Proving and refuting are fundamental aspects of mathematical practice that are intertwined in mathematical activity in which conjectures and proofs are often produced and improved through the back-and-forth transition between attempts to prove and disprove. One aspect underexplored in the education literature is the connection between this…

In undergraduate mathematics, deductive reasoning plays important roles in teaching and learning various ideas, and is primarily characterized by the concept of logical implication. This comes up whenever conditional statements are applied, i.e., one checks if a statement's hypotheses are satisfied and then makes inferences. In calculus, students…

We constructed a new taxonomy for inferential thinking, a construct called Integrative Inferential Reasoning (IIR). IIR extends Pearson and Johnson's (1978) framework of "text-implicit" and "script-implicit" question-answer relations, and integrates several other prominent literacy theories to form a unified inferential…

Research in psychology and in mathematics education has documented the ubiquity of "intuition traps" -- tasks that elicit non-normative responses from most people. Researchers in cognitive psychology often view these responses negatively, as a sign of irrational behaviour. Others, notably mathematics educators, view them as necessary…

This report documents how one undergraduate student used set-based reasoning to reinvent logical principles related to conditional statements and their proofs. This learning occurred in a teaching experiment intended to foster abstraction of these logical relationships by comparing the predicate and inference structures among various proofs (in…

This case study describes how our research team conducted the qualitative think-aloud approach (or cognitive pretesting) to obtaining cognitive validity evidence for a biology inference-making and reasoning measure for undergraduate students. The main goal of our work was to gather high-quality student think-aloud data of reasoning while they were…

In this study, the problem is limited factors relating to the learning effectiveness and teacher competence in improving the teacher performance. Therefore, this study will try to get explanations from some main issues which include the learning effectiveness issue, and teacher competence to increase teacher performance in Madrasah Tsanawiyah at…

There are many important issues in informatics and many agree that algorithms and programming are most important issues that need to be included in informatics education (Dagiene and Jevsikova, 2012). In this paper, we propose how some of these issues can be easily taught using the notion of a formal system which consists of axioms and inference…

Although the importance of reading in developing writing ability is undeniable, few competent readers in EFL contexts develop into competent writers. Since students are not aware that reading can assist them in writing, this study examined the effect of reciprocal teaching--which focuses on four reading comprehension strategies, namely…

The purpose of the research paper was to investigate the effect of eclectic learning approach on the academic achievement and retention of students in English at elementary level. A sample of forty students of 8th grade randomly selected from Government Boys High School Khurram District Karak was used. It was an experimental study and that's why…

The prealgebra curriculum presents many opportunities for encouraging students to justify their inferences. Requiring students to communicate clearly the reasoning behind their solutions, with appropriate mathematical language and notation, helps lay the groundwork for future, proof-based mathematics courses. Prealgebra students can even be…

This mixed-methods study reports psychometric properties of the 34-item Reasoning about P-values and Statistical Significance (RPASS) scale. RPASS is being designed as a research tool to assess effects of teaching methods on students' inferential reasoning. During development (Phase I), two graphical scenarios and 12 items were added to the scale,…

Universal screening has been routinely advised for determining the presence of problems for initiating problem-solving processes and models. The aim of this study was to assess the effect of two screener development methods on the validity of score inferences for two teacher screeners of child behavioral and emotional risk. The reliability and…

This study investigated whether an intervention measurably contributed to the self-regulatory processes underlying undergraduate students' learning. The Rasch model was first applied to Dynamic and Active Learning Inventory Revised (DALI-R; Iran-Nejad & Chissom, 1992) data to examine the validity of inferences made from this instrument and to…

Science teachers and science textbooks commonly introduce students to the scientific method in elementary and junior high school, but the study of scientific method and philosophy can be a life-long endeavor. This essay concentrates on a particular aspect of the scientific method--the testing of hypotheses. Concepts of hypothesis testing have…