WyzAnt Tutor Blogshttp://www.wyzant.com/resources/blogsThis is an aggregate of all of WyzAnt.com's Tutors' Blogs. WyzAnt.com is your source for tutors and students.Thu, 10 Jul 2014 10:37:15 -0500http://www.wyzant.com/images/WyzAnt_white200.gifWyzAnt Tutor Blogshttp://www.wyzant.com/resources/blogshttp://www.wyzant.com/resources/blogs277318http://www.wyzant.com/resources/blogs/277318/professional_and_patient_chinese_tutorHaosong Y.http://www.wyzant.com/resources/users/view/85234656Professional and Patient Chinese Tutor <div>China:<br /> I lived in China for 20 years and finished from Elementary school to University in China so that not only the language, but I also know China a lot in a way of how to live, communicate, culture. The most important thing is I do have the certificate of Speaking Mandarin Chinese, which is the most difficult certificate that most chinese people do not have, cannot pass or have a lower score of it. The reason I achieved this certificate was because I went to one of the top 10 Chinese Newscaster University studying in News Casting, so for each one of the Newscasters, we must not only pass the Exam but also need a high score of it to pursuit our career, and that is why I can speak standard Chinese than others. <br /> Here in America, I obtained the honor of Theater Acting B.A. at UCLA, and I have been teaching and tutoring for 2 year in the U.S.,I can speak both Chinese and English Fluently.so I do have experience of teaching. No worries, I hope I could devote all my efforts to help people from all over the world who want to study Chinese.</div>Thu, 10 Jul 2014 02:17:41 -05002014-07-10T02:17:41-05:00277249http://www.wyzant.com/resources/blogs/277249/improve_your_communication_skills_in_a_foreign_languageAndrea C. B.http://www.wyzant.com/resources/users/view/78125890Improve your communication skills in a foreign language<div>Reminders to improve your communication in the target language:<br /><br />- Pay attention to the facial expressions of the native speakers in order to understand the meaning of their talk.<br /><br />- Identify the key words in the sentences you hear. These are usually content words: verbs and nouns. <br /><br />- Determine by the intonation of the sentences if the speaker is asking or answering questions, describing, or telling a story.<br /><br />- Practice one or two new words, or small phrases regularly with native speakers.<br /><br />- Build the knowledge of the target language with small bricks: memorize nouns and verbs and use them in simple sentences (Noun + Verb + Complement). As you master the use of simple sentences in present tense you can continue progressing by learning more complex sentences and different verb tenses in order to communicate more accurately.<br /><br />- Practice each of the four skills of communication 10-15 minutes every day. These skills are: speaking, reading, listening, and writing.<br /><br />- Practice reading with the articles written by and to native speakers.<br /><br />- Practice listening by talking to native speakers at your work, or school, and by listening to authentic music.<br /><br />- Practice&nbsp;new vocabulary&nbsp;by writing down the new&nbsp;words on flash cards in order to memorize them. <br /><br />&nbsp;</div>Wed, 09 Jul 2014 17:55:03 -05002014-07-09T17:55:03-05:00277158http://www.wyzant.com/resources/blogs/277158/your_local_libraryPamela I.http://www.wyzant.com/resources/users/view/83139170Your Local Library<div>&nbsp;&nbsp;&nbsp;&nbsp; Your local public library can be an excellent resource. Not only can children borrow books at no charge (unless the items are returned late), but they can also borrow non-fiction, educational shows on DVD. And, for emerging readers, there are "read-alongs" (books accompanied by audio CDs).&nbsp; For reluctant readers, there are also books and activities created just for them. For example, in my local library, there is a program called "Paws for Reading," which is a play on words (<em>pause</em> and <em>paws</em>). This activity allows young reluctant readers to practice reading to therapy and rescue dogs in the children's activity room at our library.&nbsp; It's a great hit with the kids! I absolutely love my library. I have discovered so many excellent books and movies for teaching my subjects that I always include them, along with free printable worksheets, in my lesson plans for my tutoring sessions. I call them my "teaching" books, and they make my job so much easier and more enjoyable.</div>Tue, 08 Jul 2014 22:11:27 -05002014-07-08T22:11:27-05:00277102http://www.wyzant.com/resources/blogs/277102/my_favorite_things_to_do_indoors_summer_winter_fall_springAnne G.http://www.wyzant.com/resources/users/view/83560360My favorite things to do indoors - summer, winter, fall & spring<div>Reading is my favorite activity at any time of the year.