[Numeracy 575] Cognitive levels on the GED math section and its implications for instruction

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Mark.Trushkowsky at mail.cuny.edu Mark.Trushkowsky at mail.cuny.edu
Wed Oct 13 16:40:57 EDT 2010

I am interested in hearing what people are thinking about the kinds of
questions our students face on the GED.

Often when people talk about what is on the GED, and what students need to
learn, and what teachers need to learn, the conversation remains limited
to content areas - things like, "students struggle with the pythagorean
theorem questions".

I am looking for ways to work with teachers in exploring the model of the
three cognitive levels that the GED uses to categorize the math questions.
According to the GED Testing Service,the test "assesses different ways of
applying math skills through the use of different question types". The
three types are based on Bloom's taxaonomy and divided up as follows - 20%
of the questions are Procedural questions, 30% are Conceptual questions
and 50% are Application/Modeling/Problem Solving questions.

To read a more detailed description of each cognitive level, check out:

To go back to my earlier example, I don't think it is a procedural issue,
when students get questions dealing with the relationship between the legs
and hypotenuse in a right triangle. Students who are drilled with
examples of "A squared plus B squared equals C squared" start to make
mistakes when the GED asks a question which tests students' conceptual or
problem-solving levels of understanding. So for example, students will
often do "A squared plus B squared equals C squared", even when given the
hypotenuse and one of the legs and asked to find the other leg. They do
this because their understanding it only at a procedural level.
Unfortunately 80% of the GED math is trying to assess if they understand
math concepts at a deeper level.

Many teachers who focus on content only, also focus (often without
realizing) on procedural type questions. So for example, for students
working on area, they will work on problems where they are given the sides
of a rectangle and asked to find the area. To me, a question like this is
procedural because it only requires students to "select and apply the
correct operation or procedure to solve a problem".

But 25 out of 50 math questions are going to be
Application/Modeling/Problem-Solving - add 15 more questions at a
Conceptual level and that is 40 (out of 50 questions that require a deeper
than procedural level of understanding. Students are far more likely to
face a question like: "One of the legs of a right triangle is two feet
longer than the other leg. If the area of the triangle is 24 square
inches, what is the length of the hypotenuse?" No one can prepare for
that question on procedure alone. On a procedural level, students need to
know how to find the area of a triangle (and knowing how to find the area
of a rectangle would probably help as well), as well as how to caluclate
the hypotenuse of a right triangle when given the legs. But on a deeper,
conceptual & problem-solving level, students need to understand why they
are given the area, and how to use it. They also need to understand the
relationship between the area of a rectangle and the area of a triangle -
if they don't, they might think the legs are "4 feet" and "2 feet". And
they'll need to know how to develop a strategy to go about this problem,
to implement that strategy and to gauge whether their strategy is working.

To not help our students learn how to do math on a level deeper than
procedure is to leave many of them unequipped to do better than guess for
80% of the test.

How are other people working with teachers to help them feel more
comfortable and capable developing these deeper cognitive skills in their


Mark Trushkowsky
Mathematics Staff Developer
CUNY Adult Literacy and GED Program
101 W. 31st Street, 7th Floor
New York, NY 10001
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