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In each Know the
ISTE Standards,
an ISTE research
associate describes a
lesson from a classroom
observation and evaluates
its alignment with the
ISTE Standards for Students
( iste.org/standards/
standards-for-students).
By Talbot Bielefeldt
Standard 4: Critical Thinking, Problem Solving, &
ACTIVITY 1: No evidence of the standard.
Using values from a labeled diagram, individual students calculate
the unique surface area of a rectangle that intersects a circle through
its center on the same plane.
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This month, we focus on Standard 4, with examples of how an observer or lesson designer might assess the indicators
of higher-order thinking in a geometry lesson.
The activities described in the table below
were designed with the seventh grade Common
Core geometry standards in mind, particularly
B4: “know the formulas for area and circumference of a circle” and B6: “solve problems involving areas of two- and three-dimensional objects”
( www.corestandards.org/Math/Content/G).
The conceptual problem that the students
need to solve for this lesson involves recogniz-
ing that half the area of a circle needs to be sub-
tracted from the area of a rectangle. Once that
happens, Activity 1 is an arithmetic problem,
and Activity 2 is a more generalized algebraic
approach. Both are limited forms of the problem
that might appear on a quiz or test. Activity 3,
however, is a different animal: a project with
several multistep tasks.
Geometers and house painters have been
solving problems like this for centuries, so
none of the activities is absolutely dependent
on technology. Today, however, Activity 3
would almost certainly involve at least web
research, spreadsheets, and possibly some use
of graphics tools. Assuming that digital tools
are part of the lesson, this scenario would also
address a number of indicators under other
ISTE Standards, not to mention most of the
Common Core StateStandards for mathematical practices ( www.corestandards.org/Math/
Content/7/introduction), including:
