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 ideas.

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 (Lamon, 1999).

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 and percentages.

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