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## Math Blogs

There is no such thing as someone who doesn't get math. Instead, it is the teacher who "does not get how to teach math".   I have come across many very good teachers, and the thing that differentiates them from the less amazing ones is this: they do not have a single "tried and true" method. The teachers who do have this type of "tried and true" method always find problem students, and those students get discouraged. However, those students need to know it is not their fault.   When teaching Multivariable Calculus this past semester, which is infamous for failing engineering students at Cornell, my fellow teachers came from different backgrounds. The less experienced ones would always complain about their students "not getting it" and it was because the teachers themselves did not understand the material to a depth that they could explain the math in multiple ways to students.   In my experience, I have... read more

Often times experienced mathematicians tend to get comfortable with certain problem-solving strategies. For example, in a problem one might use a system of equations to solve a problem rather than employing a simpler more easy way to solve it. Though using system of equations are great, knowing how to solve problems using different approaches is important, not just for oneself, but for their students.   Take for example the following problem: A farmer has both pigs and chickens on his farm. There are 78 feet and 27 heads. How many pigs and how many chickens are there?   Solution 1: (Using Algebra System of Equations) 4p+2c=78 (pigs have 4 feet and chickens have 2 feet with 78 feet in total) p+c=27 (27 heads mean that the number of chicken and pigs total 27) Then by algebra p=27-c. Therefore by substitution, 4(27-c)+2c=78. 108-2c=78. 2c=30. c=15. Since, c=15, p+c=p+15=27. p=12. Therefore, the farmer has 15 chickens and 12 pigs... read more

Okay, we have all made a math mistake, but for one reason or another we never took advantage of that opportunity to commit the correct step to memory. I have news for you. You can still remedy the situation. Here is how you achieve it. 1. For every time that youâ€™ve made a wrong step in solving a problem, repeat the correct step three times. 2. If it is a multi-step problem, WRITE all the steps in the correct order at least three times. 3. READ out all the correct steps to yourself at least three times so that you HEAR the correct steps. Here is the rationale for this strategy. We have multiple ways of learning for a reason and we need to make use of multiple intelligences in order to maximize our ability to understand and memorize the correct steps. Once we commit the correct procedure into long-term memory, we are essentially freeing our short-term memory to work on other tasks. This way we won't get stumped months later when we come across the problem. So this strategy is a win!... read more

These six steps help students find a clear path toward solving word problems, and checking their answers for accuracy.  1.  Draw a picture 2.  Identify the objective -- i.e., make sure you understand the question, so you can move toward the solution 3.  Identify the available data 4.  Write an expression 5.  Solve 6.  Check

The most requested tutoring subject is MATH! Many students struggle with math (algebra, geometry, calculus) because there is no easy way to learn it. It is nice to have someone to break it down for you and talk you through your problems. But, what happens when you do not have your tutor next to you?!?!   PANIC?! OF COURSE NOT!   Although it is my duty for you to have a firm grasp on the math concepts, I may not always be there when you need me (of course, I will always try =)). What I used as a math student and what I use as a math tutor is a study "cheat-sheet" guide. I would make my own cheat sheets that broke down steps and had formulas with explanations of what each variable meant. This was a HUGE HELP when learning new concepts or having to remember old concepts for a final exam.   As you continue to learn new concepts, you add it to your cheat sheet. These should be very short blurbs like a formula or a short example of the problem... read more

One of the main complaints that students have when struggling with their math homework is that they don't understand why they need to learn this in the first place.  After all, how often do we actually use calculus or trigonometry in our daily lives?   I always make an effort to correct this false assumption in my students.  Everything that we learn in math connects to reality in often unexpected ways.  For this reason, I like to find out what it is that interests my student, or what their career goals are, so that I may show them how the math connects.   Take the example of logarithms.  For the student with an ear for music, I can explain how logarithmic scales describe the relationships between musical tones, and true understanding of musical theory requires an understanding of this field of math.  For the student who plans to go into the medical field, logarithms can be used to help model the levels of medications in a patient's... read more

There has been a link circulating recently through social media (Link below). The link describes a story in which a teacher told a student that an answer was wrong on a common core math quiz. A very loud debate has erupted in regards to Common Core Math and it's role in the education system. Some stand to defend it, and others are very much against it due to its "confusing nature." I believe that Common Core is simply not being used properly within the education system, which is why such stories described in the article exist.   I am very passionate about the debate on Common Core Math and its role in the education system. Though it is the center of much confusion and debate, Common Core is not all together bad. The issue with Common Core Math is not that the methods themselves are bad; instead, the issue resides in the fact that teachers and school boards have not been taught the actual purpose of Common Core and have not been properly trained on how to use... read more

1) THE BASE: Ask yourself where you want to start. A building is strongest and most stable at the base. So that being said, you want to build a strong and stable foundation on the subject you want to learn. Concepts, rules, understanding play a big role when learning a subject. Grasping the fundamental ideology of a subject is the beginning of formulating the bases of understanding the core concepts. So in other words get a general picture of the subject and read the history behind it.   2) START SMALL BUT BROAD: Every subject has a broad category and a specific category. The more in-depth you go, the more confusing it can become if you don't have the general knowledge or a broad understanding of that subject. For example, you're not going to understand Calculus 2 without learning Calculus. Or understand how your brain creates memories or thoughts without understanding neurons. So by researching, reading, and analyzing the broad categories of the subject you can learn... read more

