算数科の内容を一般化した理解度や数学信念が大学生の公式観に及ぼす影響

Formula belief, defined as “a way of perceiving a formula that includes feelings based on the experience of using the formula,” is a factor examined as affecting learning and performance of mathematics. However, there is room for improvement in the scales assessing formula beliefs. In study 1, the scale is shown to have four factors, adding “usefulness of formulas” to the conventional three factors of “significance of derivation,” “emphasis on memorization,” and “confusion about formulas.” As in previous findings, formula belief is influenced by learning beliefs and it influences learning strategies, which affect performance of mathematics. In study 2, the influence of university students’ essential arithmetic comprehension on their formula beliefs is investigated. Students who performed better on the essential arithmetic comprehension test had less confusion about formulas. In addition, the relationship between value perception of mathematics and formula beliefs is investigated. It is found that the factors of mathematics value perception influenced formula beliefs in various ways.