The authors propose that conceptual and procedural knowledge develop in an iterative fashion improved problem representation is 1 mechanism underlying the relations between them. Two experiments were conducted with 5th- 6th-grade students learning about decimal fractions. In Experiment 1, children's initial predicted gains knowledge, improvements knowledge. Correct representations mediated relation 2, amount of support for correct was experimentally manipulated, manipulations led to Thus,...

ages understand and what they struggle to learn, examine how instruction influences children's acquisition of both concepts procedures. The purpose the present study was explore relations between conceptual procedural knowledge in children learning principle that two sides an equation represent same quantity. Specifically, investigated about concept mathematical equivalence problem-solving procedures a procedure understanding equivalence. In addressing these issues, we also identified...

Encouraging students to share and compare solution methods is a key component of reform efforts in mathematics, comparison emerging as fundamental learning mechanism. To experimentally evaluate the effects for mathematics learning, authors randomly assigned 70 seventhgrade learn about algebra equation solving by either (a) comparing contrasting alternative or (b) reflecting on same one at time. At posttest, group had made greater gains procedural knowledge flexibility comparable conceptual...

Explaining new ideas to oneself can promote transfer, but how and when such self‐explanation is effective unclear. This study evaluated whether leads lasting improvements in transfer success it more combination with direct instruction or invention. Third‐ through fifth‐grade children (ages 8–11; n =85) learned about mathematical equivalence under one of four conditions varying (a) on versus invention a procedure (b) no explanation. Both helped learn remember correct procedure, promoted...

for equation solving

Comparing multiple examples typically supports learning and transfer in laboratory studies is considered a key feature of high-quality mathematics instruction. This experimental study investigated the importance prior knowledge from comparison. Seventh- 8th-grade students (N = 236) learned to solve equations by comparing different solution methods same problem, problem types solved with method, or studying sequentially, Unlike past studies, many did not begin equation-solving skills,...

We examined whether the overlapping waves model, originally developed to account for strategy choices in arithmetic, could also spelling. The contrast was of particular interest because arithmetic is an algorithmic domain (a that includes strategies always yield correct answers if executed properly), whereas spelling not. Thirty first‐grade students spelled words under 2 conditions, and 23 these were retested second grade. Trial‐by‐trial analysis use used identify which first graders used,...

Competence in many domains rests on children developing conceptual and procedural knowledge, as well flexibility. However, research the developmental relations between these different types of knowledge has yielded unclear results, part because little attention been paid to validity measures or effects prior relations. To overcome problems, we modeled three constructs domain equation solving latent factors tested (a) whether predictive were bidirectional, (b) interrelations moderated by (c)...

Knowledge of mathematical equivalence, the principle that 2 sides an equation represent same value, is a foundational concept in algebra, and this knowledge develops throughout elementary middle school. Using construct-modeling approach, we developed assessment equivalence knowledge. Second through sixth graders (N = 175) completed on occasions, weeks apart. Evidence supported reliability validity along number dimensions, relative difficulty items was consistent with predictions from our...

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak knowledge. An early math trajectories model proposed and evaluated within longitudinal study 517 American ages 4 to 11. This includes broad range topics, as well potential pathways preschool middle grades achievement. In preschool, nonsymbolic quantity, counting, patterning predicted fifth-grade By the end first grade, symbolic mapping, calculation,...

Abstract Young children have an impressive amount of mathematics knowledge, but past psychological research has focused primarily on their number knowledge. Preschoolers also spontaneously engage in a form early algebraic thinking—patterning. In the current study, we assessed 4-year-old children's knowledge repeating patterns two occasions (N = 66). Children could duplicate and extend patterns, some showed deeper understanding by abstracting (i.e., creating same kind pattern using new...

Elementary School, Jones Paideia Magnet and St

Feedback can be a powerful learning tool, but its effects vary widely. Research has suggested that learners’ prior knowledge may moderate the of feedback; however, no causal link been established. In Experiment 1, we randomly assigned elementary schoolchildren (N 108) to condition based on crossing 2 factors: induced strategy (yes vs. no) and immediate, verification feedback (present absent). had positive for children who were not taught correct strategy, negative with strategy. 2, in all...