MATHEMATICS

Senin, 07 September 2009

Different methods of starting a Math lesson

Well start is half done!

If a teacher is able to capture attention in the beginning of a lesson then half of the job is done. This means the first two classes of a Math lesson are very crucial. There are various methods of beginning a Math lesson in a creative manner.

#1 Making a connection- Everytime it is not essential that we are going to start a new concept. Students have some knowledge about it earlier. So, forming a connection by asking questions based on previously gained knowledge of students is a tried and tested strategy which helps in motivating students for further learning.

#2 Showing a picture - A picture says a thousand words. In a math class, one may begin a lesson by showing a picture from surroundings showing the use of some Math concept leading to introducing new concept.

#3 Story telling - This helps a lot in the beginning of a lesson. I believe we as teachers need to capture attention of students so that their focus is on the new topic. Story telling is indeed a good way to start a lesson.

#4 Realising the need to learn- Why we are learning this concept ? Why it is important ? This must be answered in the beginning.

#5 Involving students - Calling students names in between , taking their help ,taking their examples helps in capturing attention till the end of class.

#6 Showing real objects - Sometimes it is feasible to carry real objects in a classroom. Students may be asked to look around themselves to observe things also.

It is the way how a topic is introduced which matters a lot.

Soal Matematika SNMPTN

Awalnya saya mengetik kumpulan soal matematika yang ada di blog ini menggunakan word 2003, tetapi ketika mulai banyak yang menggunakan word 2007 akhirnya beralih juga untuk mengetik soal - soal dalam word 2007. Hanya masalahnya word 2007 ini kok belum bisa ya untuk upload di ziddu.com ( atau sayanya yang belum paham ), sehingga setiap file harus dirubah ke word 2003.

Masalahnya ketika file

Sabtu, 05 September 2009

Sorting and Math Teachers at Play 15

The new carnival is up.

Some of my favorite items: Kindergarten sequences (good for older kids, too) and the math skits idea.

I'm not crazy about the fractions or quadrilaterals activities, as I think both fall into some common pitfalls of the traditional thinking on these topics.

Sorting
As we started class this week, one activity we did in both my classes (geometry for K-8 and math student teacher assisting) is a Piece of Me. Students come up with one question about the class and one question about the teacher(s). They then get together in pairs/groups and decide on one of each to ask. They never ask the sort of thing you'd expect, or the sort of thing I used to share in my own introductions. It's an excellent quick pre-assessment of where they are with the class and what they care about. And, they get to discuss with other students what makes a good question. I got this activity from Dave Coffey, but I can't remember from where he got it.

The first activity I had the geometry students do was a game, that I've played with many levels of students.

In or Out
Materials: rope or chalk circle (For 20ish students a 40-50 ft rope will suffice. Of course, divide by 6 to estimate the diameter of the circle formed.)

Students stand outside of the circle. To demonstrate how a circle sorts, have a few different rules, and students who fit the rule step in. I usually use the old riddle: how many sides does a circle have? (Highlight for the answer: Two - inside and outside)

The game is a guess the rule game. Someone has a rule for the circle and people guess whether they are in or out. If they are correct, they can guess at the rule. If you guess the rule, you can make up the next rule.

I usually demonstrate the first three rules. One that is obvious, one a bit more subtle, and then a hard rule. The hardest rules are ones that change: in or out depends on body position, or on what the person before says. (Almost a guaranteed rule stumper is - you're out or in based on what the person before you guessed.) This can also be used to demonstrate the concept of function. (That's when I'm using the game in a college algebra class.)

Mostly the point is to get students thinking about characteristics. With upper elementary students or middle school students you could ask the questions I asked this time, after playing the game for awhile:

Activity: Work your way through some of the following questions.
1) What were some of the rules used?
2) Was there a rule that was easy to guess? Why?
3) Was there a rule that was difficult to guess? Why?
4) What is a rule that would divide our class into two groups of roughly the same size?
5) What are two rules that would divide our class into 4 groups of roughly the same size?
6) Why do two rules divide a population into 4 groups? Give an example.
Extension: Into how many groups would 5 rules divide a population? N Rules?

Reflection:
• Whole class: Share some of the ideas from (5). Try them out.
• Analysis: What are you doing when you’re sorting?
• Inference: What does this lesson have to do with geometry?


13 Learning Times Tables Links

Multiplication tables plays an important role in learning Mathematics. Children move away from learning them. Technology has helped teachers by offering interesting tools/games/software for helping children to learn concepts and practise.

