it demanded the students to convert the mixed fraction into an equivalent

improper fraction.

By contrast, specialized intervention did not address mixed numbers in Year 1; however, in Years 2 and 3, the focus expanded to include

improper fractions between 1 and 2 (again, the goal was to focus attention on the meaning of

improper fractions without raising the division challenges associated with

improper fractions greater than 2).

One poignant example of a video designed to address the relationship between conceptual and procedural knowledge shows Rachel, a fifth grader whose teacher normally teaches mathematics with a focus on understanding but who agreed to teach one lesson on converting between mixed numbers and

improper fractions using a procedures-only lesson.

A mixed number is usually expressed as an

improper fraction when it is to be multiplied by another mixed number, a whole number, or a fraction.

Three rules are listed below for converting a mixed number to an

improper fraction.

In the CLIPS following this introductory activity, the selected students were working with

improper fractions using pizza slices.

The other 125 students applied the shortcut algorithm for renaming a mixed number as an

improper fraction.

They did not use a traditional approach, which is to change the entire problem into fractions with like denominators and add to create an

improper fraction.

We choose not to demonstrate the consequences of rolling an

improper fraction, as we prefer this to arise naturally during the game.

This problem, if presented only as a numerical computation, might traditionally be taught by telling students to rewrite 5 1/2 as an

improper fraction, or 11/2, and then multiply 2 by 11 and 3 by 2 to get 22/6 or 3 2/3.

Figure 1 is an example of part of the experts' knowledge structure, and it demonstrates that the upper-level cognitive skills, such as "apply addition and subtraction of fractions with different denominators," are advanced cognitive skills, while low-level cognitive skills, such as "calculate addition of

improper fractions with different denominators," are basic-level cognitive skills.

Over the course of the intervention, we gradually introduced more complicated fractions, equivalent fractions,

improper fractions and a wider breadth of representations of fractions.

In some countries/textbooks, mixed numbers are converted to

improper fractions before addition or subtraction.

The recently dubbed California Teacher of the Year had 26 raps explaining everything between exponents and

improper fractions.

An integrated study of children's construction of

improper fractions and the teacher's role in promoting that learning.