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Ellen's Choice: Teach the Concept, Not the Algorithm

I hear a lot about math teachers from my students, and while every teacher is unique, some comments are repeated over and over. By far the most common one I hear is that their teacher didn't really explain something, or was incapable of elaborating when questioned and simply repeated the same lecture again. As a tutor, my first priority is to make sure the student understands the material, and if they're still confused, to find another way to explain it so that it makes sense. In order to do that, I need to have a thorough understanding of the concepts myself, so that I am not simply reading from a textbook but actually explaining a concept. In my years of tutoring math, I've developed a point of view and approach to math that I refer to as “teaching the concept, not the algorithm.” An algorithm is a step-by-step procedure for calculation. The term is used in math and computer science, but the concept of an algorithm is universal. I could tell you that I have an algorithm... read more

Math Challenge Problem #1

You are playing a game involving three dice. You can choose to bet on any number from 1 to 6. I'll roll the three dice. If: - none shows your number, you lose $1 - one shows your number, you win $1 - two show your number, you win $3 - three show your number, you win $5 What is the expected value of this game?  Email your answer so as not to ruin the challenge for others. 

The Power Of Willpower: Five Tips To Strengthen Your Discipline

Willpower is unique to humanity. It is the keystone characteristic that is directly responsible for our technological advancement over the last several hundred thousand years. Willpower can be defined as the capacity to restrain our impulses and resist temptation in order to maximize our long-term success. It is the expulsion of energy to fight off innate survival based urges to exponentially increase future advantages and benefits. It is the driving force behind all civilizations, and it is what prods humankind forward to learn and grow. When we turn down a bite of cheesecake, step away from a mind numbing reality sitcom, or push off a nap to get some work done, the credit goes to willpower. It is this ghost like aura of control and discipline that we rely on to extend our existence and maximize our accomplishments. When we watch highly successful individuals exercise routinely, read voraciously, and work tirelessly, we are impressed with their ability to resist... read more

Mathematical Journeys: Undoing the Unknown Exponent

This journey is heavily inspired by the youtube mathematician Vi Hart, whose videos describing mathematical concepts through doodling in a notebook were the inspiration for much of my mathematical journeys series. I'll put a link to her video on this topic at the end of the journey, and I highly encourage everyone to go check her out. Let's talk exponents. But to do that, first we should talk about multiplication. Multiplication is a shortcut for adding a bunch of the same number together. If I gave you: 5 + 5 + 5 + 5 + 5 + 5 = ? You could just add them normally, treating each of those 5's as a size-5 step along the number line. But since each of these addition steps is the same size, a faster way to figure out the result would be to determine two things: the size of the step, and how many steps we have. Then we can multiply the size of step (in this case, 5) by the number of steps. In this case, we have a total of 6 size-5... read more

What to Watch out for on Standardized Tests

Hey folks,  I am sure many of you have plans of going to college or finishing up that last hectic year of school.  Well with these endeavors comes not only tests and quizzes created by books and your professors/teachers, but you also have to take nation and statewide test in order to pass and/or qualify for a position in a higher learning institute.  Such tests include the SAT, ACT, MCAT, etc.  What you want to remember about taking these tests is that these tests are testing you ability to locate small mistakes and easy to miss information.  They also want you to understand this material.  You have to be prepared for these easy to miss situations.  For example, I am sure you all have done a math question, felt like you did it perfectly correct only to find out that you actually got it incorrect.  Furthermore, the answer you got appeared as one of the answer choices!  Or you were on the right track to answering correctly, but made... read more

Physics and Mathematics

Two types of studies that many people despise the most are Science and Mathematics.  Some people cannot even stand to hear them mentioned.  Truth is, whatever you are actually extremely good at, others may need some improvement.  Although there are scientists and mathematicians out there who are able to analyze and engineer scary and complex looking graphs and three-dimensional shapes and models, they do have some weaknesses.  One of my weaknesses in academia is reading (especially when it is uninteresting to me).  I have struggled with reading for quite some time and there are times where I actually have to force myself to read, not because I can't do it, because I can.  This is the same for many others, it's not that you do not like math/science, its just you were taught to memorize it and not understand it.  Back when you did adding and subtracting, math was pretty fun right?  Well I am sure you will find science and more complex... read more

WWTK: Online Resources

I've recently discovered several online resources that I find very helpful for the various subjects I tutor. Since my tutoring subjects break down into three broad categories (Math, English, and SAT Prep), I'll choose one from each category to discuss today.     SAT Prep For SAT preparation, you can't beat the College Board website ( There's no better way to prepare than to hear it directly from the test makers. In addition, twitter users can follow @SATQuestion to receive the official SAT Question of the Day on their feed each morning. Particularly now given the announcement of the impending redesign, staying connected to the College Board will keep you up to date on all the changes. There's a place on their website to sign up for email updates, so you'll never miss a thing!   Math Having recently started working with middle-school students, I found a sudden need for worksheets to practice with... read more

