2013 Conference Proceedings - University of Nevada, Las Vegas

their parents in phenotype (observable characteristics) and genotype (genetic makeup), withphenotypes being the result of genotypes growing in an environment. In reproduction of this sortthe genes of the offspring are usually some combination of two different genes from the parents;the dynamics of combining produces offspring whose genotypes are identical to their parents, orsome mixture or hybridization, etc. In addition, mutations, such as “mistakes” in copying genesor the result of external factors “interfering” with reproduction, can occur. In biologicalevolution, phenotypes - and hence, genotypes - in a population are “selected” in a probabilisticmanner through their fitness to the environment (e.g., “survival of the fittest”).Learning viewed as a genetic learning process (GLP) parallels the biological ideas ofphenotypes, genotypes, offspring, and selection. In this view, the ideas or concepts that a personholds are similar to the genes or alleles of biology. A GLP brings about new knowledge as anoffspring of previous understanding through the replication of a previous idea or the combiningof two (or more) existing ideas, or the mutation of a previous concept, and so on. The “fitness”of the offspring, however, is determined not so much by the environment as it is by thecoherence or efficiency of the new scheme as viewed by the learner. Because this view is one ofthe dynamics of learning, and not merely a taxonomy of approaches students can take, it canprovide additional insight into both teaching and learning.Genotype vs. Phenotype in GLPFirst, we note that there is an important difference between the genotype of knowledge andits phenotype. Let us consider two hypothetical students who answer the question “What is 12 ×23?” Each student (seemingly) follows the traditional algorithm, and gets the answer of 276:23× 124623_276Despite seeing the same phenotypic (observable) multiplication behavior in each student, thereare at least two quite different genotypic (but not easily observable) approaches to multiplication;often these differences become apparent only in later work. Verbal probing by the teacher mightdraw out differences between students (e.g., regarding place value or understanding of partialproducts) that could point to underlying genotypic variation.Proceedings of the 40 th Annual Meeting of the Research Council on Mathematics Learning 2013 190