Here are some interesting links
#1

1. Times tables generator You will get times table generated in click of mouse. Just type in the number and click...

#2 (Free and Downloadable )

Here is an interesting downloadable Math game which may be used for practising tables. I find it different and challenging too.Try it!

Valgetal Falling Numbers 3.23

#3 (Free and downloadable)

Another one is Multiplication Master...Free multiplication tables practice software.Fast, simple and easy to use for budding multiplication masters of all ages!Keeps your score so you can see how well you're doing.Single table mode lets you focus on one multiplication table at a time - the fastest way to improveRandom feature tests you against all the multiplication tablesIncludes reference tables to help you learn multiplication tables fastUnlimited use. Practice as many multiplications as you want, as often as you want.Completely free. No charge for this software - ever.Here is the link to download.

#4 (Free Junior edition)

This one is learn MathMatic JuniorMathmatic is a program for learning and drilling multiplication tables 1 through 12. It is dedicated to that unique task and it does it thoroughly. MathMatic generates and PRINTS DRILL SHEETS. The user can choose between Mental and Written learning modes and use the timer to measure performance. MathMatic's sounds and colors are fully user definable. The Junior Edition is Freeware and is directed towards young students (multipliers bound to low values).

#5
A free multiplication program for kids... MULTIPLICATION FACTS lets you learn and practice the basic times tables using the numbers zero through twelve. And it's FREE! MULTIPLICATION FACTS lets you work with any digit(s) you choose. Review times tables, see graphic representations of problems, or take speed drills. The program grades your performance and provides feedback. Print worksheets for practice away from the computer.

#6
Checkout Times tables activities,games and worksheets ...quite interesting!!
#7

Tables tree-an interesting game to practice multiplication tables.

#8

A complete website on multiplication for teaching learning multiplication facts.

#9

Visualising Multiplication tables using this applet.

Visual Multiplication

#10

Answer 10 multiplication questions. How much time did you take?

Tables times

#11

Multiplication flash cards on Quizlet.

#12

Interactive practice of times tables. Click on a box. Drag the right answer from the numbers given on RHS.

#13
Explore Multiplication tables in an interactive manner.

Rabu, 02 September 2009

15 Places to find Teaching Resources and Math teaching strategies

Trying to get a classroom of 20 to 30 individual thinkers to understand difficult math concepts can sometimes be challenging. Fortunately, there are many websites that offer lesson plans, activities, teaching strategies, and other resources to help you out. Here is a list of 15 sites that math teachers will find especially useful:

National Council of Teachers of Mathematics - The NCTM, a public voice in mathematics education, provides professional development strategies, lessons, journals, books, and other resources that can be used in a K-12 math classroom.

The Math Forum - This free online math warehouse offers lesson plans, activities, educational materials, teaching strategies, career development resources, and much more. The Math Forum also provides links to other resources that are useful for math education.

TeAchnology - TeAchnology, a huge database of lesson plans and classroom resources, is loaded with lesson plans specifically for math teachers. The lesson plans cover all grades, areas, and concepts.

Math.com - Even though this site was created to help students with math, Math.com features a variety of resources teachers can use as well. Under the teachers section of this site, you can find lesson plans, classroom resources, career information, standards, and other free resources.

Math-Videos-Online - This free online math site features math videos that teachers can use with their lessons to demonstrate important concepts. The site also offers interactive games, quizzes, and printable worksheets to be used in conjunction with the videos.

Rader's Numbernut - Rader's Numbernut is a site that contains interactive math games and activities for beginning and advance math. Teachers can use these activities within their lessons to illustrate important concepts.

Illuminations - The Illuminations site features a library of 103 activities that teachers can use with their K-12 students. In addition to the activities, this site also features over 500 lessons specifically for math.

TheTeachersCorner - Teachers looking for a wide range of online teaching resources will enjoy the lesson plans, worksheets, and activities offered on TheTeachersCorner. This site also features a message board, printables, bulletin board, and other general resources that teachers will find useful.

AAA Math - AAA Math provides a comprehensive set of lessons for K-8 students. The lessons come with unlimited practice to help students master concepts.

FREE - The Federal Resources for Education Excellence (FREE) features a huge list of teaching resources for algebra, data analysis, geometry, measurement, numbers and operations, and other math concepts. The teaching resources cover lesson plans, tools, learning activities, and more.

Discovery Education - Discovery Education offers free math lesson plans for elementary to high school students. The lesson plans are broken up into three sections for elementary, middle school, and high school children.

Mathematics Learning - This blog, created by an educator with over a decade of experience, provides math teachers with a place to find and share new strategies in the teaching of math. Throughout the pages of this blog, teachers will find resources, activities, and strategies that have been successful in other math classrooms.

