In this paper, we will first discuss two current meta-theories dealing with different, aspects of "truth". The first metatheory conceives of truth in terms of coherence (rationality, consistency): a body of knowledge is true when it contains no inconsistencies and has at least some credibility. The second metatheory conceives of truth as…

Wittgenstein explores learning through practice in the "Philosophical Investigations" by means of an extended analogy with games. However, does this concern with learning also necessarily extend to "education," in our institutional understanding of the word? While Wittgenstein's examples of language learning and use are always…

The expansion of technical concepts into everyday business practices suggests a need for effectively teaching difficult subjects to non-technical users. This paper describes hands-on analogy, an innovative method for teaching technically difficult concepts using interactive, experiential learning activities and a gamified exercise. We demonstrate…

Although students experience friction in their everyday life, they have difficulty understanding the scientific concept of friction. To solve this problem, various instructional suggestions have been made by researchers concerning the teaching of friction. In this study, we conducted a survey to investigate science high school students' reasoning…

Studies into the efficacy of teacher development courses for early career academics point to graduates conceiving of their teaching in increasingly complex and student-focussed ways. These studies have used pre- and post-testing of conceptions of teaching to identify this finding. However, these studies do not identify what aspects of these…

Mathematical reasoning is foundational to making sense of mathematics. Yet assessing mathematical reasoning can be challenging for teachers. This paper reports on a project where teachers taught two lessons with a specific focus on reasoning and came together with other teachers at their school to attempt to assess the reasoning of their students.…

This study was conducted to gain understanding about potential influences that learning about quadratic functions has on high school algebra students' action versus process views of linear functions. Pre/post linear functions tests were given to two classrooms of Algebra II students (N=57) immediately before and immediately after they participated…

This paper articulates a stance on the study of students' meaningful mathematics understanding with multiple representations. We integrate Thompson's theory of quantitative reasoning and Dreyfus' theory of multiple representations in our approach to frame and conduct empirical investigations of the study of meaningful understanding of function. We…

Analogical reasoning is a basic learning mechanism. Analogy in teaching science is a very popular pedagogical approach in many countries. The use of analogy is not recognized as one of the formal teaching learning strategies to facilitate students' science learning in Bangladesh. In secondary science teaching, teachers' unconscious and…

The main aim of this research is to examine the effect of an instructional design based on the Algo-Heuristic Theory of Instruction (AHTI) on students' mathematics performance and logical thinking skills in the subject of 7th grade mathematics. The research is grounded in a mixed method. In the quantitative part of the research, a…

Background: As engineering becomes increasingly incorporated into precollege classrooms, it is important to explore students' ability to engage in engineering practices. One of these practices, "engaging in argument from evidence," has been well studied in science education. However, it has not yet been fully explored in engineering…

Teaching meaningful and productive mathematical argument in school requires teachers who are comfortable with diverse forms of mathematical justification. This study examines the written and oral justifications of pre-service middle school teachers (PSTs) in a single classroom, focusing on the types of justifications they use during the patterns…

Quantitative Reasoning for Professionals is a two-semester general education sequence that teaches basic and intermediate algebra through the lens of quantitative reasoning. In this course sequence, we emphasize communication and inference-making while teaching practical algebra skills for students in programs such as business, nursing, and social…

Logic models have garnered acclaim for their usefulness and disdain for the time required to create good ones. We argue that the orderly, analytical nature of logic models is opposed to many Extension programs, and we explain developmental evaluation, an approach that highlights ongoing development, adaptations, and rapid response. We use our…

This article introduces the concept of adaptive intelligence--the intelligence one needs to adapt to current problems and anticipate future problems of real-world environments--and discusses its implications for education. Adaptive intelligence involves not only promoting one's own ability to survive and thrive, but also that of others in one's…