Calculators

As many of you know, I have strong views about using a calculator for studying.
My personal opinion is that when given the option, many students rush to the calculator too often. I saw students using a calculator for a (very) simple addition problem, or for solving a term that by simplifying it a little bit they would realize that they could bring it down to a simple answer (like 4*6/12). I encourage all my students to try and solve a question first in their heads or on a piece of paper before pulling out the calculator. Beyond improving their abilities to do more math in their heads, I often see the calculator having the exact opposite of it's intended effect - it wastes time instead of saving it. Take for example the previous example I gave - 4*6/12 . Many students get confused or scared by it's appearance and rush to the calculator to do the following - take the calculator from it's case, open it, punch in the first term (4*6), press Enter, type the result in the next term (24/12), press Enter again, and copy the answer to the page. Often that would take longer then just realizing that 4*6 is a multiple of 12, or even that 6/12 is actually 1/2 which means the term reduces to 4/2 . 
That said, I do see a lot of value in using a calculator in certain situations, especially a graphing calculator. When I was in high school, I took the American AP exam the first year calculators were allowed for it. I learned to love my TI-85 (since replaced by the TI-84 plus). It was in many ways my first handheld computer. I used it for my math and science course, I used to write games and programs for it using it's internal programming features. I once made a presentation in my high school ECON class using the calculator to simulate an economic trend. I used it to store equations, formulas, to do advance graphing, complex multi-variable equation solving and more, all through my first couple of years in university. It was a wonderful tool.
I see the value of using a calculator (for courses where it's allowed during exams), and I do recommend using the calculator for difficult calculations. When is a problem too complicated for pen-brain-paper? that's a personal questions. I believe everyone has a cognitive virtual boundary for when they are better off, time wise, turning to their calculator. Some people will do it for 4*9, some for 4*19, some only for something like 7%*17. I understand that. I just also believe that whatever your boundary is, you should always try to push it, and when I have students who rushes too fast (relative to my perception of their ability) to the calculator, i'll usually stop them and ask them to look at the problem first and try to solve it without the calculator. In effect, i'm getting them to push their own boundary forward, in order for them to be able to do  more calculations faster which will translate to more time in an exam.
On the other extreme, I see students struggle with their calculators too hard sometimes. A classic example is a student who takes close to half a minute to punch into her graphing calculator something like (4*5^2)+7^2 . Here the problem is that she is probably too used to a simple calculator and breaks the term to several basic ones (5^2 , 4*25, 7^2, 100+49) instead of just writing it out once. I also see students struggle with using graphs with their TI calculators, sometimes not knowing how to trace a simple graph, let alone use the calculator to find an interception between two lines. I try to help as much as I can, and teach calculator techniques (use the 2nd-trace options for graphs) as well as tricks (you don't need the final closing bracket, store often used terms in built-in variables), and functions (use 'solve' to find roots for functions). But my best and often given advice has always been - take the time to know your calculator, that time will pay itself back several times over during homework and especially exam time. I can't stress that enough. Just like you are more likely to make the most of your cellphone by reading (even a little bit) about what it can do, so are you ever so likely to improve you test score (or at least your time) by knowing what your calculator can do.
Just in case the instruction booklet and CD is either buried under an unknown Himalayan pile in your room, or long recycled, here are links to the manuals of the most popular graphing calculators - the TI-83 (Plus and Plus Silver) and the TI-84 (Plus and Plus Silver) (i'll put the files on my website once it's done). It shouldn't take more than 30 minutes to go through a whole chapter (like the one about graphs), but boy is it worth it.
Successful Learning!
Amir 


