Alan Cromer, a university professor of physics, seeks to inform the general reader of the serious contradiction that has evolved between the research scientist and the secondary school science teacher in respect to their thinking about both the positive sciences and the social sciences. This contradiction has been brought about by the acceptance by science teaches of the views of the post-modern philosophy called “constructivism.” This is an anti-science philosophy based largely on the work of the child psychologist Jean Piaget. It denies the objectivity of scientific observation and the truth of scientific knowledge. Such views are the opposite of those of “logical positivism,” which offers arguments for the objectivity of scientific observation and the truth of scientific knowledge.
Thus Cromer is seriously disturbed by the huge gap between the thinking of the research scientist and the science teacher at the secondary school level. He cites the case of the science teacher who believed students could discover scientific laws from a simple demonstration without prior explanation. The teacher gave the students several cylinders of equal volume but different masses. They were instructed to put each cylinder in an equal volume of water and observe which cylinders sank and which cylinders floated. After they made this observation, they were asked to weigh each cylinder and then draw their conclusion. The teacher evidently hoped they would come up with the principle of buoyancy. However, the students promptly concluded that the heavy cylinders had sunk while the light ones floated, they having not been informed that buoyancy depended on the “density,” not “weight,” for density is equal to the mass divided by the volume.
Cromer makes a good case for his philosophy of science, but his arguments might have been strengthened by presenting some theory of natural language to combat the “deconstructive” view based on the work of Jacques Derrida who argued that the meaning of natural language is “indefinite.” He also could have provided a clearer view of the relationship between natural language and mathematics. For instance, instead of its algebraic notation, the Pythagorean theorem can be expressed in natural language as “In a right triangle the hypotenuse squared is equal to the sum of the square of the other two sides.”