Preparing 21st Century Students for a Global Society

An EducAtor’s GuidE to thE Four cs
MAthEMAtiCs – 12th GRAdE
Students explore the napkin ring problem: if a
hole of height “h” is drilled through the center
of a sphere, the volume of the portion of the
sphere that remains does not depend on the
size of the original sphere; it depends only on h.
They share and critique their insights into why
this is so. Then students explore mathematician
Keith Devlin’s 2008 discussion of the problem
at www.maa.org/devlin/devlin_04_08.html,
where Devlin provides the full computation and
explains why some solutions posted online are
incorrect. Students explore solutions currently
appearing online and assess which solutions are
accurate and which are not.
Reflections on Critical Thinking
As you begin to integrate critical thinking
into classroom practices, consider the
following questions:
` `How
can you model critical thinking/
problem solving for your students?
` `What
kind of learning environment
is necessary to emphasize problem
solving skills in your classroom?
` `What
could you do to make critical
thinking and problem solving more
intentional and purposeful in your
classroom?
` `How
can you encourage students to
be better critical thinkers and problem
solvers?
`
` How can you and your colleagues
work collectively to prioritize effective
higher order thinking pedagogy
across classrooms?
P r e P a r i n g 2 1 s t C e n t u r y s t u d e n t s f o r a g l o b a l s o C i e t y
Critical Thinking and Problem Solving
Resources on Critical Thinking
The following list of critical thinking resources
is divided into “General Resources” and
“Classroom Resources.” Use these resources
to help generate dialogue and action in your
classroom, department, and school.
General Resources
The Foundation for Critical Thinking
The Foundation and its related entities aim
to improve education in all subjects at every
level by providing information, research, and
resources on critical thinking. This site provides
excellent background resources on the subject
of critical thinking.
www.criticalthinking.org
Classroom Resources
Catalina Foothills Critical Thinking Rubric
Catalina Foothills School District created a series
of rubrics to assess student critical thinking skills.
They measure critical thinking skills such as
comparing, classifying, inductive and deductive
reasoning, error analysis, and decision making.
http://tinyurl.com/ydteapw
Council for Aid to Education’s (CAE’s)
Collegiate Learning Assessment (CLA) and
College and Work Readiness Assessment
(CWRA)
These assessments from CAE measure analytic
thinking, critical thinking, problem solving, and
written communication skills. The CWRA is
available for high school use. Access the scoring
rubric at http://tinyurl.com/2vh3ugo.
http://www.cae.org/content/pro_collegework.htm.
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