scholarly journals From speck to story: relating history of mathematics to the cognitive demand level of tasks

2021 ◽  
Author(s):  
D. A. van den Bogaart-Agterberg ◽  
R. J. Oostdam ◽  
F. J. J. M. Janssen
Keyword(s):  
Prospective Teachers ◽  
History Of Mathematics ◽  
Cognitive Demand ◽  
Design Principles ◽  
Cognitive Level ◽  
Mathematics Classrooms ◽  
Cognitive Levels ◽  
History Of ◽  
High Level ◽  
And Function

AbstractIt is a challenge for mathematics teachers to provide activities for their students at a high level of cognitive demand. In this article, we explore the possibilities that history of mathematics has to offer to meet this challenge. History of mathematics can be applied in mathematics education in different ways. We offer a framework for describing the appearances of history of mathematics in curriculum materials. This framework consists of four formats that are entitled speck, stamp, snippet, and story. Characteristic properties are named for each format, in terms of size, content, location, and function. The formats are related to four ascending levels of cognitive demand. We describe how these formats, together with design principles that are also derived from the history of mathematics, can be used to raise the cognitive level of existing tasks and design new tasks. The combination of formats, cognitive demand levels, and design principles is called the 4S-model. Finally, we advocate that this 4S-model can play a role in mathematics teacher training to enable prospective teachers to reach higher cognitive levels in their mathematics classrooms.

Euler, Leonhard (1707–1783)

2018 ◽  
Author(s):  
Jeremy Gray
Keyword(s):  
Eighteenth Century ◽  
Quadratic Forms ◽  
Body Problem ◽  
History Of Mathematics ◽  
Body Motion ◽  
Integral Calculus ◽  
History Of ◽  
The Subject ◽  
High Level ◽  
Three Body

Leonhard Euler’s importance for the history of mathematics is undoubted. Not only was he the most prolific mathematician ever – his collected works so far run to 76 volumes and further editions of his correspondence are planned – he dominated the eighteenth century. He combined an extraordinary memory, a capacity for a huge range of interests, an exceptional technical facility, and an ability to work to a high level of abstraction with a natural clarity of expression. His importance extends beyond his many profound innovations in many fields, of which three can be mentioned here: - mechanics, which he built up from the motion of point masses through the theory of rigid body motion to aero- and hydrodynamics, with applications to ship design, gunnery, optics, and celestial mechanics, where he did important work on the motion of the Moon and the three body problem; - the calculus, where he successfully introduced the concept of a function as fundamental; and - number theory, including the theory of quadratic forms and the zeta function. It was also the force of his example that established the culture of publishing in mathematics, and replaced the markedly more secretive habits of Newton and Leibniz. His widespread correspondence stimulated others, his work at the head of the Academy of St Petersburg helped develop mathematics in Russia, and his textbooks on the differential and integral calculus and on algebra made the subject accessible to generations of students.

Prospective teachers’ beliefs and self-efficacy beliefs about inquiry-based teaching approach in mathematics

2018 ◽  
Vol 2 (2) ◽  
Author(s):  
Areti Chr Panaoura
Keyword(s):  
Prospective Teachers ◽  
Time Allocation ◽  
Self Efficacy ◽  
History Of Mathematics ◽  
Real Life ◽  
Efficacy Beliefs ◽  
Teaching Approach ◽  
Mathematical Concepts ◽  
Teachers Beliefs ◽  
History Of

<p align="justify">The present study focuses on the investigation of prospective teachers’ beliefs and self-efficacy beliefs about the use of the inquiry-based teaching approach in mathematics education during their studies, before and after fieldwork. The aim of the two courses they attended during their studies in a pedagogical department emphasized the understanding of the human involvement on the development of the mathematical concepts through the history of mathematics and the role of investigation and exploration at the teaching of mathematics, as a part of the inquiry-based approach. At the final year of their studies, during the fieldwork they were expected to implement the acquired knowledge about innovative processes in real life classroom situations. The study which conducted with the participation of 73  prospective teachers is divided into three main phases: a) examining their beliefs and self-efficacy beliefs after attending a course about Basic Mathematical Concepts based on the History of Mathematics, b) examining their beliefs and their self-efficacy beliefs after attending a course about the Methodology of Teaching Mathematics in primary education and c) examining the difficulties they face during their first teaching experiences in real life school situations during the last year of their studies. Results indicated that participants seemed to believe in the value of inquiry-based approach and they had high self-efficacy beliefs about using explorations and investigations which were presented at the textbooks; however they had low self-efficacy beliefs about constructing mathematical investigations and explorations by themselves and overcoming teaching difficulties which were related with children’s misunderstandings and time allocation management, during the fieldwork experience. </p>

