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I remember going to school and feeling like something was wrong with me because I was good at mathematics. Especially, since nearly every teacher felt the need to re-iterate how girls were not as good at mathematics as boys based on what ever random statistics at the time.   However, I excelled and kept going. I got a degree in mathematics. So, what made me different from all the other girls that got discouraged. Natural ability for mathematics; however, when I reflect that's not the whole story. As I went to college, there were other girls that were great at mathematics, but once again got discouraged. So, what made go on to pursue degrees is Computer Science, Mathematics, and Computer Engineering.   I got the same discouraging information as everyone else, but I kept going. Why?  1) "Fighter" Personality My personality is such that when someone tells me that I can not do something, then I wanted to fight that much harder to prove them... read more

Although new to WyzAnt, I have tutored mathematics for the past four years at college. One thing I notice among many students is a great deal of annoyance towards mathematics. They feel mathematics to be too abstract, rigorous, relentless, and just plain boring. Most students either prefer a subject they will end up using in "real life", or a subject that gives them a sense of wonder. However, the amazing thing about mathematics is how truly wonderful it is for me. Most people who see my attitude towards mathematics (including others who are reasonably adept at math) find this odd or misplaced, and I fully understand their lack of sympathy. Perhaps you are one of them. But I can assure everyone reading this there is something truly mysterious about mathematics that breaches the very foundations of astonishment and awe. Take prime numbers for example. It's pretty clear that you can take any whole number and decompose it down into a product of prime... read more

The most basic math that students will have most problems on will be Algebra.  Algebra is a whole new language to some and native to others.  Knowing and Understanding what Algebra is will be the difference between success or hardship farther down the roads.   Hi, name is Thang, and I think algebra is the stepping stone for student to succeed in any math class.  If students have basic knowledge how to recognize and utilize what they know about algebra, then they will do well in other math classes. However, if the students can manipulates and applies their understanding of algebra, then they will succeed and go farther in their mathematics' skills.   As tutors, we  can and should guide our students to learn the arts and crafts of mathematics (as well as other subjects) so it can be like their native tongue.

In mathematics, different functions has different rules and I can see a lot of students are struggling with the rules for integers. So I'll kindly discuss the rules for each operation: + - * /   Addition   (-) + (-) = (-) Ex: -9+-8=-17   (+) + (+) = (+) Ex: 4+6=10   (+) + (-)  [Remember to always take the bigger number sign and and use the opposing operation, which is subtraction to solve the equation.] Ex: 5+-3=2   (-) + (+)  Ex: -9+8=-1 [Same rule follow as above]   Subtraction   (-) - (-)  Ex: -9-(-8) = -9+8 [When two negatives are next to each other you change to its opposing operation: addition and change the 8 into a positive integer.]   (+) - (+) = (+) [Unless the first integer is smaller than the second. Ex: 5-8 then you follow the rule stated... read more

The unit circle is one of the most important concepts to understand in Trigonometry.   As a tutor who emphasizes understanding and comprehension over memorization, I try to make it as easy as possible for my students.   Here's the way I like to look at it:   1) First, realize that the unit circle is simply a few points drawn on an graph with an x-axis and a y-axis. 2) Recognize that there is an overall pattern. Every 90 degrees (0, 90, 180, 270) is a combination of 0 and 1 (positive and negative). Every 45 degrees (45, 135, 225, 315) is √2/2 (positive and negative). Every 30 degrees (30, 60, 120, 150, 210, 240, 300, 330) are combinations of 1/2 and √3/2 (positive and negative).   This means that you only have to remember three numbers: 1/2, √2/2, and √3/2 (positive and negative).   The first quadrant (0-90 degrees), has all positive numbers, just like you'd expect in any other graph. The... read more

Online tutoring is a great option for families to have on-demand access to help.  After a long day of work and school, sometimes having to go out again to a tutoring session can be very daunting.  Online tutoring allows you to bypass all of the headache and stress and get to the help you need immediately.   Typical online tutoring uses a virtual classroom which includes a whiteboard that allows the tutor and tutee to communicate in real time.  Most virtual classrooms have audio and visual components included and require no additional installation.  The only tools necessary are a computer, internet connection, speakers and microphone (or telephone depending on the connection).   To learn more or if you are interested in online math tutoring contact me, Andrea Hall.    

