This dissertation targets young students' developing knowledge relevant to a fundamental practice in academic mathematics: the use of diagrams to represent idealized mathematical objects whose properties are established by definition (as in the use of drawn dots to represent zero-dimensional points and drawn lines to represent one-dimensional…

As science teachers, we often show animations and videos in class but there is the potential for students to create their own animations to represent science concepts and thus make their conceptions visible for critique and refinement. This encourages students to be active in their own learning, creating animations rather than just viewing them.…

The last two years of primary school in Trinidad and Tobago are marked by preparation for national standardized tests. The focus on preparing for these tests impacts teaching and learning strategies, as there is a shift to teacher centered classrooms and teaching strategies that depend on rote learning and memorization. This study explored how…

Proficiency in mathematics across the United States has become an area of concern as performance on state accountability tests continues to demonstrate that less than 50% of students in 4th and 8th grade are proficient in mathematics (NCES, 2013). With such large numbers of students lacking proficiency in mathematics, systematic interventions that…

In Finland, schools' effectiveness in fostering the development of transversal skills is evaluated through large-scale learning to learn (LTL) assessments. This article presents how LTL skills--general cognitive competences and learning-related motivational beliefs--develop during primary school and how they predict pupils' CPS skills at the end…

Children sometimes solve problems incorrectly because they fail to represent key features of the problems. One potential source of improvements in children's problem representations is learning new problem-solving strategies. Ninety-one 3rd- and 4th-grade students solved mathematical equivalence problems (e.g., 3+4+6=3+__) and completed a…

Previous studies have found that children have difficulty solving proportional reasoning problems involving discrete units until 10 to 12 years of age, but can solve parallel problems involving continuous quantities by 6 years of age. The present studies examine where children go wrong in processing proportions that involve discrete quantities. A…

Teachers know their students must struggle and grapple with authentic tasks in order to grow stronger. Classroom teachers of the gifted know that their students cannot advance cognitively without facing relevant and challenging material that demands higher level thinking and reasoning. Therefore, the teacher of gifted mathematics students must…

What kind of developmental potential is present in elementary schoolchildren but hindered by the traditional type of education? Half a century ago Daniel El'konin and Vasili Davydov, the leaders of Russian Vygotskian educational psychology started answering this question. They suggested that reflection is a basic human ability and it can be…

This publication contains an updated academic standards of Arizona public schools for grade 5. The contents of this document include the following: (1) The Arts Standard 2006--Grade 5; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Foundations (Grades…

This publication contains an updated academic standards of Arizona public schools for grade 6. The contents of this document include the following: (1) The Arts Standard 2006--Grade 6; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Essentials (Grades…

This publication contains the updated academic standards of Arizona for Grade 8. The contents of this document include the following: (1) The Arts Standard 2006--Grade 8; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Essentials (Grades 4-8); (4) Reading…

This document contains the Arizona academic standards for Grade 7. The following 11 standards are reviewed: (1) The Arts Standard 2006 --Grade 7; (2) Comprehensive Health Education/Physical Activity Standards 1997--Essentials (Grades 4-8); (3) Foreign and Native Language Standards 1997--Essentials (Grades 4-8); (4) Reading Standard Articulated by…