</div> <div>&nbsp;</div> <div>I especially love to read books. Books on religions, theology, art and world cultures. &nbsp;I read them in hard copy, on-line, and on my Kindle. I also listen to audio-books and books-on-tape/cd's that i borrow from the library.</div> <div>&nbsp;</div> <div>&nbsp;In the summer I enjoy reading English "tea-cozy" mysteries. "Tea-cozy" mysteries are fun with great plots and are not &nbsp;too &nbsp;violent.&nbsp;Violent books and movies give me nightmares, so I don't do "violent".</div> <div>&nbsp;</div> <div>When I was younger and learning French and Spanish in high school and university, I would read magazines and books in these languages. (I still do.) Of course, I didn't understand all the vocabulary (and still don't) and needed to look up some words. I didn't look up all I didn't know, that would have taken too long, and I was impatient to get on with it.</div> <div>&nbsp;</div> <div>Somehow the more I read the more I was able to understand what the author was saying. I recommend that for you too.Try not to let what you don't understand stop you from continuing.</div> <div>&nbsp;</div> <div>I also enjoy painting, cooking, walking, doing yoga, and staying fit; going to art museums, and the ocean. &nbsp;I have been doing yoga for over 40 years - way before it went mainstream. I still do hatha yoga every day.&nbsp;</div> <div>&nbsp;</div> <div>How about you, what do you enjoy doing?</div>Tue, 08 Jul 2014 12:47:28 -05002014-07-08T12:47:28-05:00277087http://www.wyzant.com/resources/blogs/277087/breaking_the_iceJared M.http://www.wyzant.com/resources/users/view/85127295Breaking the Ice <div>I've noticed that a lot of students just don't ask for help that they need in algebra. This may be because they are too shy and/or feel that us tutors or other students would think they're "dumb". Students must be encouraged as much as possible to get assistance in whichever subject they are struggling in, and explain to them that everybody is good at different things and it's ok if you're not the best in math when you're probably great at another subject. Everyone has their own strong point(s).</div>Tue, 08 Jul 2014 08:47:39 -05002014-07-08T08:47:39-05:00277085http://www.wyzant.com/resources/blogs/277085/mathematical_journeys_carl_gauss_and_the_sum_of_an_arithmetic_seriesEllen S.http://www.wyzant.com/resources/users/view/75479140Mathematical Journeys: Carl Gauss and the Sum of an Arithmetic Series<div>There's a famous (and probably apocryphal) story about the mathematician Carl Friedrich Gauss that goes something like this:<br /><br />Gauss was 9 years old, and sitting in his math class. He was a genius even at this young age, and as such was incredibly bored in his class and would always goof off and get into trouble. One day his teacher wanted to punish him for goofing off, and told him that if he was so smart, why didn't he go sit in the corner and add up all the integers from 1 to 100? Gauss went and sat in the corner, but didn't pick up his pencil. The teacher confronted him, saying &ldquo;Carl! Why aren't you working? I suppose you've figured it out already, have you?&rdquo; Gauss responded with &ldquo;Yes &ndash; it's 5,050.&rdquo; The teacher didn't believe him and spent the next ten minutes or so adding everything up by hand, only to find that Gauss was right! <br /><br />So how did Gauss find the answer so fast? What did he see that his teacher didn't? The answer is simple, really &ndash; it's all about pattern recognition. Let's look at the problem more closely.<br /><br />1 + 2 + 3 + 4 + 5 +...+ 95 + 96 + 97 + 98 + 99 + 100 = ?<br /><br />Now it's true that adding all that up by hand would take forever, but we don't really need to add it all up by hand. Look at this series from each end simultaneously instead of just left to right. You'll see that we can think of this series as a set of pairs of numbers, each of which adds up to 101:<br /><br /><span class="orange">1</span> + <span class="greenText">2</span> + 3 + 4 + 5 +...+ 95 + 96 + 97 + 98 +<span class="greenText"> 99</span> + <span class="orange">100</span> = ?<br /><br />1 + 100 = 101<br />2 + 99 = 101<br />3 + 98 = 101<br />4 + 97 = 101<br />5 + 96 = 101<br /><br />and so on right through to the middle, where:<br /><br />48 + 53 = 101<br />49 + 52 = 101<br />50 + 51 = 101<br /><br />So we've got a total of 50 pairs, each of which adds up to 101. Since all our chunks are the same size, we can take a shortcut and simply multiply the size of the pair (101) by the number of pairs (50). Which is really easy to do in your head, since it's just (100 x 50) plus (1 x 50), or 5000 + 50 = 5,050.