Now, drawing the line of validity around the assumptions and intuitions recon- structed as implicitly used in the Elements is rather arbitrary – and yet this arbi- trary course was the course taken by many mathematicians, and one which continued to dominate up to the revision of the ...
We describe two mathematical representations for what have come to be called “semantic maps”, that is, representations of typological universals of linguistic co-expression with the aim of inferring similarity relations between concepts from those univ
But the concept of mathematical beauty is applied more widely than just to ideas. The expression of those ideas on paper may also be described as beautiful. Written mathematics is an exceptional, perhaps unique, language: … [mathematicians] have to express values, quantities and relationships...
If you don't quite understand it after reading it, you can click vector multiplication in the Math Library Demonstration Effect to see its practical application, reading the source code is easier to understand the concept. Dot product ...
The PAL Test Battery for Math (Berninger, in press) may have subtests for automaticity of counting and fact retrieval; concept of place value; processes of written computation; verbal, quantitative, and visual-spatial working memory; processes relevant to word-problem solving; and rapid automatic ...
Figurative drawing is a skill that takes time to learn, and it evolves during different childhood phases that begin with scribbling and end with representational drawing. Between these phases, it is difficult to assess when and how children demonstrate intentions and representativeness in their drawing...
The mental number line is an example of how numbers are grounded in space. FIVE apples are perceptibly quite distinct from FIVE cats and even more so than FIVE ringtones. What unites these examples is their FIVE-ness. To adults, the abstract concept of a small numerical value such as ...
Other psychological concepts such as “denial” and “cognitive dissonance” overlap with this concept of a rigid, difficult to change worldview. Cognitive biases seem strongest — most difficult to overcome — for elements of the worldview. ...
The concept of mathematical reasoning pertains to an individual understanding of the skill of mathematical concepts (Smit et al., 2017). It involves not only an understanding of mathematical ideas but also the ability to analyse, synthesise, and use this knowledge in various contexts. Three items...
This section is concluded with the concept of a monotone sequence of events; namely, the sequence of events {An}, n≥ 1, is said to be monotone, if either A1 ⊆ A2 ⊆… (increasing) or A1⊇ A2 ⊇… (decreasing). In case of an increasing sequence, the union ∪j...