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Wong, Monica – Mathematics Education Research Group of Australasia, 2010
Learning pathways capture the development of competence in a mathematical domain. They have been developed from empirical studies in the areas of mental computation and emergent numeracy concepts. These pathways afford teachers the opportunity to identify students' current levels of understanding, antecedent understandings and the steps that are…
Descriptors: Mental Computation, Grade 3, Mathematics, Identification
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Chesney, Marlene – Australian Primary Mathematics Classroom, 2013
Marlene Chesney describes a piece of research where the participants were asked to complete a calculation, 16 + 8, and then asked to describe how they solved it. The diversity of invented strategies will be of interest to teachers along with the recommendations that are made. So "how do 'you' solve 16 + 8?"
Descriptors: Mathematics Instruction, Mental Computation, Mathematical Logic, Addition
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Hickendorff, Marian; van Putten, Cornelis M.; Verhelst, Norman D.; Heiser, Willem J. – Journal of Educational Psychology, 2010
Individual differences in strategy use (choice and accuracy) were analyzed. A sample of 362 Grade 6 students solved complex division problems under 2 different conditions. In the choice condition students were allowed to use either a mental or a written strategy. In the subsequent no-choice condition, they were required to use a written strategy.…
Descriptors: Individual Differences, Grade 6, Item Response Theory, Computation
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Zhu, Liqi; Gigerenzer, Gerd – Cognition, 2006
Can children reason the Bayesian way? We argue that the answer to this question depends on how numbers are represented, because a representation can do part of the computation. We test, for the first time, whether Bayesian reasoning can be elicited in children by means of natural frequencies. We show that when information was presented to fourth,…
Descriptors: Mental Computation, Probability, Bayesian Statistics, Intermediate Grades
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Keiser, Jane M. – Mathematics Teaching in the Middle School, 2012
An interesting change has been occurring in the author's middle school mathematics classes. Some students have become creative, free-thinking inventors. If they have had little experience with an operation, they invent strategies of their own. Sometimes these strategies have been well informed and supported by strong mental math skills and a good…
Descriptors: Grade 8, Mathematics Skills, Mathematics Instruction, Middle School Students
Novotna, Jarmila, Ed.; Moraova, Hana, Ed.; Kratka, Magdalena, Ed.; Stehlikova, Nad'a, Ed. – International Group for the Psychology of Mathematics Education, 2006
This document contains the second volume of the proceedings of the 30th Annual Conference of the International Group for the Psychology of Mathematics Education. Conference presentations are centered around the theme "Mathematics at the Centre." This volume features 60 research reports by presenters with last names beginning between Abr…
Descriptors: Program Effectiveness, Foreign Countries, Middle Schools, Textbooks
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Brez, Caitlin C.; Miller, Angela D.; Ramirez, Erin M. – Journal of Cognition and Development, 2016
Numerical estimation has been used to study how children mentally represent numbers for many years (e.g., Siegler & Opfer, 2003). However, these studies have always presented children with positive numbers and positive number lines. Children's mental representation of negative numbers has never been addressed. The present study tested children…
Descriptors: Cognitive Processes, Numeracy, Numbers, Grade 2
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Chiras, Andreas – Science Education International, 2008
The study investigated the mental models of primary school children related to the day/night cycle. Semi-structure interviews were conducted with 40 fourth-grade and 40 sixth-grade children. Qualitative and quantitative analysis of the data indicated that the majority of the children were classified as having geocentric models. The results also…
Descriptors: Concept Formation, Models, Interviews, Time Perspective
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Clarke, Doug M.; Roche, Anne – Educational Studies in Mathematics, 2009
As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected to be undertaken mentally. The relative difficulty of the pairs was found to be close to that…
Descriptors: Numbers, Foreign Countries, Grade 6, Teaching Methods
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Robinson, Katherine M.; Arbuthnott, Katherine D.; Rose, Danica; McCarron, Michelle C.; Globa, Carin A.; Phonexay, Sylvia D. – Journal of Experimental Child Psychology, 2006
Age-related changes in children's performance on simple division problems (e.g., 6 divided by 2, 72 divided by 9) were investigated by asking children in Grades 4 through 7 to solve 32 simple division problems. Differences in performance were found across grade, with younger children performing more slowly and less accurately than older children.…
Descriptors: Intermediate Grades, Grade 4, Grade 5, Grade 6
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Witzel, Bradley S.; Allsopp, David – Mathematics Teaching in the Middle School, 2007
Research is only beginning to show the benefits of the effective use of manipulatives with students who have disabilities. This article highlights how teachers can incorporate three manipulative instructional strategies to help students with high-incidence disabilities.
Descriptors: Learning Strategies, Manipulative Materials, Special Education, Mathematics Instruction