This study aims at elaborating a well-established theoretical framework that distinguishes three modes of thinking in linear algebra: the analytic-arithmetic, the synthetic-geometric, and the analytic-structural mode. It describes and analyzes the bundle of signs produced by an engineering student during an interview, where she was asked to recall…

This paper reports from a case study which explores kindergarten children's mathematical abstraction in a teaching--learning activity about reflection symmetry. From a dialectical perspective, abstraction is here conceived as a process, as a genuine part of human activity, where the learner establishes "a point of view from which the concrete…

Teachers routinely observe and interpret student behavior to make judgements about whether and how to support their students' learning. Simulated cases can help pre-service teachers to gain this skill of diagnostic reasoning. With 118 pre-service teachers, we tested whether participants rate simulated cases presented in a serial-cue case format as…

Students often show difficulties in understanding rational numbers. Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational number tasks. Although this phenomenon has received a lot of research interest over the last two decades, research on the existence of qualitatively…

The purpose of this study is to investigate a mathematically gifted student's self-regulation behaviours while constructing and consolidating mathematical knowledge. However, the objective is to determine which self-regulation strategies influence this student's mathematical abstraction process. The case study method was used in the research. As…

There is growing interest in implementing reform-based lab courses in undergraduate physics that are student driven rather than instructor driven. In these courses, students develop and carry out experiments while simultaneously reasoning about their hypotheses, data collection procedures, collected evidence, and the relevant physics content.…

Educational systems worldwide underscore the importance of developing higher-order thinking skills (HOTS) to prepare students for the new challenges of the XXI century. Some pressing issues faced by educators include the ambiguity of the construct; the implementation of HOTS in classroom practices; and the implications for teaching students from…

The use of scientific modeling has been shown to be highly effective in the learning of science content in multiple disciplines for non-English Learners (EL). However, the benefits of using this pedagogy with ELs have not been heavily explored. This article discusses the use of modeling-based evolution and population ecology pedagogical units in a…

This case study demonstrates the ability of high school chemistry students, with varying levels of math preparation, to experience learning-gains on state and district assessments as it relates to chemical reactions, thermodynamics, and kinetics. These advances were predicated on the use of a teaching style rooted in abstract reasoning. The…

Recent research shows that teachers' level of Mathematical Knowledge for Teaching (MKT) and their beliefs about teaching and learning effect teaching practices and student achievement. Higher levels of MKT typically lead to more effective teaching abilities in terms of helping students make meaning of mathematical concepts, but beliefs seem to be…

The RBC+C abstraction model is an effective model in mathematics education because it gives the opportunity to analyze research data through cognitive actions. For this reason, we aim to examine the abstraction process of the limit knowledge of two volunteer participant students using the RBC+C abstraction model. With this aim, the students'…

Successful analogical reasoning requires an analogue in a source domain to have high degrees of structural and surface similarity with a learning task in a target domain. It also requires learners to have sufficient source- and target-domain knowledge. We review the literature and speculate that "less" might create "more"; in…

Student engagement in learning science is both a desirable goal and a long-standing teacher challenge. Moving beyond engagement understood as transient topic interest, we argue that cognitive engagement entails sustained interaction in the processes of how knowledge claims are generated, judged, and shared in this subject. In this paper, we…

Mr. Buxton is a perplexed elementary mathematics teacher. He co-teaches a second-grade classroom, with Ms. Snyder. In their classroom they have 25 students; five are identified as academically at risk, and three receive special education services. In the past Mr. Buxton successfully used an instructional approach consisting of (a) modeling, (b)…

The purpose of this study is to analyze the statistical reasoning levels of preservice elementary school teachers. With this purpose, pre-service teachers consisting of 29 groups worked on a model eliciting activity (MEA) in scope of an elective course they were taking. At the end of the class, they were asked to present their solutions while…