This study was designed to investigate children's abilities to count and make quantitative comparisons. In addition, this study utilized reasoning questions (i.e., how did you know?). Thirty-four preschoolers, mean age 4.5 years old, participated in the study. According to the results, 89% of the children (n = 30) were able to do rote counting and…

In line with the latest positions of Gottlob Frege, this article puts forward the hypothesis that the cognitive bases of mathematics are geometric in nature. Starting from the geometry axioms of the "Elements" of Euclid, we introduce a geometric theory of proportions along the lines of the one introduced by Grassmann in…

Several studies suggest that most students are not in the same level of development (Slavin, 2008). From concrete operation level to formal operation level, students experience lateness in the transition phase. Consequently, students feel difficulty in solving mathematics problems. Method research is a qualitatively descriptive-explorative…

The article aims to study the verbal collaborative interaction in both symmetrical and asymmetrical dyads according to specific individual cognitive competence. The interaction was analyzed in terms of cognitive and non-cognitive aspects. 19 dyads (38 fifth and sixth graders) participated. First, they individually solved a set of logical problems…

Paraphrasing is a signature practice of constructing intertextual discourse in academic writing. It is a story retelling technique commonly employed by academic writing classes to tackle plagiarism. However, teaching and learning of paraphrasing tend to place a very heavy emphasis on literal meanings of source messages and faithful reproductions…

The following exploratory study examines the effects of a "Harry Potter"-inspired "border crossing" analogy (HPBCA) on preservice teachers' (n = 25) Teaching English to Speakers of Other Languages (TESOL) content knowledge and disposition toward English language learners (ELLs). The analogy capitalizes on the prior and shared…

A growing body of scholarly work indicates that student performance on physics problems stems from many factors, including relevant conceptual understanding. However, in contexts in which significant conceptual difficulties have been documented via research, it can be difficult to pinpoint and isolate such factors because students' written and…

This paper reports on our use of a fine-grained learning progression to assess secondary students' reasoning through carbon-transforming processes (photosynthesis, respiration, biosynthesis). Based on previous studies, we developed a learning progression with four progress variables: explaining mass changes, explaining energy transformations,…

Like many museums, the Missouri Historical Society wants to empower students to engage with history on their own terms. In our quest to create museum literate learners and push the student-centered field trip model to its maximum, we've internalized the crucial role of metacognition, or how we facilitate opportunities for students to think about…

Connection-making among multiple representations is a crucial but difficult competence in STEM learning. Prior research has focused on one type of learning process involved in connection-making: sense-making processes leading to conceptual understanding of connections. Yet, other research suggests that a second type of learning process is…

Conceptual models have long served as a means for physical geographers to organize their understanding of feedback mechanisms and complex systems. Analytical reasoning provides undergraduate students with an opportunity to develop conceptual models based upon their understanding of surface processes and environmental conditions. This study…

Children's developing reasoning skills are better understood within the context of their social and cultural lives. As part of a research-museum partnership, this article reports a study exploring science-relevant conversations of 82 families, with children between 3 and 11 years, while visiting a children's museum exhibit about mammoth bones, and…

The article studies the verbal manifestation of critical thought in a school context. Four modes of thought--logical, creative, responsible, and metacognitive--accompanied by six epistemological perspectives, are studied from 1,730 pupils turns to speak analyzed in eight class groups. The pupils dialog about freedom. Quantitatively and gradually…

Standardized, well-established paper-and-pencil tests, which measure spatial abilities or which measure reasoning abilities, have long been found to be predictive of success in the STEM (science, technology, engineering, and mathematics) fields. Instructors can use these tests for prediction of success and to inform instruction. A comparative…

Models related to the topic of chemical kinetics are critical for predicting and explaining chemical reactivity. Here we present a qualitative study of 15 general chemistry students' reasoning about a method of initial rates task. We asked students to discuss their understanding of the terms rate law and initial rate, and then analyze rate and…