In this report, we present an analysis of two prospective secondary mathematics teachers' generalizing actions in quantitative contexts. Specifically, we draw from a teaching experiment to report how Lydia and Emma engaged in different generalizing processes for the same task. Based on these differences, we found Lydia's generalizing actions…

Ambridge argues that the existence of exemplar models for individual phenomena (words, inflection rules, etc.) suggests the feasibility of a unified, exemplars-everywhere model that eschews abstraction. The argument would be strengthened by a description of such a model. However, none is provided. I show that any attempt to do so would immediately…

In the "Republic," Plato developed an educational program through which he trained young Athenians in desiring truth, without offering them any knowledge-education. This is not because he refused to pass on knowledge but because he considered knowledge of the Good as an ongoing research program. I show this by tracing the steps of the…

A fundamental role of education is to equip students with sound justificatory reasoning capacities to support one's beliefs or actions and to guide rational decisions about complex problems. However, empirical research into justificatory reasoning among students is virtually non-existent and this impedes education research. This study illustrated…

Existing accounts of student thinking about mechanical wave propagation and superposition emphasize that students sometimes treat wave pulses as objects, saying, for example, that pulses bounce off of one another when they meet. In this paper, we present a context in which students explicitly reason about pulses as not-objects, instead describing…

Teachers routinely observe and interpret student behavior to make judgements about whether and how to support their students' learning. Simulated cases can help pre-service teachers to gain this skill of diagnostic reasoning. With 118 pre-service teachers, we tested whether participants rate simulated cases presented in a serial-cue case format as…

Mathematical problems can be divided into two types, namely, process-open and process-constrained problems. Solving these two types of problems may require different cognitive mechanisms. However, there has been only one study that investigated the differences of the cognitive abilities in process-open and process-constrained problem solving, and…

This research explored the interrelationship among Taiwanese high school students' conceptions of learning science (COLS), self-regulated learning science (SRLS), and science learning self-efficacy (SLSE). A total of 309 students participated in the study, and the self-report survey data were collected to measure these three constructs. Four COLS…

The goal of this study was to test nonverbal intelligence and neighborhood social capital as protective factors against future delinquency in early adolescent youth placed at risk by virtue of their involvement in childhood conduct problems. Analyzing longitudinal data from 3,028 youth (1,565 boys, 1,463 girls) in one cohort of the Longitudinal…

Students often show difficulties in understanding rational numbers. Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational number tasks. Although this phenomenon has received a lot of research interest over the last two decades, research on the existence of qualitatively…

This study compares the effects of object-oriented and robot programming activities on programming achievement, abstraction, problem solving, and motivation. In the study, two consecutive experimental cases were conducted to examine the consistency of findings. The research sample comprises 81 tenth-grade students undergoing vocational secondary…

Systems thinking and abstract thinking are important skills for engineers in general and hardware and software engineers in particular. Systems thinking emphasises the interdependence of system components and their synergy. Abstract thinking permits one to focus on the significant details of the current perspective, while temporarily neglecting…

Generalisation is a key feature of learning algebra, requiring all four proficiency strands of the Australian Curriculum: Mathematics (AC:M): Understanding, Fluency, Problem Solving and Reasoning. From a review of the literature, we propose a learning progression for algebraic generalisation consisting of five levels. Our learning progression is…

Classroom communication is increasingly accepted as multimodal, through the orchestrated use of different semiotic modes, resources, and systems. There is growing interest in examining the meaning-making potential of other modes (e.g., gestural, visual, kinesthetic) beyond the semiotic mode of language, in classroom communication and in student…

The purpose of this study is to investigate a mathematically gifted student's self-regulation behaviours while constructing and consolidating mathematical knowledge. However, the objective is to determine which self-regulation strategies influence this student's mathematical abstraction process. The case study method was used in the research. As…