[Numeracy 578] Re: Cognitive levels on the GED math section and its implications for instruction
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Wed Oct 13 20:21:44 EDT 2010
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I really appreciated this reminder about what is important on the GED exam. Just this month a survey was done of instructors in our program as to what they needed help with in teaching math. The answers were all procedural: percents, similar triangles, perimeter and area, etc.
Sometimes the students who are poor in reading but good in calculation do not do well on the GED predictors because they do not read the problem carefully and think through ways to solve the problem. They just do something-anything-with those numbers.
One strategy I have used is to have two students take a predictor together and talk it through as they go. This forces them to read carefully and to realize that there can be alternate strategies to solve a problem. I enjoy seeing two heads together, calculators in hand, discussing what to do--and they generally enjoy it as well. Math in real life is not a solitary activity. I think this strategy helps get rid of some of the anxiety our students have as well. We also do a lot of work with partners on more advanced review problems similar to those on the GED.
I look forward to reading lots of other suggestions!
Mary Vanderkam
Family Literacy
South Bend Community School Corporation
To: numeracy at lincs.ed.gov
From: Mark.Trushkowsky at mail.cuny.edu
Date: Wed, 13 Oct 2010 16:40:57 -0400
Subject: [Numeracy 575] Cognitive levels on the GED math section and its implications for instruction
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: http://www.acenet.edu/Content/NavigationMenu/ged/etp/math_test_descriptio.htm
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 students?
Mark
Mark Trushkowsky
Mathematics Staff Developer
CUNY Adult Literacy and GED Program
101 W. 31st Street, 7th Floor
New York, NY 10001
646-344-7301
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