The objective of this article is to describe types of mathematical reasoning evidenced by a middle school mathematics teacher, when answering two generalization questions in a figural pattern generalization task, related to quadratic sequences. Reasoning is delimited from teacher's arguments, reconstructed from a theoretical-methodological…

A few case studies have suggested students' struggles with the "temporal order" of epsilon and delta in the formal limit definition. This study problematizes this hypothesis by exploring students' claims in different contexts and uncovering productive resources from students to make sense of the critical relationship between epsilon and…

This study employed a multisite design to investigate the differential impact of deductive and guided inductive instruction for second language (L2) grammar development in ecologically valid classroom contexts. Students (n = 138) from eight intact third-year L2 Spanish classes in three public high schools in the United States received deductive…

Broad instructional methods like "interactive engagement" have been shown to be effective, but such general characterization provides little guidance on the details of how to structure instructional materials. In this study, we seek instructional specificity by comparing two ways of using an analogy to learn a target physical principle:…

Although discussions about inductive reasoning can be traced back thousands of years (Fitelson 2011), the implementation of the Standards for Mathematical Practice (SMP) within the Common Core State Standards (CCSSI 2010) is generating renewed attention to how students learn mathematics. The third SMP, "Construct viable arguments and critique…

In scientific arguments, claims must have meaning that extends beyond the immediate circumstances of an investigation. That is, claims must be generalised in some way. Therefore, teachers facilitating classroom argumentation must be prepared to support students' efforts to construct or criticise generalised claims. However, widely used…

Humans reason by analogy (Lakoff and Johnson, 1980; Gentner, 1983; 2003; Hofstadter, 2001, 2006; Pinker, 2007). Some have further argued that analogs can be scientific models (Hesse, 1966, Clement, 1989) although clearly not all analogies are models. Analogies based on mere physical similarity are not equivalent to scientific models but analogies…

We describe an evidence-based continuing professional development programme on knowledge integration (KI) for high-school physics teachers. Sixteen teachers participated in the year-long programme (about 40 face-to-face lessons and in-between computerised interactions). The teachers experienced the KI activities as learners and then engaged in an…

Researchers have regarded inductive reasoning as one of the seven primary mental abilities that account for human intelligent behaviours. Researchers have also shown that inductive reasoning ability is one of the best predictors for academic performance. Modelling of inductive reasoning is therefore an important issue for providing adaptivity in…

Clarifies the idea of prediction in science teaching by distinguishing between the two extremes of guessing and making logical deductions. Discusses the use of predictions in testing teachers' and students' explanations. (MDH)

The tendency to generalize from specific experiences leading to new, more abstract concepts is a natural aspect of human thought. Generalizations are the end result of an inductive process that begins with the identification of similarities in seemingly disparate situations. It is the existence of such generalizations that makes it possible for us…

Evaluation of a sequenced inquiry learning task with 20 normally achieving junior high students, 18 students with learning disabilities (LD), and 16 with mild mental retardation (MR) found 75 percent of the normal, 50 percent of the LD, but none of the MR students made the correct induction. LD and MR students were less likely to answer…

The 7th International Conference on Education Data Mining held on July 4th-7th, 2014, at the Institute of Education, London, UK is the leading international forum for high-quality research that mines large data sets in order to answer educational research questions that shed light on the learning process. These data sets may come from the traces…