Parents Backpack Guide to Common Core

So the school year started and so did the changes in our educational system. It used to be simple back in the days - kids went to school, teachers gave homework and parents helped to the best of their knowledge. And now, all of a sudden all these fancy words like Common Core, Data Driven instruction, placement tests, standardized assessments come into play. How does one make sense out of them? Textbooks now look so complicated that many parents can't even figure out what should their child carry to school or bring from school for that matter. Well, luckily Engage NY is a great resource that tries to make a little sense out of this educational cluster. I have accidentally come across a little brochure called "Parents Backpack Guide to Common Core". This publication is priceless! It helps with understanding the basics of the Common Core ELA and Mathematics standards and gives suggestions on how to best help your child as a parent.   So, I felt I have to... read more

Better Than SAT/ACT Test Prep

The following article takes well known anecdotal evidence and makes it much more real - as if it were a punch to the stomach or whack to the head. Do not let it intimidate you in the least. The issue is not about the money…..and this is the key point! It is not the actual tangible money - it is the BEHAVIOR of how people think and what they do which makes the largest difference. The issue is about EXPOSURE. Money can allow for wealthy families to have their children gain MORE EXPOSURE OVER LONGER PERIODS OF TIME to the material within the SAT and ACT. In reality, anyone can gain more exposure over longer periods of time. The idea of last minute test prep and cramming for these exams is where most families have it all wrong - even those with money. It is about the number of times... read more

My Favorite Online Resources

Following are some of my 'go to' online resources. They help keep me up to date and also help me provide positive technology tools for my students.  By sharing these, it is my hope that you find something here useful and interesting. Math Blaster The Free Dictionary Eutopia Reading Rainbow Teaching Resources We Are Teachers Happy Teaching! Sharon H.

Tutoring and this week's Southern California weather (2/24/14 Forecast)

Hello!   To start my first blog post I wanted to say a little something about how much I love tutoring and the weather forecast for Southern California since my main passion is meteorology. Tutoring is something I started in the latter half of college once I started to take upper level math courses. I loved tutoring and wished I had a team of tutors to help me when I was struggling in some of my courses at the time. Sometimes teachers can only do so much or you cannot feel like you can approach them or ask them for questions. Tutors on the other hand are always eager to help students in their studies. It's more than just helping the student, you are creating a brighter future with every student you tutor. Additionally, each time you tutor you feel even better and learn each time you do it. It's both a learning and rewarding experience.   Also, for those that live in Southern California (San Luis Obispo, Santa Barbara, Los Angeles, San Diego, and even... read more

Mathematical Journeys: The Unperformed Operation

Come with me on a journey of division. I have here a bag of M&Ms, which you and I and two of your friends want to share equally. I'm going to pour the bag out on the table and split it into four equal piles. For this example, “one bag” is our whole, and the best number to represent that whole would be the number of M&Ms in the bag. Let's say there were 32. If I split those 32 M&Ms into four equal piles and asked you how many were in one pile, you could certainly just count them. But a quicker way would be to take that 32 and divide it by the number of piles I'd made, which in this case is 4. You'd probably write that as: 32 ÷ 4 = 8 So there are 8 candies in each pile. Seems easy enough with a large number of M&Ms, right? But what if there were less candies – what if our “whole” was less than the entire bag? Well, for a while we'd be okay – if there were 16, for example, we'd do the same thing and come up with piles of 4 instead... read more

Parallel, Skew, and Perpendicular Lines

I've found that most students have little to no difficulty understanding the difference between parallel and perpendicular lines when only one plane is involved. Either they never touch, or they intersect at a 90 degree angle, or they just plain intersect. This concept is relatively easy to visualize because it is completely 2 dimensional.  Where the difficulty lies, is visualizing these same types of lines when different planes are involved, since it is 3d. To help, I utilize flash cards, or small pieces of paper. Have students draw a series of lines on each flash cards, making sure there is at least a set of parallel lines, perpendicular lines, and intersecting lines on each, and give each line a name. Then move the flashcards in different ways, either stacking them or making parallel planes, and quiz them about the new relationships between the lines. 

