In this paper, we present a case study of a secondary mathematics teacher, Isaac (pseudonym), and his considerations for teaching with multiple methods for solving missing-value problems. While his students preferred methods that drew more closely on their intuitive understanding of proportionality, Isaac emphasised the algorithmic…

Structural reasoning is a combined ability to "look for structures, recognize structures, probe into structures, act upon structures, reason in terms of general structures, and see how a piece of knowledge acquired resolves a perturbation experienced" (Harel and Soto, 2017). The purpose of this study was to explore the cognitive…

Due to increased need of professionals on the future labour market with competence in programming, many countries have integrated programming in kindergarten to grade 12 (K-12) education. In 2017, programming was integrated in Swedish primary and secondary school curriculum and the courses of Mathematics and Technology. Research has highlighted…

COVID-19 contributed to the largest student performance decline in mathematics since 1990. The nation needs cost-effective mathematic interventions to address this drop and improve students' mathematics performance. This study presents a cost-effectiveness analysis (CEA) of three algebraic technological applications, across four conditions: From…

COVID-19 contributed to the largest student performance decline in mathematics since 1990. The nation needs cost-effective mathematic interventions to address this drop and improve students' mathematics performance. This study presents a cost-effectiveness analysis (CEA) of three algebraic technological applications, across four conditions:…

This study examined if and how thinking time, defined as the time from the start of the problem to the students' first action to solve, influences their problem-solving efficiency, defined as the number of steps taken to solve the problem, using Graspable Math, a web-based mathematical tool. We found that: (1) students who took longer to think…

In the present study, we were interested in the appraisal by teachers who have had experience with an individual form of differentiation of the efficiency of grouping learners into homogenous or heterogeneous groups. In the study, seven aspects were thus considered: (1) the learning performance and motivation of learners, (2) the learners'…

This study compared the effectiveness and efficiency of an error-correction procedure, response repetition, to a prompting procedure, simultaneous prompting, on the acquisition and maintenance of multiplication facts for three typically developing 3rd grade students. This study employed an adapted alternating treatments design nested in a multiple…

Prior research found that without the naming cusp, children did not learn from instructional demonstrations presented before learn units (IDLUs) (i.e., modeling an expected response twice for a learner prior to delivering an instructional antecedent), however, following the establishment of naming, they could. The present study was designed to…

When teachers do not know the history of science well, when they misunderstand and underestimate its educational importance, it becomes a serious obstacle for the improvement of their methodological skills. This paper has a goal to describe author's method how to teach the history of mathematics. This method is aimed at training math teacher's…

We recently developed the "Framework of Achievement Bests" to explain the importance of effective functioning, personal growth, and enrichment of well-being experiences. This framework postulates a concept known as "optimal achievement best," which stipulates the idea that individuals may, in general, strive to achieve personal…

Even in primary school, mathematics achievement depends upon the efficiency of cognitive, metacognitive and self-regulatory processes. Thus, for pupils to carry out a computation, such as a written calculation, metacognitive mechanisms play a crucial role, since children must employ self-regulation to assess the precision of their own thinking and…

Background: This study investigated learning outcomes and user perceptions from interactions with a hybrid intelligent tutoring system created by combining the AutoTutor conversational tutoring system with the Assessment and Learning in Knowledge Spaces (ALEKS) adaptive learning system for mathematics. This hybrid intelligent tutoring system (ITS)…

The effect of simulation-based probability teaching on the prospective teachers' inference skills has been examined with this research. In line with this purpose, it has been aimed to examine the design, implementation and efficiency of a learning environment for experimental probability. Activities were built on modeling, simulation and the…

Despite extensive scholarship about the importance of teaching mathematics with multiple strategies in the elementary grades, there has been relatively little discussion of this practice in the middle and high school levels or in the context of introductory algebra. This article begins our exploration of this practice by addressing the following…