Shelfari: Book reviews on your book blog

Saturday, July 19, 2014

Masterpost- deal with later

I adore this textbook on Second Language Acquisition: Making Communicative Language Teaching Happen 2nd ed by James Lee and Bill VanPatten


College by 12?

These parents got their kids into college by age 12 through some non-traditional teaching methods. I love the idea of teaching kids to follow their interests. If something interests a person they are more likely to enjoy doing the work required for it. I hope I can find a way to tap into this concept as well.

https://shine.yahoo.com/experts/how-we-got-our-kids-into-college-by-age-12-175102493.html





Sites I want to save for later use:
Virtual Nerd


Snipping Tool: This tool allows me to copy things from online without having to retype it all up. It's extremely useful for making lesson plans and creating worksheets.



This one teacher did a few videos with her students covering some math concepts:


I really enjoy this site for the short, concise videos which explain how to perform certain mathematical processes by hand: http://www.virtualnerd.com/

An interactive website which shows 1-400 and greys out multiples of prime numbers when you click on them. You start with 2 and go on up. I could see myself using this with students to show them a visual representation of how the sieve works. I will definitely use it when teaching prime numbers. http://www.hbmeyer.de/eratosiv.htm


I really like this site because it is a fun way to do grammar exercises and it gives explanations for why things are correct or incorrect. http://www.colby.edu/~bknelson/SLC/pret_imp.php



Favorite Translating Site: http://www.wordreference.com/

http://rubistar.4teachers.org is a great site to make rubrics with, so I've been told. I haven't actually used it yet, but I figured it would still be a cool resource to share.

Edit: Another example of a better way to teach math: https://secure.lipscomb.edu/ayers/Video/Play/6

Example of Japanese classroom using the teaching  methods I am now learning to use: Structured problem solving: http://timssvideo.com/49





My aunt is a math teacher and she uses this song. But the more remarkable part is that she accidentally taught it to her three-year-old granddaughter in the car one day by singing it a few times. My baby cousin is adorable already but even more so when she's singing this. 

I would love to see a comparitive math question in which a student at an anime convention is trying to decide whether to buy manga at one station or another at an anime convention based on the sales they are having. Geek culture is growing and I think it would apply. 

I noticed a teacher who counted down from 5 to get the students to pay attention. By the time she got to 1 they were all quiet and ready to listen. I think this would be effective and anyone still talking at 0 would get a warning and so many warnings would merit a detention.


I think it would be cool to occasionally have my Algebra students work out problems to figure out which HW problems they have to do. Ex: 4-2i with the condition i = 0-20. I know of another teacher who did this and I think the concept is neat.


I'm thinking that every January I will hold a contest of some kind that will run from when class starts in January up until March 13. The winning class will get homemade pie on March 14 (or the Friday closest if it's on the weekend).


Math Pickup Lines FACTS

There are no clever pickup lines. But these aren’t pickup lines. These are mathematical facts applied to real life as if they were pickup lines. Similar, but not the same. Easy to confuse though. But show your Valentine just how clever you are with some of these wonderful facts:

You must be the square root of -1 because you can’t be real.

Love is like pi; irrational and never ending.

Students could respond with more clever math lines (that are clean and mathematical) for points toward pi day. I think I will open up this point opportunity the first day of February and give students until the 14th to participate. Participation would of course be voluntary.




One teacher, a Professor R. Smullyan, wrote of a method he used in a geometry class in his book 5000 B.C. and Other Philosophical Fantasies that I found interesting (http://www.cut-the-knot.org/pythagoras/index.shtml). He drew a right triangle and then drew squares on both the legs and the hypotenuse. Then he told his students to pretend the squares were gold and he asked them if they would rather have the large square on the hypotenuse or the two smaller squares on the legs. Students gave a variety of answers, but were surprised when he informed them that it did not matter because of the Pythagorean Theorem which states “The area of the square built upon the hypotenuse of a right triangle is equal to the sum of the areas of the squares upon the remaining sides.”


I like this method. It provides a visual representation as well as a real world connection. I know it’s not a proof, but I still like it to use to segue into a proof which uses squares. 






Game: Unders and Overs

For teachers who like an activity-based approach to the study of statistics and probability, Unders and Overs is a rich introductory activity that can be studied by students with various levels of mathematical maturity from upper primary school to year 11 Maths.

