On I.Q. tests and in other places, one is often confronted with problems of the form: “What’s the next element in the following series: 1, 4, 9, …” Technically, such questions have no right answer, because there are a multitude of ways to generate the initial elements of the series, and each way can produce a different result for how the series should continue. What is being sought is the generator for the series that is somehow the simplest, cleverest, most obvious, or most elegant. There is an esthetic at work in determining the preferred solution. For example, for the series above, an obvious answer is 16, because the initial elements of the series are the squares of the first three natural numbers, and so the obvious way to continue the series is with the squares of the subsequent natural numbers. The series is given by sn = n2. A similar type of question involves a mapping between a series of expressions and values. In that case, the preferred... read more
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Lately I've realized just how stressful economics can be, particularly for students with English as a second or third language. Trying to explain utility and utils to someone a few days ago, all I could think about was my own AP Econ professor, with his southern drawl, and a look he reserved for confused students. Someone would ask a question. There'd be a pause. Wearing his varsity football coach jacket, he'd sigh, and make eye contact with whoever had asked the question. Then, it was more like he was looking at you for something in particular - did you really not understand the concept, or were you confused by how the word was being used? Different questions would require very different answers. As a student who was frequently confused with the use of terms in a different context than I was used to, I hated that look. For the first month of classes, I was convinced he hated me, and that I was going to fail miserably. Every time we got a test or quiz back,... read more
I am thankful for mainly my father who first introduced me to the guitar. One day, he was playing his electric on the couch and something changed inside me and I had the urge to learn it. He had books on chord shapes and scales. After getting me started on the basic chord shapes of C and A major, he sent me on my own and I took off from there. I am also thankful for everyone I played music with over the years. Mainly my friends in high school. It is extremely important to play music with others any time you can because you will always learn something, every time and no matter how big or how small, it will make you a better musician.
I will never forget my favorite math teacher. Mr. Lazur taught ninth grade CAS Geometry (my school's version of AP) and also twelfth grade IB Calculus, so I was fortunate enough to have him as a high school freshman and then again as a senior. I'm incredibly thankful for Mr. Lazur because his fun and informal teaching style got even the most anxious students to actually enjoy math. In his classes I learned to think about math on a more “macro” scale, thinking about the concepts and how they related to each other rather than getting bogged down in numbers. He also knew exactly when and how to give a practical demonstration of a confusing concept so that none of us would ever forget it again. One of these demonstrations has stuck with me ever since, and I don't think I'll ever lose the knowledge it provided. We were in Geometry, working on volumes of solids. The previous day we'd learned the formulas for volume for cubes and cylinders, and today we were supposed to... read more
Okay! Call me old and grouchy. In fact, I am getting old but I'm still going to recommend Strunk & White's "Elements of Style" for two reasons: 1) That's how I learned the vagaries of grammar, punctuation, usage, etc. and I've used "the little book" successfully in ESL, composition, literature and creative writing classes. 2) The major reason is that no student wants to spend--or needs to spend--hours going through interminable grammar and punctuation exercises. Instead, use E. B. White's marvelous book to learn the fundamentals. Then, student and tutor can begin to learn how to write, edit and re-write. A far more profitable and enjoyable line of work. I have written professionally for over forty years. Far more helpful than grammar and punctuation tests is a good ear. If something sounds wrong, it most likely is! The last thing to try to memorize are dozens of meaningless rules. Spend that precious time on developing a topic and re-writing for impact and clarity... read more
"With the backing of (Bill) Gates and Google, Khan Academy and its free online educational videos are moving into the classroom and across the world. Their goal: to revolutionize how we teach and learn. Sanjay Gupta reports." For more information, here is a 60 Minutes interview on The Future of Education, Salman Khan's TED talk, and Bill Gates' interview.
