There has been a long-standing debate on situational and symbolic mathematics, which is associated with how to design and execute mathematics education for all students. Brain studies can give some clues for how to deal with the debate. There are situational, verbalized, and visuospatial brain networks and the connectivity among the networks,…

The electronic and molecular structure of the acylium cation ([CH[subscript 3]CO][superscript +], 1) receives varied treatment in undergraduate textbooks and online resources. The overall structure of 1 is typically represented as an equal combination of resonance structures containing C-O triple and double bonds, the latter structure occasionally…

This paper addresses the use of Excel tables to convey information to blind students that would otherwise be presented using graphical tools, such as Data Flow Diagrams. These tables can supplement diagrams in the classroom when introducing their use to understand the scope of a system and its main sub-processes, on exams when answering questions…

Technological advances continue to reshape the skill sets necessary for students to succeed both in the classroom and in the workforce. The ability to communicate information verbally and graphically can be viewed as a necessary skill that should be developed in a secondary technology education curriculum (Silva, 2008). This article outlines a…

It is common for both algebra and calculus instructors to use power functions of various degrees as well as exponential functions to examine and compare rates of growth. This can be done on a chalkboard, with a graphing calculator, or with a spreadsheet. Instructors often are careful to connect the symbolic and graphical (and occasionally the…

The "Titanic" caught the attention and imagination of the public when, in 1985, the sunken ship was discovered 370 miles off the coast of Newfoundland (PBS, 2012). Since that time, scientists have conducted numerous expeditions using high-resolution SONAR working in tandem with remote-operated vehicles (ROV) to collect information used…

Ontologies are one of the most popular and widespread means of knowledge representation and reuse. A few research groups have proposed a series of methodologies for developing their own standard ontologies. However, because this ontological construction concerns special fields, there is no standard method to build domain ontology. In this paper,…

Intelligent Tutoring Systems (ITS) are effective tools for education. However, developing them is a labour-intensive and time-consuming process. A major share of the effort is devoted to acquiring the domain knowledge that underlies the system's intelligence. The goal of this research is to reduce this knowledge acquisition bottleneck and better…

In the Walking Out Graphs Lesson described here, students experience several types of representations used to describe motion, including words, sentences, equations, graphs, data tables, and actions. The most important theme of this lesson is that students have to understand the consistency among these representations and form the habit of…

This article describes a mathematics session in which students explored a challenging combinatorics task, a topic shown to be difficult for students when taught traditionally. The students developed a progression of personal representations, increasingly symbolic and abstract, which they used to find a solution and justification. (Contains 8…

In order to make a dramatic change in the way teachers approach science writing, the authors found it necessary to address both science instruction as a whole and the use of writing during various stages. To guide them in this endeavor and communicate a concrete idea of an ideal foundation for highly effective science writing to teachers, the…

Despite a growing development of virtual laboratories which use the advantages of multimedia and Internet for distance education, learning by means of such tutorial tools would be more effective if they were specifically tailored to each student needs. The virtual teaching process would be well adapted if an artificial tutor can identify the…

Genetic algorithms (GAs) are a problem solving strategy that uses stochastic search. Since their introduction (Holland, 1975), GAs have proven to be particularly useful for solving problems that are "intractable" using classical methods. The language of genetic algorithms (GAs) is heavily laced with biological metaphors from evolutionary…

It is assumed that cooperative learning continuously constructs and extends the shared knowledge of a group of learners with respect to a specific learning domain. Experiences with Computer-Supported Collaborative/Cooperative Learning (CSCL) environments indicate that an explicit representation of the shared knowledge is helpful with regard to two…

An appreciation of the relationship between novice and expert knowledge frameworks may help develop an understanding of the process of transition from one to the other. Recommends the use of concept mapping. (DDR)