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johnstutoring

my thoughts on learning math

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math https://johnstutoring.wordpress.com/category/math/
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math skills are built https://johnstutoring.wordpress.com/2015/06/02/math-skills-are-built/
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fun with numbers https://johnstutoring.wordpress.com/2015/06/02/fun-with-numbers/
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math test taking skills https://johnstutoring.wordpress.com/2015/06/02/math-test-taking-skills/
minus vs negative https://johnstutoring.wordpress.com/2015/06/02/minus-vs-negative/
test preparation and the battle at home https://johnstutoring.wordpress.com/2015/06/01/test-preparation-and-the-battle-at-home/
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johnstutoring my thoughts on learning math menu skip to content search for: fun with numbers june 2, 2015mathcswgs in the year 2011 we experienced 4 unusual dates 1-1-11 1-11-11 11-1-11 11-11-11 now for some fun: take the last 2 digits of the year you were born plus the age you will be this year and it will equal = 111 it works for those born in 1900 – 1999 if you were born in the year 2000 or later it only adds up to = 11 can you calculate what happens if you were born in these centuries past? calculated if they were still alive today – someone born in january 1111 would be 900 years old this month – 11 + 900 = 911 can you see the interesting trend if you were born in these centuries? 1800 – 1899 (211) 1700 – 1799 (311) 1600 – 1699 (411) 1500 – 1599 (511) 1400 – 1499 (611) 1300 – 1399 (711) 1200 – 1299 (811) 1100 – 1199 (911) math skills are built june 2, 2015mathcswgs a couple years ago my wife and i broke down and finally purchased a wii home game system. my two sons spend quite a bit of time perfecting their skills on their favorite game. i recently asked if i could play with them. the game was a mario race track of some sort. the graphics flew past me and there were too many controls, tricks, and turns for me to be even minutely successful. my kids got mad at my lack of skills and yelled at me. they actually used the word “stupid” which i do not allow in the house. i thought it quite unfair that they expected a higher performance from me on my first exposure to the game. so they gave me a few more chances. however, my success was slow to come even after an hour on the system. why was this? well, not only had i never seen the game, i had never used one of those game controllers, i wasn’t familiar with the interface, i didn’t even know who mario was or anything else dealing with this system or the game. i grew up on real pinball machines and i even owned an original pong for tv. they on the other hand have never had anything other than a game controller and have seen mario in multiple game formats such as their hand held game systems. math is much the same way. the skills you learn in elementary school become the building blocks to higher math. addition, subtraction, division and multiplication become the “controller” for all future math courses. if you took short cuts in these basic skills to “get by”, you will suffer for it in algebra i. if you don’t master algebra i, then the calculations you must do in geometry will be difficult. you learn some new skills in algebra 2 to add to the others, and so on. it is common for me to find high school students that do not understand how to add and subtract negative numbers or are stumped by fractions. unfortunately, if you want to succeed, you can’t short cut any of these steps. just like mario kart, i can’t simply push one lever forward and race straight to the end. there are all kinds of turns and bumps and traps and buttons. if i want to win the race i need to know how to use them all. if your student has always struggled in math, you may find that he/she needs to step back and learn some of these basic skills. sometimes this is simply a “refresher” while other times bad habits have to be broken and good habits have to be learned. a good tutor can identify these weaknesses and build the proper skills. after many frustrating experiences playing the different games my sons enjoy i asked if i could pick a game. wii olympics has an archery game. they had played it before, but it was not exciting enough for them to spend much time on it. my first effort at wii archery i blew their scores away. they couldn’t believe that “stupid” dad did so well on his first try. i didn’t tell them that i had my first recurve bow in 2nd grade and that by 9th grade i was the archery instructor for ra camps across texas. learning proper skills will stay with you a life time. math test taking skills june 2, 2015mathcswgs it is common for students that typically perform well on daily work to not perform well during tests. in my experience the number 1 reason for this is test anxiety and the number 2 reason is information overload. that is the confusion that occurs because the test includes multiple skill sets at once while the daily work address only 1 or 2 at a time. one of the many habits a student should acquire is the habit of proper testing skills to avoid the anxiety and overload that occurs without them. before i explain the good test habits, let me describe some of the bad test habits. first, students tend to pick up the test and scan all the questions before starting any work. the drawback to this is that your brain has gotten a glimpse of the upcoming problems and starts to wander and worry instead of focusing on the