Search results for "Language of mathematics"
showing 6 items of 6 documents
The Interpersonal Dynamics of Collaborative Reasoning in Peer Interactive Dyads
2003
Abstract The authors investigated the microlevel processes of collaborative reasoning in heterogeneous peer dyads working on an open-design task in elementary geometry. Special attention was paid to the nature of student social interaction, problem-solving strategies, and mathematical language and how they shape collaborative problem-solving processes. Qualitative case-based analyses of 3 focal dyads reveal that collaborative reasoning was supported by equal participation in social interaction, consisting of joint negotiation of problem-solving strategies and active conceptualization and visualization of the situation. Challenges to collaboration were manifested in the existence of divergen…
Quantum Mechanics as a Semantic Problem
2018
Physics, like all science, is grown out of a desire to understand the world. However, modern physics with its mathematical form has become increasingly removed from the world of everyday experience and visual imagination. In quantum mechanics it is impossible to visualize the reality represented by the theory. All we have is a consistent mathematical structure. Although the theory works perfectly well instrumentally, the question remains, how can the mathematics of the theory impart understanding? If we look at mathematics as a language, we are faced with the semantic problem: how does the language of mathematics acquire meaning? In an attempt to answer this question, I study Derrida’s earl…
A Concept for Quantitative Comparison of Mathematical and Natural Language and its possible Effect on Learning
2017
Starting with the question whether there is a connection between the mathematical capabilities of a person and his or her mother tongue, we introduce a new modeling approach to quantitatively compare natural languages with mathematical language. The question arises from educational assessment studies that indicate such a relation. Texts written in natural languages can be deconstructed into a dependence graph, in simple cases a dependence tree. The same kind of deconstruction is also possible for mathematical texts. This gives an idea of how to quantitatively compare mathematical and natural language. To that end, we develop algorithms to define the distance between graphs. In this paper, w…
On Mathematical Language: Characteristics, Semiosis and Indispensability
2021
Mathematicians and others often discuss mathematics as a universal language, and say that mathematics holds a special status among sciences. In particular, it is the language of science. In some way, it is the basis of the physical world, but globally it is beyond any other science, and it is not a mere servant of sciences. Apparently, mathematical language is simple, with a little grammar and a limited vocabulary, but very different from others. Unlike natural languages, it is a rigorously defined and unambiguous one. This characteristic constitutes its greatest advantage: its complete lack of ambiguity. Although it is limited in the range of things that can express, it can be adapted to t…
A Qualified Kolmogorovian Account of Probabilistic Contextuality
2014
We describe a mathematical language for determining all possible patterns of contextuality in the dependence of stochastic outputs of a system on its deterministic inputs. The central principle contextuality-by-default is that the outputs indexed by mutually incompatible values of inputs are stochastically unrelated; but they can be coupled imposed a joint distribution on in a variety of ways. A system is characterized by a pattern of which outputs can be "directly influenced" by which inputs a primitive relation, hypothetical or normative, and by certain constraints imposed on the outputs such as Bell-type inequalities or their quantum analogues. The set of couplings compatible with these …
Analysis of the psicometric properties of a multiplication and division processes assessment scale
2019
Esta comunicación se encuentra disponible en la siguiente URL: http://www.infad.eu/RevistaINFAD/OJS/index.php/IJODAEP/article/view/1464/1321 Este número está dedicado a la "Psicología de la Educación y Saberes Originarios". The domain of multiplication and division operations depends on both algorithm management and the ability to identify the semantic structure of the problem and to translate it into mathematical language. Many students present difficulties in identifying the semantic structure of the problem but not applying the algorithm when the problem is presented numericaly. The aim of the study is to validate an assessment tool of the processes involved in multiplication and divisio…