Introduction To Using Comparison Charts In The Mathematics Classroom printable pdf download

Dare to Compare?

Introduction to Using Comparison Charts in the Mathematics Classroom

Dave Damcke (University of Portland), Tevian Dray (Oregon State University), Maria

Fung (Western Oregon University), Dianne Hart (Oregon State University), Lyn

Riverstone (Oregon State University)

The geometry team at the Oregon Mathematics Leadership Institute (OMLI) created and

delivered a course for K-12 teachers called “Comparing Different Geometries.” A major

part of this course was spent on creating extensive comparison charts aimed at

synthesizing newly acquired knowledge that teachers gained in Spherical and Taxicab

geometries, and connecting this knowledge to ideas in the school geometry curriculum.

In this article, we discuss using comparison as a method for reviewing, looking back, and

extending mathematical knowledge. We can also imagine it working well as part of an

on-going process; as students construct new knowledge, they may spend time revising

and editing their charts based on formative feedback from the teacher. We believe that

comparison charts are an interesting and invaluable tool for supporting students as they

make connections between different mathematical ideas (NCTM, 2000).

What to Compare?

Mathematics is a subject rich in interrelations and surprising analogies. There are

numerous possibilities for comparing different objects, operations, or properties. We will

suggest several very different examples to illustrate how comparison can be used in the

mathematics classroom.

• In geometry, students often struggle with definitions. Remembering which properties

define special types of quadrilaterals can be tricky for many students. Using a

comparison chart where students compare, for instance, squares with rectangles,

rhombi with parallelograms, and trapezoids with parallelograms, could be a great way

to remember the characteristic properties of these different polygons. Students could

be given the task of describing in detail the similarities and differences between each

pair. Once this activity is completed and thoroughly discussed, students could also be

given the task to compare and contrast pairs of different types of triangles (e.g.

isosceles and right triangles, scalene and right triangles, etc.).

Another geometric topic students could be asked to focus on is circles. What

properties do all circles share? Students may consider that

is the ratio of the

circumference to the diameter of any circle, for example. Are there properties that

depend on the specific circle we are considering? By looking for ways to compare

circles in this way, students would have the opportunity to look back at the concepts

of radius, circumference, and area, to discuss their definitions and to consider

examples.

Introduction To Using Comparison Charts In The Mathematics Classroom