scholarly journals From Euclid's Elements to the methodology of mathematics. Two ways of viewing mathematical theory

1970 ◽  
Vol 10 ◽  
pp. 5-15
Author(s):  
Piotr Błaszczyk
Keyword(s):  
Prospective Teachers ◽  
Mathematical Theory ◽  
History Of Mathematics ◽  
Mathematical Meaning ◽  
Common Features ◽  
Historical Texts ◽  
History Of ◽  
Euclid’S Elements

We present two sets of lessons on the history of mathematics designed for prospective teachers: (1) Euclid's Theory of Area, and (2) Euclid's Theory of Similar Figures. They aim to encourage students to think of mathematics by way of analysis of historical texts. Their historical content includes Euclid's Elements, Books I, II, and VI. The mathematical meaning of the discussed propositions is simple enough that we can focus on specific methodological questions, such as (a) what makes a set of propositions a theory, (b) what are the specific objectives of the discussed theories, (c) what are their common features. In spite of many years' experience in teaching Euclid's geometry combined with methodological investigations, we cannot offer any empirical findings on how these lectures have affected the students' views on what a mathematical theory is. Therefore, we can only speculate on the hypothetical impact of these lectures on students.

scholarly journals Understanding the development of amblyopia using macaque monkey models

2019 ◽  
Vol 116 (52) ◽  
pp. 26217-26223 ◽  
Author(s):  
Lynne Kiorpes
Keyword(s):  
Macaque Monkey ◽  
Therapeutic Approaches ◽  
Ongoing Research ◽  
History Of ◽  
Visual Motor ◽  
Perceptual Abilities ◽  
High Level ◽  
And Function ◽  
The Brain ◽  
Insight Into

Amblyopia is a sensory developmental disorder affecting as many as 4% of children around the world. While clinically identified as a reduction in visual acuity and disrupted binocular function, amblyopia affects many low- and high-level perceptual abilities. Research with nonhuman primate models has provided much needed insight into the natural history of amblyopia, its origins and sensitive periods, and the brain mechanisms that underly this disorder. Amblyopia results from abnormal binocular visual experience and impacts the structure and function of the visual pathways beginning at the level of the primary visual cortex (V1). However, there are multiple instances of abnormalities in areas beyond V1 that are not simply inherited from earlier stages of processing. The full constellation of deficits must be taken into consideration in order to understand the broad impact of amblyopia on visual and visual–motor function. The data generated from studies of animal models of the most common forms of amblyopia have provided indispensable insight into the disorder, which has significantly impacted clinical practice. It is expected that this translational impact will continue as ongoing research into the neural correlates of amblyopia provides guidance for novel therapeutic approaches.

scholarly journals Tracking the evolution of crossmodal plasticity and visual functions before and after sight restoration

2015 ◽  
Vol 113 (6) ◽  
pp. 1727-1742 ◽  
Author(s):  
Giulia Dormal ◽  
Franco Lepore ◽  
Mona Harissi-Dagher ◽  
Geneviève Albouy ◽  
Armando Bertone ◽  
...  
Keyword(s):  
Occipital Cortex ◽  
Neural Activation ◽  
Visual Responses ◽  
Auditory Responses ◽  
Before And After ◽  
Crossmodal Plasticity ◽  
History Of ◽  
Sight Restoration ◽  
High Level ◽  
And Function