Math Anxiety: What It Is And How To Defeat It

Let me guess… the question that is currently floating through your brain is as follows: what the heck is “math anxiety?” While it may sound bizarre and made up, math anxiety is an actual condition that is quite common amongst students. It is similar to other sorts of anxiety or fear a person might encounter when doing something that is personally terrifying such as public speaking, interacting with strangers, or being around scary animals. The symbols and the operations can feel overwhelming for some, and that can trigger a subsequent anxiety reaction that completely stifles one’s brain and prevents a person from properly absorbing any material. The Cause Of Math Anxiety Math anxiety is a learned reaction. Students who have negative experiences with math early on tend to have bad emotions and limiting beliefs tied to mathematics. Once these reactions and beliefs are established, students will subconsciously return to those bad feelings whenever mathematics... read more

SAT Prep - How To Boost Your Math Score

So you just took a practice test and you’re devastated by your results. You thought you would net more points, but lo and behold, your score is painfully below your expectations. Your math score is especially poor, but you’ve never been good at math. What is a good plan of action? Let the math score linger at a subpar level while focusing all of your energy on the verbal portion, right? Wrong. First of all, even if you’ve historically done poorly in math, you can easily turn that around with a few months of devoted practice. Second, math is the area where you can see the most marked transformation as far as testing abilities. You can certainly improve your score in the verbal section, but the base of knowledge for both the writing and reading sections is far broader. The English language is highly complex, and it takes most of us a great many years before we learn and understand all the intricacies. Math, in comparison, is much simpler. The rules and terms are... read more

Tailoring Math Education To Different Learning Styles

Math can be a puzzling and often frustrating subject for students. Some pupils seem to effortlessly pluck A+’s from the heavens, while others grind away to earn average grades at best. Why the discrepancy? Are some brains simply predisposed to math success, while others are hopelessly misaligned? Of course not. If I believed that, I wouldn’t be teaching math. So what’s the deal? Why the blaring gap in math performance? One key factor is learning styles. Despite what your folks might say, people learn in different ways. Some students naturally thrive in standard Prussian style classroom settings; others, however, only truly soar in different environments that are better tailored to their particular strengths. If a student is struggling in math at school, it could be because the standard curriculum is not in sync with his/her learning style. This article will (1) run through the seven learning styles, (2) explain how to identify where students fit on the learning style spectrum,... read more

6 Things To Consider In A Math Tutor

Finding an excellent tutor can make a tremendous impact on a child’s ability to succeed academically. While some kids are able to independently digest in class lectures and textbook explanations, others benefit greatly from an additional system of support. Parsing through the material after school with a guiding hand can fully illuminate subjects that are otherwise difficult to grasp. Translation: with the right set of mentors, all students can develop into confident adults with healthy GPAs. Most parents are well versed in the art of finding a nicely fitting academic institution, but very few are aware of the highly nuanced process for vetting a tutor. Here are six key components that parents should evaluate when searching for a tutor: 1. Experience Tutoring Or Teaching – it goes without saying that experience is critical in any field. It is particularly important in teaching, however, because there are a wide variety of students and respective learning styles. Some... read more

6 Tips For Math Excellence: How To Go From An "A" To An "A+"

A new student of mine came to me with a difficult problem: “how can I go from an ‘A’ to an ‘A+?’” Now, I know what you’re thinking… she needs to get a grip. An “A” is an excellent grade, right? Certainly. But my student yearns to jump to the honors mathematics section, which is only reachable via an “A+.” So now that I’ve established that this is a totally valid request, how do I make it happen? How can someone, who is already achieving a high level of success, bridge that final gap to test taking perfection? Here are six ways an “A” student can modify their routine to grab the highly coveted and often elusive “A+.” 1. Master Mental Math – yes indeed, mental math will come in handy here. For most students struggling to nab that 100%, speed (or lack thereof) is often the culprit. One of the key reasons why students can’t get through an exam quickly is because their mental arithmetic is lagging. They spend an unnecessary amount of time either writing out... read more

Let Your Units Be Your Pilot

I am studying stoichiometry with a student right now. It can be confusing sometimes to think about the two or three steps required to reach your final answer. We ran into a problem that required converting weight to moles of reactants, converting moles of reactants to moles of product using mole ratio, converting moles of product back to weight, and then finally calculating the percent yield. Anybody can get lost in this soup. Take the time to write down the units at each and every step. If your units don't add up, then you know that you didn't do the problem right.    When you're down and they're counting When your secrets all found out When your troubles take to mounting When the map you have leads you to doubt When there's no information And the compass turns to nowhere that you know well   Let your units be your pilot Let your units guide you They will guide you well

Assumptions and Academic Success

Assumptions make up the basic fabric of Mathematics.  Every problem in mathematics makes assumptions.   As a student, when you see a problem on a test or in homework, the first thing you need to do is figure out what assumptions the question writer has in mind.  It may be that a problem has multiple solutions, and knowing the assumptions will allow you a better chance to answer the question in the correct context.     Many people who are trained in teaching write questions for the ACT or SAT make commonly accepted assumptions without realizing it. They do this because they don't have sufficient training in Mathematics and Logic to understand what assumptions they are making.   Teachers often lack training, and many homework problems make unstated assumptions which confuse students and cause them to fear Mathematics.  In my opinion, a student's fear of Mathematics is often a fear of being tricked by unwarranted assumptions.   As... read more

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