In a well-publicized paper that
addressed why some students were not learning to read, Reid Lyon (2001)
concluded that children from disadvantaged backgrounds where early childhood
education was not available failed to read because they did not receive
effective instruction in the early grades. Many of these children then required
special education services to make up for this early failure in reading
instruction, which were by and large instruction in phonics as the means of
decoding. Some of these students had no specific learning disability other than
lack of access to effective instruction. These findings are significant because
a similar dynamic is at play in math education: the effective treatment for
many students who would otherwise be labeled learning disabled is also the
effective preventative measure.
In 2010 approximately 2.4 million
students were identified with learning disabilities — about three times as many
as were identified in 1976-1977. (See http://nces.ed.gov/programs/digest/d10/tables/xls/tabn045.xls
and http://www.ideadata.org/arc_toc12.asp#partbEX).
This increase raises the question of whether the shift in instructional
emphasis over the past several decades has increased the number of low
achieving children because of poor or ineffective instruction who would have
swum with the rest of the pack when traditional math teaching prevailed. I
believe that what is offered as treatment for learning disabilities in
mathematics is what we could have done—and need to be doing—in the first place.
While there has been a good amount of research and effort into early
interventions in reading and decoding instruction, extremely little research of
equivalent quality on the learning of math in the United States exists. Given
the education establishment’s resistance to the idea that traditional math
teaching methods are effective, this research is very much needed to draw such
a definitive conclusion about the effect of instruction on the diagnosis of
learning disabilities.1
Some Background
Over the past several decades, math
education in the United States has shifted from the traditional model of math
instruction to “reform math”. The traditional model has been criticized for
relying on rote memorization rather than conceptual understanding. Calling the
traditional approach “skills based”, math reformers deride it and claim that it
teaches students only how to follow the teacher’s direction in solving routine
problems, but does not teach students how to think critically or to solve
non-routine problems. Traditional/skills-based teaching, the argument goes,
doesn’t meet the demands of our 21st century world.
As I’ve discussed elsewhere, the criticism of
traditional math teaching is based largely on a mischaracterization of how it
is/has been taught, and misrepresented as having failed thousands of students
in math education despite evidence of its effectiveness in the 1940s, ’50s and
’60s. Reacting to this characterization of the traditional model, math
reformers promote a teaching approach in which understanding and process
dominate over content. In lower grades, mental math and number sense are
emphasized before students are fluent with procedures and number facts.
Procedural fluency is seldom achieved. In lieu of the standard methods for
adding/subtracting, multiplying and dividing, in some programs students are
taught strategies and alternative methods. Whole class and teacher-led explicit
instruction (and even teacher-led discovery) has given way to what the
education establishment believes is superior: students working in groups in a
collaborative learning environment. Classrooms have become student-centered and
inquiry-based. The grouping of students by ability has almost entirely
disappeared in the lower grades—full inclusion has become the norm. Reformers
dismiss the possibility that understanding and discovery can be achieved by
students working on sets of math problems individually and that procedural
fluency is a prerequisite to understanding. Much of the education establishment
now believes it is the other way around; if students have the understanding,
then the need to work many problems (which they term “drill and kill”) can be
avoided.
The de-emphasis on mastery of basic
facts, skills and procedures has met with growing opposition, not only from
parents but also from university mathematicians. At a recent conference on math
education held in Winnipeg, math professor Stephen Wilson from Johns Hopkins
University said, much to the consternation of the educationists on the panel,
that “the way mathematicians learn is to learn how to do it first and then
figure out how it works later.” This sentiment was also echoed in an article
written by Keith Devlin (2006). Such opposition has had limited success,
however, in turning the tide away from reform approaches.
The Growth of Learning Disabilities
Students struggling in math may not
have an actual learning disability but may be in the category termed “low
achieving” (LA). Recent studies have begun to distinguish between students who
are LA and those who have mathematical learning disabilities (MLD). Geary
(2004) states that LA students don’t have any serious cognitive deficits that
would prevent them from learning math with appropriate instruction. Students
with MLD, however, (about 5-6% of students) do appear to have both general
(working memory) and specific (fact retrieval) deficits that result in a real
learning disability. Among other reasons, ineffective instruction, may account
for the subset of LA students struggling in mathematics.
The Individuals with Disabilities
Education Act (IDEA) initially established the criteria by which students are
designated as “learning disabled”. IDEA was reauthorized in 2004 and renamed
the Individuals with Disabilities Education Improvement Act (IDEIA). The
reauthorized act changed the criteria by which learning disabilities are
defined and removed the requirements of the “significant discrepancy” formula.
