Determining evidence-based practices helps guide educators on how to teach. In this study, researchers replicated, updated, and extended the review of the literature on mathematics interventions for students with MID by Hord and Bouck (2012). The researchers determined the current state of the literature on academic mathematics interventions for…

This paper discusses the mathematical and didactical problems of teaching indefinite integral in the context of the ubiquitous availability of online integral calculators. The symbol of indefinite integral introduced by Leibniz, unfortunately, does not contain an indication of the interval on which the antiderivatives should be calculated. This…

What comes to mind when one thinks about building? One may envision constructions with blocks or engineering activities. Yet, constructing and building a number system requires the same sort of imagination, creativity, and perseverance as building a block city or engaging in engineering design. We know that children invent their own notation for…

Various features have been found hidden in the Pascal triangle. In this paper, some very well-known properties of the Pascal triangle will be presented, as well as the properties related to different extensions of the triangle, namely the Pascal pyramid. Given that in the textbooks of the tenth grade, respectively in the school, where we realised…

The interactions young children have with adults are of vital importance in developing mathematical reasoning. This paper describes the behaviours of teachers who work with young children in school yet manage to have individual and natural mathematical conversations with children. These mathematical interactions young children have with their…

This study investigated two undergraduate mathematics students' meanings for derivatives of univariable and multivariable functions when creating linear approximations. Both participants completed multivariable calculus at least two semesters prior to participating in a sequence of four to five exploratory teaching interviews. One purpose of the…

Humans have the remarkable ability to solve different tasks by simply reading textual instructions that define the tasks and looking at a few examples. Natural Language Processing (NLP) models built with the conventional machine learning paradigm, however, often struggle to generalize across tasks (e.g., a question-answering system cannot solve…

Learning transfer has been studied for over a century, though studies are primarily through the lens of the researcher or an expert. The purpose of this project was to better understand the student perspective in transfer by examining how they approached transfer tasks and how these approaches related to classroom instruction. The Actor-Oriented…

Optimization is introduced to teaching in secondary school, focussing on functions of one variable with the first derivative criterion for critical points and monotonicity of functions. The second derivative criterion is also used to determine the nature of the critical points. Similarly, in university-level teaching, algebraic work using criteria…

In this article, the authors focus on five instructional approaches with a strong evidence base for the teaching and learning of math: (a) plan, model, and practice: systematic and explicit instruction; (b) focus on the language of math; (c) use multiple representations, including number lines; (d) build fluency; and (e) provide word problem…

This study used a qualitative, holistic case study to explore obstacles tutors faced when implementing high cognitive demand (HCD) tasks and the possibility of using embedded educative curricular supports to overcome them. Much prior research has explored using educative supports in classrooms with teachers (Davis et al., 2017), but more research…

Our work investigated how six primary school students used a non-traditional method for adding and subtracting: the ABN method, a Spanish acronym for Open (method) Based on Numbers. Commognitive theory [Sfard, A. 2008. "Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing." New York: Cambridge…

Background/purpose: This study aimed to investigate the differences among the equations used in estimating the reliability coefficient using the half-split method. These equations demonstrate Spearman-Brown's, Rulon's, Guttman's, Mosier's, Flanagan's, and Horst's. Materials/methods: The study instrument was a 43-item scale for evaluating the…

This study explored teachers' self-efficacy in teaching mathematics (SETM) as related to their teaching profile and pedagogical practices. Using data from 327 New Zealand primary teachers, a multilevel structural equation model was constructed and analyzed that looked at the relationships among SETM and effective pedagogical practice scales and…

This paper investigates how mathematics teachers describe their ethical decision making related to instructional practices, drawing on frameworks that incorporate both rational and non-rational approaches. We employed a multiple-case study method, selecting three teachers as cases through criterion sampling. Data were collected via four…