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One of the things I love most about the Latin language is how its writers can massage it to add information and imagery without having to add more words.  I call this, personally, writing in two dimensions.  Here's an example:   At one point in the Aeneid, Aeneas and Dido are having a lovers' tryst in a hidden cave, which was dedicated to a god.  Because Latin is a highly inflected language, word order carries little grammatical information (unlike English), but can add quite a bit of what I call "two-dimensional" information.  So, in English the line might be written:   Aeneas and Dido were in the holy cave.   But Vergilius writes instead (only in Latin):   In the holy Aeneas and Dido were cave.   Thus, even in terms of word order, Aeneas and Dido are INSIDE the cave!  I find things like this absolutely thrilling.  But it's not my favorite half-line in Latin poetry.   That... read more

  For those of you who may have purchased Apple's spiffy $79 external CD/DVD burner (or Superdrive as they call it), it may not have worked when you plugged it into your older Mac. A lot of times a person's built-in optical drive fails, and they see the new external at the Apple Store. They naturally grab one assuming it'll work because they'll be using it with a Mac. Hopefully there's a "Genius" selling it to them who's going to ask which Mac they plan on using it with. I'd think probably not. It turns out it's only the fairly newer Macs that support it. When you plug it in, your older Mac might very well inform you that "This Apple External CD/DVD drive is not compatible with this Mac. Please go to Apple Support to read more." What they show you is a compatibility matrix that seems to makes no sense. I haven't compared every spec of every Mac they list, but 2009 seems to be the general cutoff.   Perhaps Apple requires USB 3, and... read more

NOTE: For today's Math Journey, please refer to the image file “Image for Math Journey: Road Trip Around A Problem” under my WyzAnt files. Link: Let's go on a road trip! When I teach geometry, especially geometry involving angle measures like this problem, I like to describe the process of solving a problem as taking a little road trip. I describe it this way because this is how I personally feel when solving a problem like this – my eyes rove around the figure from one intersection to the next, and I hop in my little math car and drive along lines and stop at intersections to figure out where I am. Geometry is a very visual discipline, and as a visual learner, I have the most fun when I can trace a physical journey around the problem, solving things as I go. So let's hop in our math car and chase this problem down! The first step in any problem like... read more

I recently had the experience of arranging to meet a new client's high-school student for their first time using online tutoring with me. We had already exchanged messages on the platform we intended to use in an attempt to ensure everything was ready for that night's session when the student would be ready.   However, we encountered some problems!  Although we were both logged into the video-conferencing application, and had earlier exchanged IMs through the application, neither of us appeared to be online to the other! After trying the usual restart-the application, restart-the-machine first trouble-shooting steps, to no avail I asked the client to try checking their application for any available updates.  Well, evidently there must have been some updates that hadn't run for quite some time (or perhaps an antivirus program or firewall interfered with the update process, or perhaps the operating system was out-of-date too, or ... could have been any number of... read more

Infinity is a term with which most people are familiar, but few truly understand. Infinity is not an actual value, like the number 3 -- it is an abstract concept. In math terms, it is used as a "limit", where a value can approach infinity by getting continuously larger, but it will never actually get there. Consider the act of cutting a pizza into slices. You can cut it in half, then cut those halves in half, then cut those halves in half, etc. As the slices get smaller, the number of slices gets larger; therefore, as the size of each slice approaches zero, the number of slices approaches infinity. Again, in math terms, this means that as x approaches zero, the value of 1/x approaches infinity. Some go so far as to say that 1/0 equals infinity, but this would not be entirely correct; nothing can actually "equal" infinity, since it isn't a value, but an abstract limit that can only be "approached". Here's another example. You are standing a... read more

Wyzant has a policy to allow new students to meet with a tutor of their choice and if they don't find the tutor meets their needs, they may contact another tutor without charge (as I understand it). This is a customer-friendly policy that makes students feel more comfortable in contacting a potential tutor. However, it works both ways. A tutor will also need to review the information a potential student provides to determine if possible how well the tutor can provide the help requested. The problem lies when the student gives no information.   When a student writes only "I need help", or "when can you meet", or writes no message at all, it is impossible for a tutor to determine if he/she can help. A tutor must determine the student's specific subject and area of need, level, school or work situation, possible schedule (e.g. evenings only), and other factors to see if he/she can help. It becomes a waste of time to write back and forth when the student... read more