<br /><br />This reasoning can actually be extrapolated to work with any arithmetic series, and in fact is how we get the formula for the sum of an arithmetic series. Check it out:<br /><br />Each pair added up to the same number, so we could actually use the mathematical expression for any one of those pairs in our formula. Since the first and last term are the ones most often known, let's use those. Remember, the last term in the series is written as a<sub>n</sub>, where n is the number of terms in the series. So that 101 will be represented by:<br /><br />The first term (a<sub>1</sub>) + the last term (a<sub>n</sub>), or (a<sub>1</sub> + a<sub>n</sub>)<br /><br />Check out the first term in each of our pairs above. They range from 1 to 50, so there are 50 terms &ndash; exactly half the number of terms in the series. Which makes sense, since we're pairing up the terms and that by definition gives us half as many pairs as terms. <br /><br />So 50 in our example is represented by one-half of n, or n/2. <br /><br />And what are we doing with these two bits of information? Multiplying them together. So our final formula would be:<br /><br />&Sigma;&nbsp;= (n/2)(a1 + an)<br /><br />Now, sometimes you see this formula written as n(<span style="text-decoration: underline;">a1 + an</span>), <br />&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;2<br /><br />or the number of terms times the average of the first and last terms. Practically that is exactly the same thing as the way we wrote it first, it's just written a little differently. But they both have the same value, so if it's easier for you to remember it as the average times the number of terms, do so.<br /><br />This formula works for any arithmetic series, so the next time you come up against one, remember Gauss and his pairs of terms!</div>Tue, 08 Jul 2014 08:21:06 -05002014-07-08T08:21:06-05:00277041http://www.wyzant.com/resources/blogs/277041/keep_up_your_language_skills_over_the_summerAlbert K.http://www.wyzant.com/resources/users/view/85054505Keep up Your Language Skills Over the Summer!<div>Are you taking a foreign language in school? Maybe it is Spanish, or Japanese, or French? Well, that's great! However, summer is typically the time that most of what you have learned in these second languages during the school year wears away, and very fast too.</div> <div>&nbsp;</div> <div>That's why it's recommended that you keep practicing reading, writing, listening, and speaking in your second (or third) language throughout the summer months. That way, you'll be prepared not only for the next class in the series in the fall, but also keep you from forgetting all of the intricate details that you have mastered already. Don't know how? Well here are some tips to get you started:</div> <div>&nbsp;</div> <div><ol> <li>Ask your teacher or school librarian to see if you can borrow a used copy of your foreign language book, or perhaps loan out a copy of next year's book early. This way, you can review everything that you have already studied during last school year and even start looking ahead into what's coming up next!</li> <li>If you're taking a second language in college, courses typically require students to purchase an online package that grants you premium access to online materials such as an electronic version of your textbook, videos, grammar tutorials, online workbook activities, and more. Logging in regularly while you still have access over the summer is a great way to retain what you have mastered during the school year and keep the material fresh in your mind.</li> <li>Invest in time-tested foreign language materials like the Pimsleur Audiobook Series. This is especially true if you are extra-busy during the summer with work, internships, or even other college classes. Pimsleur is one of the most effective and proven programs out there that allow you to retain and <em>increase</em> your speaking and listening foreign language abilities naturally through repetition. In fact, you can learn these lessons in small sections of your day which are typically wasted-- such as when you're in the car during a commute, waiting for a bus, standing in a long line, or even while your eating lunch or dinner.</li> </ol></div>Mon, 07 Jul 2014 19:26:11 -05002014-07-07T19:26:11-05:00277039http://www.wyzant.com/resources/blogs/277039/defeat_the_dreadBob R.http://www.wyzant.com/resources/users/view/76968540Defeat the Dread<div>You practice Geometry Proofs, memorize dates for History, and review flashcards for Spanish. But how do you practice writing? Writing is the one skill you&rsquo;re guaranteed to use for the rest of your life. <br /><br />The challenge every writer faces is to understand and manage the dynamic between creating and crafting. These are two very different skills that conflict with each other--leading to frustration not to mention procrastination.<br /><br />I'm offering 3 Sunday afternoon dynamic and fun (no grades! no rubrics allowed!) writing workshops with a focus on &ldquo;hands-on&rdquo; work.&nbsp;I want to give you insight and confidence as you develop your personalized writing process.</div> <div><br />You&rsquo;ll discover how writing is as much a strategy as it is a skill. Invest some time this summer and we know you&rsquo;ll be less likely to dread your first writing assignment in the fall!