Elucidating the Effects of Diagram Use Training for Math Word Problem Solving
Hiroaki Ayabe, Emmanuel Manalo and Noriko Hanaki
Abstract.
In solving math word problems, diagram use is generally considered effective. However, although teachers often demonstrate diagram use, students do not use them spontaneously, and when they do, they tend to use them ineffectively. The prevalence of student difficulties in problem solving can at least in part be attributed to these problems. Recently, we demonstrated that both knowledge about diagram use and practice are necessary to promote spontaneous use, and result in improvements in correct answer rates [4]. However, the components of instruction necessary for diagram use mastery, and the corresponding physiological consequences (brain activity) remain unclear. Thus, we clarified these issues in the present study. Sixteen participants (aged 15.7 ± 2.9 years) were given math word problems for which the use of tables was deemed effective for generating a solution. Data collection was in three phases: No- Instruction-or-Training, Asked-to-Use-a-Table, and After-Table-Use-Training. We measured their math word problem solving performance, and frontal brain/cerebral blood flow using fNIRS (Functional near-infrared spectroscopy). Only after the Table-Use-Training did participants show improvements in correct answer rates (pre- and post-training comparison, t (15) = 2.54, p= .022), corresponding with an increase in table use (t (15) = 7.93, p < .001). Furthermore, following training, participants showed blood flow increase in the left frontal area of the brain (dorsolateral- and ventrolateral-prefrontal cortex) while solving the problems. These results indicate that simply asking students to use diagrams is not adequate: appropriate training is necessary for effective use. They also provide evidence for physiological/brain consequences of successful learning/skills acquisition.