Materials
Two dice; one large table; five poker chips for each player plus fifty or so chips for the bank; one white board marker.  Optional - armband, croupier’s eyeshade, bowtie, a vest and hair slicked back with Bryl Cream.

The Activity
Bill is at the front of the room, dressed like a croupier, behind a large table. Not too large, it is important that he can easily reach all parts of the table. On the table directly in front of Bill is a white board marker and piles of poker chips.

[Comment: In the old days you could often find a game of Unders and Overs at the local school fete, being run by one of the parents.  It was illegal but this was generally ignored as the gambling activity raised money for the school.]

‘Come on down, come on down.  You’ve got to be in it to win it.  If you don’t speculate you can’t accumulate.’

The students gather around the table.
‘Ladies and gents, the name of the game is Unders and Overs.  Here is how you play.’

Bill takes the white board marker and draws two lines on the table, dividing it into 3 sections.  In one section he writes ‘Under 7’, in the middle section he writes, ‘7’ and in the remaining section he writes, ‘Over 7’.  Bill looks around furtively.

‘I hope the boss doesn’t catch me doing this.  Now I am going to toss two dice.  There are three possible outcomes - the total is Under 7, the total equals 7 or the total is Over 7.’

Bill rolls the dice a few times.  The patter changes depending on the outcomes, eg,
‘Under 7; and Under 7 again.  It looks like Under 7 hot.’  Under 7 again.  There - an Over 7, that balances things up a bit.’

Bill now explains how to bet.
‘Ladies and germs, boyz and girlz, you can bet on Under 7.’  Bill places a small stack of chips in the Under 7 section. 
‘If the total of the two dice is under 7, ladies and germs, you win even money.’  He places a stack of equal height next to the first stack. 

If you bet on Over 7 and the total is over 7, ladies and germs, you win even money.  Bill repeats his actions in the Over 7s section.

And if you bet on 7 and the total is 7, ladies and germs, I pay out not even money, not 2 to 1 but ladies and germs I pay 3 to 1 on a total of 7.’  Bill places a three stacks. each as high as the original one, next to the original stack.

‘Just think about it - there are only 3 possibities and on 7s I pay out 3 to 1.  You walk away with four times your bet.  Ladies and germs I will probably lose my shirt on this, but that’s the sort of generous guy I am.’

Bill now places a few chips in each section, rolls the dice and demonstrates how he pays out, by placing a stack of chips from the bank next to the winning stack and then taking up the losing chips.

He then passes out 5 chips to each player.
‘OK, ladies and germs, place your bets, place your bets.   You’ve got to be in it to win it.  If you don’t speculate you can’t accumulate.  You have to bet big to win big.  Under 7 pays even money, Over 7 pays even money and 7 pays 3 to 1.

Students place one or more chips in various sections of the board.
‘If you don’t bet big you can’t win big.  Any more bets?  OK, the table is closed, no more bets.’

Bill rolls the dice.  They come up 4 and 2, say.
‘4 and 2, that’s 6, that’s Under 7.  Under 7 pays even money.’

Bill places a stack of chips next to each winning bet and then clears away the losing bets.
‘OK, place your bets, If you don’t speculate you can’t accumulate.....’ etc

The students play a couple of rounds.
‘I seem to be doing OK, so I’ll tell you what.  Being a magnanimous chap, I’m going to increase the payout on 7s to 4 to 1.  That’s right, ladies and germs, if 7s comes up, for every chip you bet on 7s you win 4 more chips if 7 is the total.

The students play 2 or 3 more rounds.
‘Now lets have a show of hands - who is well ahead?  Who is about even?  Who is losing?  Who is broke?’

Usually the majority of students are broke, a few are about even and a few are well ahead.  Bill points out how well the back has fared, then collects up the chips and asks the students to return to their seats.
‘Now that we’ve played a few rounds, and you have a feel for the game, I want you to think about a strategy that will give you the best chance of winning.  You can talk it over with your mates if you wish.  Once you have your strategy figured out I want you to write your strategy down.’

The students are given a few minutes to do this.  Common strategies are to wait for a run and then either bet on the same outcome (‘the lucky streak theory’) or on the opposite outcome (‘the law of averages theory’).  The class members should share some of the strategies.

