Woohoo I LOVE email! My love of email may go so far as to be distracting, but that is a completely different topic. Just make a note: If you ever have any questions about doing well in math, send ‘em my way! You can get a hold of me through jerimi@mathbootcamps.com. (and NO I won’t do your math homework for you)

Last week, a reader asked if it was possible for him to do well in his calculus course even though he had never studied any trigonometry. According to him, his algebra skills are solid and so far he has been able to manage the course work.

There is a reason why a lot of high schools and colleges combine trig with algebra in a course like precalculus. If you are willing to put in a little bit of outside effort, many topics in trig are easy to pick up and there are really only a few key skills/ideas. Don’t get me wrong, there is a whole lot of memorization and things like solving a trig equation WILL come up in a calculus course. But, for someone who is able to learn math on their own, picking it up along the way is possible.

Will it be easy? No way. I warned our friend that instead of being able to focus on the new calculus topics by themselves like everyone else, his studying time will also be filled with learning the trig. Calculus is already a challenging course by itself!

For anyone else considering this, I recommend against it unless you are the type who generally can learn math on their own, and is willing to work through a book like schaum’s outlines at the same time as working through your calculus problems. Even then, it will be a tough road and you might not get the grade you would have if you had been able to focus on the calculus alone. It is all about how much time you are willing to put in and how well you use all the resources available to you.

Everyone (yes, EVERYONE) who learns new math struggles at first and then slowly puts the pieces together. The only difference is that the people with more experience learning math know what to expect and how to push through it. This is the key to not only understanding math but really to doing anything tough in life.

Think about how it feels when you start a new topic in math. Can you identify these stages in your process? Do you let yourself get caught up in frustration before you push through?

• Stage 1: Bewilderment – I’m sorry. The fact that no one uses this word anymore made it all the more important to me that I manage to use it in a sentence today. Anyway, back to our topic: This is the stage where you have literally no idea what is going on. All you know is that someone is writing symbols on the board and they might as well be making them up. You try to look in the book and it looks more made up than the stuff you saw on the board! Pushing through this stage means asking tons of questions and truly reading your math book. When I say reading, I mean sitting with a pen and paper and trying the examples right along with the book.
• Stage 2: Stumbling – You know you have hit stage 2 when you can do problems in the book, but only if you have your notes. In other words, you get the first step or two and then get stuck. BUT — All it takes is a look at the notes or an example (and a few minutes of frustration) and you can figure out where to go. A lot of people get stuck here because they haven’t learned that the frustration they’re feeling is no different than “feeling the burn” when working out. Those little trip ups and times when you are trying to find you mistake? Those are exactly the moments your brain is building the connections it will need for the next problem.
• Stage 3: Robotic Understanding – After a while of working problems and stumbling about you will find yourself at this stage. Things are starting to feel much different now. While you may not always know WHY you do certain steps, you can do problems on your own and are getting the right answers most of the time. You’re seeing connections between this and things you learned before even though some of the ideas are still fuzzy. This is a good place to be and a place to be careful! Plenty of people figure they got it at this stage and stop practicing/studying. Don’t fall for that! Keeping the work up now will pay off with…
• Stage 4: True Understanding – Truly understanding a math concept or idea means that you can work problems that use it (even if you get stuff wrong here and there – that’s normal!), see how it is connected to other ideas, and even be creative with it (as in do a problem that is different from anything you have seen and apply this new idea to it). In my personal experience, there are probably 100 levels of “true understanding”. Even with all my experience, there have been times where I suddenly realize something about a topic I learned 10 years ago! If you are taking math class, you won’t necessarily reach this stage until you have had a few new topics that your mind can start to connect together. In my experience, the difference between accepting being in the “robotic understanding” stage and pushing to the “true understanding” stage is what separates the A/B’s from everyone else.

