An Investigation of the Relationships Between Musical Training and Mathematical Problem Solving
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The 2007 Trends in International Mathematics and Science Study (TIMSS) revealed that American sixth and eighth grade students are falling significantly behind students from Singapore, Hong Kong, Chinese Taipei, Japan, England, and the Russian Federation in mathematics (Gonzales, Williams, Jocelyn, Roey, Kastberg, & Brenwald, 2009). Students’ difficulties with mathematics extend into post-secondary education where introductory mathematics courses, such as college algebra, can act as gatekeepers to college success by blocking the academic progress of hundreds of thousands of students each year (Reyes, 2010; Small, 2002). Despite the large body of research suggesting that music can have beneficial effect on spatial reasoning and mathematics performance, schools continue to cut funding for music programs. A correlational research design employing chi-square tests, analyses of variance, and ordinal logistic regressions was used to explore the relationships between music background and the mathematical problems-solving strategies utilized by students enrolled in first-year credit-bearing algebra-based university mathematics courses. Participants’ music background was measured by the researcher-created Music Background Survey while data regarding the utilization of problem-solving strategies were collected through a problem-solving assessment consisting of three mathematical tasks. Spatial and analytic reasoning ability were also measured and used as control variables. Analysis of participants’ music background revealed that over 25% of the participants, “Low Music” participants, had no music instruction through either school music programs or private music instruction and had not participated in any formal instruction in music theory. In contrast, the participants deemed “High Music” reported means of approximately 11 years of private music instruction, approximately 7 semesters of music participation at the middle school level, and approximately 12 semesters of music participation at the high school level. The investigation of the relationship between music training and the utilization of mathematical problem-solving strategies revealed one significant difference in the way “Low Music” and “High Music” participants utilize strategies while engaged in mathematical problem-solving tasks. Results indicated that participants with high levels of music training relied more heavily on the use of the construction of tables and lists as a mechanism for finding patterns than participants with low levels of music training. In general, when comparing problem-solving strategies utilized by participants with high and low levels of analytic reasoning ability and high and low levels of spatial reasoning ability, results were inconclusive. However, when comparing participants with high and low levels of analytic reasoning ability, participants with low analytic reasoning ability reported being more reliant on remembering familiar procedures as a problem-solving strategy than participants with high analytic reasoning ability. The results of the current research provide an initial look at the relationship between musical training and mathematical problem-solving. Further research investigating the relationship between musical training and mathematical problem-solving should include the collection of demographic data and data related to incidental music participation.