In the last years special "ovals" appear increasingly often in diagrams and applets for discussing crucial items of statistical inference (when dealing with confidence intervals for an unknown probability p; approximation of the binomial distribution by the normal distribution; especially in German literature, see e.g. [Meyer,…

Since 2018, institutions of higher education have been aware of the "enrollment cliff" which refers to expected declines in future enrollment. This paper attempts to describe how prepared institutions in Ohio are for this future by looking at trends leading up to the anticipated decline. Using IPEDS data from 2012-2022, we analyze trends…

Most existing solutions to the current replication crisis in science address only the factors stemming from specific poor research practices. We introduce a novel mechanism that leverages the experts' predictive abilities to analyze the root causes of replication failures. It is backed by the principle that the most accurate predictor is the most…

Multimodal learning analytics (MMLA) has increasingly been a topic of discussion within the learning analytics community. The Society of Learning Analytics Research is home to the CrossMMLA Special Interest Group and regularly hosts workshops on MMLA during the Learning Analytics Summer Institute (LASI). In this paper, we articulate a set of 12…

Reading comprehension is the goal of reading, and making inferences is vital. Authors usually expect readers to make multiple types of inferences, including anaphoric, background knowledge, predictive, and retrospective. Common core assessments include all of these, yet instructional materials focus mostly on only one type, retrospective. This…

Traditional school laboratory exercises on a system of moving objects connected by strings involve deriving expressions for the system acceleration, a = (?F)/m, and sketching a graph of acceleration vs. force. While being in the form of rational functions, these expressions present great opportunities for broadening the scope of the analysis by…

This article presents a fundamental advance in the theory of mental models as an explanation of reasoning about facts, possibilities, and probabilities. It postulates that the meanings of compound assertions, such as conditionals ("if") and disjunctions ("or"), unlike those in logic, refer to conjunctions of epistemic…

As part of Japanese Lesson study research focusing on "comparing and describing likelihoods", fifth grade elementary students used real-world data in decision-making. Sporting statistics facilitated opportunities for informal inference, where data were used to make and justify predictions.

Oftentimes physics is portrayed as merely a list of facts that we know about the world around us, when in fact it is a way of knowing about that world. At times physics claims to understand the inner working of objects that cannot be directly observed, such as the core of the planets and Sun, or the structure of an atom. It is important for…

Statistics is one of the most widely used topics for everyday life in the school mathematics curriculum. Unfortunately, the statistics taught in schools focuses on calculations and procedures before students have a chance to see it as a useful and powerful tool. Researchers have found that a dominant view of statistics is as an assortment of tools…

There is a general agreement that critical thinking is an important element of 21st century skills. Although critical thinking is a very complex and controversial conception, many would accept that recognition and evaluation of assumptions is a basic critical-thinking process. When students use simple mathematical model to reason quantitatively…

The activities described in this article, Prediction Path and Quotation Cafe, are adapted from the IRA book "Building Reading Comprehension Habits in Grades 6-12." They highlight the reading comprehension habit of making inferences and predictions, which can be used across content areas and grade levels. In creating this toolkit of activities, the…

This study aims to examine a) whether vocabulary knowledge, captured in the Vocabulary Levels Test (VLT), is related to the performance on the five types of reading comprehension items tested in TOEFL, i.e., Guessing Vocabulary, Main Idea, Inference, Reference, and Stated Detail; and b) whether EFL learners with different levels of vocabulary…

Too often, teachers scratch their heads and ask, "What were my students thinking?" then answer, "I don't want to know." But teachers should want to know, and students should question their own thinking, as well. Critical thinking involves not just problem solving, creativity, analysis, and synthesis but also self-awareness of learning and learning…

Many kinds of common and easily observed causal relations exhibit property transmission, which is a tendency for the causal object to impose its own properties on the effect object. It is proposed that property transmission becomes a general and readily available hypothesis used to make interpretations and judgments about causal questions under…