[Phys-L] NAEP math:Can 8th graders do fractions, decimals, percents?
From: jane.jackson at ASU.EDU (Jane Jackson)
Date: Sun Dec 12 20:37:28 2004
[Since physics and math are intimately related, here's a link to a
provocative new study on middle school math teaching and learning, issued
by the Brookings Institution. Some questions posed are these: are recent
gains in NAEP math tests false? Do 8th graders understand fractions,
decimals, percents?]
THE 2004 BROWN CENTER REPORT ON AMERICAN EDUCATION:
How Well Are American Students Learning?
(with studies of NAEP math items, middle school math teachers, and the
revamped Blue Ribbon Schools awards)
by Tom Loveless
November 2004
INTRODUCTION
...
The NAEP has publicly released more than 500 items from its mathematics
tests. In the first section of this report, after reviewing test data
released in 2004, we analyze a sample of NAEP items and discover that the
mathematics required to solve many of the problems is extraordinarily easy.
Most of the arithmetic one would need to know to solve the average item on
the eighth grade NAEP is taught by the end of third grade. The second
section of the report presents a survey of middle school math teachers,
focusing on their educational background and professional development. A
significant number of math teachers at this level lack formal undergraduate
training in mathematics, and the professional development they are
receiving appears to be inadequate to remedy the problem. ...
View Full Report (PDF-672 KB)
[excerpt from page 12]
A couple of things stand out in the
fourth grade portion of Table 1-3. First, the
problem solving items on NAEP are not very
challenging - at least not in the arithmetic
required to answer them. Content taught in
first and second grades is at least two years
below grade level for fourth graders. But that
is the level of difficulty of more than four out
of ten (43.6%) problem solving items on
NAEP. The second surprising finding is that
even though the NAEP items are so easy,
fourth graders do not do very well on them.
The first and second grade items demand
nothing more than being able to add and
subtract whole numbers and knowing basic
multiplication facts. Yet a majority of the
nation's fourth graders miss the average item
pitched at this level.
Even more dramatic findings are
evident at eighth grade. The eighth grade
items are only slightly more difficult than
those on the fourth grade test (3.4 mean
grade level). Almost four out of ten items
(39.6%) address arithmetic skills taught
in first and second grade-six years below
the grade level of eighth graders taking the
test. Indeed, more than three-fourths of
the items (33/43) are at least four years
below grade level, taught in the fourth grade
or lower. Yet the percentage of eighth graders
answering problem solving items correctly
is an unimpressive 41.4%. Problem solving
items on the eighth grade NAEP only require
knowledge of very simple arithmetic.
Despite this, eighth graders have trouble
getting them right.
The Dominance of Whole Numbers:
What makes NAEP items so easy? The short
answer is the dominance of whole numbers
on the test. ...
[excerpt from page 15]
This study casts the dramatic NAEP gains of
the past decade in a new light. It appears that
even if American students are making
progress in mathematics, the arithmetic on
which the gains are being registered is not
very challenging, certainly no more demanding
than that taught in third grade. ...
... Math reformers in the
1990s, including the National Council
of Teachers of Mathematics, stressed
that schools should teach mathematics as
a problem solving activity. The data
presented here support that position by
confirming widespread difficulty
with problem solving. Students cannot
solve problems employing even the
simplest arithmetic.
[excerpt from page16]
The short-fall in students' current learning has two
dimensions. One dimension is insufficient
problem solving skills; the other is
insufficient arithmetic skills. If students do
not possess the tools to solve problems
involving fractions, decimals, and percents-
if students do not grasp forms of numbers
other than whole numbers - then the
only problems they will ever be able to solve
will be mathematically trivial. The NAEP test
measures problem solving skills and tracks
student performance over time. It does
not do so in arithmetic, and as indicated by
the data presented here, assesses only the
most rudimentary skills in that domain.
...
Jane Jackson, Co-Director, Modeling Instruction Program
Box 871504, Dept.of Physics & Astronomy,ASU,Tempe,AZ 85287
480-965-8438/fax:965-7331 <http://modeling.asu.edu>
"Scientists explore the physical world for REPRODUCIBLE
PATTERNS, which they represent by MODELS and organize
into THEORIES according to LAWS." - David Hestenes