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Cheat Sheets

I often encourage my students to write their own cheat sheets. For one, it's a great way to review all the information. Also, writing something helps with memorization (that's why it's a good idea to take notes in class, even if you are handed a summary, or if the teacher is just reviewing the book's material).
A good cheat sheet is, first of all - meant for studying, not cheating. Sometimes you will have to memorize it, sometimes you will just need it to do your homework, sometimes you will actually be allowed to bring it to an exam. If you are not - don't! . I am partial of sheets that can fit on just a few pages, written in an organized but condensed way. Basically it should read like a map - where it's easy to find the formula you're looking for quickly (10 seconds max), even though it contains tons of information.
That said, sometimes you don't have the time to write everything down, or you know you'll be getting some of the information on a test, or sometimes you just need to use a formula you learned the previous year. For those cases, prepared formula sheets can go a long way. There are many good ones available out there, but I would like to highlight just a couple (i'll post most recommendations with time)
Probably the most useful one will be a trig sheet - this trig sheet (developed by a Lamar University instructor) is a favorite. In the first two pages you get all the ratios, the half and double formulas and a few identities. Then you get the unit circle (which you should be able to develop by yourself based on my system) in the third page. The forth page elaborates on the first two, but can really be derived easily from it.
Another good sheet is this calculus sheet from a Radford University professor. It's basically a two page sheet - one for integration, one for derivation. Each includes all the basic formulas, plus the trig ones and a few extra's (natural logs, hyperbolics, etc). But what I really like about it is that it also includes a summary of all the major methods - chain, product, and quotient rules for derivation, and for integration - substitution rules and integration by parts. It also leaves a lot of empty space on the page which I would use to add techniques such as how to solve related rates using derivatives, bodies of revolution for integration etc. . As you can see, no one sheet is perfect, and any one will invariably have more and less than what you need. But that can be a wonderful opportunity for you to personalize and add in the edges the missing pieces, the tricks that have worked for you, the tips you've seen. Like I mentioned, you'll probably improve your memory of all those tricks just by writing them out and by doing so - you'll cheat yourself into learning better.
Successful learning to all,
Amir

A letter to your teacher

Dear teacher, I hope this is a beginning of a long, fruitful, bi-directional communication. We don’t know each other, we’ve never met. I have heard of you and you might have heard of me, our relationship is a little ambiguous, something I would like to correct. Though really it’s not going to be easy, first of all, I’m not writing this specifically to you, I’m writing this to you and to all of your peers – all highschool teachers, university profs, classroom TAs, who are involved in helping and educating our students. You are many, I am one. Yet this is not an attack, not an accusation, in fact, I don’t even see us as working on separate sides or with separate goals. We are part of the same team, you are the educator in the classroom setting, and I am the private tutor for our students after class is dismissed.

First let me clarify – I have a lot of respect for classroom teachers, I used to be one for a short time in my life. I know the challenges, I know the difficulty, I know that a part of you does (or at least should) care for all your students, wants them to succeed, struggles with students who are struggling, and gets excited when students ‘get it’. I also know that the hours you spend every day in front of a class, can be both exhilarating and wearing. I know the struggle to keep the class going, to keep the information flowing, to keep up with a curriculum that you might or might not agree with, even though you know that some students need a more one-on-one, slow pace attention, one that you can’t give at that point in time. I know you sometimes just have to move on ‘for the sake of the class’ knowing that some students won’t be able to follow you and be lost on the way.

I understand that, it’s not easy, and you do your best. This letter is not about that.

This letter is about the students, and their struggles. It’s about those 20 or more pairs of eyes that are facing you every morning, keen to learn, knowing that knowledge is their key in life, or at least for now. Knowing that they don’t know, and knowing that knowing and knowledge is what they need, and fearing that they might not know even how to learn, at least not what you are trying to get them to know. It’s about those students, who after hanging by every word of yours, want and struggle and try. And they all want and struggle and try, they all wish to succeed, even that kid in the back row who shows up to, what might appear to you to be, just stare and make noises, and interfere. They all want to learn, but not all get it. Not at this hour, not this material, not with this explanation. They don’t. So they come to me, those who realize they need more attention, and who are willing to make the necessary investment, they come seeking help, seeking the insight that was there in the air in the classroom, the insight that was hovering and winding, and occasionally touching their peers in an a-ha moment that seemed to elude them, they come to me.

And my job is to finish the work that started in your class. You might have done it yourself, if you had more time, more scheduling leniency, but you can’t, and so I do.

