國小學生數學文字題知識結構之評量

The Measure of Elementary School Students' Knowledge Structure of Mathematical Word Problems

解題者對數學文字題所產生的問題表徵品質，會影響解題的成功與，而解題者所具有的數學知識結構，是影響問題表徵品質優劣的重要因素。因此，本研究旨在評量216位國小六年級學生的數學文字題知識結構，並探討其與數學解題表現的關係。研究結果發現：（一）不同數學能力學生在數學文字題知識結構測驗的三項數值（PRX數值、GTD數值、PFC數值），達顯著的差異。高數學能力與中數學能力學生的三項數值，皆顯著高於低數學能力學生的三項數值。（二）國小六年級學生在數學文字題知識結構測驗上的PRX數值、GTD數值和PFC數值，皆與數學解題表現有顯著的相關。（三）排除GTD和PFC兩個知識結數值的影響力後，國小六年級學生的PRX數值與數學解題表現的淨相關為.340，達顯著相關的水準（p < 0.1）。

The problem solvers’ problem of representation of mathematical word problems has great influence on the causes of mathematical problem solving. Thus， the mathematical knowledge structure problem solving. Thus， the mathematical knowledge structure problem solver is an important factor to influence problem representation quality.The purpose of the research is to evaluate 216 elementary school students of the sixth grade and to understand their knowledge structure of mathematical word problems and the relationship with the presentation of mathematical problem solving. The findings of the research are below：（1）The students with different mathematical abilities have significant differences on knowledge structure problems tests. High and middle mathematical ability students’ PRX， GTD and PFC values are significantly higher than low mathematical ability students’.（2）The students’ PRX， GTD and PFC values on the test of mathematical word problem knowledge structure showed significant correlation with mathematical problem solving.（3）To exclude the influence of GTD and PFC， the students’ partial correlation between PRX and mathematical problem solving is .340， and it has a significant correlated level.（p ＜ 0.1）