| I tested the effects of mastery of writing mathematical algorithms on the emergence of complex problem solving using a time-lagged multiple probe design across matched pairs of participants. In Experiment 1, 6 participants enrolled in third grade, ranging in age from 8 to 9 years, were selected because they were unable to write mathematical algorithms despite mathematical proficiency. The dependent variables were pre and post algorithm instruction probes consisting of verbally governing algorithm probes and abstraction to complex problems. Abstraction to complex problems was defined as solving untaught complex problems by applying taught algorithms. Verbally governing responses were defined as a functional algorithm on how to complete the mathematical problem. The independent variable was algorithm instruction which consisted of two teacher antecedent models for less complex problems, using an algorithm to complete the problem, then writing the algorithm, followed by learn units to the participants who served as writers. A peer-yoked contingency was implemented to teach the functionality of writing algorithms by providing an establishing operation for participants. The writer solved a mathematical problem and then wrote the algorithm on how to solve the problem. If, after one attempt, the reader solved the problem correctly, both participants moved up on the game board, however, if the reader was unable to solve the problem correctly, the experimenter moved up a space on the game board. In Experiment 2, the effects of the algorithm procedure were further tested with 4 new participants enrolled in second grade and ranging in age from 7 to 8 years. The differences between Experiment 1 and 2 were the age and grade level of the participants as well as the mathematical content taught. The mathematical content taught in Experiment 1 was fractions and multiplication and addition and fractions in Experiment 2. Results of the study show all participants acquired the capability to abstract more complex mathematical skills and write functional algorithms for mathematical problems solved. Participants' overall mathematical skills increased from skill levels prior to algorithm instruction. After serving as a writer, participants were able to abstract two more complex mathematical problems without receiving additional instruction. |
