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?
- 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.
- 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.
- 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!
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.
Did I miss something? Do you know of a great blog or site? Please tell me about it in the comments!
One thing I did that really helped me when first learning math was head off to the library and look at different textbooks. Sometimes just seeing a definition stated a different way, or just seeing one more example was enough to make everything “click”.
Whether you are just starting to learn calculus, reviewing it, or looking for a reference book, this text should help you along the way. The high points: Nice straightforward explanations with a large number of exercises. Beyond that, I have never been one to be able to write a great book review so instead I will share with you a review by a student (posted on amazon.com):
I had the privilege of using this book for my calculus course as a senior in high school. I am now in college and very often refer back to this text because it is so comprehensively written. The book is easy to understand, but still covers a great deal of the very broad subject of CALCULUS!. More Reviews
How to enter
This giveaway is CLOSED! Watch the front page for the next one!
Lectures might not be the most exciting thing to sit through (well unless you are in MY class, yeah couldn’t resist saying it, of course I do more than lecture but lets get back on track…) but let’s face it: most math classes are strictly lecture oriented. Therefore, if your plan is to do well, you MUST figure out the way to get information this way even if your learning style is a little different.
Hmmm…This may look awesome, but if your notes look like this you could have a little trouble following them.
- Try to look at the book beforehand – I know that in reality, it is hard to find the time to look at things before class. You don’t have to read and understand the whole chapter though! Here, a quick read through to make mental notes about anything that seems particularly confusing can help you focus on those things during the lecture (and will help you ask better questions as well)
- Don’t write down EVERYTHING! – Definitions are in your book as well as proofs and “rules”. Instead of writing them down again, use the time in class to really try and understand them and ask questions. If they’re raelly confusing, make yourself a quick note to go and research it more.
- Focus on examples and the “why” – Hopefully your teacher or professor does some examples in class that are different from the text. These are studying GOLD. Every worked problem you have in your hands is a problem you can practice later on your own (with a full solution to see what you got wrong if you mess it up). This is where you should be writing the most careful notes. Also pay close attention to the “why”. Why do you use this method and when. This can be tough to follow in a math book so its worth writing down pointers for yourself.
- If you think you are “getting it” then test yourself – Suppose the professor is doing two examples and you really “got” the first one. Ok, try to solve the second one before he does! This way you can see if you really are understanding things and if you get stuck, you are in the perfect position to ask a good question.
- Try using different color pens or pencils – I know this sounds crazy, but I even do this when I use the board in my classes. It is so much easier to read notes (or the board) when the problems are black, the solutions are blue, and confusing parts or things you want to ask questions are in red.
- Rewrite your notes as part of studying – Now if you write slow, my previous tip may not work for you. But you could take your notes like normal and then rewrite them later in this color coded format. In fact this would be a really nice way to catch anything confusing and help solidify the information in your head. I had a friend in grad school that rewrote all her notes as part of studying and it worked wonderfully for her!
- Please ask questions. PLEASE! – The professor really wants you to ask a question. Seriously. Questions help us transition into new ideas and see how well our students are understanding things. The rest of the class wants you to ask a question (well except for that guy in the back who doesn’t care and wants out early, but he shouldn’t be there anyway). They are nervous and probably have the same question its just that someone needs to break the ice. I know everyone says it all the time but its true, so ask questions already!
I’m sure there are tons more tips out there so what are yours? What have you done in math classes that has helped you? Or if you teach, what do you wish your students would do?
When I was first starting out in math, the more math books I could read the better! This has lead to quite the collection of math book – from textbooks to novels. Now there are way too many math books filling up the bookshelves here at Math Bootcamps and it is time to share some of that math love with all of you!
