Purpose: Research shows that postsecondary students are largely unaware of the impact of algorithms on their everyday lives. Also, most noncomputer science students are not being taught about algorithms as part of the regular curriculum. This exploratory, qualitative study aims to explore subject-matter experts' insights and perceptions of the…

In this note we demonstrate two instances where matrix multiplication can be easily verified. In the first setting, the matrix product appears as matrix element concatenation, and in the second, the product coincides with matrix addition. General proofs for some results are provided with a more complete description for 2×2 matrices. Suggested for…

Computational thinking (CT) is becoming increasingly important as a learning content. Subject-integrated approaches aim to develop CT within other subjects like mathematics. The question is how exactly CT can be integrated and learned in mathematics classrooms. In a case study involving 12 sixth-grade learners, CT activities were explored that…

The training of non-specialists, particularly engineers, in mathematics requires designing specific didactic proposals that make the importance of mathematics evident. One approach to creating such proposals consists in analyzing the mathematics used in authentic contexts of engineering research and then effectuating a didactic transposition to…

The aim of this paper is to present a teaching proposal for the theoretical part relating to the first- and second-order linear difference equations with constant coefficients suitable for the first-year students at various types of universities. In contradistinction to the methods often applied (memorization of algorithms without a proper…

Every educator knows the sinking feeling of a lesson gone wrong. As teachers look around the room and realize that many of their students are just not getting it, they often feel like failures. However, the struggle students experience as they persevere through high-quality challenging tasks is not a sign of failure, but rather a key aspect of…

Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific…

The authors have found that having students learn accessible standard algorithms by explaining them using mathematics drawings increases students' sense of place--value numbers and enables students to articulate their understanding of what is actually happening with the numbers and why. In this article, they will discuss three standard algorithms…

This study sought to compare the effectiveness of teaching with manipulatives versus algorithms and procedures. Assessment data were collected before instruction, after instruction with algorithms and procedures, and after instruction with modeling and manipulatives. Data were collected from 113 students from the 5th, 6th, and 7th grades within…

The importance of computational thinking (CT) as a 21st-century skill for future generations has been a key consideration in the reforms of many national and regional educational systems. Much attention has been paid to integrating CT into the traditional subject classrooms. This paper describes a scoping review of learning tools for integrating…

Adaptive tutoring systems often model student knowledge in ways that break away from a "one size fits all" approach to learning. Nonetheless, the strengths of these systems can often be limited, as knowledge representations are not easily interpreted by teachers, which make these systems difficult to integrate into pedagogical practices.…

This paper demonstrated how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. Using a data-driven approach, we examined 1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance (i.e. posttest math knowledge scores) prediction and 2)…

This paper demonstrated how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. Using a data-driven approach, we examined: (1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance (i.e. posttest math knowledge scores) prediction; and…

In our investigation of university students' knowledge about real numbers in relation to computer algebra systems (CAS) and how it could be developed in view of their future activity as teachers, we used a computer algorithm as a case to explore the relationship between CAS and the knowledge of real numbers as decimal representations. Our work was…

This paper demonstrates how to apply Machine Learning (ML) techniques to analyze student interaction data collected in an online mathematics game. We examined: (1) how different ML algorithms influenced the precision of middle-school students' (N = 359) performance prediction; and (2) what types of in-game features were associated with student…