With the increasing attention and surge of empirical research in providing academic instruction for students with autism spectrum disorder (ASD) comes the need to provide teachers with research-supported strategies. Using one evidence-based strategy for teaching mathematics to students with high incidence disabilities, and another for teaching…

The mathematical proficiencies in the "Australian Curriculum: Mathematics" of understanding, problem solving, reasoning, and fluency are intended to be entwined actions that work together to build generalised understandings of mathematical concepts. A content analysis identifying the incidence of key proficiency terms (KPTs) embedded in…

There are relatively few studies in Australia and South-East Asian region that combine investigating models of math growth trajectories with predictors such as reasoning ability and reading comprehension skills. Math achievement is one of the major components of overall academic achievement and it is important to determine what factors (especially…

In earlier research the writer was constrained by the variables which were continuously appearing in both experimental class teaching experiences and various psychological experiments to distinguish four levels of cognitive sophistication in so far as mathematical material was concerned between the ages of 7 years and 17 years. In current research…

Discusses the spatial aspects of Greeno's model of conceptual domains and applies the theory to geometry learning. Examines the relationship between mathematical and spatial thinking in light of Greeno's environmental/spatial view of learning. (Contains 16 references.) (MDH)

Piaget has hypothesized that concrete and formal operations can be described by specific logical models. The present study focused on assessing various aspects of four concrete operational groupings and two variations of two formal operational characteristics. Six hundred twenty-two 9-14 year old students participating in the Human Sciences…

About 25 children in each of grades 3, 5, 7, 9, and 11 were tested in their ability to solve linear syllogisms, such as: John is taller than Mary. Mary is taller than Pete. Who is tallest--John, Mary, or Pete? Response latencies and error rates decreased across grade levels and sessions. Component latencies also generally decreased with increasing…

Many writers have suggested that comprehension occurs at several levels (e.g., literal, inference, and conclusion). However, many teachers spend as much as two-thirds of their time on lower-level skills such as phonics and literal-level comprehension skills. Some authors have suggested ways of assisting readers in achieving comprehension at more…

This paper presents a cross-sectional investigation of adolescents' and young adults' reflective epistemological development. Three groups of 8 subjects (4 male and female) ages 10, 14, and 18 were given Piagetian tasks, the Kohlberg moral judgment questionnaire, and an epistemology interview covering such concepts as knowledge, thought, feeling,…

Examples of high school case studies are used to illustrate prototypical mathematical images and the use of imagery in metaphoric and metonymic ways in mathematics. Discusses pattern imagery and other types of imagery as central components in a model of mathematical reasoning. (34 references) (MDH)

Focusing on the role of language in learning, this paper discusses schemata and symbolic thinking that help students learn from unfamiliar experiences. The first part of the paper introduces the idea of symbolic thinking by comparing students encountering new ideas with convention-goers making their way around a new city. The section suggests that…

Cognitive science research offers hope for the development of innovative science teaching strategies that facilitate the development of optimally interconnected procedural and declarative knowledge networks. Improving students' neural networks should improve their abilities to think critically, reason logically, learn more efficiently, and solve…

Theory and research regarding four levels of concept attainment and three uses of concepts as specified by the conceptual learning and development (CLD) model are described. Assessment batteries were developed to assess each child's level of concept attainment and also the related use of the concepts equilateral triangle, cutting tool, and noun.…

Compared formal reasoning responses of seventh-and eighth-grade students on three tests of formal reasoning. The three tests differ only in the mode of equipment presentation on identical test items and problems. Tests included three-dimension demonstration (Lawson), two-dimension showing drawings of materials used in three-dimensional test, and…