Teaching through Problem Solving (TtPS) is an effective way to teach mathematics "for" understanding. It also provides students with a way to learn mathematics "with" understanding. In this article, the authors present a definition of what it means to teach through problem solving. They also describe a professional development vignette that…

We describe the difficulties that advanced undergraduate and graduate students have with quantum measurement within the standard interpretation of quantum mechanics. We explore the possible origins of these difficulties by analyzing student responses to questions from both surveys and interviews. Results from this research are applied to develop…

The Virtual Genetics Lab II (VGLII) is an improved version of the highly successful genetics simulation software, the Virtual Genetics Lab (VGL). The software allows students to use the techniques of genetic analysis to design crosses and interpret data to solve realistic genetics problems involving a hypothetical diploid insect. This is a brief…

There is a reciprocal relationship between mathematics and reading cognition. Metacognitive training within reading-enhanced problem solving should facilitate students developing an awareness of what good readers do when reading for meaning in solving mathematical problems enabling them to apply these strategies. The constructs for each cognitive…

Early childhood teacher education courses must prepare students for the types of challenges they will face in communities and classrooms after graduation. By adopting a scenario-based approach, teacher educators and others designing online environments can help prepare students for these challenges. Solving complex problems inherent in a…

It can be difficult to connect with parents of students in upper elementary grades, because as they get older, students generally seek independence and do not want their parents involved as much as they have been in their younger years. Teachers must work at finding a way to reach out to parents. The author started parent science nights so she…

Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

Students can use geometric representations of numbers as a way to explore algebraic ideas. With the help of these representations, students can think about the relations among the numbers, express them using their own words, and represent them with letters. The activities discussed here can stimulate students to try to find various ways of solving…

For students who have difficulty envisioning how the mathematics that they are learning is used outside the classroom, an adventure as field mathematicians can be enlightening. Measuring stream discharge is a field experience that allows students to engage in a hands-on (and boots-on) real-world, problem-solving activity and that integrates…

This activity introduces students to the concept of reduction-oxidation (redox) reactions. To help students obtain a thorough understanding of redox reactions, the concept is explored at three levels: macroscopic, submicroscopic, and symbolic. In this activity, students perform hands-on investigations of the three levels as they work at different…

The ability to couple problem solving both to the understanding of chemical concepts and to laboratory practices is an essential skill for undergraduate chemistry programs to foster in our students. Therefore, chemistry programs must offer opportunities to answer real problems that require use of problem-solving processes used by practicing…

Students often view mathematics as a set of unrelated facts and procedures and fail to make the connections between and among related topics. One role of a teacher is to help students understand that mathematics is an interrelated discipline. Another role is to assist students in the scaffolding of their knowledge so that they can make connections…

This article tackles the problem of what should be done with real textual data that are contaminated by errors of recording, particularly when the data contain words that are misspelt, unintentionally or otherwise. (Contains 5 tables and 2 figures.)

We consider a problem appearing in an Australian Mathematics Challenge in 2003. This article considers whether a spreadsheet might be used to model this problem, thus allowing students to explore its structure within the spreadsheet environment. It then goes on to reflect on some general principles of problem decomposition when the final goal is a…

This article gives an elementary proof of the famous identity [image omitted]. Using nothing more than freshman calculus, the present proof is far simpler than many existing ones. This result also leads directly to Euler's and Neville's identities, as well as the identity [image omitted].