May I help you with that?
The Tutoring Room is a place where people can ask questions. Daily Kos has some very smart people as users and it makes sense for them to have a place to share.
Despite my user name (which is what I do...), this doesn't have to be just a place about math. This diary is about learning and it recognizes that sometimes it's hard to learn, even when you're motivated. If I can't help you, I'm sure there are other kossacks who can and will.
Link to last week's (which includes an introduction and more):
http://www.dailykos.com/...
This diary series is in alliance with plf515's diary series Daily Kos University, which appears on Saturday mornings, and cfk's Bookflurries:Bookchat. They also offer tutoring.
On college:
"I didn’t know what I didn’t know until I took the mid-term."
My college undergraduate experience was completely changed by the above sentence. Actually, it was me talking and I said, "You didn’t know what you didn’t know until you took the mid-term." I said it to a guy sitting in my living room who had just received his American History mid-term grade, which was an F. He was baffled by his grade; he thought he’d get at least a C. He thought he was ready for the test and even thought the test was "kind of easy." His next grade for the class was to be a paper comparing Hamilton and Jefferson and since I was the only History major in the entire building, he’d been told to come see me.
The guy in my living room had barely any knowledge of Hamilton and Jefferson. He did not know how to effectively use the index of the required textbook. He did not know how to use the campus library (this was pre-internet days). When he brought me a draft of his paper, I discovered that his writing was nearly incoherent and did not address the subject of the paper, which was to compare the views of government held by Hamilton and Jefferson. He wrote biographies. I did what I could and received a six-pack for my trouble. When the guy told me his career goal was to be a lawyer like his father, I covered a burst of laughter with a coughing jag.
It is my opinion that the typical college-bound high school graduate is not prepared for what college expects from students. I formed that opinion in my living room thirty years ago and nothing has changed. Because I am a renowned soft-touch, I average somewhere between three to six young people per year- nephews, nieces, friends of so and so, sons and daughters of so and so- in my home looking for help. Not all are college students but every high school student I’ve helped has been college-bound, or so it is expected by the parents.
Successful high school students do a lot of work and meet a lot of deadlines, including daily homework deadlines. Read this; answer the questions at the end. Do problems 1 through 20. There’s a vocabulary test every Friday. Do the lab and write up the results. So on and so on and so on. Sometimes I think the amount of work a college-bound high school student does is a way of checking up on his or her teachers. Any teacher not making his or her students do the expected amount would be an object of investigation by parents and administrators. If anything, No Child Left Behind reinforces this constant demand to produce because of the pressure to cover every tested Standard. Nobody wants a college-bound student to see a high-stakes, multiple-choice test question that he or she doesn’t know anything about. The college-bound are supposed to score "advanced" or "proficient" on all tests, after all.
But college is different, at least in every lower-division class I’ve ever heard of. Course grades can be based on a mid-term, maybe two mid-terms, and a Final. Maybe there’s a mid-term, a paper and a Final. Whatever the combination of these things, the point is that college students are supposed to prepare themselves and be ready to produce when the time comes. No fooling, no second chances. Some classes are designed to weed out the weak.
I sat down with my college daughter and talked about what she would have to do to succeed in her college classes. My daughter refers, laughing when she says it, to herself as a "cool nerd." I told her to be cool on the weekends and a nerd during the week, which starts some time Sunday afternoon.
We talked about language (Know and use the words that are used in the lectures and the book; make lists and test yourself until the words are ordinary for you), reading (Never just read anything; every page or so, write down what you read and then skim the reading to see if you forgot anything useful), writing (Never turn in a paper until you have someone as smart as you are read it first and with enough time for you to fix what’s wrong), preparation (Look at all your notes; what would you ask about on a test? Write answers ahead of time or at least outlines of answers. I became so adept at this that I always had a prepared answer for every exam question in my upper division classes) and attitude. Students who don’t take command of their own education in college get whacked. Students who rejoice over not having to do homework in college get whacked. Students who coasted through high school and believe they’ll do the same thing in college get whacked.
My daughter’s college works on the quarter system. She did very well in her first quarter. Over Winter Break, she told me that she knew lots of people at her school who were crazy-scared at Finals time while she was busy-tired.