<br /><br />The Seminars are designed for High School/College level students who are comfortable with basic grammar but want to have an edge when they sit down to write anything from College Applications to Term Papers.<br /><br />The $295 Fee covers all three 90-minute sessions to be &nbsp;held at WyzAnt&rsquo;s Offices in Bucktown: Sessions are 1:00 PM Sunday July 27, Sunday Aug 3, Sunday Aug 10.<br />Register with a friend or sibling and you each pay $250<br />Sign up Soon--very limited space</div>Mon, 07 Jul 2014 19:15:46 -05002014-07-07T19:15:46-05:00277033http://www.wyzant.com/resources/blogs/277033/inputs_and_outcomesBob R.http://www.wyzant.com/resources/users/view/76968540Inputs and Outcomes<div>One of the challenges for Parents making the case for the value of schoolwork is a student&rsquo;s perfectly cogent question, &ldquo;How is learning about (fill in the blank, you've heard it enough times) going to help me later?&rdquo; Fair question and one that today&rsquo;s tools make even more challenging to answer.<br /><br />I like to remind the students I work with that being smart isn't &ldquo;knowing the answer to every question&rdquo;&mdash;it&rsquo;s knowing where to find the answer. And with practically any answer just a click away memorization of dates, places, events and names can seem even more impractical.<br /><br />You can&rsquo;t credibly make a case to your kids that they will be writing geometry proofs or discussing the causes of the Civil War as adults. But you can help them understand &nbsp;by helping them see the practical application of education in general: It's the Learning Process&mdash;learning how to understand, think about, write about and solve problems and complete assignments.<br /><br />Information and media tools to engage with &ldquo;what they want, when they want it, and on what platform they want&rdquo;, now surround the generation in school. My Media Business colleagues are wresting with this dramatic remodeling of the mobile/digital world. In the classroom, there are smart applications and tools that now integrate teaching and learning techniques&mdash;the online textbook with links to the backgrounds of the historical figures they write about is one. <br /><br />One technique that&rsquo;s helped some of my students to get a sense of engagement and reward from their Language classes is to take an on-line story about a subject they like (Sports for sure works here) and source it from sites like ESPN Deportes or CBC (French Canadian service) both of which cover content familiar to them allowing the student to decode vocabulary words and grammar more confidently. <br /><br />On a higher level, there&rsquo;s a practical and applicable way to describe and view the writing process for papers or similarly proofs for mathematics: it&rsquo;s not the assignment or problem per se but rather strategically understanding a directive and executing it. (We&rsquo;ll talk about the process for organizing all this in a subsequent Blog). A lawyer has to build a case from facts. An analyst has to make the case for buying or selling a company&rsquo;s stock. Someone writing code has to communicate goals and objectives. <br /><br />Access to information is surely not a guarantee of mastering it. And being able to recite rote facts and figures isn't &nbsp;necessarily learning. But having the skills to find and incorporate information in assignments has value throughout school and work.</div>Mon, 07 Jul 2014 18:47:21 -05002014-07-07T18:47:21-05:00277018http://www.wyzant.com/resources/blogs/277018/5_ways_to_get_smarter_this_summerJeremy B.http://www.wyzant.com/resources/users/view/797096805 Ways to Get Smarter This Summer<div>There are two things that happen to the brain during the summer: either it gets smarter, or it gets dumber. &nbsp;If you work on making it smarter this summer, then you'll have a stress free school year when it comes.</div> <div>&nbsp;</div> <div>To help you on your path of smart awesomeness, I have put together this list of 5 ways to get summer this summer.</div> <div>&nbsp;</div> <div><ol> <li><strong>Video Games: &nbsp;</strong>Your mom is wrong. &nbsp;You should play video games. &nbsp;Show her this YouTube video the next time she gets on your case:&nbsp;<a href="http://www.youtube.com/watch?v=lfBpsV1Hwqs">Jane McGonigal: The Game that Can Give You 10 Extra Years<br /></a></li> <li><strong><span style="text-decoration: line-through;">Exercise</span> Play:</strong> Your mom is right. &nbsp;To become smarter, your brain needs oxygen. &nbsp;The only way to get oxygen to your brain is to move your body. &nbsp;But don't do something as lame as exercising. &nbsp;Get out there and find something fun. &nbsp;To tell you the truth, I'm such a geek that I like to walk trails while reading my Kindle or listening to music. &nbsp;Nature is lame. &nbsp;But, if you are into sports, that will work. &nbsp;Honestly, if you are lazy, then 30 minutes of walking around the block will do the trick.