Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side…

Students with Autism Spectrum Disorders (ASD) have unique educational needs. The concrete representational abstract (CRA) instructional sequence has been shown effective in teaching students with mathematical difficulties. The purpose of this study was to examine the effects of the CRA sequence in teaching students with ASD. A multiple baseline…

This study investigated the effects of gender, academic performance and preschool education on mental rotation skills among Turkish prospective teachers. A total of 525 undergraduate students (364 female) from a government university located in western Turkey completed the Mental Rotation Test (MRT). A three-way [2 (gender) × 5 (academic…

Building upon previously developed and more general dual-process models, this paper provides empirical support for a multidimensional thinking style construct comprised of linear thinking and multiple dimensions of nonlinear thinking. A self-report assessment instrument (Linear/Nonlinear Thinking Style Profile; LNTSP) is presented and…

For multinational corporations, the need for efficiency and control has motivated the choice for a corporate language. However, increasing internationalisation has forced corporations to rethink their language policies to cater to the changing demands of the multicultural and multilingual workplace. This paper explores two related issues. First,…

The article presents an account of how action learning principles were implemented to alleviate complex problems in universities. It focuses on the registrars and administrators under the academic Registrar's department. The Marquardt model of action learning was used in combination with the constructivist theories of learning, namely community of…

For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

The high prevalence of anxiety symptoms in individuals with autism spectrum disorders has now been well documented. There is also a positive relationship between autistic traits and anxiety symptoms in unselected samples and individuals with anxiety disorders have more autistic traits compared to those without. Less is known, however, regarding…

I advance a theoretically and empirically-grounded case for designing for and learning from failure, and instantiate it in a learning design called Productive Failure (PF). I describe the key mechanisms and the design principles of PF. The PF learning design comprises a generation and exploration phase followed by a consolidation and knowledge…

The development of expertise in writing is a complex but important achievement for young children as they become literate. Writing is a critical component of literacy development, yet there are few accounts of change over time in early writing development that attend to both changes in writing behaviors, the complexity of written messages, and the…

This study reports teachers' insights and challenges after one year of adopting a curricular material designed to move students through carefully engineered, small steps and encourage learners through success and accessible challenges. The analysis of interviews showed that teachers 'followed' the material in different ways, not necessary in-line…

Students often memorize and apply procedures to solve mathematics problems without understanding why these procedures work. In turn, students demonstrate limited ability to transfer strategies to new problem types. Math curriculum reform standards underscore the importance of procedural flexibility and transfer, emphasizing that students need to…

This paper presents a preliminary study of three six year-old children's use of functional language when engaging collaboratively on a mathematics task. The analysis is presented as an illustration of young children's authority and agency in mathematics as evidenced in their discourse. Modality, as a function of language, was seen to indicate…

While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks…

Do your students think a triangle can be constructed from any three given line segments? Do they believe that a transformation affects only the pre-image--not the whole plane? Do they understand that examples--no matter how many they find--cannot prove a conjecture but one counterexample is sufficient to disprove it? "What tasks can you…