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…

Understanding a student's problem-solving strategy can have a significant impact on effective math learning using Intelligent Tutoring Systems (ITSs) and Adaptive Instructional Systems (AISs). For instance, the ITS/AIS can better personalize itself to correct specific misconceptions that are indicated by incorrect strategies, specific problems can…

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…

A critical part of supporting the development of students' algorithmic thinking is understanding the challenges that emerge when students engage with algorithmatizing tasks--tasks that require the creation of an algorithm. Knowledge of these challenges can serve as a basis upon which educators can build effective strategies for enhancing students'…

Self-directed learning is a critical competence for living and working in our increasingly complex and unpredictable world. The concept of self-directed learning grew out of the adult learning field and scholars highlight the need to examine how self-directed learning competence can be fostered during childhood. However, there are very few…

This study aims to examine the construction process of the square root concept of secondary school students in Realistic Mathematics Education (RME) based environment. The study was carried out in an 8th-grade classroom with 16 students from a secondary school in a city in the Black Sea Region. The research was designed qualitatively as a case…

Crystalline concept is the main concept used as the reference by students in algebraic verification. This concept divided the way of solving algebraic verification into two types: symbolic and embodied compression. This research aimed to explore the students' mathematical thinking process in solving algebraic verification based on the Crystalline…

Objective: Explicit instructions to students to use the index finger to trace out specified elements of mathematics worked examples have been shown to improve mathematics learning outcomes; however, there is limited research on whether the magnitude of tracing actions impacts these outcomes. Method: Using an experimental design, 34 adults were…

Based on previous research, Computational Thinking (CT) Skills and attitudes can be influenced by gender differences. In addition, attitudes also have a correlation and influence on CT Skills. However, research on CT skills, attitudes, and gender for mathematics subjects and the relationship between CT skills for mathematics and attitudes is still…