<br /><br /></li> <li><strong>Khan Academy</strong><strong>:</strong> &nbsp;This is like push-ups for your brain. &nbsp;Don't go all crazy and try to do 5 hours a day. &nbsp;Do just 15-30 minutes a day and you will destroy everybody in your math class the next year. &nbsp;You want to know a little secret? &nbsp;I'm a math teacher and I still do a little Khan Academy every once in awhile.</li> <li><strong>Eat:</strong> &nbsp;Smartness isn't just about books. &nbsp;It's a combination of physical, mental, and emotional. &nbsp;To keep your physical state at peak mental ninja level, make sure to chow down on all the summer ripe fruit this summer. &nbsp;Fruit has healthy sugar. &nbsp;Your brain uses sugar to think. &nbsp;The more fruit you eat, the more you can think.</li> <li><strong>Sleep:</strong> &nbsp;This is the one that everyone forgets! &nbsp;You don't get smarter while learning. &nbsp;You actually get smarter while sleeping. &nbsp;Actually, if you're not sleeping enough, then you basically just wasted your time. &nbsp;Your brain will remember NOTHING! &nbsp;So take advantage of not having to wake up for school and stay in bed until your body says its ready. &nbsp;I remember staying up until 5:00 a.m. when I was in high school, but you're smarter than me and won't do that...right?</li> </ol></div>Mon, 07 Jul 2014 14:40:59 -05002014-07-07T14:40:59-05:00277013http://www.wyzant.com/resources/blogs/277013/reading_tv_to_improve_english_skillsSarah S.http://www.wyzant.com/resources/users/view/85163457Reading TV to Improve English Skills<div>Now that its getting warmer this summer, many of us our spending more time watching TV. But how can watching TV help to improve our English/ESL skills?</div> <div>&nbsp;</div> <div>One way is to mute the TV and display the closed captioning at the bottom of the screen. That way, you can practice reading English and still enjoy catching up on your favorite shows.</div> <div>&nbsp;</div> <div>Let me know how it works for you, and have a great summer!</div>Mon, 07 Jul 2014 12:07:19 -05002014-07-07T12:07:19-05:00276974http://www.wyzant.com/resources/blogs/276974/summer_tutoringJudy L.http://www.wyzant.com/resources/users/view/76289240Summer Tutoring<div>I so admire parents and students who decide to attend tutoring during summer vacation. &nbsp;These are the folks who realize that they must put in effort and time to get the desired educational results. &nbsp;They are not lazy. &nbsp;They do what it takes. &nbsp;This is an admirable trait in them, that they choose to attend tutoring during what could just be a lazy, relaxing time. &nbsp;They bring their student for tutoring and the student does his best to cooperate and learn. Results are not always immediate -- they will come in time. &nbsp;As long as parents and students keep reaching out for education, even when school is not in session!</div>Sun, 06 Jul 2014 21:22:31 -05002014-07-06T21:22:31-05:00276959http://www.wyzant.com/resources/blogs/276959/on_paramount_importance_of_mental_mathAndrei K.http://www.wyzant.com/resources/users/view/79746510On Paramount Importance of Mental Math<div><strong>Summary:&nbsp; </strong><em>Mental math teaches students to see short, efficient solutions&mdash;rather than to blindly follow</em> <em>the brute-force, cookie-cutter, one-size-fit-all, show-all-your-work procedures taught at school.</em></div> <div>&nbsp;</div> <div>To my youngest students, I lie&mdash;by omission&mdash;that vertical arithmetic does not exist.&nbsp; I can usually get away with it for about a year. Until the school shows them the light.&nbsp; Say, how to add 25 and 8 <em>vertically</em>, with the carry-over 1 carefully written on top of the 2.&nbsp; By that time, my students are proficient in <em>mental</em> addition and subtraction of <em>3-digit</em> numbers: carrying, borrowing, and all.&nbsp; Of course, they make me proud.&nbsp; Yet, my goal is by no means to turn them into human calculators.&nbsp; So then, why bother?</div> <div><br />Vertical arithmetic is a convenient method for computing numerical answers.&nbsp; Especially when the numbers to manipulate are multidigit.&nbsp; But it is a <em>procedure</em>, requiring&mdash;once learned&mdash;little thought.&nbsp; The entire process is delegated to the mechanics of paper&mdash;and, essentially, to the spinal cord. It is almost as bad for one's brain as using a calculator. Further, in carrying out vertical arithmetic, one rarely deals with more than two digits at a time.&nbsp; This encourages a math version of the <em>tunnel vision</em>: focusing on a small, narrow portion of the task, at the expense of seeing the big picture.&nbsp; Finally, with the exception of division, vertical arithmetic is performed right-to-left, which is <em>unnatural</em>.