Terri Husted - The Terri Husted site is designed specifically to give math teachers information and ideas on how to improve their teaching strategies. Throughout this site, you will find information on classroom management, new teacher resources, math activities, homework assessments, and much more.

National Library of Virtual Manipulatives - The National Library of Virtual Manipulatives is a free online activities site that teachers can use with their K-12 classrooms to visually demonstrate numbers and operations, algebra, geometry, measurement, and data analysis.

Math Drills - Math Drills provides thousands of free printable math worksheets that are great for assessing student's abilities, giving extra practice, and teaching new strategies.

Guest post from education writer Karen Schweitzer. Karen is the About.com Guide to Business School. She also writes for OnlineCollege.org, an online college resource.

Rabu, 26 Agustus 2009

Soal Latihan Integral

Kalau pada postingan sebelumnya saya menyajikan tentang materi integral seputar pengertian dan beberapa contoh soal integral tak tentu, integral tentu dan beberapa integral trigonometri, maka postingan berikut ini saya ingin berbagi beberapa soal integral yang saya comot dari beberapa tempat.

Seperti file saya yang lainnya soal latihan integral kali ini pun saya sajikan dalam bentuk microsoft

Selasa, 25 Agustus 2009

Motivation

Good thing to be thinking about as school starts. I'm a bit skeptical about Dan Pink, but several people I know and respect have a high opinion of him. It feels sometimes like he's selling creativity.

But on his recent TED talk, he reports (link to his talk) some social psychology experiments that help me understand a big divide in teaching: incentives in classroom management. A simplification of his point would be that incentives work best on simple, direct tasks. On more challenging problems rewards don't work and, in fact, impede. What does work? Choice! Autonomy! (Conditions of Learning chalk up another point.)

Plus he's pretty entertaining.


Picture click leads to a Florida reading teacher site.

Jumat, 21 Agustus 2009

Riddles and Reasoning and Math Teachers at Play 14

When is a carnival full of problems? Besides like every circus movie ever?

The new carnival is up, hosted this week by Susan Van Hattum at Math Mama Writes.

My favorites include the Math Recreation post on origami and a clever lesson using statistics to catch cheaters which also uses bad jokes.

The bad jokes thing reminded me of a lesson I use with riddles about reasoning.

Reasoning and Riddles
The framework David Coffey and I use for reasoning, based on the NCTM process standards of course, is:
Mathematicians are engaged in reasoning when they:
-Make sense of something (sorting, understanding a problem, interpreting a representation)
-Make a conjecture about something (initial answer, plan of attack, possible relationship)
-Make an argument for something (justification, verification, proof)

I then give the students a list of riddles and ask them to figure out the answers. As we look at their answers, and more importantly, how they got their answers, they generate lots of examples of making sense, making conjectures, and arguing for why their answer fits.
(General riddles and Halloween riddles are posted at my faculty page. Click the links for the pdfs.)

We then explore a more math-centric riddle (it's usually a geometry class):

Four Sided Riddle

1) Taking the clues for a mystery shape in order, put a checkmark next to the last clue you need to know exactly the type of shape that the mystery shape is. Then explain your answer.
1. It is a closed figure with four straight sides.
2. It has two long sides and two short sides.
3. The two long sides are the same length.
4. The two short sides are the same length.
5. One of the angles is larger than one of the other angles.
6. Two of the angles are the same size.
7. The other two angles are the same size.
8. The two long sides are parallel.
9. The two short sides are parallel.

2) Using one less clue than your answer to number (1), draw a shape that satisfies all those clues BUT is different than the mystery shape, or explain why this cannot be done.

There is also a nice Van Hiele connection here as students at different levels approach this task very differently.


Dinosaur Comics are perfectly qwantzian. Click the cartoon to see it full size, click the link to get to the web comic's home. (T-Rex does not always subscribe to human norms of taste and good form, obviously, so, at your own risk.)

Eventually I'll work all my favorite webcomics in here.

Selasa, 18 Agustus 2009

Running Out of Options

This game was a favorite for Paul Rettinger, a brilliant grad school room-mate I had at Penn State. He went from a Master's of Fisheries and Wildlife to a law degree. Amazing guy. I was lucky to ever win.

Last Letter Loses


Players take turns adding a letter to a word. The first player to be forced to spell a word (at least three letters) loses. A player can challenge the previous turn if they think there is no such word. If there is such a word, the challenger is out. If there is not, the challenged player is out.