On reducing fractions:
Repeat after me: fractions are division. The top number is divided by the bottom number.
When students are first taught how to reduce fractions, their first problems tend to be fractions that can be reduced by using the number two. For example, six-eighths. Divide the top by two, divide the bottom by two and now you have the reduced three-fourths.
A problem for a lot of students is that they never really progress past the number two. Lots of my students want to divide everything by two (including those hideously massive fractions that prove, by their existence, that people who create those problems hate children), and then another two, and maybe another two and so on until they get the answer or give up. Lots of my students don’t even try bigger numbers until I retrain them.
Most textbooks talk about reducing fractions as "Find the number that..." I don't care for that approach because books rarely emphasize how to "find" that number. My Algebra book before the most currently adopted included what's below in a "supplemental" section and didn't include it in the sixth- or seventh-grade books at all.
Have your student(s) learn this sequence; it will help them "find" the number to use to reduce:
10 and 5
9 and 3 (and if 3, advanced students should check 2 right now)
Check 7
2
Any number that ends in zero can be divided by ten. If you can, divide ten out to the fraction first.
Any number that ends in zero or five can be divided by five. If you can, divide five out of the fraction.
Add the digits of the numbers in the fraction. For example, eighteen over twenty-seven is one plus eight, nine, and two plus seven, also nine. If the sums can be divided by nine, divide nine out of the fraction.
Let me stop right here and point out what might not be obvious. The whole point of reducing fractions is to do the division that is possible; that’s simplifying the fraction. If you’re going to divide, why not divide by the biggest numbers you can so that you’ll be finished faster? Ten, five and nine are a lot bigger numbers than two. The other good thing about this sequence is that you eliminate numbers as you work your way down. If ten doesn’t work at the beginning of reducing, it will never work. Once five is used up, it will never need to be considered again. Then you won't have to think about nine, and so on down.
Go back to the sums you did for the top and bottom of the fraction. Can those sums be divided by three?
Check seven. Seven has no special rule.
Now check two. Any number that ends in zero, two, four, six or eight can be divided by two.
The advanced thing? Any number that can be divided by three and by two can be divided by six. Now let me put that another way; a number can be divided by six only if it can be divided by three and by two. If not both, it cannot be divided by six. The only reason I call this "advanced" is because it requires doing something out of its turn, so to speak.
On Pre-Algebra:
Algebra is full of times when numbers and letters, written in an established order, can tell you what something looks like on a graph. Pre-Algebra, which is becoming the normal seventh-grade math class for much of the country, starts teaching about this.
The slope-intercept form of a line (aka "function form"): y=mx+b
Many students have a hard time connecting how something written in this form is a line they can see on a graph.
Some realities: if you see the y-axis (the vertical, up-and-down number line) as where the start of the graph could be, the "b" is where the graph starts. The y equals the b. Put a point there. The slope (the "m") now tells you where to go from that spot. And remember that slope is a set of directions written like a fraction, how many up or down and then how many to the right.
For example: y=3x+2. Put a point where y=2. Now from that point, go up 3, then right 1 (3 is 3 divided by 1).
Another: y=-2x-4. Put a point where y=-4. Now from that point, go down two, then right one (-2 is -2 divided by 1)
A fraction: y=3/4x+3. Put a point where y=3. Now from that point, go up 3 then right 4.
By the way, if you think of slope as how many up or down, then how many to the right, you won’t get messed up with negatives. A negative just means go down first, then right. And zero slope means flat line. No heartbeat. Horizontal. Dead. Y is he dead? He's been x'd out. And "undefined" slope is when the stupid thing is going up and going down at the same time, otherwise known as vertical.
And by the way, why is it always going to the right? Because time does not go backwards; it goes forwards. Time is positive and positive is to the right. (Every year, I have to remind my Algebra students that time does not go backwards except in the movies and objects do not "fall" up.)
Canadian History
Well, I don't know much. Can anybody recommend a better book than A Few Acres of Snow, by Leckie, about the French colonies and the French-English conflicts before 1763?