Your goal: Next time you are feeling overwhelmed and frustrated learning math, remember: It is part of the process. You will have to find your own way to push through it, but I am hoping just knowing this much will keep you motivated!

math anxiety, math success, studying tips, test-taking

Every semester I have a few students that have put themselves in a really tough situation. Dreading math and being convinced they’re no good at it, they put off taking any math requirement to their last couple of semesters. The moment I hear this, I imagine jumping in a time machine, finding them in their first semester – just as they are registering and saying:

Sign up for a math class now! Take your math courses in your first year! Please! Not only will you do better, you will be so happy you got it done!

This is what a time machine looks like.

Math is a skill and like any other skill, it gets rusty over time. Even if your major only requires one or two math courses, you want to do well right? The idea is – take it while the math from high school is still fresh. Even if it has been a couple of years, that will be easier than when it has been four or even six years!

If you already have a math phobia, then making it the one thing that is keeping you from graduating in your last semester isn’t exactly helpful. If you are taking it in your first year, you can be more relaxed (knowing that you can drop if you must). Being more relaxed will make learning easier and probably help you do better than if you had all kinds of “my last semester” stress.

If you are a college or high school student, do me a favor. Right now, look at your schedule for next semester. Have you taken your math requirements yet? If not, make sure you are signed up for a math class next semester. Get it done.

I realize that for a lot of people, taking math courses can be stressful especially if you are just used to “getting it” before and now having trouble. Personally, I think there is something we could do with the way we teach math that would help everyone relax and appreciate math more but that’s for another post on another day .

To do my part to help, I’ve written about how you can do well in calculus, and even had a guest post filled with tips for NOT FREAKING OUT when you hit your first really tough math class.

Based on how much people are reading the calculus articles, I’m betting a lot of you guys are engineering or science majors. If so, you definitely should check out this article over on College Info Geek: Tips for Engineering Students. In fact, if you are taking any math class whatsoever, I would follow these tips – regardless of your major!

My favorite sentence in the whole article “Take an active interesting in learning.” ::nods::

Everyone who has studied math has felt overwhelmed, confused, and downright frustrated at one time or another. The real stuff starts to happen when you decide how you are going to handle it. Are you going to give up and try to avoid it all as much as possible or learn to adjust a bit (kinda like working out hard – hey everyone gets sore sometimes but that doesn’t mean you stop!).

Today, Laura Laing was kind enough to drop by and offer some advice. And she knows what she is talking about too! She is the author of the book and blog “Math for Grownups” which is all about being REAL in math. In other words, answering questions like “how do you actually use this stuff in life?”, and “why is it this way?” in a completely laid back, nice to read way. Definitely worth checking out! On to her tips…

By the time you hit high school or college math, you might have a similar realization as Dorothy’s in The Wizard of Oz: “Toto, I’ve a feeling we’re not in Kansas anymore.” Even if you’ve done well in math before, you may find that the problems look a lot different and the concepts are more difficult to understand.

That’s because math is much, much bigger than most people might think. Mathematicians usually end up specializing—in statistics, abstract algebra or calculus, for example. But until you get to that point, you will need to learn a little bit of everything. And that can get pretty darned overwhelming.

So how do you handle feeling overwhelmed in a subject area that you once felt comfortable with? Or how do you get through a class when the math just isn’t clicking?

Breathe deeply
It never pays to panic. If you feel yourself getting overwhelmed—or worse, thinking that you are too dumb to understanding the material—practice some deep breathing and look for ways to reframe your thinking. Be your own internal cheerleader, or find others who can boost your confidence.

Take small bites
By definition, feeling overwhelmed means there’s too much going on. Instead of looking at the big picture, try tackling smaller pieces. With homework, this can mean really focusing on each problem individually and taking breaks between problem sets. In lectures, focus on asking specific and concrete questions. Make notes to ask your instructor for more information, if something doesn’t make sense.

Look for connections
We all have some sense of the math around us. And with years of math education behind you, you definitely have some math skills that you can build on. The trick is to draw on this experience, even in math classes where all of the material seems brand new. Look for touch points in your classes—information that is familiar or that you can connect to skills you already have.