I've been creating mad-libs to use with my middle school French students. If anyone else would like to use them, feel free. Many of them are created from non-copyrighted short stories, not my original writing.    Mad Lib 1   1. un mois 2. un profession 3. un lieu 4. une Fete 5. une chose 6. un verb avec ils 7. un prenom d'une femme 8. un verb avec elle 9. une chose pluriel 10. un verb avec elle Nous sommes en __________(1). Gilles est ________(2) dans un/une ________. C’est bientôt la __________ (4) et Gilles a acheté un nouvel ________ (5). « ____________ (4) est un lundi cette année », dit le _________ (2) à sa femme. Ensemble, ils _________ (6). La femme de Gilles s’appelle ________(7). Elle _________ (8) dans un magasin de décorations en ville. Durant le mois d’octobre, elle a souvent beaucoup de _______. L’automne est une période où _______(7) ________ (10) beaucoup.     Mad... read more

My Cancellation Policy I consider time very valuable, both to me and to my students. In order to be a more effective tutor, I am implementing my cancellation policy as follows: - Student Cancels with more than 24 hours Notice: No fee - Student Cancels with 6-24 hours Notice: 1/2 price of session - Student Cancels with 1-6 hours Notice: Full price of session - Student no-show with No Notice: Full price of session and student may be dropped I am committed to providing an excellent experience during each tutoring session. I promise to value your time. In the unlikely event that I am late or need to cancel a session last-minute, I agree to the following: - I am more than 15 minutes late to session: Student charged 1/2 price of session and make-up time, if possible - I cancelled a session with less than 24 hours Notice: Next session is free   My schedule is very full, and I prefer to schedule my students on a certain day of... read more

Ellen's Rules for Effective Time Management, Part 2 3. Know when it’s time to take breaks. Spending a good chunk of time on one subject is good; it helps you settle into a rhythm and lets your brain get into the correct frame of reference for the subject. But there exists a horizon beyond which no progress can or will be made. It’s the point at which your brain has become over-saturated with the current material, and if you continue on you’ll just end up working yourself into circles of frustration. In paper writing, it’s the point at which anything you wrote would make sense to you regardless because you’ve been reading the same few paragraphs to yourself for hours. In math, it’s the point at which you will just end up confusing yourself more and more as you try desperately to work it out. When that moment arrives, you know it’s time to take your break. 4. TAKE BREAKS. I don’t care how much work you have, there’s always enough time for a fifteen-minute break... read more

I became pi day challenge genius #181 at 3:14 on Sunday :-) Less than an estimated 10% of those who play do all 37+ (some have groups of puzzles). You can still play at any time at #pidaychallenge Pi Day Challenge throughout the year. They're not just math/physics puzzles.   Per the owner of the site, I calculated the genius percentage incorrectly.  About 10,000 people took the challenge, so becoming a “genius” is pretty rare.   One of my elementary age students this year started answering some of the hard ones even faster than I did. I don't know if he'll complete all the puzzles, but each year his lateral and creative thinking improves.  Having these extra-curricular activities helps youth have FUN!!!   Try a few out... even if you think you're stuck.  It's amazing what the brain can do with a good night's sleep. Barbara W.

The Seven Learning Styles Visual/Spatial:You prefer using pictures, images, and spatial understanding. Aural/Auditory: You prefer using sound and music. Kinesthetic/Physical: You prefer using your body, hands and sense of touch Verbal/Linguistic : You prefer using words, both in speech and writing. Solitary: You prefer to work alone and use self-study Social: You prefer to learn in groups or with other people. Logical/Mathematical: You prefer using logic, reasoning and systems.   The Seven Learning Styles Visual/Spatial:You prefer using pictures, images, and spatial understanding. Aural/Auditory: You prefer using sound and music. Kinesthetic/Physical:  You prefer using your body, hands and sense of touch Verbal/Linguistic : You prefer using words, both in speech and writing. Solitary: You prefer to work alone and use self-study Social: You prefer... read more

Good project ideas for rainy (or just lazy) weekends:     Have the kids read aloud to you. Choose a word that you think they may not know the definition. Then start a "Look up that word" game: I know some friends of mine who used to play this game often, I recall there were brothers and were very much into sports and competition, if they didn't know a word that was spoken or in their homework assignments, they would race to a dictionary to see who could find the meaning first. By the way, now they are articulate men with an awesome vocabulary! You can ask "Who can look this word up and create a sentence? The fastest one is a winner!" Some kids may not think this is too much fun at first so plan a preferred meal or movie as a reward! They may start to really enjoy the word race game over time as they play it!

