Due to growing interest in twenty-first-century skills, and critical thinking as a key element, logical reasoning is gaining increasing attention in mathematics curricula in secondary education. In this study, we report on an analysis of video recordings of student discussions in one class of seven students who were taught with a specially…

This study aims to develop a computer program for the identification key to insect orders (Arthropoda: Hexapoda) and to investigate its effectiveness as teaching material. Secondly, this study is aiming at whether this program improves students' computational thinking skills or not longitudinal quasi-experimental design. Firstly, the study is…

This study aims to investigate the relationship between learning styles and the efficacy of routine and non-routine problem solving. It also compares these relationships with respect to routine and non-routine problem types. The study sample consisted of 356 eighth-grade students in four different schools. In this study, correlational and…

Mathematics teaching and learning goes beyond computations and procedures; it rather includes complex problem-solving and critical thinking. Kilpatrick, Swafford, and Findell (2001) identify five mathematical competencies that are present in mathematics learning: conceptual understanding, procedural fluency, adaptive reasoning, strategic…

Despite the critical role of teachers in the educational process, few advanced learning technologies have been developed to support teacher-instruction or professional development. This lack of support is particularly acute for middle school math teachers, where only 37% felt well prepared to scaffold instruction to address the needs of diverse…

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…