first question to be solved. thoughts start to creep into your mind such as “do i know how to do problem #3 on the second page? didn’t the teacher say we weren’t going to be tested on that material? what if that was the thing i was having so much trouble with?” now your mind is needlessly worried about something that you are not even looking at and you become distracted and confused. the next bad habit i see is poor handwriting & cramming work into small spaces between test questions. when you practiced with homework you had unlimited blank paper on which to work out the problems but on the tests, blank paper is generally not present and the problem solving skills practiced at home on paper are not used during the test. you can avoid this issue by finding out the teacher’s policy on scratch paper prior to any test and then planning accordingly. some teacher’s allow you to use your own scratch paper, some prefer to provide it, and many require you turn it in with the test. i’ve only come across 1 teacher that didn’t allow scratch paper at all & i recommended the parents speak to the counselor about the issue. the third problem i see is skipping difficult questions and going on to the next. this creates similar issues to the first habit i described of scanning all the problems, but it adds the risk of either forgetting to come back to the problem or when you do, you don’t fully read the instructions the second time. so, the correct skills are basically to do the opposite of the bad skills listed above. don’t scan the whole test when you get it, simply start working the first problem. don’t cram your handwriting into small spaces, use the same writing skills taught to you by the tutor. and, finish difficult questions the best you can before continuing with the rest of the test. there is one more skill that i teach not only for test taking but for everyday homework. it is the most important thing you can do when taking a test. before starting any work or looking at any problems write down all the core knowledge that is to be on the test on the scratch paper, if allowed, or on the back of the test or top of the test if scratch paper is not allowed. you already knew what the test was about from your syllabus or class review. it might have said “friday test, chapter 5, graphing and solving linear equations”. well, there is certain core knowledge attached to that chapter and that topic. so write down what you know before you start, such as formulas, facts, equations, definitions, etc. this helps your brain to switch gears to math, it will reduce your anxiety, and if a problem confuses you, you simply look at what you’ve written and search for the missing data in the problem. think of it this way. you are going out to play soccer with your team on saturday morning. part of the preparation is to put on your cleats, put on your shin guards, put on your jersey, and do some stretching or warm up exercises before you go on the field. you don’t wait to slip on your team shirt only when it is your turn to go on the field, you already have it on. you don’t stand on the field and wait for the ball to come and then slip on your shoes only when it is your time to kick the ball. no, you have everything on and ready to go before the game starts. it is the same thing with a math test and writing down this core knowledge. you put it all down and have it all ready when you start. you don’t wait until a graphing question comes up and then try to remember how to find slope. you already thought of it, you already have it in front of you and you are ready. you will be amazed how writing down the core knowledge before starting homework or a test will not only make the work easier, it will also eliminate your test anxiety and your grades will improve immediately. this learned skill should become a habit in all your subjects and makes the differences between simply passing a class and actually mastering the knowledge of the class. your friends will be calling you the math genius before you know it. minus vs negative june 2, 2015mathcswgs one of the ways i identify the strength of a student’s foundation in mathematics is to give them a simple equation: –5 – 3 = ? what i usually get back from the student is the question “is that a minus 3 or a negative 3?” to which i reply “huh?” you see, i couldn’t understand why students today think that a “minus” and a “negative” are different things. to me they are the same thing and are only called differently depending on where they appeared. for instance if the symbol “–“ appeared in front of a number that stood alone, we called it a “negative”. if it appeared between numbers in an equation, we called it a “minus”. but truthfully, “minus” and “negative” act the same way. so, although the above equation is properly read: negative 5 minus 3 it could just as easily be read: minus 5 minus 3 or even negative 5 negative 3. my confusion got to the point that in one of my high school algebra classes, several students wanted to argue that they were different. you know what they used as evidence that they are different things? they showed me their calculators. the high-tech calculators of today have a – sign and a (–) sign. the first is called a “minus” and is used as the “operation” command. the second is called a “negative” and is used to denote a number with a “negative” value. wow, what do i say to that? we have to realize that calculators simply aren’t that smart. you’ve heard the term “trash in trash out”. that means that the accuracy of a calculator or any computer is only as good as the information you give it. the newer