Almost no one likes homework, especially mind-numbing drill and practice.  Problem after problem, over and over again... does this really accomplish anything?  The answer, according to the literature, is "yes!"     As a tutor, I recommend the website to all primary and secondary students as the best way to practice math, but is it the best way?  To investigate this, I turned to the peer-reviewed literature, which turned up some interesting results about the importance of practice.     In a 2005 study on a diverse group of Texas math students, researchers Nguyen and Kulm randomly placed students in two different groups.  One group had old-fashioned pencil-and-paper homework, while the other group had randomized online homework.  Students in both groups had the opportunity to rework homework and improve grades.  The students were given a pretest before the study and a post test after.  The results... read more

Q: Where do you go when it is cold? A: In the corner of the room because it is 90 degrees!   Q:Why is a math book always sad? A: Because it has too many problems!   Q: Why did the mutually exclusive events break up? A: Because they had nothing in common!   Q:What did one math book say to the other? A: Don't bother me I got my own problems! Q:Why do you never serve beer at a math party? A: Because you can't drink and derive!

Here are 48 of my favorite math words in 12 groups of 4. Each group has words in it that can be thought of at the same time or are a tool for doing math.   between on over in   each multiply of many   ratio divisions distribution compartments   limit neighborhood proximity boundary   infinite infitesmal mark differentiation   graph width height depth   circle sphere point interval   hyper extra spacetime dimensional   geometry proportion sketch spatial   four table cross squared   target rearrange outcome result   area volume space place   What are your favorite math words? If you aren't sure, search for "mathematical words" and pick a few.

It has come to my attention that a lot of people do not enjoy math. As a math tutor, I probably hear this complaint more than most, but most people probably know a person (or are that person!) who just does not like math. I would like to say that if you think you don't like math, you might just be wrong. Mathematics is an extremely diverse discipline that stretches across all aspects of life. What a lot of people don't realize is that they are engaging in mathematical activities without even thinking about it. When you're driving and start to hit the breaks early so you can coast to a gentle stop, you're using calculus. When you're running and feel the air cool as it's passing your face, that’s thermodynamics. When you're asked to make a password with numbers and letters, that’s cryptography. When you can't find what you're looking for on Google and try rephrasing your search, that’s set theory. You're using math every day all the time. So maybe "solving for x"... read more

This course represents a transition from basic mathematical formulas and equations into a bigger concept of learning about the origins or proving theories of math and created formulas. Taking this course requires the use of logic and concepts which you must understand deeply in order to write out correct proofs to back up your theories of math.

But there's always MORE math! That's what I told one of my students a month ago, and I meant it. I've dealt with math in every role from student, to teacher, to tutor and I can honestly say that the more I learn, the more I'm sure that I've barely scratched the surface of what's out there. A scary thought considering I've been educated in the subject for nearly 25 years. So what is a high school student to do these days with so much scary math out there?   I have one piece of advice: focus. That does NOT mean fixating on every minor detail you come across in order to then extract meaning from each individual piece of information and then put it all together at the end. That's not focusing, that's suffering. Nobody learns the ABC's all at once. Neither should you attempt to do it with math.   In order to focus, it helps to (temporarily) ignore the minor details and devote your attention to "the big picture." You want to quickly identify and master... read more

I can't count how many times I've sat and watched a student erase half a page of her hardest math work just because the end result didn't come out right - or because it didn't fit neatly on the page.  I'm not sure if this is a new thing, this preoccupation with making one's homework look nice and flow perfectly from Point A to B.  But it makes me sad to see my students erasing some of the most important records in their academic lives.   Mistakes are not failures.  Mistakes show you how hard you worked, how far you got and exactly where you went wrong.  They are beautiful pieces of your mental history.  They show you what kinds of things you need to watch out for in the future.  Do you often forget to distribute your negatives?  Do you get exponent rules mixed up?  Maybe you're not so great at remembering when to rationalize the denominator.  Whatever your personal "weaknesses" are, they are uniquely yours.  Acknowledging... read more

