Sudoku is a puzzle that has a unique solution. No matter how many methods are used, the result will always be the same. The player thought that the number of givens or clues, the initial value on the Sudoku puzzles, would significantly determine the difficulty level, which is not necessarily correct. This research uses two search algorithms,…

In contrast to normative ethics, which emphasizes determining whether a person or action is good or bad and developing codes to govern individual behaviors, applied ethics focuses on the application of ethics to real-world problems and contexts of practice (Ethics Unwrapped, n.d.). In design-oriented disciplines such as instructional design and…

We adapt the Lanchester combat model to represent conflict between vampires and humans. It is assumed that vampires attack humans during the hours of darkness whilst humans attack vampires during the hours of light. The right-hand side of the differential equation model therefore depends upon the hour of the day. A key insight is that to answer…

This paper contains an analysis of some early thinking of 94 young children aged 5 years 7 months to 6 years 5 months. These children were interviewed as part of a larger study of the multiplicative thinking of children who were midway through their first year of school in Australia. They had not been formally taught multiplication or division at…

A very common Applied Optimization Problem in Calculus deals with minimizing a distance given certain constraints, using Calculus, the general method for solving these problems is to find a function formula for the distance that we need to minimize, take the derivative of the distance function, set it equal to zero, and solve for the input value,…

Understandability and completeness are essential in modern collaborative digital platforms and their learning systems. These platforms have shaken up the traditional education setting, particularly in leveraging the coauthoring approach in problem-solving and streamlining the learning behavior of cowriting or corevising. Such a learning context…

Public education in the United States is breaking down on two dimensions: its bureaucratic organization and its conceptualization of the learning process. These breakdowns result from attempts to deliver public education using business models and have failed to support the needs of both students and teachers. This breakdown has been further…

Previous research has shown the importance of conducting early interventions in mathematics in disadvantaged children. Solving arithmetical word problems is a field in which children particularly fail. In this study, preschoolers from disadvantaged French public schools (n = 101; M[subscript age] = 5-6) were taught strategies for using fingers to…

Students, even as young as kindergarten, are natural problem solvers (Carpenter et al., 2017). Even before they learn to count, they can make sense of mathematical problems and real- world situations (National Council of Teachers of Mathematics, 2022). Kindergartners can make sense of complex story problems, including Separate Start Unknown…

In his work leading professional development, Peter Klosterman found that teachers specifically asked for help teaching optimisation more effectively. To address challenges students often experience solving optimisation problems, he explains useful pedagogical strategies to support the teaching of optimisation and student learning in this topic.

Self-explanation prompts in example-based learning are usually directed backwards: Learners are required to self-explain problem-solving steps just presented ("retrospective" prompts). However, it might also help to self-explain upcoming steps ("anticipatory" prompts). The effects of the prompt type may differ for learners with…

This study reports a secondary analysis from a randomized control trial study conducted with third graders with mathematics difficulty (MD; N = 75). We used simple linear regression to investigate whether students' performance on a word-problem vocabulary assessment predicted their performance on a measure of word-problem solving. Additionally, we…

The purpose of this study is to provide reliable evidence of the observable correlates of the Aha! moment and what this means for moving from surface to deep thinking. The study analyses facial expressions and body language from video recordings of students solving problems, followed by interviews, focus groups, and surveys. The problem-solving…

To fully execute multitiered systems of support (MTSS), schools must have access to screening and progress monitoring measures that are defensible and appropriate for intended use yet also must be usable within the intended context. Usability is the extent to which a measure, process, or system is acceptable and can be feasibly used by…

Mathematical problem-posing and modeling are essential skills in developing students' analytical thinking and problem-solving abilities. This study aims to examine correlation between 9th-grade students' problem-posing and mathematical modeling skills within the learning domain of numbers and algebra. Additionally, it evaluates students'…