Middle school is an important crossroad in a student's academic journey. As students enter middle school, their academic achievement and engagement frequently declines. This is true particularly for Black and Latinx students. Poor middle school grades are often a harbinger of poor performance in high school and beyond. In particular, having a…

The "Academic Mindsets and Behaviors, Prior Achievement, and the Transition to Middle School" study examined the relationship between 2016/17 grade 5 student responses to a Clark County School District (Nevada) survey on levels of academic mindsets and behaviors and the predicted probability of earning a low GPA (below 2.0) at the end of…

Cognitive scientists have studied internal cognitive structures, processes, and systems for decades in order to understand how they function in human learning. Nevertheless, questions concerning the diagnosis of changes in these cognitive structures while solving inductive reasoning tasks are still being scrutinized. This paper reports findings…

In the Basic Local Independence Model (BLIM) of Doignon and Falmagne ("Knowledge Spaces," Springer, Berlin, 1999), the probabilistic relationship between the latent knowledge states and the observable response patterns is established by the introduction of a pair of parameters for each of the problems: a lucky guess probability and a careless…

Reports on (n=11) student attempts at 3 combinatorial questions focusing mainly on 3 aspects of strategy: (1) listing; (2) subdivision into cases; and (3) use or misuse of 4 standard formulas. (MKR)

Describes a study that investigated probabilistic intuitions held by students (N=98) from grade 7 through college through the use of a questionnaire. Of the misconceptions that were investigated, availability was the only one that was stable across age groups. Contains 20 references. (DDR)

Investigated are three misconceptions of probability and the differential effect of two activity-based instructional units. Response categories (law of averages, law of small numbers, and availability) are identified. Treatment differences (evaluation or no evaluation) appear to influence subjects' interpretations of the information. (YP)

Examined the effects of perceived control and close alternative outcomes on counterfactual generation (thoughts of what could have been). Subjects played a "wheel of fortune" game in which they controlled one of two wheels. Results supported the idea that people generate counterfactuals about events over which they have perceived…

Examined impact of outcome controllability on counterfactual thoughts (thoughts of what could have been). Two studies showed that outcome controllability affected counterfactual direction: thoughts on how things could have been better were more frequent following controllable outcomes, and thoughts on how things could have been worse followed…

Reviews research indicating that students' cognitive models hold random events to be equiprobable Examined 87 students between the ages of 15 and 17 to determine whether masking a random event using geometric figures would affect the students' view of the event as equiprobable. Results indicated that masking overcame the equiprobable bias of the…

Decades of education research have shown that students can simultaneously possess alternate knowledge frameworks and that the development and use of such knowledge are context dependent. As a result of extensive qualitative research, standardized multiple-choice tests such as Force Concept Inventory and Force-Motion Concept Evaluation tests…

The concept of probability is not an easy concept for high school and college students to understand. This paper identifies and analyzes the students' alternative frameworks from the viewpoint of constructivism. There are various interpretations of probability through mathematical history: classical, frequentist, and subjectivist interpretation.…

This paper illustrates a model of the layperson's reasoning patterns under conditions of uncertainty, the "outcome approach," which was developed from analysis of videotaped problem-solving interviews with 16 undergraduate students. According to the outcome approach, the goal in questions of uncertainty is to predict the outcome of an…

One of the most common misconceptions about probability is the belief that successive outcomes of a random process are not independent. This belief has been dubbed the "gambler's fallacy". The belief that non-normative expectations such as the gambler's fallacy are widely held has inspired probability and statistics instruction that attempts to…

To investigate the origins and nature of intuitive obstacles affecting the learning of elementary probability theory, 618 Italian elementary and middle school students were interviewed about their methods of solution for several problems dealing with probability. The discussion focuses on four varieties of obstacles to learning prevalent within…