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
Spanish project idea: http://www.collegehumor.com/embed/6942161/student-makes-telenovela-parody-for-spanish-class
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
Quadratic Formula Game https://jeopardylabs.com/play/quadratic-formula-game
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
Lesson Plan Ideas: http://www.readwritethink.org/search/index.html?page=1&grade=17-20&resource_type_filtering=6-16-18-20-126-56-58-66-68-94&resource_type=6
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.
American version: http://www.mathsisfun.com/numbers/multiplication-long.html
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.