1) THE BASE: Ask yourself where you want to start. A building is strongest and most stable at the base. So that being said, you want to build a strong and stable foundation on the subject you want to learn. Concepts, rules, understanding play a big role when learning a subject. Grasping the fundamental ideology of a subject is the beginning of formulating the bases of understanding the core concepts. So in other words get a general picture of the subject and read the history behind it.   2) START SMALL BUT BROAD: Every subject has a broad category and a specific category. The more in-depth you go, the more confusing it can become if you don't have the general knowledge or a broad understanding of that subject. For example, you're not going to understand Calculus 2 without learning Calculus. Or understand how your brain creates memories or thoughts without understanding neurons. So by researching, reading, and analyzing the broad categories of the subject you can learn... read more

WHAT: Does the student know what they are trying to learn? Some classes move so fast that they don't even know what topic they are on anymore. WHERE: Does the student know where to apply what it is that they are learning? WHEN: Does the student know when to apply what they are learning? They may understand what they are doing, but do not know when to use it. WHY: Does the student know why they are doing what they are doing? Do they know why the answer is right? This is the most important question. Does the student actually comprehend or are they just repeating? HOW: Does the student know how to apply what they have learned at any given time? Do they know how to use these tools they were given in everyday life?   I want to have the answer to all of these questions an unhesitating "YES"

Never have I ever done a tutoring job like this before.  I am looking forward to partaking in this website and venture as a side job because it seems like a reasonable way to generate income on the side without stressing yourself out. I'm looking forward to teaching kids and passing on my knowledge of subjects through tips and tricks to make their learning easier, like it did for myself.  Most of all, I can't wait to see the results from my students when they receive their grades or start to perform better at the sports I coach them in.

There are so many great math curricula out there.  Some are very heavy on drills: and who can deny that drills are extremely important?  Others are wonderful at demonstrating concepts....the thought processes behind working out problems.  Drills can easily bore a student to death and make them feel like math is a punishment, rather than an interesting investigation.  However, they seem to have some mastery of math when, in reality, they don't understand the language of math. Some children pick up on concepts so quickly that a teacher or parent begins to think the student is a prodigy and is past the drills. So the teacher tends to "zoom" through lessons, allowing the student to lose important ground that has already been gained.  Eventually, this leads to a halt in the student's progress.      Obviously, this means that both concepts and drills are equally important, and a tutor should never sacrifice one for the other... read more

On Friday my TV broke. Kind of a bummer, but we'd had it for many years and it was time for it to go. Now we needed to get a new one, so we headed out to the store. In the process of our search, we realized that our old TV was at the extreme smaller end of the TVs they now sell, so we were going to need to buy a bigger one. We found one we liked, that was only slightly bigger than our old one. The big question, though, before we plunked down our hard-earned cash, was this: would it still fit on our entertainment center? Our current TV was sold as a 40-inch model, and the one we liked was 43-inch. However, TVs are measured across the diagonal, not the width, so we needed to know what the actual width would be. My hubby got out a tape measure, and I got out a pencil and paper. He measured our 40-inch TV across the diagonal and found that 40 was actually just the screen size; the full diagonal with the frame was 42.5 inches. We knew the new one's frame was no larger... read more

If you intend to write for more than 30 minutes, please consider using a text editor like Microsoft Word or Notepad. That way, you can copy and paste your finished post into the submission form and not risk losing your work because of a timeout.

We all have one: that one subject that our brains just refuse to understand, and no matter how much we study or how hard we work, we never feel like we really truly GET what is going on.   For me, that subject was always Physics. No junior high or high school teacher could ever answer the unending string of "...but WHY?" questions that I needed answered before I could understand even the most basic concepts of our Introductory course. It wasn't that I couldn't understand, but rather that I wasn't being taught these ideas in a way that made sense to me.    As an adult, Physics is now actually one of my favorite subjects to read about because I have found some books written for people just like me, people who need explanations fulls of examples and explanations and lots of pictures! I may never discover black holes or split an atom, but I now know enough that I can understand the people who do those things. :-)     So,... read more

Math is a subject that I've always been excited about! So it was easy for me to do my homework. What if you don't like math? Let me ask you a question. Is math a subject that is required for you to take in order to be promoted from one grade to the next? Do you have the choice of not taking it? My point is simply this. There are many things which you and I have to do that we don't like if we want to make it or survive. Instead of telling yourself that you don't like math or that you hate it; simply say that you love what learning math can do to your quality of life or how you can conquer your fears and I promise that you will find yourself solving problems that you thought only Einstein could do. Get it? Got it? Good!

When I start a tutoring session,I first check up on my students and inquire about what they are up to or what is on their mind. Then I relate to that and segue into our goals for the next hour or so (session length). Second, I always bring up how I learn and how everyone learns a little bit differently. Thus, I encourage my students to let me know if they are not following my lead or have questions or concerns. Third, I always have my students "illustrate" outwardly how their minds are working through a problem by working entirely without assistance until they feel they have done their best. This fosters perseverance and lifts self-esteem and goes a long-way towards generating a "can-do" attitude. Then, I always make up games or riddles that challenge my students in what they are studying (Since, I predominately tutor in chemistry and math and SAT/ACT math prep, these "puzzles" are mathematical in nature.). Lastly, I mention something that relates the... read more

Sure, we have all heard our math teachers say "Study for your test tomorrow." While we can all agree the importance of studying and getting prepared for an exam, not many math teachers actually tell you HOW to study. I am sure we have all spent time making flash cards, staring at our notes, or watching last minute videos on youtube, only to realize the test results often don't correlate to our effort. Before long, these upsetting experiences and test results created a scar in our minds, that statement we have all heard before: I am just not good at math.   The truth of the matter is, many people who have expressed their inability to understand and perform well on mathematics simply don't know how to study for a math exam. After all, those negative signs and multiple choice questions are often so tricky, even though you calculated every step correctly until the very end, all it took was one single mindless error that can well ruin the entire result. If we closely... read more