In this study, the author examined the relationship of probability misconceptions to algebra, geometry, and rational number misconceptions and investigated the potential of probability instruction as an intervention to address misconceptions in all 4 content areas. Through a review of literature, 5 fundamental concepts were identified that, if…

Energy is a critical concept in physics problem-solving, but is often a major source of confusion for students if the presentation is not carefully crafted by the instructor or the textbook. In the first three articles in this series we discussed several issues related to the teaching of energy concepts. We have saved a major single issue for this…

Algebra uses symbols for generalizing arithmetic. These symbols have different meanings and interpretations in different situations. Students have different perceptions about these symbols, letters and signs. Despite the vast research by on the students' difficulties in understanding letters in Algebra, the overall image that emerges from the…

We report on the contents and results for 360 students of a mathematics assessment administered at the start of the second-semester introductory chemistry course required for science and engineering majors at the University of Minnesota. This calculator-free, 20-question, 30-minute, multiple-choice, diagnostic quiz includes questions selected…

Ensuring that young children have safe, secure environments in which to grow, learn, and develop healthy brains and bodies is not only good for the children themselves but also builds a strong foundation for a thriving, prosperous society. Science shows that early exposure to circumstances that produce persistent fear and chronic anxiety can have…

This study investigated the effectiveness of multiple scaffolding tools in helping students understand a complex problem. In order to support students with this task, a multimedia learning environment was developed based on the cognitive flexibility theory (CFT) and scaffolding through computer-based tools. Seventy-nine 10th-grade students in an…

Problem-based learning focuses on small groups using authentic problems as a means to help participants obtain knowledge and problem-solving skills. This approach makes problem-based learning ideal for teaching lean manufacturing, which is driven by a culture of problem solving that values learning as one key output of manufacturing production.…

Chemical phenomena can be described using three representation modes: macro, submicro, and symbolic. The way students use and connect these modes when solving conceptual problems was studied, using a think-aloud interview protocol. The protocol was validated through interviews with six faculty members, and then applied to four graduate and six…

Students are often told to use representations to solve mathematics problems, yet it may be a hindrance for many. This article contains an approach, the Graphic Representational Analysis Process, that teachers can use to analyze representations and focus future instruction. (Contains 7 figures.)

The purpose of this study was to determine (1) strategies students use when solving composition problems and the difficulties they encounter; (2) conceptions and/or misconceptions students have with respect to composition of functions; and (3) the effect of using dynamic visualization during instruction on students' understanding of composition of…

Both upper- and lower-level chemistry students struggle with understanding the concept of buffers and with solving corresponding buffer problems. While it might be reasonable to expect general chemistry students to struggle with this abstract concept, it is surprising that upper-level students in analytical chemistry and biochemistry continue to…

In this paper we consider prior definitions of the terms "ill-defined domain" and "ill-defined problem". We then present alternate definitions that better support research at the intersection of Artificial Intelligence and Education. In our view both problems and domains are ill-defined when essential concepts, relations, or criteria are un- or…

The authors examined the impact of manipulative-based instruction on 2 independent cohorts of preservice elementary teachers. In Study 1, 50 participants engaged in problem solving with operations on whole numbers and fractions using concrete and representational manipulatives over 5 classes. Pre- to posttest performance on a mathematics survey…

In order to think, to interpret and judge correctly, the humans have to comprehend what they have learned. Concepts are the abstract representatives of the classifications that are formed by objects, events, ideas and behaviors which have common specifications. (Fidan, N., 1985). Concepts reduce the complexity by simplifying the environment that…

"Mathematics is more than skills... it is also the excitement of discovery." This is how Derek Holton, one of the contributing authors to this book, defines mathematics. His enthusiasm and energy are echoed throughout by many of the other writers. This is a book to delight mathematics teachers at all stages: experienced and inexperienced;…