There is a clear tendency among college students to have strong fears when faced with an algebra class. There must be some kind of deep fear when it comes to learning algebra, and especially, when they have an intense fear of failing the class. This strong aversion stems from the fear of failure, which sets off alarms and creates a state of constant agitation. This retroactive scenario makes everything more difficult, as these fears tend to feed off each other.
Learning mathematics, especially at the college level, is a process that requires preparation and continuity. Mathematical concepts and ideas collide with each other, and missing links can create a gap that is simply impossible to bridge. Many introductory college math courses require a path of solidly learned concepts that builds over time, and that is something that simply cannot be improvised over time. The problem is not easy, because it is fair to say that very modest learning objectives are not usually achieved by the average college student.
One of the initial things we need to do is find out where this gap is being created. We can say that university programs for teaching algebra and mathematics in general make total sense, with abundant examples and solved problems, coming from textbooks and online resources. However, despite a clearly well-crafted curriculum, you will find that university professors find that goals are seldom met satisfactorily. They don’t seem to understand why students perform the way they do. In fact, considering all the resources made available to students (tutors, online resources, websites offering solved problems), it is simply difficult for a college math instructor to understand.
The problem does not seem to be the structure of the university curricula, but in some earlier stages. In fact, if the student came to their first algebra class in college equipped with the tools and background they’re supposed to have, we’d probably have a full row of A’s all the time. But that’s not the case, indicating that our assumption is broken. In other words, the student does not arrive at the university adequately prepared. This lack of preparation also often implies a lack of emotional preparation.
So what is homework company the origin of this? Personally, I think the problem begins in the high school years. Children learn some basic algebraic concepts early in their lives (fractions, numbers, geometry, etc.) but are exposed to these new “math objects” until they are in the eighth grade. Then at the high school level, they just get in the habit of memorizing and not understanding. Most of the concepts have already been learned during the first few years. Suddenly, they are not learning new things anymore, they are just memorizing. I think the key to the problem is realizing how little new concepts are learned in high school.
There is a difference in that students who took calculus in high school tend to do better in college math than those who did not. Is that because they “pushed” to keep learning about new math objects during the high school years that makes all the difference? I think it’s time to rethink how we teach our kids math during their high school years. Otherwise, all efforts to teach mathematics at the university level are more or less doomed to failure.