One question I just received on a different blog was how to handle the 4-star ratings that come up. No matter how good you are, someone will not be satisfied. I personally have received two 4-stars here on WyzAnt, one when I was just starting out, and one just today. For the 4-star early on, it was from a weekly student who only rated the very first meeting as a 4-star. When I learned it was him (either WyzAnt didn't let us see ratings back when I began or I just hadn't figured out how), I approached him about it at the end of our next meeting. One thing I've learned in life is to ask questions instead, so I simply inquired as to why the first lesson was a 4-star to him. He thought back and couldn't really remember why; the session had gone well to him, and he couldn't remember anything in particular that went wrong; he simply thought that 4-stars was still "good". When I explained to him that it wasn't really how things worked on WyzAnt, how only 5-stars is "good" and... read more
Identify all 20 consonant letters of the alphabet. (Consonant letters make the sound.) Identify 2 for 1 consonant combinations (two letters one sound). Highlight all consonant combinations one color. Identify 6 short and long vowels of the alphabet. Highlight short vowels one color and long vowels a separate color. Identify vowel combinations. Highlight all vowel combinations one color. Highlight silent letters with your choice of color. Highlight "c" when it has an "s" and a "k" sound. You can only hear a sound, but you can't see it.
Times are definitely changing in the world of education. Today, as with all things twenty-first century, there are no limits to a student's education. This is absolutely exciting since so many 'schools without walls' have adopted various technologies during the past few years to enable students excel academically. As an advanced tutor, it makes me dance in my shoes. Universities such as Harvard, Princeton, and MIT have posted several free virtual lectures for the average student on education applications via android devices, iPads, iPhones, and iPods. Today, I want to introduce some fantastic techniques to approach tutoring that will benefit the student who cannot meet physically with a tutor, or maybe a student who is in a town on one end of the United States while their tutor is at the opposite end of the map. Yes, tutoring can now be employed with the use of fantastic applications such as Skype and Scribblar. Skype: This is a tool by which a tutor can see his/her... read more
Meeting with internationals has been one of the great pleasures of pursuing International Relations and Spanish studies. When I chat with people from other counties, the topics of culture and traditions inevitably come up. One of the most interesting topics I share is Thanksgiving. Since it is a uniquely American holiday, internationals love to hear about the food, family, and fun that surround the holiday. It is worth the effort to learn the Spanish vocabulary for Thanksgiving so that you can easily share your festive experiences with other people. It may open the door to a fascinating discussion of interesting holiday traditions in other cultures. Here are a few key phrases to help describe the day: Día de Acción de Gracias Thanksgiving Day Yo doy gracias por... I give thanks for...
This is another way to find a distance between two parallel lines. This derivation was suggested to me by Andre and I highly recommend him and his answers to any student, who wants to learn math ans physics. This derivation requires the knowledge of trigonometry and some simple trigonometric identities, so this may be suitable for more advanced students. Once again, we have two lines. y=mx+b1 (1)--equation for the first line. y=mx+b2 (2)--equation for the second line. Now recall that the slope of the line is the tangent of an angle this line forms with the x-axis. Indeed, m=(y2-y1)/(x2-x1), where x1, x2, y1, y2 are the x- and y-coordinates of any two distinct points on the line. If one draws the picture, it will be immediately obvious that m is the tangent of the angle between the line and the x-axis. The difference b2-b1 gives the relative displacement along the y-axis of two lines. Since b2 is the y-intercept of the second... read more
FRIENDLY DISCLAIMER I assure you, this post is rated G. Tell the children they can come back now. Exquisite Corpse is a writing exercise that was first introduced to me in 10th grade AP English. My teacher at the time (who is, by far, my favorite ever) was trying to rid us of the awful writing techniques ingrained in us from the TAKS test. There is a good chance you or your child has gotten a nice Texas-sized dose of these in school. We were so regemented that, even though we were all gifted in Reading and Language Arts, lots of us had gotten 2s and 3s on the writing portion of the test. We lost the fun. We lost the creativity. How did we get it back? Exquisite Corpse. What in the world is Exquisite Corpse? It's the Galaxy X totin', New age cousin of the old parlor game "Cadavre Exquis" in which multiple people would contribute to a sentence. The first would write an adjective, the next, a verb, then the... read more