Get some help
No, you don’t need a psychiatrist, but it may be a good idea to ask for assistance from your instructor or find a tutor. This is not a sign of weakness. Everyone needs help sometimes—even mathematicians. In fact, most of history’s greatest mathematicians collaborated at least occasionally. Now is not the time to let your pride get in the way of success.

Write about math
One of the best ways to check your understanding is to restate the concepts in your own words. You don’t need to keep a math journal, but it can be helpful to summarize your class notes—especially if the concepts are challenging and your understanding of them is fleeting.

It can be upsetting to walk into a class and feel lost. But with a few strategies, you can get past feeling overwhelmed and right to the task at hand: learning the math.

I’ve been on a little bit of a graphing calculator kick here lately but its only because Graphing calculators are powerful tools! Once you get used to working with them, it is amazing how you will find yourself understanding things in a much deeper way. Even so, they are EXPENSIVE tools. If you decide to buy one of the more advanced models, you may find yourself spending more money than you did on the textbook!

So what are the alternatives? Well, don’t skip out on getting a hold of a graphing calculator if it is required for the course but DO talk to your professor to make sure you will actually use it. Sometimes, it is part of the syllabus only because the department wants professors to use it even though some of them don’t. Let’s say you know for sure you are going to need one – what can you do?

1. Rent One! – For textbooks you have sites like Chegg and for calculators, you have Graphtor and RentCalculators.org. Both companies offer a cheap plan to get a hold of the popular TI series of calculators. My advice: if you only need one or two math courses then look into this – otherwise you might need it so long it won’t be worth it.
2. Buy Used – I personally do not understand why anyone would buy a graphing calculator brand new. With a little planning, you can save a significant percentage off the new cost by buying one someone needed for just one class. I mean, just look at amazon’s prices! I have seen them sold even cheaper than this by students on campus as well.
3. Skip it Completely – Maybe you know you won’t be taking many technical courses and your professor doesn’t require a graphing calculator but says it might help. There are plenty of free alternatives online that will help you graph equations and make routine calculations. One I have talked about before is http://www.wolframalpha.com/ and this calculator by desmos is one of the best free online graphing calculators I have seen!

Finally, if none of these options work, check with your college. Some have programs to loan calculators to students. This may be a part of the library or the math department. Don’t get discouraged! College is expensive, but think about it this way – learning to make things happen now will only help you later in life – look for those deals and ways to save your cash – you will not regret it!

resources, TI83/84

I feel like I have to warn you, this is completely a “non-math” post. (I know, I know…If you really need your math fix today, how about this post about the quotient rule? or this list of ways a math tutor can be helpful?)

Back to the post at hand: I’m betting that a lot of my readers are students. In fact, from what I can tell, a lot my readers are SERIOUS students. You want to succeed at whatever it is you are trying to do, and you are willing to put the work or research into things to make it happen!

While most of these sites focus on college, there is still good information for high school or homeschooling students. If you are planning on going to college, understanding things like CLEP tests and how to pick a class are things to start thinking about.

• Study Hacks – Run by a computer scientist who wrote the books “How to Win at College” and “How to be a High School Superstar”, this blog covers life goals and academic success. I like articles like “How to be a Math Wiz” (short, sweet, and so very true!) and “How to Cure Deep Procrastination“.
• Campus Splash – This site is all over the place yet entertaining and informative. Right along side silly/fun articles about not embarrassing yourself at a party, you will find very valuable articles like “What the HECK is the CLEP test?“. (Hint: The CLEP test is one way I saved a ton of money and finished my bachelors in just under 3 years)
• Chegg Blog – Chegg is the first company I saw take textbook rentals mainstream. Since then, a lot of colleges and publishers are trying to do the same thing. (BTW renting your textbooks saves a ton of $$). Turns out they also have a blog! I’m a sucker for articles with great tips, so I have to link to “Ten Habits of Successful College Students“
• College Info Geek – This site reminds me of a lifehacker designed for college students. Written BY college students, you will find things like “How to Get Boxes for Your Move” (seriously why is this always so hard?!) and “42 Things I Learned Freshman Year“

Did I miss something? Do you know of a great blog or site? Please tell me about it in the comments!