**Purpose**

Developed by Ogle (1992) for the purpose of scaffolding readers' prior

knowledge to new knowledge, the KWHL strategy initiates active engagement

in the reading/learning task. The strategy creates an instructional framework

where students list (1) what they know, (2) what they want to find out, (3) how

they plan to find new information, and (4) what they have learned or still want

to learn. This activity can be used individually, in small groups , and with
whole

class activities. This strategy allows students to share what they learn with

others, learn that there are many sources where information can be found, and

to summarize their findings .

** Rationale **

In this story the number devil addresses some rather complex math concepts

which are suitable for 7^{th} graders but can be used to address Algebra 2 concepts

such as factorials or expanding polynomials ( multiplying a polynomial with 2 or

more terms with another that contains 3 or more terms). He does it in a way

that is easy to understand and engaging. This activity will help the students

connect the mathematics in the text with the deeper development of the

concepts in the course and the world.

**Directions**

STEP ONE .—Hand out the KWHL worksheet to the students and instruct

them to brainstorm on the topic of polynomials (or the topic of your choice,

see a list of topics at the end of this document). Explain what each of the four

boxes on their worksheet stands for and prompt them with some of the

following questions:

**Know**

• What do you know about polynomials?

• What kinds of applications do polynomials have ?

• Who are the contributors to the development of polynomials in history?

**Want**

• What do you want to know more about?

• What questions would you like answered ?

**How**

• How can you find out?

• Where can you look for answers?

Initiate the discussion as a class and then have the students first complete
the

worksheets on their own. Let them know that they will be coming back to the

final box (“Learn”) later. Let them discuss ideas with peers if needful.

STEP TWO .—After students have completed their worksheets individually,

compile a class list on the board of some of the things students wrote in each

category. Tell the students they can add to their worksheets as they hear

something new that interests them.

STEP THREE.—Instruct students to pick at least one of their questions that
they

would like answered. At this point, you should assign a follow-up assignment

such as one of the following:

• Students read an article on the topic that interests them and write a

review

• Students write a research paper on the topic that interests them

• Students research more information about a topic and give a

presentation or mini -lesson in front of the class.

STEP FOUR.—After students have completed their own individual research,

return to the KWHL worksheet and have them fill in the “learn” column.

Prompt them with the following questions:

**Learn**

• What did you learn?

• Which ideas are most important?

• What kinds of real world applications might these concepts have?

Open up to a class discussion on ideas students learned in their research.
Then,

tie ideas into those presented in the novel and discuss what they are now able

to understand better. Finally lead into a mathematical unit addressing more

fully the concepts discussed in class expanding the Learn column periodically.

Try to answer (or let the students answer) as many of the questions as possible

from the “Want to find out” section of the KWHL.

**Assessment**

The teacher will use the activity to informally assess what the students already

know about polynomials. Then the teacher will be able to use this information

to scaffold learning and teach new concepts. Students should be given credit

for completing their KWHL worksheets and associated projects. Assessments

for the related research projects will vary, depending on the type of project.

**Alternative Topics**

In the explanation for this strategy I used the topic of polynomials as the

subject of the KWHL inquiry. As there are various topics in math and various

courses to which they may be applicable I thought it would be useful to suggest

a list of other topics that could be investigated in relation to this book. The
list

is not meant to be comprehensive; it is merely given as a list of suggestions

Number Systems

Exponents

Geometric Shapes

Geometric Proofs

Fractals

Pythagorean Theorem

Series and sequences

Combinations and permutations

Pascal’s Triangle

Factorials

Uncountable sets (set theory)

Imaginary Numbers

Algorithms

Mathematicians