Category: Discussion

Students often struggle to apply abstract mathematical concepts to real-world problems. These might be word problems assigned as math homework, which often appear in a section titled Applications, at the end of a chapter in their math textbooks. These might be problems appearing in one of their other classes like Chemistry, Hospitality Management or Engineering. Or these might be problems that students are solving in their heads in their day-to-day lives, without even realizing that they are applying abstract math concepts.

Tutors may not realize that they can help students with such topics when they pop up in other disciplines, but a tutor’s expertise can be extremely valuable here. The tutor should have a firm grasp of the big picture (the abstract math concept) and the ability to recognize how and when it is applied in different contexts. The tutor has the chance to help the student realize that, “Hey, this is the same math concept, just dressed up in different ways!”

In this post, we tackle a topic that appears in each of these three realms: unit conversion. Continue reading

We touched only briefly on the topic of limits at December’s meeting, so I wanted to follow up here. The concept of a limit is absolutely fundamental in a calculus class, but it’s also one that causes the most trouble for students. One possible reason for this is that in most college calculus classes, the formal definition of limit is not even given! The reason that the formal definition is often skipped is that it can look scary to someone who hasn’t seen it before, and it can take a long time to develop an intuitive understanding of what a limit is from the definition. While a tutor will probably never discuss this formal definition with a calculus student, the tutor himself or herself should have an understanding of the formal definition as well as how it implies the intuitive definition we usually give students.

The formal definition

Let be a function. We say “” if for all there is a such that whenever .

Quite a mouthful, eh?! Continue reading

One of the topics we discussed at our December meeting was symmetry of functions. This topic is covered in MAT 1375 when students are learning about graphing functions, but it may appear in any course that includes functions of real numbers and their graphs.

Even or odd or….???

One issue that sometimes gives students trouble is the language that is used. An integer is either even or odd, but a function is either even or odd….or neither even nor odd! This difference between how the words are used to describe integers and how they’re used to describe functions can be really hard to process, since even and odd are such familiar concepts for integers. This difference also obfuscates a really important feature of functions: that most of them are neither even nor odd! Symmetry is a really special feature for a function to have; if you try to think of a random function, odds are that you’ll come up with one that does not have any symmetry. (Pun intended.)

Add to this the fact that there are other names that some people use instead of even and odd. An even function is said to have symmetry with respect to the y-axis and an odd function is said to have symmetry with respect to the origin. Continue reading