&nbsp; Indeed, we read numbers left-to-right, we call our answers left-to-right, and, perhaps most importantly, numbers diminish in significance left-to-right.&nbsp; Consequently, when right-to-left vertical arithmetic is performed, the feeling of whether the answer makes sense has typically been lost along the way.&nbsp; Combine this with the tunnel vision, and the ground for &ldquo;silly mistakes&rdquo; is laid.</div> <div>&nbsp;</div> <div>The situation is quite different with mental arithmetic.&nbsp; When performed correctly, it is done left-to-right.&nbsp; Thus, one typically begins with the most significant portion of the answer, and then augments it with less and less significant modifications, as necessary.&nbsp; The sense of magnitude is maintained at each step&mdash;reducing the possibility of &ldquo;silly mistakes.&rdquo;&nbsp; As an added bonus, one can usually begin calling the answer before its less-significant digits have been figured out&mdash;creating the impression that the answer has been obtained almost instantly.</div> <div><br />Next, mental arithmetic requires mathematical imagination and short-term memory&mdash;therefore developing both.&nbsp; A bad short-term memory is responsible for those &ldquo;silly mistakes&rdquo; which one makes due to forgetting&mdash;or rather incorrectly remembering&mdash;the results of prior steps.&nbsp; A <em>long</em>-term memory benefits as well, as some numbers begin ringing the bell.&nbsp; For example, I <em>know</em> off the top of my head that 16 &times; 3 = 48,&nbsp; 17 &times; 3 = 51,&nbsp; 25<sup>2</sup> = 625,&nbsp; 38 / 2 = 19, etc.</div> <div><br />Yet, the main benefit of mental arithmetic is found elsewhere.&nbsp; Nobody is thrilled about doing a lot of work in his mind.&nbsp; Thus, one is forced to look for easier ways to approach a particular computation.&nbsp; (Such ways include performing the operations in a more convenient order, using the distributive property, rounding, reducing, doubling and halving, etc.)&nbsp; Each computation is approached as a little puzzle, in which not just any, but the most efficient, solution is sought.&nbsp; In that, the entire problem must be taken in as a whole&mdash;as opposed to the vertical arithmetic&rsquo;s 2-digits-at-a-time tunnel vision.</div> <div><br />The importance of this search for an efficient solution is hard to overemphasize.&nbsp; It seems that during their entire secondary-school tenure, children are taught, and required to follow, brute-force, cookie-cutter, one-size-fit-all, show-all-your-work procedures.&nbsp; A student who sees a shortcut, a simpler way to solve a problem, is more likely to be penalized than rewarded.&nbsp; Gradually, even the best students tend to abandon what we loosely term &ldquo;thinking&rdquo;&mdash;a search for the simplest and most elegant solution&mdash;in favor of what the school miscaracterizes as &ldquo;applying learned skills&rdquo;: almost mindlessly following prescribed protocols.</div> <div>&nbsp;</div> <div>It is in overcoming these school-instilled habits that his work is cut out for a math tutor.&nbsp; This is when mental arithmetic&mdash;and, more generally, mental math&mdash;come to the rescue.&nbsp;</div> <div>&nbsp;</div> <div>The math portion of the SAT is a case in point.&nbsp; I have tutored some [gifted] 7th graders to get the perfect score of 800 on this test.&nbsp; It would seem then that everybody who is above average should be able to get the 800 say by grade 10.&nbsp; Yet, achieving the 800 is beyond their wildest dreams for 98% of high-school seniors. Why is that?</div> <div>&nbsp;</div> <div>A typical SAT problem can be solved as follows: one reads it slowly and thoughtfully (say, 10&ndash;20 seconds), ponders it briefly (5&ndash;10 seconds), sees a simple solution, and computes the answer mentally (5-10 seconds). Total time: 20 to 40 seconds. No calculator. Nothing is written.</div> <div><br />By contrast, upon reading the problem, a typical high-school student plunges himself into quickly writing lines upon lines of mathematical expressions, or clicking away on his calculator.&nbsp; Those 20 to 40 seconds later, he may still have precious little idea of where he is heading with all that work, rather hoping that something good is going to come out of it eventually.</div> <div><br />The first thing which I tell my high-school students when I tutor them for the SAT math, is to put away their calculators, and do all their arithmetic mentally.&nbsp; It is very uncomfortable for them at first. For they had sworn, and have been intending to stay true to, the school-math version of the Rifleman&rsquo;s Creed: &ldquo;<em>This is my calculator.&nbsp; There are many like it, but this one is mine. My calculator is my best friend. &nbsp;It is my life.&nbsp; I must master it as I must master my life. My calculator, without me,</em> <em>is useless. Without my calculator, I am useless.