This study builds on two lines of research that have so far developed largely separately: the use of additive methods to solve proportional word problems and the use of proportional methods to solve additive word problems. We investigated the development with age of both kinds of erroneous solution methods. We gave a test containing missing-value…

Previous research (e.g., De Bock, 2002) has shown that--due to the extensive attention paid to proportional reasoning in elementary and secondary mathematics education--many students tend to overrely on proportional methods in diverse domains of mathematics (e.g., geometry, probability). We investigated the development of misapplication of…

The aim of the study was to analyze the development of children's adaptive expertise in computing sums and differences up to 100. We defined the adaptive nature of children's strategy choices on the basis of problem (addition, subtraction), achievement, and strategy performance (accuracy, speed). Sixty-nine 2nd graders of high, above-average, or…

We examined the relation between self-explaining and encoding among kindergartners. For 5 days, children (n = 27) took turns solving addition problems with an adult expert who always used an advanced addition strategy. During the game, children explained the expert's answers (Explain-Expert), explained their own answers (Explain-Novice), or did…

Examines the hypothesis that problem comprehension and computational processes interact during the solving of arithmetic word problems. Results suggest the absence of any interaction between the two processes. Questions the notion that automatized retrieval facilitates problem solving, as well as assertions suggesting that increasing computational…