Only that I don’t have to follow your curriculum, I am not bounded by the textbook, or the methods it teaches, or by the specific order even that it teaches the material. I just need to be focus on our student’s success. I have the freedom that you might not have, or have forgotten that you have. And I have that one-on-one time that you don’t.

So I teach, and I change my curriculum and my method every time I sit with a student. I borrow ideas, illustrations, examples and parallels from wherever I can, and use whatever will work. With one student I’ll talk about apples, with another about sports, another about space, or people, or hiking, or computers, or even political theory. I will use whatever tool I can think of (and I can think of a lot) to illustrate a point, to generate that insight, to realize that a-ha moment. I will use ideas from different books, or different teachers, or will come up with a brand new way on the spot that I think might explain things better to a student. And I’ll keep at it, and keep at it, and keep at it, until they get it, until they understand enough to solve the textbook questions. And then I might go some more, to give them different options for different ways of solving the same problem. Just in case. And then I’ll also show them tricks and rules-of-hand of what to do when they have forgotten all those methods in the middle of an exam. And then I might give them some exam taking tips, and some questions to test their knowledge, and congratulate them for figuring it out, because I need to teach them not only the material but also how to believe in themselves and in their own ability, and how to trust themselves, and their brains, and their intelligence. Because they are all capable, even though they are often their own greatest critics and doubters.

Perhaps you would have done the same, perhaps you would have. I know that when you or your peers try to do after-hours tutoring for free or not, that you try. But when you are part of a system that teaches only one technique, one topic, one subject at a time, you will be challenged to be more than a classroom teacher.

You see, we are a team, you and I, and together we can introduce success to the minds and abilities of our students. Each in our own way, each with our own abilities, yet still being on the same side.

The student’s side.

Yours truly,

Amir Taller

Private Tutor

5 tips for success during midterms

It’s that time of the year again – Midterms!

Whether you’re in highschool or in university, midterms can be a very frightening time. For many students this is the time they realize how behind they have been on their school work, and they start a frantic race to catch up in the seemingly little time left till the first (and last) midterm.

But midterms can also be a wonderful opportunity. For one, consider the fact that once you do catch up with all the topics being taught then you’ll have an almost ‘clean start’ for the second, usually more difficult, part of the semester.

Here are a few things you should always keep in mind when studying for a midterm:

1. Your teachers/instructors/profs use midterms to check your knowledge on the earlier chapters of the semester. Once that is established, they know they don’t have to spend too much effort (questions) on the final exam asking questions about those chapters. That is why usually midterms are slightly more skewed toward the earlier chapters of the half-semester than the final is. So make sure you understand the topics that were taught in the first month of the semester at least as well as those taught later.
2. Don’t panic! In many courses, the midterm has a diminished weight in the final grade, a mistake in the midterm does not reduce your final grade as much as you fear.
3. Plan ahead - Here is a good strategy - starting a week before the midterm, set aside some time every day to go over one of the chapters that will be tested in the midterm. Make yourself a study sheet - take notes, make summaries, write equations, whatever is relevant – on a special study sheet, then when you start studying in earnest all you’ll have to do is just review this sheet. An added benefit is that when you’ll be studying for the final you will already have these papers and will only have to summarize the latter half of the semester.
4. Know what you don’t know – Make a list of all the topics you are struggling with and need to know by the time of the midterm. While studying, when you feel you’ve nailed down a topic – scratch it off! It will give you a sense of accomplishment each time and a sense of perspective of where you are in your studying goals.
5. Plan your time and your priorities – studying is difficult as it is, with school, family, work, extracurricular activities. Set aside in advance time for you to study, and if you need to – delay commitments till after the midterms. Look at previous semesters and try to remember what commitments made it the most difficult for you to study. Then try to figure out how to avoid/delay/preempt whatever you reasonably can so that you have a clean slate as much as possible for your studying. That said, don’t forget to plan for some reenergizing ‘down time’ for yourself during your studying.

Midterms are a difficult time, but with careful preparation and with good time and effort management, they could become very manageable. A good grade could mean a strong ‘safety net’ for the final, which can never be a bad thing.