Practice ◽  
National Curriculum ◽  
Pedagogical Issues ◽  
Mathematical Activity ◽  
Generic Level ◽  
Anthropological Theory ◽  
Didactic Knowledge

This paper investigates how Japanese mathematics teachers produce and share didactic knowledge together. It is a case study of a post-lesson reflection meeting so-called open lesson. The crucial idea of this study is the dialectic between the specific and generic level of foci of the participants’ reflections about the observed teaching practice; namely, about applied teacher’s specific didactic technique for achieving a specific mathematical goal, and more general pedagogical issues such as realisation of the objectives of mathematics education. This dialectic is mediated by the meso-level notion of mathematical activity, described in the guidelines for Japanese national curriculum. The application of the scale of levels of didactic co-determination, provided by the anthropological theory of the didactic into the analysis shows in what way the dialectic interplay between the teachers’ comments with focus of the specific and generic levels influences the development and establishment of the Japanese teachers’ shared professional scholarship.

Cultural Tools and Mathematical Learning: A Case Study

1995 ◽  
Vol 26 (4) ◽  
pp. 362-385 ◽  
Author(s):  
Paul Cobb
Keyword(s):  
Conceptual Development ◽  
Second Graders ◽  
Mathematical Activity ◽  
Sociocultural Perspective ◽  
Mathematical Learning ◽  
Mathematical Development ◽  
Constructivist Perspective ◽  
Cultural Tools ◽  
Conceptual Advance

This study investigates the role that four second graders' use of the hundreds board played in supporting their conceptual development over a 10-week period. Particular attention is given to the transition from counting by ones to counting by tens and ones. The analysis indicates that the children's use of the hundreds board did not support the construction of increasingly sophisticated concepts of ten. However, children's use of the hundreds board did appear to support their ability to reflect on their mathematical activity once they had made this conceptual advance. The constructivist perspective exemplified in the analysis is contrasted with a sociocultural perspective on mathematical development. The differing roles attributed to cultural tools are clarified, and potentially complementary aspects of the two perspectives are discussed.

The Genesis and Internal Dynamics of El Salvador's People's Revolutionary Army, 1970–1976

2014 ◽  
Vol 38 (01) ◽  
pp. 102-129
Author(s):  
ALBERTO MARTÍN ÁLVAREZ ◽  
EUDALD CORTINA ORERO
Keyword(s):  
Latin America ◽  
El Salvador ◽  
Early Years ◽  
Left Wing ◽  
Internal Dynamics ◽  
Internal Coherence ◽  
The 1960S

AbstractUsing interviews with former militants and previously unpublished documents, this article traces the genesis and internal dynamics of the Ejército Revolucionario del Pueblo (People's Revolutionary Army, ERP) in El Salvador during the early years of its existence (1970–6). This period was marked by the inability of the ERP to maintain internal coherence or any consensus on revolutionary strategy, which led to a series of splits and internal fights over control of the organisation. The evidence marshalled in this case study sheds new light on the origins of the armed Salvadorean Left and thus contributes to a wider understanding of the processes of formation and internal dynamics of armed left-wing groups that emerged from the 1960s onwards in Latin America.

Culture and the plasticity of perception

2020 ◽  
Vol 43 ◽  
Author(s):  
Michael Lifshitz ◽  
T. M. Luhrmann
Keyword(s):  
Cultural Context ◽  
Sensory Experience ◽  
Cultural Learning ◽  
The World

Abstract Culture shapes our basic sensory experience of the world. This is particularly striking in the study of religion and psychosis, where we and others have shown that cultural context determines both the structure and content of hallucination-like events. The cultural shaping of hallucinations may provide a rich case-study for linking cultural learning with emerging prediction-based models of perception.

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

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