en klassieke aanpak van het rekenen kan volgens een recente AERA-studie
rekenproblemen voorkomen (zie bijlage).
In het boek 'Rekenen
tot 100' (Raf Feys, Wolters-Plantyn, Mechelen) beschreven we uitvoerig zo'n
aanpak. We namen er ook - en volgens de recente AERA-studie terecht - afstand van de constructivistische
en context-gebonden aanpak van het Nederlandse Freudenthal-Instituut. Vanaf de
jaren zeventig bestreden we de te
abstracte en hemelse Moderne Wiskunde (New Math) en met succes. Zie b.v. Moderne
wiskunde: een vlag op een Modderschuit, Onderwijskrant nr. 24, april 1882. Bij het verdwijnen van de Moderne Wiskunde
dreigde die extreme benadering vervangen te worden door het andere extreem: de aardse,
contextgebonden en constructivistische wiskunde à la Freudenthal-Instituut.
Volgens de AERA-studie gebruiken Amerikaanse leerkrachten
veelal een ineffectieve methodiek in de richting van de constructivistische -
en child-centred-aanpak. In Vlaanderen deden we de voorbije decennia
ons best om dergelijke aanpakken te bestrijden. Net als voor het leren lezen en
spellen werkten we voor wiskunde aanpakken uit waarmee we ook zwakkere
leerlingen vlot kunnen leren rekenen.
We stelden de voorbije decennia ook vast dat aanpakken die
rendeerden voor zwakkere leerlingen, ook rendeerden voor sterkere leerlingen.
Met onze Directe SysteemMethodiek (DSM) voor het leren lezen (Beter leren lezen,
Acco-2010), leren o.i. niet enkel de zwakkere leerlingen, maar ook de sterkere
vlotter lezen. Samen met collega Pieter Van Biervliet werkten we ook aan
effectieve aanpakken voor het spelling-onderwijs en aan een meer
gestructureerde aanpak met afzonderlijke spellingpakketten.
Bijlage: AERA Study: Teachers More Likely to Use Ineffective
Instruction When Teaching Students with
WASHINGTON, D.C., June 26, 2014 ─ First-grade teachers in
the United States may need to change their instructional practices if they are
to raise the mathematics achievement of students with mathematics difficulties
(MD), according to new research published online today in Educational
Evaluation and Policy Analysis, a peer-reviewed journal of the American
Educational Research Association.
VIDEO: Co-author Paul L. Morgan discusses key findings.
Which Instructional Practices Most Help First-Grade
Students with and without Mathematics Difficulties? by Paul L. Morgan of
Pennsylvania State University, George Farkas of the University of California,
Irvine, and Steve Maczuga of Pennsylvania State University, examined nationally
representative groups of first-grade students with and without MD to determine
the relationship between the instructional practices used by teachers and the
mathematics achievement of their students.
The study, funded by the U.S. Department of Education and
the National Institutes of Health, found that first-grade teachers in
classrooms with higher percentages of students with MD were more likely to be
using ineffective instructional practices with these students.
When first-grade classes had larger percentages of students
with MD, their teachers were more often using non-traditional instructional
practices, in which students use manipulatives, calculators, movement, and
music to learn mathematics. The researchers found these types of practices were
not associated with achievement gains. These practices were ineffective for
both MD and non-MD students.
Instead, the researchers found that only use by first-grade
teachers of more traditional, teacher-directed instruction in which teachers
used textbooks, worksheets, chalkboards, and routine practice to instruct
students in mathematics facts, skills, and concepts was associated with
achievement gains for students with MD.
According to study findings, the most effective
instructional practice that first-grade teachers could use for students with MD
was to provide them with routine practice and drill opportunities to learn
mathematics. The findings held true for first-grade students who had shown
either persistent or transitory MD in kindergarten. Results were extensively
controlled for students prior mathematics and reading achievement, family
income, and other factors.
Use by first-grade teachers of non-teacher-directed
instruction is surprising and troubling, given our findings and what prior
research has shown about the instructional needs of students with MD, said
lead study author Paul L. Morgan. It suggests that first-grade teachers are
mismatching their instruction to the learning needs of students with MD.
Our findings suggest that students with MD are more likely
to benefit from more traditional, explicit instructional practices, Morgan
said, This is particularly the case for students who are more likely to
persistently struggle to learn mathematics.
Effectively instructing students with MD at an early age
matters immensely to their future academic achievement and opportunities in
life, said Morgan. We know that students who continue struggling to learn
mathematics in the primary grades are highly likely to continue to struggle
throughout elementary school. Others have reported that students who
subsequently complete high school with relatively low mathematics achievement
are more likely to be unemployed or paid lower wages, even if they have
relatively higher reading skills.
For students without a history of MD, teacher-directed
instruction is also associated with achievement gains. However, unlike their
schoolmates with MD, the mathematics achievement for these students is also
associated with some, but not all, types of student-centered instruction, which
focuses on giving students opportunities to be actively involved in generating
mathematical knowledge. Student-centered activities associated with achievement
gains by first graders without MD include working on problems with several
solutions, peer tutoring, and activities involving real-life math. Students
without MD benefited about equally well from either more traditional
teacher-directed instruction or less traditional student-centered instruction.
While previous research has identified instructional
practices that can be used by elementary school teachers to increase reading
achievement for those with and without reading difficulties, very few empirical
studies have tried to identify instructional practices being used by teachers
that are effective in increasing the mathematics achievement of their students
with and without MD.
For their study, the researchers analyzed survey responses
from 3,635 teachers and data from a subsample of 13,393 children in the Early
Childhood Longitudinal Study, Kindergarten Class of 199899, a nationally
representative dataset maintained by the U.S. Department of Educations
National Center for Education Statistics.
About the Authors
Paul L. Morgan is an associate professor of education at
the Pennsylvania State UniversityUniversity Park College of Education, and the
director of the Educational Risk Initiative.
George Farkas is a professor at the University of
CaliforniaIrvine School of Education.
Steve Maczuga is a research programmer/analyst at the
Pennsylvania State UniversityUniversity Park Population Research Institute.
The American Educational Research Association (AERA) is the
largest national professional organization devoted to the scientific study of
education. Founded in 1916, AERA advances knowledge about education, encourages
scholarly inquiry related to education, and promotes the use of research to improve
education and serve the public good. Find AERA on Facebook and Twitter.