Ellen’s Rules For Effective Time Management, Part 3 5. Mix up your subjects. Spending all day working on the same project can lead to feelings of frustration and inadequacy. Mixing up your subjects helps the brain to stay engaged, since it can’t fall into the trance of working on the same thing for hours. If you’re writing a paper and starting to feel annoyed or frustrated with it, take a break and work on your math for a bit. You’ll sit back down to the computer feeling refreshed and relaxed, even if you haven’t stopped for more than fifteen minutes at a time all day. 6. Make the delineations between subjects clear and firm. When mixing up your subjects, keep them distinct and separate from each other. Take a short break between subjects, or place the rest of your notebooks on the other side of the room so that you’re forced to get up and move around in order to change subjects. Give your brain several minutes to clear and reorganize for the next... read more

I've had several potential students contact me recently without reading my profile page carefully. I'm not involved with social media, so I don't know if that page resembles a social media platform. I doubt it, but perhaps people are so used to looking at information online with half an eye, without really reading or absorbing the content, that when they come here they feel the “information” is the same as elsewhere. It's not. On my profile page, my location is stated. Yet potential students from other time zones sometimes feel I must work close to them. They are surprised when they finally realize I don''t live in their state. That also means I can't meet them at a local coffee shop for face-to-face work. Again they are surprised, despite the fact that their tutoring request clearly states: “preferred lesson location: online”. If I live far from you, and you have asked for online tutoring, then why would you be surprised that we would work online, not face-to-face at a local... read more

The complaints against WyzAnt’s 40% commission demands a response. Suppose a tutor with 15 hours of work time through WyzAnt charges $40 an hour. Of that amount, WyzAnt will automatically deduct $16. This deduction is based on WyzAnt’s commission rate, which is 40% for the first 20 hours of work time. So the tutor is not earning $40 an hour; rather, the tutor is earning $24 an hour. According to a number of individuals, WyzAnt’s 40% commission rate is too high, way above average. Some folks, oddly enough, have even posted complaints on other websites. Why? Here's some food for thought. 1. Twenty-four dollars an hour is higher than any state’s hourly minimum wage. 2. You can create your website for tutors and charge a lower commission. 3. If you tutor for an hour you will be paid $24. 4. If you don’t tutor for an hour you will not be paid $24. 5. Twenty-four dollars is more than zero dollars. 6. You don’t have to stay with WyzAnt, but before you leave... read more

Well, okay, it's not incorrect, but it's flawed and by a mathematician's standards: morally wrong.   I'm sure at one point you boringly learned the order of operations. These are the set of rules that tell you whether you should do multiplication before division or addition before subtraction to get the correct answer on your math problem.  1) Parentheses (brackets) 2) Exponents x^x 3) Multiplication 2*2 4) Division 2/2 5) Addition 2+2 6) Subtraction 2-2 7) Get the right answer :)   Except, you don't always get the right answer.   For example: 8-2+1. Is it 5 because 8-3=5? Or is it 7 because 6+1=7?   Is 6/3/3 equal to 2/3 or 6/1?   The issue here is that focusing on the order of operations can lead to ambiguity and obscures the real beauty of mathematics.   A mathematician will tell you that 8-2+1 is actually 8+(-2)+1, which is unambiguously equal to... read more

This was a really hard essay to write. Not because I couldn't figure out what to write about; I knew almost from the moment I read the prompt that I wanted to write about Dracula. On the contrary, it was hard because I had TOO MANY ideas for this essay – I had so many thoughts buzzing excitedly around in my head that my outlines kept coming out really scattered and disorganized. I went through, no joke, at least FOUR different outlines for this essay – and I refused to even start writing a draft until I'd sorted out what precisely was wrong with my outline, scrapped it for the third time, and started over from scratch. I went through several different organizational schemes, starting with one centered around a favorite Hitchcock quote about suspense that was a good idea, but ultimately, had no place in this particular essay. My outline eventually settled on the format that probably should have been obvious from the start – the one that related most closely to the prompt. My outline... read more

10 Tips to Advance Your Second-language Learning Process Speaking a second language is a wonderful tool to have at your disposal. Not only is it fun and cool, but it opens doors to experience another culture in new, exciting and personal ways. And if you're working on speaking a language that others speak in your community, it can also open doors for you professionally. So, if you're itching for some tips to help advance your language learning process, have no fear…I'm here to share with you 10 of my trusty tips for how I learned to speak my second language! (How well do I speak it, you ask? Well, native Spanish speakers often think I’m a native Spanish speaker, just to give you some context.) These are all things that I did myself, so I’m confident in recommending them all to you! :) Let’s get started with some specific tips, and then move on to my more “philosophical” and general advice: 1. Watch television shows, movies and videos in your target language For those working... read more

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