  "I don't need to learn math because I want to be a truck driver". I love hearing that or similar comments. Especially from a 12 year old. How does a 12 year old who never drove a car know he wants to be a truck driver? There is nothing wrong with being a truck driver. Some truck drivers make over $100,000 a year. Many office workers fantasize what it would be like to be on the road away from the drudgery of the cubicle. However, being a truck driver is hard work; which is why it pays well (sometimes). You never see your family, have few friends and face real dangers. But does a truck driver need math? I would say yes; some are immediately apparent, some are not. The immediately apparent reasons are truck drivers need to have a good understanding of weights and heights. How many times have we seen that truck hit a bridge because the driver did not realize his truck was too high? How many trucks have crashed because the weight of the freight was too much... read more

Rather than droning on about each subject in math at this point, I'm going to make a shift. I'm currently engaged in a conversation with a friend, and my most recent reply to him expresses my opinion on how math is being taught today:   ...The beauty of math is something that I have seen most of my life, and it stands in my mind as one of my fundamental motivations for studying math. As a person with that emotional tie to math, I realize that many students would find it difficult to identify with my assertion that math is beautiful. As a result, I often take a stance that might be a little self-protective, and offer an answer that seems to be weaker but more universal. In short, some aspects of math are of universal benefit, such as the skill of basic calculation, or the benefits of mental exercise. There are some benefits that apply only to a portion of the population, such as the ability to factor polynomials, or to find missing sides of triangles... read more

One of the biggest frustrations for students is getting something wrong that they know how to do. What is usually the problem?  Careless errors. Do students really care less? Probably, they care less for writing everything down step by step. They care less about labeling the formulas.  They care less about thinking about why they keep making that mistake. For some reason, I have found that students have the perception that smart people don't write stuff down. Students believe that "smart"  people hold it all in their heads. Well, here's the real deal. Smart people write almost everything down with meticulous attention to detail. They know that the "blackboard " in their head gets erased quickly. There's nothing more frustrating than trying to figure out what you did wrong when you don't have a record of what you did. I call it the dance in your head that leads nowhere!  What's the cure? If you believe that your student is being careless  Tell... read more

Hello! I wanted to share something with everybody which seems obvious to me, but I'm not sure everyone is on the same page. Have you ever had a terribly boring school teacher? I bet you have because we all have at some point! It doesn’t mean that these teachers are all uneducated in their subject, (although they might be…) it just means that either: A. They aren’t involved enough in their field to have passion for it or B. They don’t know how to transmit that passion to students effectively To be able to have fun or at least gain respect, understanding, or interest in a subject - the subject must be presented in an interesting way. It seems obvious when you put it that simply, but some or most teachers don’t care enough to even pretend to be excited, passionate or involved in their field. This makes learning from these teachers very difficult, especially if the students are self-sufficient learners. ——That is where... read more

A question that I have heard many times from my own students and others is this: "When am I ever going to use this?" In this post and future posts, I'm going to address possible answers to this question, and I'm going to also take a look at what mathematics educators could learn from the question itself.   Let's look at the answer first. When I was in school myself, the most common response given by teachers was a list of careers that might apply the principles being studied. This is the same response that I tend to hear today.    There is some value in this response for a few of the students, but the overwhelming majority of students just won't be solving for x, taking the arcsine of a number, or integrating a function as part of their jobs. Even as a total math geek, I seldom use these skills in practical ways outside my tutoring relationships.   Can we come up with something better, that will apply to every student? I say that... read more

Since it's Thanksgiving week, let's think about pie for a second. No, not mathematical pi, just actual real edible pies. For Thanksgiving I'm in charge of making dessert, so I'll be bringing two pies, one pumpkin and one apple. Let's say that I sliced the apple pie into 12 pieces, and the pumpkin pie, since it held together better, into 18. Fast forward to the end of the evening. My pies were a big hit, and I have almost none left. In fact, all I have is three pieces of apple and four pieces of pumpkin. I want to combine the remaining slices into a single pie pan, so that they take up less space in the fridge. How do I figure out if my remaining pie will fit in one pan? Well, let's start by writing down the remaining amounts of pie in the form of fractions. Remember, one of the definitions of a fraction is parts of a whole, so let's apply that definition to figure out our starting fractions. The apple pie was cut into 12 pieces, and we have three out... read more

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