Whether you are a student taking a math course or a parent with a child struggling to learn new concepts, I encourage you to read the rest of this blog post to discover a few extra tools meant to drive excellence in mathematics.
The technological boom of the last two decades has brought with it vast resource improvements to aid in student success. Computer-aided visualizations, video lectures, tutorial websites, and online learning programs (e.g., WebAssign, MyMathLab, and ALEKS) are just a few of the many resources designed to positively impact a student's ability to learn mathematics and attain a conceptually strong grasp of the material.
Despite the abundance of these aids, I find that many students are either unaware of these resources, or just don't know how to use them appropriately. This is why I have decided to list some of the top learning tools available and how a student may wish to use them to achieve a better understanding of mathematics. In each of the items listed below, I speak as if you are the student; however, if you are the parent of a student, then obviously this advice should be delivered to your child. Finally, I encourage you to read each resource, even if it is not flashy or new (e.g. textbooks, office hours, and classmates).
The Good 'Ol Textbook
Beyond attending lecture (which is a given), this is the very first resource you should be using. The exercises that you are assigned for homework are likely from this resource and, therefore, the material required to do these problems is probably covered sufficiently in the reading.
I cannot stress enough how important it is that you read the assigned text. Speed reading is out of the question. Education gives you as much as you put into it. So if you decide to skip reading important material, it will only hurt your knowledge-base in the long run.
If you can fit it into your schedule, I highly recommend getting some of your specific questions answered in your instructor's office hours. It may surprise you how a five-minute conversation with your instructor could save you hours of searching online. Face-to-face, you can articulate your stumbling blocks more clearly than if you were to email or search online.
Talking through material with fellow classmates is a great way to get a better understanding of the material in the course. As the saying goes, "Two heads are better than one." You can easily benefit from the different perspectives of your classmates. A peripheral benefit is that you will likely have to describe your thinking to someone in your study group at some point. Teaching is a very powerful learning technique. Personally, this is why I became so proficient with mathematics - I would discuss mathematical concepts with anyone who would listen, bouncing ideas off of them and seeing if they had a fresh perspective.
Do you notice that the top resources are still the same resources used forty years ago? This is not coincidence. Learning is an innately human experience and, as such, you get the "biggest bang for your buck" by interacting with the material and discussing this with others.
Google Hangouts or Skype
Now we are getting into the newer resources; however, the most important of these are still focused on human interaction. We live busy lives and often cannot travel across town to meet up with fellow students for a study session. A simple solution is to meet with fellow students digitally via Google Hangouts or Skype. This allows for human interaction and "face-to-face" study sessions while in the convenience of your home or workplace.
You should also consider emailing your instructor an invite. While he or she may be busy, you can entice them with a sentence like, "We would love it if you digitally attended. We would not expect you to actively participate (because you likely have a ton of grading and other business), but it would be awesome if you 'lurked' in the background, just listening every once in a while, and popped in when we got too far off track."
Let's face it, if there is a topic you are struggling with, there are likely 300 videos to help you with it on YouTube. Some of these are worthwhile, but many are only going to give you a superficial understanding of the concept. If you are interested in understanding the material in your math course, then you should be very careful about which videos you choose to watch.
In contrast to what most students want, I tend to only recommend video resources where the instructor/teacher/video carefully guides you through the concepts. These videos are usually less focused on a "quick fix" or a "shortcut", and instead are designed to derive an entire concept so that any gaps in your education get filled in appropriately. So, what are the good video resources?
- MathemAddicts Lecture Series (www.youtube.com/MathemAddictsCom): Yes, I understand it is somewhat self-serving to have a link to my own videos, but I truly think these videos are incredibly strong from a rigor standpoint.
- Khan Academy (www.khanacademy.org): The Khan Academy has a pretty robust library of videos available. Unfortunately, many of these offer "quick-fix" methods, which I am not in support of; however, Salmon Khan does a good job with many of the videos trying to teach the content.
I know that is not a long list of video resources, but that is only because I am quickly writing this blog post. Leave video suggestions in the comments field below and I will take a look to see if they fall into "trick" videos or rigorous development videos.
Wolfram Demonstrations Project (demonstrations.wolfram.com)
This is a database of awesome simulations and visualizations for common mathematical concepts (it also houses simulations for many of the sciences). Whether you are learning how to graph linear equations or to use an integrating factor to solve a linear, first-order differential equation, this is an incredible resource to get a visual of how things are done.
Wolfram Alpha (www.WolframAlpha.com)
While this may seem like a "cheater's" website, it is actually an incredibly powerful resource. I would need another blog post to talk about the richness of this resource... so I think I will do that at some point.