Children's ability to place fractions on a number line strongly correlates with math achievement. But does the number line play a causal role in fraction learning or does it simply index more advanced fraction knowledge? The number line may be a particularly effective representation for fraction learning because its properties align with the…

When a new student comes to play an educational game, how can we determine what content to give them such that they learn as much as possible? When a frustrated customer calls in to a helpline, how can we determine what to say to best assist them? When an ill patient comes in to the clinic, how do we determine what tests to run and treatments to…

There is an ongoing debate over the psychophysical functions that best fit human data from numerical estimation tasks. To test whether one psychophysical function could account for data across diverse tasks, we examined 40 kindergartners, 38 first graders, 40 second graders and 40 adults' estimates using two fully crossed 2 × 2 designs, crossing…

How do children map number words to the numerical magnitudes they represent? Recent work in adults has shown that two distinct mechanisms--structure mapping and associative mapping--connect number words to nonlinguistic numerical representations (Sullivan, J., 2012). This study investigated the development of number word mappings, and the roles of…

Consciousness remains a mystery--"a phenomenon that people do not know how to think about--yet" (Dennett, D. C., 1991, p. 21). Here, I consider how the connectionist perspective on information processing may help us progress toward the goal of understanding the computational principles through which conscious and unconscious processing…

Nonoverlap is widely used as a statistical summary of data; however, these analyses rarely correct unwanted positive baseline trend. This article presents and validates the graph rotation for overlap and trend (GROT) technique, a hand calculation method for controlling positive baseline trend within an analysis of data nonoverlap. GROT is…

I conduct a study of learning in HMAX-like models, which are hierarchical models of visual processing in biological vision systems. Such models compute a new representation for an image based on the similarity of image sub-parts to a number of specific patterns, called prototypes. Despite being a central piece of the overall model, the issue of…

Gifted children with autism spectrum disorder (ASD) are often referred to as twice-exceptional, the term that highlights the co-occurrence of exceptional challenges and exceptional giftedness. This study performed secondary data analysis on samples of twice-exceptional children from the Pre-Elementary Education Longitudinal Study and the Special…

Moving among levels of abstraction is an important skill in mathematics and computer science, and students show similar difficulties when applying abstraction in each discipline. While computer science educators have examined ways to explicitly teach students how to consciously navigate levels of abstraction, these ideas have not been explored in…

Conventional teacher-led instruction remains dominant in most elementary mathematics classrooms in Taiwan. Under such instruction, the teacher can rarely take care of all students. Many students may then continue to fall behind the standard of mathematics achievement and lose their interest in mathematics; they eventually give up on learning…

The aim of this study is to develop a self-efficacy measuring tool that can predict the computational thinking skill that is seen as one of the 21st century's skills. According to literature review, an item pool was established and expert opinion was consulted for the created item pool. The study group of this study consists of 319 students…

In the last years, a growing trend in different educational contexts focused on Computational Thinking (CT) skills acquisition for both in-service teachers and students. But very low attention has been paid to pre-service teachers' education in regards to CT skills. To solve this issue, an empirical experimentation has been carried out with 141…

Students learning the skills of science benefit from opportunities to move between the scientific problems and questions they confront and the mathematical tools available to answer the questions and solve the problems. Indeed, students learn science best when they are actively engaged in pursuing answers to authentic and relevant questions. We…

This paper presents primary school teachers' perceptions associated with their engagement in a project aimed at building Year 3 and Year 4 students' number fact and computational fluency. Throughout the project, teachers were provided with classroom ideas and suggestions for engaging students in number fact practice and for generating student…

Increasingly, researchers are interested in questions regarding treatment-effect variation across partially or fully latent subgroups defined not by pretreatment characteristics but by postrandomization actions. One promising approach to address such questions is principal stratification. Under this framework, a researcher defines endogenous…