‘OK come on down, come on down.   You’ve got to be in it to win it, if you don’t speculate you can’t accumulate, to win big you have to bet big.’

The above scenario is repeated.   Usually it takes longer for the students to lose their chips as students are more cautious in their betting, but the final outcome is the same.  The bank is the big winner.  The students turn in their chips and return to their seats.  Bill passes out a table of random numbers generated in a spreadsheet that uses the correct probability for each total of two dice.  He explains how the table can be used to simulate the tossing of two dice.’

‘What are the chances of winning each of the bets?  We can use the Unders and Overs Simulation sheet to help us find out.’  Pick a starting spot and a direction at random.  Select 50 numbers and record them as either Under, Over or Sevens.  Then total up how many are in each category.’

Bill demonstrates how to do this on an overhead transparency.  He then gives the students time to gather the data.  The class can pool their results to find the experimental probability of each of the outcomes.  Depending on the sophistication of the class, the theoretical probability can now be calculated and compared to the class results.

It is instructive to have students use the Unders and Overs Simulation sheet to test their strategy.   Here is an example.

‘We can also use the table to see what happens after we get a run of three Under 7s.  Move your finger along a randomly chosen row or column until you get three numbers under 7 in a row.  Record the next number.  Repeat this until you have recorded 20 numbers.’

The students carry out this simulation.  The class results can be quickly collated on the board.  The students will see that a run of Under 7s doesn’t alter the chance of an Under 7 coming up next.

This activity closes with a discussion of who really wins these games, and what the almost certain outcome is for folks who gamble often.

 From the Exploring Data website - http://curriculum.qed.qld.gov.au/kla/eda/
© Education Queensland, 1997


More Probability Games: http://www.scholastic.com/probabilitychallenge/

Predicting uniqueness of DNA with probability. http://nrich.maths.org/6680

MUSIC IN MATH: http://nrich.maths.org/5478

Rock, Paper, Scissors: http://www.math.wichita.edu/history/activities/prob-act.html#rock
Could go a number of ways with this: What's the probability of you winning all of them. Probability of tying with scissors, getting scissors, or etc.

http://www.bbc.co.uk/schools/teachers/ks2_activities/maths/probability.shtml






Japanese multiplication.


I feel like the American version makes it clear that we are dealing with numbers more so than the Japanese version. The Japanese version feels a bit like magic. I am still amazed that it works. The explanation links it to foiling. I think this is a difficult concept to grasp, but it is neat that it links to something students will learn later in high school. They learn how to use this method in elementary school and build on it in high school. I think that is fascinating. It allows teachers to take something the students are comfortable with and introduce something new that they are uncomfortable with. 


In terms of usability, this method is quick and easy, though on the blog a commenter noted that it can be a pain to draw out all those lines and then count them. While I see his point, I also feel it is an effective method. After all, it is basically counting. Once the concept is down, it is pretty straightforward and simple. However, students in a rush are often known to multiply incorrectly when using the method taught in American schools. In fact I had to look up how to multiply by hand and I even messed up when multiplying two random large numbers to test both methods out.

Both methods are easy to understand. Both methods consistently give accurate answers. However, both had efficiency issues. In the American long multiplication, students may panic and multiply incorrectly in their heads. At the same time, students might draw their crosshatch incorrectly, for example drawing lines too close together, or obsess about drawing it perfectly. They may also panic and miscount. I would teach both. I think they are both useful to learn and students can always decide which one to use in the moment. For example, with larger numbers, 99 x 88, students may want to use the long multiplication to avoid drawing a lot of lines. But in smaller things 33 x 44, students can draw the lines. Honestly, it is really up to the students which one they feel they can use most efficiently and accurately. To be honest, the method they are most comfortable with which the mess up the least is going to be the one they use. 




Homework idea:
I thought this was a great idea and something I wouldn't have come up with personally. Since I lose access to the class once the semester is over I wanted to have a copy for myself: 

Thomas M: 
I am now attempting to implement more interactive homework assignments instead of simply book assignments. One idea is to have the student take a problem from class or from the book and explain to someone how to work the problem. Or take a problem or concept and give a real world application for the problem. Another example would be to illustrate a problem. Maybe it would allow the students to step into a more comfortable area for them. So that would be my advice, to try some different strategies that may be more interesting to the students while still accomplishing the goal of extending or reinforcing the student's learning.