That formula identified students as learning disabled if they performed
significantly worse in school than indicated by their cognitive potential as
measured by IQ. IDEIA required instead that states must permit districts to adopt
alternative models including the “Response to Intervention” (RtI) model in
which struggling students are pulled out of class and given alternative
instruction.
What type of alternative instruction
is effective? A popular textbook on special education (Rosenberg, et. al,
2008), notes that up to 50% of students with learning disabilities have been
shown to overcome their learning difficulties when given explicit instruction.
This idea is echoed by others and has become the mainstay of the Response to Intervention
model. What Works Clearinghouse finds strong evidence that explicit instruction is an effective intervention,
stating: “Instruction during the intervention should be explicit and
systematic. This includes providing models of proficient problem solving,
verbalization of thought processes, guided practice, corrective feedback, and
frequent cumulative review”. Also, the final report of the President’s National Math Advisory Panel
states: “Explicit instruction with students who have mathematical difficulties
has shown consistently positive effects on performance with word problems and
computation. Results are consistent for students with learning disabilities, as
well as other students who perform in the lowest third of a typical class.” (p.
xxiii). The treatment for low achieving, learning disabled and otherwise
struggling students in math thus includes math memorization and the other
traditional methods for teaching the subject that have been decried by
reformers as having failed millions of students.
The Stealth Growth of Effective
Instruction
Although the number of students
classified as learning disabled has grown since 1976, the number of students
classified as LD since the passage of IDEIA has decreased (see Figure 1). Why
the decrease has occurred is not clear. A number of factors may be at play. One
may be a provision of No Child Left Behind that allows schools with low numbers
of special-education students to avoid reporting the academic progress of those
students. Other factors include more charter schools, expanded access to
preschools, improved technologies, and greater understanding of which students
need specialized services. Last but not least, the decrease may also be due to
targeted RtI programs that have reduced the identification of struggling and/or
low achieving students as learning disabled. .
Having seen the results of
ineffective math curricula and pedagogy as well as having worked with the
casualties of such educational experiments, I have no difficulty assuming that
RtI plays a significant role in reducing the identification of students with
learning disabilities. In my opinion it is only a matter of time before
high-quality research and the best professional judgment and experience of
accomplished classroom teachers verify it. Such research should include 1) the
effect of collaborative/group work compared to individual work, including the
effect of grouping on students who may have difficulty socially; 2) the degree
to which students on the autistic spectrum (as well as those with other
learning disabilities) may depend on direct, structured, systematic
instruction; 3) the effect of explicit and systematic instruction of
procedures, skills and problem solving, compared with inquiry-based approaches;
4) the effect of sequential and logical presentation of topics that require
mastery of specific skills, compared with a spiral approaches to topics that do
not lead to closure and 5) Identifying which conditions result in
student-led/teacher-facilitated discovery, inquiry-based, and problem-based
learning having a positive effect, compared with teacher-led discovery,
inquiry-based and problem-based learning. Would such research show that the use
of RtI is higher in schools that rely on programs that are low on skills and
content but high on trendy unproven techniques and which promise to build
critical thinking and higher order thinking skills? If so, shouldn’t we be
doing more of the RtI style of teaching in the first place instead of waiting
to heal the casualties of reform math?
Until any such research is in, the
educational establishment will continue to resist recognizing the merits of
traditional math teaching. One education professor with whom I spoke stated
that the RtI education model fits mathematics for the 1960s, when “skills
throughout the K-8 spectrum were the main focus of instruction and is seriously
out of date.” Another reformer argued that reform curricula require a good deal
of conceptual understanding and that students have to do more than solve word
problems. These confident statements assume that traditional methods—and the
methods used in RtI—do not provide this understanding. In their view, students
who respond to more explicit instruction constitute a group who may simply
learn better on a superficial level. Based on these views, I fear that RtI will
incorporate the pedagogical features of reform math that has resulted in the
use of RtI in the first place.
While the criticism of traditional
methods may have merit for those occasions when it has been taught poorly, the
fact that traditional math has been taught badly doesn’t mean we should give up
on teaching it properly. Without sufficient skills, critical thinking doesn’t
amount to much more than a sound bite. If in fact there is an increasing trend
toward effective math instruction, it will have to be stealth enough to fly
underneath the radar of the dominant edu-reformers. Unless and until this
happens, the thoughtworld of the well-intentioned educational establishment
will prevail. Parents and professionals who benefitted from traditional
teaching techniques and environments will remain on the outside — and the public
will continue to be outwitted by stupidity.
- See more at:
http://www.educationnews.org/education-policy-and-politics/barry-garelick-math-education-being-outwitted-by-stupidity/#sthash.VpaBihFf.dpuf
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