Much of the education research on implicit differentiation and related rates treats the topic of differentiating equations as an unproblematic application of the chain rule. This paper instead problematizes the legitimacy of this procedure. It develops a conceptual analysis aimed at exploring how a student might come to understand when and why one…

This paper aims to revisit and clarify the term problem context and to develop a theoretical classification of the construct of levels of context use (LCU) to analyse how the context of a problem is used to formulate a problem in mathematical terms and to interpret the answer in relation to the context of a given problem. Two criteria and six…

The purpose of this study was to examine the differences between Finnish and Taiwanese textbooks for grades 7 to 9 on the topic of solving systems of linear equations (simultaneous equations). The specific textbooks examined were TK in Taiwan and FL in Finland. The content analysis method was used to examine (a) the teaching sequence, (b)…

A seminal study by Chi "et al." firmly established the paradigm that novices categorize physics problems by "surface features" (e.g., "incline," "pendulum," "projectile motion," etc.), while experts use "deep structure" (e.g., "energy conservation," "Newton 2," etc.). Yet, efforts to replicate the study frequently fail, since the ability to…

This account of practice explores the concept of resistance in action learning. Resistance is conceptualized as an attempt of self-protection that is manifested in action learners' struggles with their sense of self-efficacy and their social Self. These struggles are an inherent part of the action learning process and may elicit defensive…

In Japan, only a few public libraries provide e-mail reference services. To help public libraries start e-mail reference services, the authors investigated reference questions received by libraries via e-mail and traditional face-to-face services. The authors found that research questions are more frequently observed among e-mail questions and…

A multiple-baseline design across math-fact sets was used to evaluate the effects of a taped-problems intervention on students' performance with addition facts and their inverses in an intact, rural, second-grade classroom. Results suggested that the procedure was effective in improving fluency on math facts as well as their inverses. Across 3…

While it is recognised that prior knowledge is a key factor in determining future learning, its influence on learning to teach is less well known. This study investigates two cohorts of teacher candidates studying for a one-year, graduate qualification for primary teaching, who completed two tasks at entry to their initial teacher education…

A MC (multiple-choice) question can be defined as a question in which students are asked to select one alternative from a given set of alternatives in response to a question stem. The objective of this paper is to analyse if MC questions may be considered as an interesting alternative for assessing knowledge, particularly in the mathematics area,…

The residue number system (RNS) has been an important research field in computer arithmetic for many decades, mainly because of its carry-free nature, which can provide high-performance computing architectures with superior delay specifications. Recently, research on RNS has found new directions that have resulted in the introduction of efficient…

We describe an investigative laboratory module designed to give college undergraduates strong practical and theoretical experience with recombinant DNA methods within 3 weeks. After deducing restriction enzyme maps for two different plasmids, students ligate the plasmids together in the same reaction, transform "E. coli" with this mixture of…

How does early feedback change the programming problem solving in an online environment and help students choose correct approaches? This study was conducted in a sample of students learning programming in an online course entitled Introduction to C++ and OOP (Object Oriented Programming) using the ANGEL learning management system platform. My…

Learning about linear relationship with one unknown, middle school students may often demonstrate a certain degree of proficiency manipulating algebraic symbols. When encouraged, they can verbalize and explain the steps they perform, thereby demonstrating awareness of the procedures with symbols according to fixed rules. It is well known that…

In what unique ways can mathematics tasks contribute to pre-service teachers' understanding of subject matter and pedagogy? And what school mathematics tasks can usefully be included in a pre-service program? To contribute to answering these questions, we report on the selection and choice criteria for mathematics tasks that we use in an…

The "Cognitive Tutor[R] Algebra I" curriculum, published by Carnegie Learning, is an approach that combines algebra textbooks with interactive software. The software is developed around an artificial intelligence model that identifies strengths and weaknesses in each individual student's mastery of mathematical concepts. It then…