calculators have 2 symbols because in higher math the order of operations can get confusing when using a – sign such as negative exponents. so, my counter argument is that addition and subtraction is simply the movement along a number line. therefore, the – symbol simply denotes the location or the direction on that number line. for instance our sample equation can be illustrated as follows: although we started at -5 (negative 5), we actually started at 0 and first subtracted the 5 to get to the starting point of negative 5. then we subtracted 3 more to get to -8. before you get to comfortable with that, let me point out that the – symbol means to move “in the opposite direction”. it does not mean “to move left”. we read left to right, so the default direction is right. the – direction would be left. so if we have the following equation: –5 – –3 = ? we again start at negative 5, but the first – means left and the one after that means move in the opposite direction or to the right. so we get: to me, this is simple to understand, but for students it can be confusing. so, here are “rules” for addition and subtraction problems that the students seem to grasp. if the signs of both numbers are the same, add the numbers together and keep that sign. if the signs of the numbers are different, find the “difference” and keep the sign of the larger number. keep, change, change. my students use this a lot to deal with subtraction problems. it means to keep the sign on the first number, change the subtraction to addition & change the second number to a negative. so the equation 5 – 3 becomes 5 + -3. for some reason 5 plus negative 3 is easier for them to understand. here are a couple examples for these rules: rule 1:    5 + 3 = 8 (same sign add & keep sign) -5 – 3 = -8 (same sign add & keep sign) rule 2:   -5 + 3 = -2 (diff. signs, find diff, keep sign of larger number) 5 – 3 = 2 (diff. signs, find diff, keep sign of larger number) rule 3:    5 – 3 becomes 5 + -3 = 2 (keep, change, change) -5 – 3 becomes -5 + -3 = -8 (keep, change, change) 5 – – 3 becomes 5 + + 3 = 8 (keep, change, change) corrects the double negative dealing with negative numbers should be second nature to a student at least by the time they are in 7th grade. i’ve seen students that can be taught algebra, but then get poor grades because they aren’t handling negative numbers correctly. if you aren’t sure about your student, then ask them to solve this equation: –5 – 3 = ? if they can’t give the answer instantly & correctly, then it might be time to get a tutor. test preparation and the battle at home june 1, 2015mathcswgs test preparation and the battle at home the school year is almost over. taks is behind us and students are already looking forward to summer. but it isn’t quite complete yet. we still have the hurdles of a 9 week test and a semester final. with that in mind, i thought it a good idea to review test preparation advice. just before taks week, the school sent home a letter encouraging the parents to give their child every advantage for success. some of the suggestions in the letter included: get plenty of sleep the night before the test eat a healthy breakfast high in proteins drink plenty of water, stay hydrated wear clothes that are comfortable these of course are some of the same things that i encourage my students to do all the time. but while helping students prepare this taks season, i had a new thought. maybe parents of older students already thought of this, but i have not had to face it with my own children yet. keep tv and other electronics off (or to a minimum) during test week (tv, xbox, internet, cell phone, etc) i’m guessing for many of you, this is an on going battle in your homes. you see, the human brain is not only capable of processing large volumes of data, it needs to, and will process large volumes of data one way or another. the question is, do you want your brain processing the latest sitcom, xbox battle, or facebook page during an important test week or do you want it focused on the subject at hand. you and i learned growing up that work came first and rewards came later. however, our society teaches a “just do it” now attitude where instant gratification is a right not a privilege. our children are so over stimulated with electronics, social networks, instant communication, etc. that they can literally go into withdrawal without it. however, the brain is an amazing creation. it is capable of learning and adapting to almost anything. as parents, we not only want them to excel in school, we want them to be mature and successful in life. by the time they hit high school, we have to start being smarter about how we teach them these life lessons. they need to feel like it is their idea and you need to stay in control. so, don’t take the electronics away as punishment or as incentive. instead let your student know how proud you are of all the hard work they have put into getting good grades so far and how the sacrifice of electronics for a couple days in order to be successful on a major exam is very mature of them. then let them know they can reward themselves after the test with their own little electronic overload. good luck to you and to your student in these final 4 weeks. math for autumn june 1, 2015mathcswgs what do you get if you divide the circumference of a pumpkin by its diameter? pumpkin pi! learning math recent posts fun with numbers math skills are built math test taking skills minus vs negative test preparation and the battle at home create a free website or blog at wordpress.com.


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