Professors in proof-based mathematics courses often intend that the feedback they provide on students' flawed proofs will promote proof comprehension. In this theoretical article, we investigate how such feedback can be formulated. Drawing on Lakatos's process of proof and refutation, we propose the notion of "heuristic refutation…

Understanding chemical models can be challenging for many university students studying chemistry. This study analysed students' understanding of molecular structures using the Lewis structure as a model, and examined what hinders their understanding. We conducted pre- and post-tests to analyse students' conceptions and changes in them. The…

Word problems are among the most difficult kinds of problems that mathematics learners encounter. Perhaps as a result, they have been the object of a tremendous amount research over the past 50 years. This opening article gives an overview of the research literature on word problem solving, by pointing to a number of major topics, questions, and…

The periodic table is recognized as one of the most powerful tools in science. While it is included in virtually all high school and undergraduate general chemistry curricula, it remains a mystery to many chemistry students who find it impossible to decode. Students are often able to predict periodic trends concerning atomic radius, ionization…

Most current models of sentence comprehension assume that the human parsing mechanism (HPM) algorithmically computes detailed syntactic representations as basis for extracting sentence meaning. These models share the assumption that the representations computed by the HPM accurately reflect the linguistic input. This assumption has been challenged…

The concept of mathematical problem solving is an important mathematical process in mathematics curricula of education systems worldwide. These math curricula demand that learners are exposed to authentic problems that foster successful problem solving. To attain this very important goal, there must be mathematics teachers well versed in content…

By bringing together the national German sports game community and an international scientific community in a joint conference, the 6th International Teaching Games for Understanding Conference (TGfU) Meets the 10th German Sports Games Symposium of the German Association of Sport Science (DVS), held July 25-27, 2016, at the German Sport University…

In several domains of psychology it has been shown that mood influences the way in which we process information. So far, little is known about the relation between mood and processes of language comprehension. In the present study we explore, whether, and if so how, mood affects the processing of syntactic anomalies in real time by recording…

Children find object relative clauses difficult. They show poor comprehension that lags behind production into their fifth year. This finding has shaped models of relative clause acquisition, with appeals to processing heuristics or syntactic preferences to explain why object relatives are more difficult than subject relatives. Two studies here…

A large body of research demonstrates the incredible power of initial conceptions, scripts, and stereotypes that result from our naive theories. Prior knowledge compatible with information introduced by instructors enhances encoding and retrieval, but hinders learning when in conflict with it. Theories and facts contradicting existing beliefs are…

Demonstrations of judgment heuristics typically focus on how heuristics can lead to poor judgments. However, exclusive focus on the negative consequences of heuristics can prove problematic. We illustrate the problem with the representativeness heuristic and present a study (N = 45) that examined how examples influence understanding of the…

This study investigates the relationship between the students' understanding of the aims of an investigative activity and their performance when conducting it. One hundred and eighty-one year nine students from a public middle school in Brazil took part in the study. Students working in pairs were asked to investigate two problems using a…

Examines tasks from the heuristics and biases literature in light of the understanding/acceptance principle of P. Slovic and A. Tversky (1974). Shows how the variation and instability of responses can be analyzed to yield inferences about why descriptive and normative models of human reasoning and decision making sometimes do not coincide.…

Research on language comprehension has focused on the resolution of syntactic ambiguities, and most studies have employed garden-path sentences to determine the system's preferences and to assess its use of nonsyntactic sources information. A topic that has been neglected is how syntactically challenging but essentially unambiguous sentences are…

A framework is presented for characterizing competence for cognitive tasks, with a detailed hypothesis about competence for counting by typical 5-year-old children. It is proposed that competence has three main components that are called conceptual, procedural, and utilizational competence. Conceptual competence, which is discussed in greatest…