</em>&rdquo;&nbsp; After the initial shock has subsided, I begin insisting that they do not write down <em>anything,</em> doing not just the arithmetic part, but the entire solution, mentally.</div> <div><br />I have found this approach indispensable even with the most gifted of my students, when preparing them for math competitions such as the AMCs.&nbsp; School habits die hard.&nbsp; I keep on reminding them that when practicing, the objective is not to arrive at the answer at any cost, but to learn from each problem.&nbsp; Solving introductory to intermediate problems mentally forces them to abandon brute-force routes in favor of gems of solutions.</div> <div>&nbsp;</div>Sun, 06 Jul 2014 18:45:33 -05002014-07-06T18:45:33-05:00276887http://www.wyzant.com/resources/blogs/276887/act_prep_timeNicole D.http://www.wyzant.com/resources/users/view/80997500ACT Prep Time!!<div>ACT 2014-2015 prep season is here! The first test is only 10 weeks away, so now is the time to start ACT tutoring for your high school student. &nbsp;Please feel free to email me if you have any questions about ACT prep strategies, goal scores, or general test prep questions. :)</div>Sat, 05 Jul 2014 21:42:30 -05002014-07-05T21:42:30-05:00276886http://www.wyzant.com/resources/blogs/276886/reading_a_bookAisha R.http://www.wyzant.com/resources/users/view/85207034Reading a book<div>Read a book with a friend and then text your friend back and forth your reaction to the book chapter by chapter</div>Sat, 05 Jul 2014 21:22:16 -05002014-07-05T21:22:16-05:00276795http://www.wyzant.com/resources/blogs/276795/two_recommendations_when_learning_spanishLourdes M.http://www.wyzant.com/resources/users/view/80398510Two recommendations when learning Spanish<div>&nbsp;</div> <div>When you learn Spanish there are a couple of recommendations:</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;1.- Know your English grammar.- Most students have no idea of grammatical functions. When they start studing Spanish and the teacher talks to them about pronouns, direct objects, adverbs and so on; they feel lost and confused. Its hard to understand&nbsp; how a pronoun works in Spanish if you don't in English. If you know the diferences between adverbs, verbs, nouns, etc. learning Spanish will be easier.</div> <div>&nbsp;</div> <div>2. Be Analitycal.- Spanish methods are always advertising to have you speaking in less time. Learning in less time has no meaning if you don't understand what you are doing.&nbsp; Memorizing or associating words will get you by but will not give you a full command of language. Understand, analyze the language structures</div> <div>; this will make it easier to find patterns and understand the rules.</div> <div>&nbsp;</div> <div>Hasta la pr&oacute;xima y buena suerte!!!! Lourdes</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div> <div>&nbsp;</div>Fri, 04 Jul 2014 05:56:49 -05002014-07-04T05:56:49-05:00276789http://www.wyzant.com/resources/blogs/276789/learning_in_the_summer_timeMarc H.http://www.wyzant.com/resources/users/view/82781430Learning in the summer time<div>Playing board games is a great way to pass the summer time. Especially when it is raining. Jigsaw puzzles or building models of planes, trains doll houses are also great ideas.&nbsp;</div>Thu, 03 Jul 2014 22:10:56 -05002014-07-03T22:10:56-05:00276787http://www.wyzant.com/resources/blogs/276787/how_to_balance_chemical_equations_easilyChris P.http://www.wyzant.com/resources/users/view/85101531HOW TO BALANCE CHEMICAL EQUATIONS EASILY<div>When balancing chemical equations, follow these 3 easy steps:</div> <div>&nbsp;</div> <div>1. &nbsp;<strong>BALANCE THE SKELETAL EQUATION:</strong>&nbsp;This means to complete the equation first. &nbsp;Whether it is a double displacement or other type of equation, write out the basic equation first.</div> <div>&nbsp;</div> <div>2. &nbsp;<strong>BALANCE THE INDIVIDUAL CHARGES: &nbsp;</strong>This means to balance each individual compound based on individual charges. &nbsp;To adjust these charges so the overall compound charge is 0 add&nbsp;<strong>subscripts.</strong></div> <div>&nbsp;</div> <div>3. &nbsp;<strong>BALANCE THE ENTIRE EQUATION:</strong> &nbsp;This means to be sure that you have the same amount of each element on the left of the equation that you do on the right. &nbsp;You do this by adding&nbsp;<strong>coefficients</strong> to the front of the compound.</div> <div>&nbsp;</div> <div>Good Luck!</div>Thu, 03 Jul 2014 20:23:50 -05002014-07-03T20:23:50-05:00276744http://www.wyzant.com/resources/blogs/276744/evolution_and_time_understanding_4_billion_yearsKatharine D.http://www.wyzant.com/resources/users/view/85221348Evolution and time: understanding 4 billion years<div>One of the great challenges in teaching evolution is understanding the flow of time.&nbsp; Humans have 75-year lifespans, on average.&nbsp; Our generations are approximately a third of that.&nbsp; Our existence as anatomically modern humans has only lasted for about 200,000 years.