Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

This article discusses how teaching via problem solving helps enact the Mathematics Teaching Practices and supports students' learning and development of the Standards for Mathematical Practice. This approach involves selecting and implementing mathematical tasks that serve as vehicles for meeting the learning goals for the lesson. For the lesson…

How better to begin the study of linear equations in an algebra class than to determine what students already know about the subject? A seventh-grade algebra class in a suburban school undertook a project early in the school year that was completed before they began studying linear relations and functions. The project, which might have been…

Life tables are mathematical tables that document probabilities of dying and life expectancies at different ages in a society. Thus, the life table contains some essential features of the health of a population. Probability is often regarded as a difficult branch of mathematics. Life tables provide an interesting approach to introducing concepts…

This practice-sharing piece outlines two main approaches to flexible summative assessment schemes, including for each approach one example from my practice and another from a published study. The bento approach offers the same assessments to all students but a variety of grade weighting schemes, allowing students to change weighting during the…

Sustaining engagement with a mathematics task is not a novel suggestion for effective mathematics teaching. "Principles and Standards for School Mathematics" (2000) specified that "students need to know that a challenging problem will take some time and that perseverance is an important aspect of the problem-solving process and of…

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…

Jennifer Miller is a special education preschool teacher at Grant Elementary School in Muscatine, Iowa. In this article, she describes how she created and implemented a learning center with three-to-five-year-old students in an integrated morning class (nine students; four on IEPs) and an integrated afternoon class (10 students; four on IEPs) to…

Proving a child has been adequately educated is manifest through assessments evaluating the recall of facts or the deciphering of codes. How this information is taught and learned is the issue. Webb's depth of knowledge (DOK) and Bloom's taxonomy are cognitive models that drive instruction in today's classrooms. According to these models,…

Traditional assignments that aim to develop and evaluate creative problem solving skills are frequently foregone in large marketing classes due to the daunting grading prospect they present. Here, a new assessment method is introduced: the "snapsignment." Through photography, individual projects can be assigned that promote higher order…

Most educators who teach the advertising campaigns course require students to work as groups. A review of cooperative learning and group dynamics literature, however, suggests that unless students are systematically prepared for group work instructional goals will be difficult to achieve. This article describes how pre-training activities in group…

Learning curves have proven to be a useful tool for understanding how a student learns a given skill as they progress through a curriculum. A learning curve for a given Knowledge Component (KC) is a plot of some measure of competence as a function of the number of opportunities the student has had to apply that KC. Consider the case where each…

Service-learning can provide a range of literacy learning experiences for children as they work to solve real world problems and engage in inquiry, collaboration and reflection. Rather than being an extracurricular activity, service-learning projects are designed to meet standards and align with existing curriculum. This article explores how…

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…

In the "Australian Curriculum," the concept of mathematical induction is first met in the senior secondary subject Specialist Mathematics. This article details an example, the Tower of Hanoi problem, which provides an enactive introduction to the inductive process before moving to more abstract and cognitively demanding representations.…