Practal — Practical Logic: A Bicycle for Your Mathematical Mind

This is a first sketch of the design of Practal, an interactive theorem proving system for practical logic.

MIND MAPPING MATA PELAJARAN MATEMATIKA UNTUK KELAS IX SEMESTER GANJIL

The study s a qualitative descriptive approach, and his research type is the study of library studies. Researchers aim to project sub-sub materials through the mathematical mind mapping of major semester ix classes, researchers are trying to collect data by reading, studying understanding and analyzing books as well as research journals, accessing Internet sites, or documents related to mind mapping. Mind mapping is the most effective and efficient way to input, store and extract data from the brain or into the brain. It works according to the natural workings of our brain, thus optimizing all the human brain's potential and capacity. The manufacturing of the mind mapping process requires that a number of basic characteristics are attained. There is also the basic characteristic; Paper, colour, line, letter, keyword, key image, and structure. Thus basically the mind mapping process is based on the development of the mind mapping process, resulting in a mind mapping that can help teachers and students in the mathematical process during the difficult part of the semester, and can make learning more meaningful and enjoyable because the learning material is visible to the whole so that students can readily understand the material given.

Number concepts: abstract and embodied

Numerical knowledge, including number concepts and arithmetic procedures, seems to be a clear-cut case for abstract symbol manipulation. Yet, evidence from perceptual and motor behaviour reveals that natural number knowledge and simple arithmetic also remain closely associated with modal experiences. Following a review of behavioural, animal and neuroscience studies of number processing, we propose a revised understanding of psychological number concepts as grounded in physical constraints, embodied in experience and situated through task-specific intentions. The idea that number concepts occupy a range of positions on the continuum between abstract and modal conceptual knowledge also accounts for systematic heuristics and biases in mental arithmetic, thus inviting psycho-logical approaches to the study of the mathematical mind. This article is part of the theme issue ‘Varieties of abstract concepts: development, use and representation in the brain’.

The visual number world: A dynamic approach to study the mathematical mind

In the domain of language research, the simultaneous presentation of a visual scene and its auditory description (i.e., the visual world paradigm) has been used to reveal the timing of mental mechanisms. Here we apply this rationale to the domain of numerical cognition in order to explore the differences between fast and slow arithmetic performance, and to further study the role of spatial-numerical associations during mental arithmetic. We presented 30 healthy adults simultaneously with visual displays containing four numbers and with auditory addition and subtraction problems. Analysis of eye movements revealed that participants look spontaneously at the numbers they currently process (operands, solution). Faster performance was characterized by shorter latencies prior to fixating the relevant numbers and fewer revisits to the first operand while computing the solution. These signatures of superior task performance were more pronounced for addition and visual numbers arranged in ascending order, and for subtraction and numbers arranged in descending order (compared to the opposite pairings). Our results show that the “visual number world”-paradigm provides on-line access to the mind during mental arithmetic, is able to capture variability in arithmetic performance, and is sensitive to visual layout manipulations that are otherwise not reflected in response time measurements.