The Math War between traditional and “realistic” mathematics education and its research. An analysis in institutional economics on research on education in arithmetic and algebra, with a focus on long term memory of pupils and using a causal model for valid testing on competence

Institutional economics investigates how institutions affect empirical events. The term "institution" can be taken widely, and may also represent engrained mental conceptions by organised groups of actors. There is a curious but counterproductive combination of three groups also at universities in Holland w.r.t. research on education in arithmetic and algebra: (1) adherents of "realistic" mathematics education, an ideology that compares to astrology or homeopathy, (2) traditional mathematicians, who have no expertise on the empirical science of didactics of mathematics either, (3) psychometricians, who look at statistical data but who have no expertise on the empirical science of didactics of mathematics either. This combination needs deconstruction and the present paper focuses on (3), though with influence from (1) and (2). Some psychometricians seem to have a sound dislike of both the ideologues from (1) and the discussion between (1) and (2), but they are less aware that (2) are ideologues too. Some psychometricians also throw away the child with the bathwater by disregarding (4) the proper science of didactics of mathematics. Measuring competence in arithmetic and algebra requires consideration of long term memory of students. What you learn in elementary school tends to stay with you for the rest of your life. What you learn in highschool has the property of "use it or lose it". Algebra in highschool requires competence in the traditional algorithms of arithmetic, best learned in elementary school. "Realistic" mathematics education has reduced the competence of students at elementary school which affects them not only for algebra in highschool but also for the rest of their lives in both arithmetic and algebra. Inadequate testing by psychometricians allows this detrimental state to continue. The paper presents a causal model that identifies the engrained mental conceptions by psychometricians and where they would have to accept insights from didactics of mathematics. There is also a role for the Dutch Academy of Sciences KNAW that supported an inadequate report in 2009.