"As a guitar player, I am always looking for new resources to help me get better at my craft. I have gone through book after book that held some good tips for improving my playing. Some better than others. I have been playing the guitar for 40 years now and still consider myself a rhythm hack. I must confess that I do not spend the time like I should but that is another article. A friend of mine recently released a book titled Guitar Tips - What Every Guitar Player Should Know. I love this guitar manual for a ton of reasons. It's practical, easy to follow and gives some great tips for advancing my playing and understanding of music and the instrument I so love. I have a degree in music but often fail to implement the basics of theory in my arranging of worship music. This book is not so much a "how to play the guitar better" as it is a "how to use your guitar in a band setting". Ric F. is an amazing guitarist, performer, arranger, musician, composer, teacher and... read more
Hi again. I thought I'd start with something simple. Here's an everyday application of math, science, and graphing skills that I think you'll find useful. Enjoy! A while back, the Tap Dancing Engineer was visiting some tap dancing friends in Canada. We ended up talking about recent strange weather, which of course led to a discussion of converting between temperature scales. The equation to convert from C to F, as I learned it, is the following: F = (9/5)*C + 32 OR F = 1.8*C + 32 Its simple Algebra to figure out the reverse: C = (F - 32)*(5/9) Converting from Celsius to Fahrenheit is generally encountered more often, especially an American. This is because many other countries, as well as the majority of the scientific community, use Celsius. As an American you often encounter situations where you need to convert in order to understand the situation. 23C degrees sounds cold to us, but thats actually a very comfortable... read more
Have you ever received a graded essay handed back with the phrase, "Needs more structure," or "structure needs work?" Creating a structure for any written word, whether it is poem, essay, news brief, or novel, is an integral part of the message you intend to convey. Using long, convoluted sentences as means to convince the reader that your argument is very simple will usually only give the opposite impression; simple arguments are best conveyed with short, simple sentences. (For example, the opposite is true in Jonathan Swift's essay, "A Modest Proposal," in which he uses didactic and complex language in an effort to "convince" the people of England that the solution to their hunger and poverty problem is to eat their starving infant children; his complex sentences reflect the sarcastic and satiric nature of his essay, reflecting that he does not see cannibalism as a real solution.) Structure also helps you keep your thoughts organized. It is a way to say... read more
WyzAnt wants to know: Which teacher from your past (or present) are you most "thankful" for and what lesson did they teach you? I am most "thankful" for my 5th, 6th and 7th grade Math teacher. She opened my mind and truly showed me what it means do think through and write up a rigorous mathematical proof. The key concepts I learned then, I still used up to the time I finished college.
I find oftentimes that one of the biggest stumbling blocks for algebra students is that beginners have difficulty seeing the "chunks" in an expression. Instead, they see a big jumbled mess of symbols. An analogy is an orchestra. A person who has never played a musical instrument, or doesn't have much experience with listening to music, hears the orchestra as one big sound. The trumpets, flutes, strings, percussion all happening at once. An experienced musician can isolate each instrument, and let the rest of the orchestra fade, focusing on the single melody or harmony line. Likewise, an experienced mathematician can isolate the sections of an expression, focusing on the single term or operation that needs to be dealt with at the moment, allowing the rest of the expression to fade away for the time being, until the term or operation has been dealt with. Consider the following problem; can you see the four operations required to solve the... read more
Entering Variables into SPSS: Working with the Data Editor 1. Once an SPSS file is open CLICK ON “VARIABLE VIEW” found as a tab on the left bottom portion of the file 2. Type the names of your variables under the heading “NAME” (e.g. ethnicity, annual salary) 3. By clicking on the “TYPE” column you will find options for the type of variable you would like to have. Most common type is “Numeric.” A variable whose values are numbers. For example, annual salaries, anxiety scores, GDP, LDL levels, score on a certain test, such as SAT, GRE. If you see that your variable's type is “String,” this means that SPSS does not consider this variable's values (scores) numeric and therefore you cannot use this variable in your analyses. There are 2 common reasons why your variable is a string variable. First, it has letters instead of numbers. For example, you entered "M" for male and "F" for female under a variable "Gender." In this case, see... read more
If you are interested in earning a certificate that offers courses in Church History, Old Testament, New Testament, Theology, World Missions and Biblical Interpretation then the Ockenga Institute of Gordon-Conwell Theological Seminary's Dimensions of the Faith Certificate program is for you. Also, it is absolutely free and totally online. I have gone through this program myself and highly recommend it to anyone interested. If you wish to take only some of the courses and not necessarily go for the certificate that is an option. Enjoy!
All students who live in Queens and want to learn English please get in touch with me through my profile. Thank you very much.