Today, I will be giving away a novel that anyone with the slightest curiosity about how mathematicians work will enjoy: Uncle Petros and Goldbach’s Conjecture: A Novel of Mathematical Obsession. Not sure if its for you? Here is what a couple of reviewers on Good Reads said:
Uncle Petros and Goldbach’s Conjecture tells the story of a brilliant mathematician obsessed with proving Goldbach’s Conjecture (as reformulated by Euler: every even number greater than two is the sum of two primes). Despite the seemingly difficult mathematical subject, the book is a quick and easy read. This is a testament to the clear and simple prose of the author, himself a mathematician by training.
I am surprised that I enjoyed this book as much as I did, given the fact that mathematics is definitely not my forte. The main character spends nearly his entire life trying to prove Goldbach’s Conjecture – a quest which becomes an obsession.
The winner was chosen and the book was mailed off! Sorry if you missed it, but please subscribe to our the blog to find out about the next giveaway!
***If you would like to enter into the giveaway, just post a comment here and I will randomly select a person later in the week to send the book out to! Please don’t post your address etc – I will email whoever is selected.***
Yesterday, I ran across a great article on Math for Grown Ups about different ways of attacking math problems. While this article talks about day to day math, I was wondering how many people really think about this for more advanced topics like algebra or calculus.
I have a habit of giving my students a problem and asking them to find *at least* a couple of ways to find an answer. (In fact, I did one of these as a calculus problem of the week recently). A lot of time, I find that the students are worried they will get confused if they know more than one way – they are simply too focused on just getting an answer! Talking about this always leads to a great discussion which I tend to start off with these two questions:
How do you know what method makes the most sense to you until you have seen several different methods?
How can you be sure you really understand something until you can look at it from a different perspective?
If you have found yourself able to “go through the motions” of math without much understanding then this is a great exercise to try. In fact, this is something that anyone who is trying to understand something better should try! Stop focusing on just getting the answer and start trying to see how things work together. There are patterns hidden all throughout math waiting to be noticed. It’s these patterns that can help you get a deeper understanding and get better at finding fast or efficient ways to “problem solve”.
Try finding another way to do the problem, or change the problem a little and see how the answer changes – basically I say, let yourself explore the topic. Use the textbook problems as a starting point (thats really what they are) and go from there – all you need is paper! Remember, math isn’t about just finding the answer, but instead about problem solving skills.
Students ask me all the time: “Should I get a tutor!?” and my answer is almost always a resounding “YES! OF COURSE!”. The only part that bothers me about this question is that it is usually asked towards the end of the semester by students who are in danger of failing. If I were to recommend when to hire a tutor, it would be to do it at the start of a class before your grades suffer! I guess the natural question is – why do I think that getting a tutor is so great?
- Forced Practice on a Fixed Schedule – The only real way to learn math is through practice and that doesn’t mean doing 100 problems the night before the test. Think of it like something athletic – you have to build up and be consistent. Instead of 100 problems before the test, it should be 100 problems over the few weeks before the test. If you know that you are meeting with a tutor at 3pm every Friday then at the very least you will be practicing your math at that time every week. More likely, to get the most for your money, you will be practicing earlier in the week so that you have lots of questions for your tutor! It’s just another way to keep yourself on track.
- Hearing it Explained Another Way – In the classes I teach, I have students explain ideas to eachother all the time. Why? Well, over and over again, I have seen students who don’t understand the way I explained it hear the same idea explained from a friend and then suddenly understand! Even if it is exactly the same process, everyone has a different way of explaining things and hearing these other ways can help you develop your own understanding.
- A Tutor Can Focus on Your “Style” of Mistakes – I have been doing math practically full time for the past 15 years I can still get all caught up in a problem and miss a negative sign if I’m not careful. I know this and have learned to always do a quick double check of my signs. We all have mistakes we tend towards and since these can be very individual, they usually won’t get addressed in a class. A tutor however, can notice that you always forget to divide by 2a in the quadratic formula and help you figure out how to handle that. You may have a habit that it holding you back that you don’t even know about but working with a tutor can help identify and address it.
