There is an insightful study that looks at the application of the Constructivist theory in mathematics education which can be found in http://ejournals.ph/article.php?id=222 . The study was conducted by Dr. Auxencia A. Limjap where she showed that the deductive reasoning of five teachers was significantly enhanced in a constructivist-based environment. The study described deductive reasoning as a manifestation of logico-mathematical intelligence, the latter being one of the multiple intelligences identified by Gardner. It also further described deductive reasoning as the ability to reason from necessary premises to their necessary conclusion. By invoking accepted rules of logic, teachers can infer statements from a given set of statements through different cognitive abilities. The validity or invalidity of the premises and the conclusion are said to be establishable. The enhancement therefore of proficiency in deductive reasoning is important as school mathematics has a strict hypothetico-deductive nature.
It was also argued that deductive reasoning can be best enhanced in an inquiry-based environment or the so-called constructivist environment. If we check on Wikipedia, we can see the philosophers behind the theory, one of whom is the eighteenth century philosopher Giambattista Vico who claimed that “humans can only understand what they have themselves constructed”. However, it was really the French psychologist Jean Piaget who clearly developed constructivism as applied to classroom and childhood development. Ernst Von Glaserfield also advanced the principle that “Knowledge is not passively received either through the senses or by way of communication. Knowledge is actively built by the cognizing subject.” It was further cited in the study that “the function of cognition is adaptive, in the biological sense of the term, tending towards fit or viability.” And that “cognition serves the subject’s organization of the experimental world, not the discovery of an objective ontological reality”. This contradiction is quite puzzling to me. But the study explained the principle clearly as “knowledge is not transferred directly from the environment or duplicated from one person’s mind into the mind of another person.” This is the reason why the “teachers communication does not transmit a single meaning to all learners, but rather evokes different meanings to different learners.” It is therefore argued that ‘mathematical meaning is built up actively by the learner from pre-existing mental objects within his/her mind.” This may explain why teachers find it difficult to teach learners who lack a good foundation in math.
Most importantly, it was found out in the study that the constructivist-based instructional design moved the level of one out of five teachers to the reflective level. Thus, it was maintained that “the best environment for the enhancement of deductive reasoning and most of mathematics learning is a constructivist environment”.