Meer gestructureerde 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 Mathematics Difficulties

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 1998–99, a nationally representative dataset maintained by the U.S. Department of Education’s National Center for Education Statistics.

About the Authors

•Paul L. Morgan is an associate professor of education at the Pennsylvania State University–University Park College of Education, and the director of the Educational Risk Initiative.

•George Farkas is a professor at the University of California–Irvine School of Education.

•Steve Maczuga is a research programmer/analyst at the Pennsylvania State University–University Park Population Research Institute.

About AERA

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.