GeoGebra is a dynamic software that is frequently used and of increasing importance in mathematics teaching processes in our digital age. Accordingly, in this study a new perspective has been brought to the proofs of the "two square difference identity" expressed for the square, which is a flat polygon, made with different approaches.…

It's often useful extending students beyond the limiting geometry of triangles and quadrilaterals to regularly consider generalizations of results for triangles and quadrilaterals to higher order polygons. A brief heuristic description is given here of the author applying this strategy, and which led to an interesting result related to the…

This paper describes a study that used a novel method to investigate conceptual difficulties with mathematical induction among two groups of undergraduate students: students who had received university-level instruction in formal mathematical induction, and students who had not been exposed to formal mathematical induction at the university level.…

A multiple probe across participants design was used to examine the effects of intervention on reality-based fictional narratives. Four boys with autism spectrum disorder (ASD) and language disorder, aged 9-10, participated in a 1:1 intervention targeting the narrative macrostructure elements of character, setting, problem, feelings, and fix.…

We perform dynamic investigation of two surprising geometrical properties, each of which involves additional properties. In the first task the property belongs to two regular polygons with the same number of sides and with one common vertex. It is found that all the straight lines that connect corresponding vertices of the two polygons intersect…

Using a multiple probe design across peer buddy-target child dyads, we evaluated the effects of an intervention package (i.e., brief training, system of least prompts, visual supports) on peer buddies' use of stay-play-talk (SPT) with their classmates who were socially isolated (target children). All six peer buddies increased their use of SPT…

This document introduces, describes and exemplifies the technical features of some recently implemented automated reasoning tools in the dynamic mathematics software GeoGebra. The new tools are based on symbolic computation algorithms, allowing the automatic and rigorous proving and discovery of theorems on constructed geometric figures. Some…

In the most general sense, mathematical thinking can be defined as using mathematical techniques, concepts, and methods, directly or indirectly, in the problem-solving process. In this study, efforts were made to include the Graph Theory of mathematics, which is found abundantly in physics, chemistry, computer networks, economics, administrative…

Across many years of teaching Research Methods and assessing many applications for admission into higher degree studies which require an understanding of theories, principles, strategies and skills needed to complete a higher degree such as a Masters or a PhD, one of the things I have found problematic for many students is the inability to…

Generalization and proof are a foundation of mathematical practice and as such should be integral to K-12 mathematics instruction. However, if generalizing and proving are to become popular within K-12 mathematics classrooms, we must consider how to effectively enlist pre-service teachers (PSTs) into supporting these activities in their…

Deficits in social communication and interaction have been identified as distinguishing impairments for individuals with an autism spectrum disorder (ASD). As a pivotal skill, the successful development of social communication and interaction in individuals with ASD is a lifelong objective. Point-of-view video modeling (VM) has the potential to…

Researchers have previously shown that video prompting can promote vocational skill acquisition for students with autism, and in a prior study, we demonstrated a model to train a paraprofessional to implement this practice. In this study, we evaluated (a) the degree to which the paraprofessional generalized implementation to new students and…

The researchers in this study used a multiple baseline design across dyads to examine the effects of professional development with coaching to train general education teachers to use a simultaneous prompting procedure when teaching academic core content to students with autism and the effects of the procedure on the students' outcomes. Three…

In this study, we revised the "Metacognitive Awareness of Reading Strategies Inventory" (MARSI), a self-report instrument designed to assess students' awareness of reading strategies when reading school-related materials. We collected evidence of structural, generalizability, and external aspects of validity for the revised inventory…

The authors of this study evaluated the acquisition of instructive feedback information presented to four kindergarten children with mild delays taught in dyads using a constant time delay (CTD) procedure. They also assessed the learning of observational (dyadic partner) information within this instructional arrangement. A multiple probe design…