Cognitive Models Underlying Students' Formulation of Simple Linear Equations
Data are presented to show that errors in formulating algebraic equations are not primarily due to syntactic translation, as has been assumed in the literature. Furthermore, it is shown that the reversal error is common even when none of the previously published causes of the error is applicable. A new explanation is required and is proposed in this paper. An examination of students' errors leads us to suggest that students generally construct from the natural language statement a cognitive model of compared unequal quantities. They formulate equations by trying to represent the model directly or by drawing information from it. This hypothesis is supported by research on the comprehension of relationships by linguists, pyscholinguists and psychologists. Data were collected from 281 students in grade 9 in free response format and from 1048 students in grades 8, 9, and 10 who completed a multiple-choice item.
The constant of integration, typically denoted by $C$, is essential in indefinite integrals to account for the vertical shift of the original function.
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Westinghouse 16" 15-Amp 2-in-1 Electric Dethatcher and Scarifier with Collection Bag
Westinghouse 16" 15-Amp 2-in-1 Electric Dethatcher and Scarifier with Collection Bag
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- ONE MACHINE. TWO STEPS. BETTER LAWN: This 2-in-1 dethatcher and slice aerator removes hidden buildup that can smother grass, then cuts narrow soil channels to help air, water, and nutrients reach deeper roots with less disruption than plug-style aerators
- STEP 1 - REMOVE THE HIDDEN BARRIER: Steel dethatching tines lift and collect built-up thatch, dead grass, and organic debris from above the soil, refreshing the lawn surface and clearing the way for healthier growth
- STEP 2 - SLICE YOUR SOIL FOR BETTER ROOT ACCESS: Easily switch to the slice aerator blade, also called a scarifier, to cut narrow channels into dense soil so water, air and nutrients can go deeper into the root zone without the yard mess of plug aerators
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