The ability of analysing and designing an algorithm is quite essential for computer science education. The students in the Analysis and Design of Algorithms (ADA) course are expected to be able to solve problems by choosing one of the proper design methods and to analyse the algorithm's performance in terms of various aspects. Instead of using…

Mathematical models that are constructed through modeling activities should be appropriate for the situation at hand. In this study, we seek to monitor the modeling routes of different learners as well as their modeling sub-competencies in order to learn how these are related to the semiotic characteristics of the resulting mathematical models.…

Studies on the productive failure (PF) approach have demonstrated that attempting to solve a problem prepares students more effectively for later instruction compared to observing failed problem-solving attempts prior to instruction. However, the examples of failure used in these studies did not display the problem-solving-and-failing…

A well known physics problem is to calculate the friction forces required to support a ladder against a wall. A more tractable problem is to calculate the friction forces needed to support an inclined beam on a ball or a cylinder. In the latter case there are three rather than two points of sliding support. Measurements and calculations are…

Recently, Lima lamented on the 'time-consuming and tiresome' pedagogical nature of repeated integration by parts, throwing down the challenge of providing a pencil-and-paper solution to a related problem in a few seconds. Lima put forth a simple formula as an alternative. In this work, I offer a response to Lima's challenge and his formula.…

In collaborative problem solving, children produce and evaluate arguments for proposals. We investigated whether 3- and 5-year-olds (N = 192) can produce and evaluate arguments against those arguments (i.e., counter-arguments). In Study 1, each child within a peer dyad was privately given a reason to prefer one over another solution to a task. One…

Promoting mathematical creativity is an important aim of mathematics education, which may be promoted by engaging students with open-ended tasks. Most studies of students' creativity have investigated the creativity of students working individually. This study concerns the mathematical creativity of students working as individuals as compared with…

Recently, Christopher C. Tisdell questions some claims and results that appear in our article [Rivera-Figueroa A, Rivera-Rebolledo JM. A new method to solve the second-order linear difference equations with constant coefficients. Int J Math Educ Sci Technol. 2016;47(4):636-649.] regarding the novelty and simplicity of a method to solve…

Many theories and models describe the various cognitive processes individuals engage in as they solve ill-structured problems. While diverse in perspectives, these theories and models uniformly agree that essential aspects of complex problem solving include iteration and inquiry. This paper further argues that an important yet overlooked component…

As part of its project on instructional leaders at the middle tier, International Institute for Educational Planning (IIEP) and Education Development Trust (EDT) conducted case studies in five jurisdictions, exploring the professional practices and perceived impacts of instructional leaders and the enabling factors present in the systems in which…

Technology-based, open-ended learning environments (OELEs) can capture detailed information of students' interactions as they work through a task or solve a problem embedded in the environment. This information, in the form of log data, has the potential to provide important insights about the practices adopted by students for scientific inquiry…

We investigated whether three interventions -- studying incorrect worked examples, studying correct worked examples, or receiving feedback -- improved children's 0-1,000 (Experiment 1) and adults' 1 thousand--1 billion (Experiment 2) number-line estimation precision relative to a no intervention control group. At pretest, participants estimated…

This cross-national study examined students' evaluation of strategies for solving linear equations, as well as the extent to which their evaluation criteria were related to their use of strategies and/or aligned with experts' views about which strategy is the best. A total of 792 middle school and high school students from Sweden, Finland, and…

Problem-solving is a skill of fundamental importance for populations with developmental delays, and especially for students with Autism Spectrum Disorder (ASD). Training students with ASD to solve ill-defined problems is a challenging objective for educational and therapeutic teams. This is due to the myriad of unpredictable situations presented…

In the Hungarian "Guided Discovery" approach to teaching mathematics, teachers' planning work plays a crucial role. Teachers following the approach develop teaching trajectories based on "series of problems". This work includes the choice, creation, transformation, organization and networking of problems with regard to various…