</div> <div>&nbsp;</div> <div>Only!</div> <div>&nbsp;</div> <div>A popular analogy for conceiving geologic time on Earth is the clock, or the calendar, where humans occupy the last second or the last chunk of December 31.&nbsp; This still doesn't give you a very good idea of how long 4 billion years is.</div> <div>&nbsp;</div> <div>I suggest therefore a new analogy, which compares time with distance.&nbsp; For the purposes of this blog post, let's say <strong>1 year = 1 meter.</strong></div> <div>&nbsp;</div> <div>1 meter is an easily conceivable length, and so is 1 year.&nbsp; Divide it into days, and each day is about one-fourth of a centimeter.</div> <div>&nbsp;</div> <div><strong>100 years = 100 meters.</strong>&nbsp; Google any one of Usain Bolt's record-breaking 100-meter dashes and see how far he runs.&nbsp; 100 years ago, it was about 1914.&nbsp; This was the age of World War I and the Titanic.</div> <div>&nbsp;</div> <div><strong>400 years = 400 meters.</strong>&nbsp; A standard high school track is a quarter-mile, which is 400 meters.&nbsp; 400 years ago, it was 1614, and Pocahontas was alive.</div> <div>&nbsp;</div> <div><strong>1,600 years = 1,600 meters.</strong>&nbsp; A mile is 1,600 meters.&nbsp; 1,600 years ago, it was 414, and the Byzantines were puttering around in the remains of the Eastern half of the Roman Empire.</div> <div>&nbsp;</div> <div><strong>160,000 years = 160,000 meters.</strong>&nbsp; 100 miles is 160,000 meters.&nbsp; You can drive this distance in about 3 hours.&nbsp; 160,000 years ago is the lower end of the estimation for <em>Homo sapiens</em>' emergence in Africa.</div> <div>&nbsp;</div> <div><strong>3,500,000 years = 3,500,000 meters.</strong>&nbsp; This is the length of the American Appalachian Trail, from northern Georgia to the middle of Maine.&nbsp; 3,500,000 years ago, we were puttering around in the Pliocene epoch, relatively late in geological time.&nbsp; <em>Australopithecus</em> was alive.</div> <div>&nbsp;</div> <div><strong>40,233,000 years = 40,233,000 meters.</strong>&nbsp; This is the circumference of the Earth at the Equator.&nbsp; We have still not gotten back to the point in time where dinosaurs were alive.&nbsp; In fact, this period of time is the Eocene epoch.&nbsp; Australia had just split from Antarctica.</div> <div>&nbsp;</div> <div><strong>132,462,000 years = 132,462,000 meters.</strong>&nbsp; This is the diameter of a geosynchronous orbit around the Earth.&nbsp; 132,462,000 years ago was the middle of the Cretaceous.&nbsp; You might run into a T-rex out here.</div> <div>&nbsp;</div> <div><strong>384,400,000 years = 384,400,000 meters.</strong>&nbsp; This is the distance from the Earth to the Moon.&nbsp; 384400000 years ago, dinosaurs hadn't even emerged yet.&nbsp; The first FORESTS were emerging.&nbsp; Everything was fish and inverts.</div> <div>&nbsp;</div> <div><strong>4,250,000,000 years = 4,250,000,000 meters.</strong>&nbsp; You're two-thirds of the way to Mars.&nbsp; Life emerges.</div> <div>&nbsp;</div> <div><strong>13,798,000,000 years = 13,798,000,000 meters.</strong>&nbsp; You're past Mars.&nbsp; But barely to anywhere else.&nbsp; The Universe comes into existence.</div> <div>&nbsp;</div> <div>Chew on that for a bit.</div>Thu, 03 Jul 2014 14:56:20 -05002014-07-03T14:56:20-05:00276742http://www.wyzant.com/resources/blogs/276742/replace_pi_with_tauRobert S.http://www.wyzant.com/resources/users/view/78405400Replace Pi with Tau?<div>I must admit I was unaware of this controversy, but it makes some sense to stop using the constant pi, and to use a new term, tau, instead. Tau is defined as 2 times pi, which would be 6.283. &nbsp;This is explained in a fun article in a recent Scientific American story: &nbsp;</div> <div>&nbsp;</div> <div>http://www.scientificamerican.com/article/let-s-use-tau-it-s-easier-than-pi/</div> <div>&nbsp;</div> <div>Tau relates the properties of a circle to the circle's diameter, whereas pi is related to the radius (r). So the equation 2*pi*r, which gives the circumference of the circle based on a measure of the radius, is replaced with the simpler version, tau*diameter, where the diameter is simply twice the radius. I always wondered, when bored in class, why mathematicians used the radius in calculations instead of the diameter. The article cites some of the history of pi, and why that constant was chosen. <br /><br />Mathematically, it makes no difference. The argument for changing everything to tau is based on the observation that using the radius always involves a "2" multiplier, which sometimes makes the resulting expression somewhat less obvious. Examples used in this Scientific American article show how the use of pi always adds an additional "2" in an expression, sometimes degrading the apparent simplicity/beauty of fundamental equations in the process. <br /><br />Interesting topic, especially if you enjoy math.</div>Thu, 03 Jul 2014 14:24:08 -05002014-07-03T14:24:08-05:00