- Reviewing that Stuff You’re “Supposed to Know” – Who remembers everything they learned in every class ever? Well, if you do you are lucky as most of us don’t. Unfortunately in math, there can be little topics here and there that come up again in future classes in fact this is pretty much 100% guaranteed. Double unfortunately (ok go with me on that phrase lol), there may not even be time in class to remind you of these tricks or skills. This is where having a tutor is incredibly helpful as they can help you go back and practice this “old stuff” so that it doesn’t hold you back with the new stuff.
If you do decide to hire a tutor, you should really look into all of the options first. Your school may already have a free tutoring program that you can take advantage of. Do your research and remember – tutoring is an investment just like paying for your tuition or books – so take it seriously and try your best to get the most out of it that you can.
Anyone taking the general GRE in August (or later) will be taking a brand new version with some major changes to the test question types and overal design of the questions. This means that if you have been studying with some of the older review books or classes, that you should take the test BEFORE August if possible!
If you are studying the new format and haven’t registered for the test yet, ETS (the company that runs the GRE) is offering a 50% discount on the test fee if you take the test between August 1 and September 30. The only catch is that your scores won’t make it out until mid-November. Considering that the regular fee is a whopping $160, this is something to seriously consider taking advantage of!
What are some of the changes on the new test? Well among some general test format changes like the ability to skip around on the computer based test and an on screen calculator, there are also some major changes to the question types.
- Math Questions are More “real life” – It seems as though they are trying to get away from mindless calculations and focus more on questions that test your reasoning abilities. HOWEVER, they still say about 100 times on their own site that you still must have the same math skills as you would have on the old test.
- New Math Question Types – There are two new types of math questions: numeric entry, where instead of choosing an answer, you type it in and “multiple select” questions where there may be more than one right answer that you need to choose. You can also expect to see more data interepretation.
- No More Antonyms and Analogies – It has been many years since I took the GRE but I am jumping for joy as I read this! ETS says they will no longer test vocabulary “out of context” and instead will have more reading comprehension questions and new question types such as text completion and questions that have you determine if two sentences have the same meaning.
You can read more about the revised GRE here: http://www.ets.org/gre/revised_general/know
In my opinion, multiple choice math tests are the most difficult type of test you can take. Instead of the usual partial credit, everything becomes all or nothing! Miss a negative sign somewhere? You may end up with no credit.
As a student, the best thing you can do is understand how these tests are written. Both poorly written and well written tests follow typical patterns that, if you know about, will give you a much better chance than guessing on the questions you are unsure of.
The incorrect answer choices in multiple choice tests are called distractors. In a well written test, these are found by purposely doing the most common errors that students do and then making that an answer choice. The idea is that a student who knows what they are doing will not make these mistakes.
How can you use this to your advantage? Know the common mistakes for the type of problem you are doing and try to use this to eliminate answers. I’ll show you an example:
Let’s pretend you are completely stuck on this problem because you forgot how to multiply. What’s a common mistake here? Well, usually people mess up the sign when they are dealing with negative numbers right? If you know that the sign MUST be negative, you can eliminate answer choices (C) and (D) and increase your chance of guessing right!
This works on any level of math test but does require you to know what you are doing at least a little bit. So, pay attention to what your instructor points out as the “obvious” mistakes or what your common mistakes are to help you when you get stuck! I have used this method to write these types of questions even for calculus exams and know that others do as well. Do students always forget to distribute? (answer: yes)… figure out the answer you would get without distributing and eliminate it!
Note: Unfortunately in a poorly written test, the answer choices may just be made up making this method useless! Luckily, it is often true that a poorly written multiple choice tests makes the correct answer obvious since several of the answers will not be realistic.
Over the next few weeks, I will add more tips specifically about this type of test. If you have your own tips, please share them!
Today, I’m doing research into the math that is used on the MCAT (this is the test that students take to go to medical school) so that I can address these topics better here on the site. Through my research, I ran across this great guide with practice problems and solutions that I thought I would pass along!