Although student understanding was the initial focus of the research, other data was collected on the teacher candidates as well, since their own knowledge of fractions and rational numbers
is key to the success of the students they will eventually teach.
Summarizing, we can state that roughness of parameters of real physical system modeled by finite N in (2) leads to inhomogeous fractal distribution of rational numbers
along number axis.
On the mathematical, cognitive and instructional foundations of the rational numbers
This simplest drawing shows that rational numbers
are distributed inhomogeneously in the Minkowski number plane.
Partitioning, equivalence, and the construction of rational number
8) led them to conclude that proportional thinking is an underlying factor associated with achievement in equivalent fractions, supporting the hypothesis that postponement of teaching certain rational number
concepts until secondary school is a viable alternative.
These students will need re-teaching, that should include visual and verbal reasoning activities that build a conceptual understanding using the part-whole relationship of rational numbers
infinity]] is exactly the set of rational numbers
and is dense in K.
the even numbers, and the rational numbers
(quotients of counting numbers, such as 3/4 and 101/763).
The remedial math program will stress seventh-grade math concepts, including fractions, decimals, integers, rational numbers
Cauchy (1789-1857) gave a beautiful way of defining real numbers in terms of rational numbers
, but he used a defective notion of limit that led him to believe that the limit of a convergent sequence of continuous functions was necessarily continuous.
Expanded Curriculum Includes Fractions, Decimals, and Integers Lessons; New Adaptive Virtual Manipulatives Develop Understanding and Fluency with Rational Numbers