This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…

Conflicting explanations and unrelated information in science classrooms increase cognitive load and decrease efficiency in learning. This reduced efficiency ultimately limits one's ability to solve reasoning problems in the science. In reasoning, it is the ability of students to sift through and identify critical pieces of information that is of…

We investigated the effect of emphasising the realistic modelling complexity in text or in the accompanying picture on the solution of P-items, in relation to pupils' grade. 290 pupils from the 5th and 6th grade of various elementary schools in Flanders (Belgium) made a paper-and-pencil task with 7 word problems that are problematic from a…

Problem solving in mathematics has been a goal for students for decades. In the reviewed literature, problem solving was most often treated as the dependent variable and was defined very broadly; however, few studies were found that included problem solving as a treatment or independent variable. The purpose of this study was to investigate the…

Data from open modelling sessions for year 10 and 11 students at an extracurricular modelling event and from a year 9 class participating in a programme of structured modelling of real situations were analysed for evidence of Niss's theoretical construct, "implemented anticipation," during mathematisation. Evidence was found for all…

This paper provides examples of Aid-to-Thought uses in urban decision making, classroom laboratory planning, and in a ship antiaircraft defense system. Aid-to-Thought modeling and simulations are tools students can use effectively in a STEM classroom while meeting Standards for Technological Literacy Benchmarks O and R. These projects prepare…

Assimilating an algorithmic course is a persistent problem for many undergraduate students. The major problem faced by students is the lack of problem solving ability and flexibility. Therefore, students are generally passive, unmotivated and unable to mobilize all the acquired knowledge (loops, test, variables, etc.) to deal with new encountered…

"Designing backwards" is presented here as a means to utilize human-centered processes in diverse educational settings to help teachers and students learn to formulate and operate design processes to achieve three sequential and interrelated goals. The first entails teaching them to effectively and empathetically identify, frame and…

Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

Software programs such as Tinkerplots ® or Geometer's Sketchpad ® can help students solve problems in mathematics classes, but may not be available to them after high school. In contrast, many students who become familiar with Internet tools and programs in office packages (word processing, spreadsheets, etc.) may use them daily to enhance their…

This conceptual article explores teaching as design work, arguing that a critical thing teachers do is design systems that enable their students to learn. Designing occurs when teachers generate new learning activities or modify curricular programs to create coherence for themselves and their students. Nonetheless, few teacher education programs…

The purpose of this study was to explore supervision group leaders' conflict management strategies in Turkey. This research was conducted as a survey using a descriptive method. The population of the study consisted of 2493 inspectors working in 81 provinces geographically divided in seven regions. The data were collected by "Conflict…

If a person has "a problem" to solve and knows the solution and just has to apply it (retrieve it from memory and re-act), it is not a problem--it is a task; if a person does not know the solution and has to create it--this is a problem. Using this language, there are only two situations: (a) one has to perform a task; or (b) one has to…

Paper folding, or origami in Japanese, is a traditional craft that has been enjoyed by both children and adults for hundreds of years. Mathematicians have long studied the mathematics of paper folding. They use square papers to construct mathematical shapes (for example, folding an equilateral triangle from a square paper or trisecting an angle),…

Usually, distribution electricians are called upon to solve technical problems found in electrical substations. In this project, we apply problem-based learning to a training program for electricians, with the help of a virtual reality environment that simulates a real substation. Using this virtual substation, users may safely practice maneuvers…