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Department of Mathematics

Teaching

E-books (Online Textbooks)

Modern technology offers a broad variety of interactive tools that can be used to aid understanding. The Q-Center is developing interactive online texts to be used in precalculus and differential equations. These e-books feature multiple pathways allowing an instructor or student to tailor his or her book experience to their individual needs, interactive tools such as diagrams to illustrate relationships between changing quantities, and full integration with the online homework system. With the generous support of our alumni, these e-books are being made fully mobile compatible, enabling students not only to carry their textbook on their cellphone or iPad, but also to complete their assignments on these devices.

 

Studio College Algebra

a live activity Students in College Algebra learn to carry out specific manipulations by rote, and sometimes, they do not see the point in what they are learning and are unable to apply this knowledge in later courses. In order to help students make sense of what they are learning, it is important that they get a chance to work through an entire situation, and not just a book exercise. In the studios, we give them a chance to find and/or collect data about a situation, develop a formula to describes the data, use their algebraic skills to analyze the formula, and apply their analysis to answer questions about the original situation. The contexts for these studios include social and natural science, commerce, and sports.

our computer lab A key feature of the studio is that the students work together. There are 20 computers for the 60 students in a studio section. If students are going to learn to use mathematical language, they need the opportunity to discuss mathematics with other students, and group work makes it easier to master the technology involved.

The primary technological tool we use is the spreadsheet, the same tool students will likely use in their future workplaces to analyze data. While our studio room has PCs with Excel 2007, we have provided instructions (to the extent feasible) for students using Excel 2003 and 2007 for both PC and Mac and also for students using OpenOffice (a free open-source spreadsheet program) so that they can carry out work on their own computers with whatever software they have. Since different groups work at different speeds, particularly with computers, most studios have bonus sections so students finishing early can explore the material in more depth for extra credit. Since students can work at home (or in any public lab on campus), everyone has the opportunity to earn the extra credit no matter how quickly they work.

Typically there will be a first studio where students explore the graphical meaning of algebraic operations, followed by a second studio where they apply their understandings to a particular context. A good example of the first type of studio is Translating Graphs, where we have embedded sliders in the studios so the students can get a kinesthetic sense of what changing f(x) to f(x+2) does. In a particular studio of the second type, students determine whether a power law or an exponential law is a better model for predicting how the the world record in the 100 meter dash changes over time.

It should be noted that the studio version of College Algebra entails more than just the studios. Financial and space constraints force us to have one large lecture and one traditional recitation per week. We are now using iClickers to engage students during the lecture. We are also using online homework to address mechanical skills to free up recitation time for discussing applications of the material.

The studio version of college algebra has been very successful with the C or better rate increasing from 60-67% to 75-80%. Furthermore, students who pass the studio version do just as well (actually slightly, but not statistically significantly, better) in subsequent courses.

Additional Documentation

The video link below demonstrates what happens in the Translating Graphs Studio; it is part of the feedback received by students that miss questions related to the studio. Also, one can find the instructions and spreadsheets students use below. Since different versions of spreadsheet programs have slightly different interfaces, we provide students with multiple sets of instructions so that they will have instructions matching the program they use.