As we get closer and closer to the end of the academic year, a lot of math students will be studying for exams. Some of these tests are comprehensive exams that cover everything from day one to the day before the test. I believe that as tutors, we need to help those we teach with ditching old, faulty study habits in favor of successful, incremental approaches.
What is the biggest bad study habit you might ask? Cramming...
Cramming, at best, will help students remember the material the day of the test and promptly forget it the next or, at worst, actually degrade their academic performance.
Researchers at UCLA have found that excessive "cramming" actually makes students perform worse on average than those who adopted daily study habits. This was published in the Journal of Child Development in 2012. In another study conducted by Time.com in 2011, the average student who crammed for the exam only passed...
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Learn to count: | is 1, || is 2, ||| is 3, |||| is 4, ||||| is 5, |||/// is 6, ||||\\\ is 7, ||||//// is 8. |||||\\\\ is 9, |||||///// is 10
Alexei M.

I mentioned this problem from one of my earliest blog posts with one of my students last week, so I thought I'd bring it back as this week's Math Journey. Enjoy!
~
The SAT messes with your head. Don't feel embarrassed, it messes with everyone's head. It's designed to. The SAT is a test of your critical reasoning skills, meaning it's actually far more about logic and figuring out the correct course of action than it is about actually knowing the material. This is nowhere more evident than on the Math section.
The SAT Math trips up so many students because they expect it to behave like a math test. The truth is, the SAT Math is about figuring out how to answer each problem using as little actual math as possible. It's all about working quickly, and the questions are structured such that they conceal the quick logic and context-based route behind the facade of a more complicated math question. They're trying to psych you out; to make you...
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To keep your math skills sharp, try Khan Academy. They have numerous math resources, and even more computer science exercises. You can learn how to program. Go there today.

To my fellow educators and students,
I know that it is very tempting to give your students answers to their questions immediately, but sometimes it's best to let a student struggle a little. Asking students why they are doing what they are doing can help students to make lasting connections that go beyond that next test or ACT exam. This approach can be frustrating for both teachers and students at times, but it is quite rewarding.
I have a student who was completely scared about sharing their opinion on an answer they gave. Throughout most of the lesson i refused to give them a yea or nay answer. I asked them to talk it out and see if they could understand why they did what they did. The student was correct, but having students explain their answer and even get frustrated with me some helped this student achieve deeper understanding of the material.

A few summers ago I wrote a blog post about finding math in unexpected places as a way to keep skills sharp through the summer break. One of the unexpected places I talked about was the world of tabletop Role-Playing Games (RPGs) such as Dungeons & Dragons. Such games are essentially communal storytelling exercises which use chance elements to help guide the story via a set of polyhedral dice.
I've been running a D&D game for a group of friends for several months now, serving as “Game Master.” As Game Master I serve as lead storyteller for the group, while the others each create a character to experience the story firsthand. My job is to create the framework for the story. I devise and flesh out the world that the story takes place in, present challenges for the players to overcome, and rationalize the effect their actions have upon the world. Overall, my goal is to create circumstances that will allow the players to be heroes. Today I'd like to delve a little deeper...
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Many of my students come to me needing to learn, or at least review, on how to handle operations involving fractions. I have found that the mere appearance of a fraction in a problem can invoke anxiety in some students. My goal for this post, and any that follow relating to this topic, is to not only teach you how to work with fractions, but to also help you gain confidence.
First, we will start by looking at the parts of the fraction. The number before the slash is the numerator, and the number after the slash is the denominator. In this case, the numerator is 1, and the denominator is 2.
1/2
To work with fractions it is also necessary to understand equivalent fractions, which are different fractions that represent the same number. You might be wondering how this can be true, so I will do my best to explain it.
Since one half is the most easily understood and recognized of the fractions, I will use it in my example. Say you want to divide...
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Math is all around us. We use math to calculate the speed of the earth rotating about its axis. We use math to calculate the radius and height of a water tank to store enough water for a town. We use math to calculate the amount of carpeting material to purchase for our houses, and we use math to calculate the amount of fabric material to purchase to sew a pillowcase for our pillows. This means that you cannot run away from math. Even the dosage of painkiller medicine that your body needs depends on your weight and the use of math.
I have another example of the applications of math in our everyday lives. Movie theaters like any other for-profit business, have a budget with expenses and income columns. In order for the movie theater to break even, it needs to sell a minimum amount of tickets. This movie theater needs to sell a minimum of 100 tickets as the sum of the of tickets purchased. Also it needs to make a minimum of $100 from the sum of the tickets purchased in order to break...
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We're going back to basics today with a Math Journey covering the three broad categories of symbols. I've found this concept very handy when introducing Algebra to middle school students. So let's go!
Math is a language, and I find it often helps to think of it as such right from the beginning. Just as there are different parts of speech in a language, so there are different 'parts of speech' in math. Where a spoken language includes parts of speech such as nouns, verbs, and adjectives, math has three major types of symbols: constants, operators, and variables. Let's go over each one in detail.
Constants
These would be the equivalent of your nouns. A Constant is a number – it has a single, discrete place on the number line. Even if the number itself is ugly – a non-terminating decimal, for example – it still does exist in a specific spot somewhere on the number line. In addition to the obvious constants, math frequently uses what I refer to as 'special constants'...
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Happy Pi Day everyone!
In honor of the mathematical constant with the delicious name, let's revisit my Thanksgiving-themed Math Journey about storing leftover pie! You can check it out
here.
Enjoy everyone!
~Ellen

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...
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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...
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Hello again. I hope everyone had a great break, but please don't take too much time away from studying, from learning. Maybe you need a little extra something to get you going. Here is a great four week course to guide you on how to learn: Learning How to Learn.

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 you’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!...
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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...
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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...
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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...
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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...
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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