Literature suggests that "current characterizations of the terms procedural knowledge and conceptual knowledge are limiting and are, in fact, impediments to careful investigation of these constructs" (Star, 2005, p. 405). We examined secondary mathematics teachers' understanding of procedural and conceptual knowledge at superficial and…

This paper discusses the significance of model-based teaching on the topic of ionic and metallic bonding in Year 12 Chemistry in a New Zealand secondary school. Based on the conceptualization of the sub-macro level understanding of the bonding structure and properties of ionic and metallic compounds, models and drawings were used as an effective…

This three-article dissertation explores Learning by Evaluating (LbE), an educational approach that enhances student learning through the process of assessing and providing feedback on peer work. Leveraging principles of comparative judgement, students evaluate pairs of exemplars side-by-side to determine which is better and provide a rational for…

Problem-solving is one of the 21st-century skills. However, students still have difficulty solving sequences and series word problems. The purpose of this research is to analyze students' errors in solving sequences and series word problems based on problem-solving steps of Polya. The research method is descriptive qualitative. The research…

Professional learning strategies often rely on the belief that teaching and learning outcomes are best when teachers have a clear understanding of students' thinking. This may seem like common sense -- after all, students are active participants in the learning process, so their thinking impacts the outcome. But does research support the…

In this paper, a learning progression for geometric transformations is developed based on research that demonstrates the importance of viewing transformations as functions of the plane. The 5 levels of the progression reflect a student's evolving understanding of transformations as functions and their evolving understanding of the domain of these…

In response to the wide-scale proliferation of "the cone of learning"--a fanciful retention chart confounded with Dale's Cone of Experience--the authors make four major claims debunking this fantasy and provide documentary evidence to support these claims. The first claim is that the data in the mythical retention chart do not make…

Critics have been attempting to debunk the mythical retention chart at least since 1971. The earliest critics, David Curl and Frank Dwyer, were addressing just the retention data. Beginning around 2002, a new generation of critics has taken on the illegitimate combination of the retention chart and Edgar Dale's Cone of Experience--the corrupted…

The authors are attempting to set the record straight regarding the sources frequently cited in the literature of the mythical retention chart and the corrupted Dale's Cone. They point out citations that do not actually connect with relevant works; provide correct citations of sources that are often cited erroneously; add references for overlooked…

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

In this paper we describe two episodes of instructional interaction, in which examples are used in order to help students face their misconceptions. We introduce the notions of pivotal example and bridging example and highlight their role in creating and resolving a cognitive conflict. We suggest that the convincing power of counterexamples…

The central place of the learning environment and the personal characteristics of the learner in influencing whether students adopt deep or surface approaches to learning is well evidenced in the literature (for example, Marton & Saljo, 1976; Biggs, 1987; Entwhistle, 2001; Ramsden, 2003). For this reason, tertiary educators are constantly…

The aim of this study is to investigate Emiratii high school students' understandings of stoichiometry, their use of metacognitive strategies, and the influence of students' use of metacognitive strategies on their understandings of stoichiometry. Two instruments were used in this study, the first to measure students' understandings of…

Four experiments investigated children's ability to notice and remember events in which the acquisition of factual information occurs. Results indicated that children tend to report they have known newly learned information for a long time, suggesting that children have some understanding of knowledge acquisition, but not at the level of adults.…

Discussed is a constructivist model of science learning and its possible use in the treatment of science misconceptions. Science learning as conceptual and methodological change is described. (KR)