Solving arithmetic operations: a semantic approach
Emmanuel Sander · eScholarship (California Digital Library) · 2001
Systematic errors observed when solving arithmetic operations are often considered as being procedural.Rules induced by the learner and the errors committed are viewed as resulting by use of general problem solving methods.In this study, in the case of solving column subtractions, we show that some errors may be semantic: they are due to analogies involving different sources that guide the interpretation of both operations and procedures already learned.Two sources have been identified: (i) subtracting considered as removing something and (ii) subtracting considered as covering a distance between two elements.Results of the 2 experiments reported here show that (i) not only all of the predicted semantic errors were observed among beginner children, but also that (ii) semantic errors were still observed among more advanced learners, in a decreasing proportion for higher level of instruction.These results support the idea that (i) semantic aspects have a major influence in the learning process, and (ii) that this kind of errors still intervene in the learning process even if the procedural aspects become more influent (advanced students).These results suggest that a procedural approach might be articulated with a semantic approach.