Visual deprivation leads to massive reorganization in both the structure and function of the occipital cortex, raising crucial challenges for sight restoration. We tracked the behavioral, structural, and neurofunctional changes occurring in an early and severely visually impaired patient before and 1.5 and 7 mo after sight restoration with magnetic resonance imaging. Robust presurgical auditory responses were found in occipital cortex despite residual preoperative vision. In primary visual cortex, crossmodal auditory responses overlapped with visual responses and remained elevated even 7 mo after surgery. However, these crossmodal responses decreased in extrastriate occipital regions after surgery, together with improved behavioral vision and with increases in both gray matter density and neural activation in low-level visual regions. Selective responses in high-level visual regions involved in motion and face processing were observable even before surgery and did not evolve after surgery. Taken together, these findings demonstrate that structural and functional reorganization of occipital regions are present in an individual with a long-standing history of severe visual impairment and that such reorganizations can be partially reversed by visual restoration in adulthood.

Riemann–Weyl in Deleuze's Bergsonism and the Constitution of the Contemporary Physico-Mathematical Space

2015 ◽  
Vol 9 (1) ◽  
pp. 59-87 ◽  
Author(s):  
Martin Calamari
Keyword(s):  
Field Theory ◽  
Gauge Field ◽  
Fibre Bundle ◽  
History Of Mathematics ◽  
Gauge Field Theory ◽  
Contemporary Science ◽  
Explicit Mention ◽  
History Of ◽  
Key Features ◽  
Bernhard Riemann

In recent years, the ideas of the mathematician Bernhard Riemann (1826–66) have come to the fore as one of Deleuze's principal sources of inspiration in regard to his engagements with mathematics, and the history of mathematics. Nevertheless, some relevant aspects and implications of Deleuze's philosophical reception and appropriation of Riemann's thought remain unexplored. In the first part of the paper I will begin by reconsidering the first explicit mention of Riemann in Deleuze's work, namely, in the second chapter of Bergsonism (1966). In this context, as I intend to show first, Deleuze's synthesis of some key features of the Riemannian theory of multiplicities (manifolds) is entirely dependent, both textually and conceptually, on his reading of another prominent figure in the history of mathematics: Hermann Weyl (1885–1955). This aspect has been largely underestimated, if not entirely neglected. However, as I attempt to bring out in the second part of the paper, reframing the understanding of Deleuze's philosophical engagement with Riemann's mathematics through the Riemann–Weyl conjunction can allow us to disclose some unexplored aspects of Deleuze's further elaboration of his theory of multiplicities (rhizomatic multiplicities, smooth spaces) and profound confrontation with contemporary science (fibre bundle topology and gauge field theory). This finally permits delineation of a correlation between Deleuze's plane of immanence and the contemporary physico-mathematical space of fundamental interactions.

A Confrontation between Two Doctrines: The Birth of Struggle for Hegemony in Hebrew Children's Literature during the 1930s and 1940s

2008 ◽  
Vol 1 (2) ◽  
pp. 139-155 ◽  
Author(s):  
YAEL DARR
Keyword(s):  
Children's Literature ◽  
Educational System ◽  
Single Channel ◽  
Children’S Literature ◽  
The Political ◽  
Literary Creation ◽  
History Of ◽  
High Level ◽  
First Time ◽  
Literary Quality

This article describes a crucial and fundamental stage in the transformation of Hebrew children's literature, during the late 1930s and 1940s, from a single channel of expression to a multi-layered polyphony of models and voices. It claims that for the first time in the history of Hebrew children's literature there took place a doctrinal confrontation between two groups of taste-makers. The article outlines the pedagogical and ideological designs of traditionalist Zionist educators, and suggests how these were challenged by a group of prominent writers of adult poetry, members of the Modernist movement. These writers, it is argued, advocated autonomous literary creation, and insisted on a high level of literary quality. Their intervention not only dramatically changed the repertoire of Hebrew children's literature, but also the rules of literary discourse. The article suggests that, through the Modernists’ polemical efforts, Hebrew children's literature was able to free itself from its position as an apparatus controlled by the political-educational system and to become a dynamic and multi-layered field.

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