Example:
1- A
2- A-M (doesn't lose because less than 3 letters)
1- A-M-E (P would lose, even if you're thinking of 'amplify', since amp is already a word.)
2- A-M-E-R (thinking of america)
1- (thinking they're in trouble) A-M-E-R-I
2- (happily) A-M-E-R-I-C
1- (inspiration strikes) A-M-E-R-I-C-I
2-(thinking what? that's not a word!) Challenge
1-Americium! I still would have lost but thought you might not remember that word. (It's an element.)

In that example Paul would have been player 1, snatching victory from the jaws of defeat.


(From a repository of free educational clipart, click the image.)

That inspired the following game, which I use to introduce prime number decomposition.


Last One Loses

Players take turns breaking down a number by multiplication. The first player starts with a whole number. The next player makes a string of two numbers that multiply to give the first. The next player then can break down one of the two numbers, making a three number string. The last player who can break it down is the loser of the game. Numbers chosen must be able to be broken down more than twice. A player may challenge if they disagree with a breakdown, or if they say it's the end but it's not. Players may not reuse starting numbers. 1 may not be used in the breakdown. You can't use a number that's been used this session.

Example 1:
A- 24
B- 3x8
A- 3x4x2
B- 3x2x2x2 - augh! (loses)

Example 2:
A- 112
B- 2x56
A- 2x2x28
B- 2x2x4x7
A- 2x2x2x2x7 - curses! (loses)

Instructional uses:
Have students keep track of which numbers make first player lose, and which numbers made second player lose. When the data is collected, students will see that the same number almost always has the same effect. (Although there's usually a number that was mis-factored.)

Pose the questions: what if you break the number down in a different way? Is it always the same number of steps? Is the end result always the same?

Several important ideas about the prime decomposition will come out immediately, including the idea of prime numbers! Also why 1 is not a prime. (And 1 is NOT a prime.)

I allow calculators for numbers bigger than 144. Follow up investigations can be things like: find a number that takes 6 steps and is between 500 and 1000, or trying the Sieve of Eratosthenes.

Minggu, 16 Agustus 2009

Materi Integral

Mengajarkan integral kepada siswa memang agak sedikit sulit, apalagi kalau dasar - dasar dari turunannya tidak kuat. Yup, turunan menjadi sangat penting untuk memahami materi integral karena sebenarnya integral adalah kebalikan dari proses turunan. Ketika materi baru sampai pada dasar - dasar integral mungkin siswa tidak terlalu kesulitan, tetapi ketika materi sudah mulai merambah ke integral

More Math Correlates to Higher Income

The blog where I saw the study referenced: Free Exchange at the Economist.

The study the blog is citing: Joshua Goodman

The cartoon that teaches correlation:


(XKCD is occasionally profane, almost always funny, and frequently geeky. Clicking the cartoon leads to the site.)

Jumat, 14 Agustus 2009

ThatQuiz for teachers

Children love to learn in a playway method. Why not try evaluating their knowledge using readymade quizzes ? Recently, I was exploring some recreational Math resources for teachers and I stumled upon ThatQuiz.
ThatQuiz for Teachers is a free testing service for teachers to use with their classes. Multiple choice tests and math tests can be administered to students using this website. All grades are immediately reported to the students. Teachers receive complete record keeping of test results, including all grades and wrong answers.
Here is the link.

Kamis, 13 Agustus 2009

Ken Robinson Answers

I've written about Ken Robinson a few times (One and Two). The idea of creativity in mathematics was a sub-theme for my summer calculus class. Students at the end felt that some of the open-ended assignments (projects of their choice), non-standard problems (like the mobiles) and emphasis on problem solving helped open them up to creativity in math. But they suggested more specific demonstrations of how to be creative. (Boy, is that insightful.)

TED occasionally has question and answer sessions with their speakers who really ignited something with their presentation, and Sir Ken recently did this. (Here's the article.) He addresses math specifically:

"If you want to promote creativity, you need, firstly, to stimulate kids minds with puzzles and questions which will intrigue them. Often that's best done by giving them problems, rather than just solutions. What often happens in classrooms is, kids sit there trying to learn in a drone-like way things of not much interest that have already been figured out.

The best math teachers I know, like the best English teachers, are always giving kids puzzles. They're given things to work on where math skills are required but may not be the focus of the activity. There giving them problems to solve. Or they're made to engage with age-old mathematical problems. For example, I'm thinking about the problem of latitude. How do you go about measuring the planet? I mean, somebody had to do that. How do you do it? Professional mathematicians have such a cornucopia of fascinating puzzles, questions, proposals and conundrums. A great math teacher really has endless opportunities to stimulate kids minds and get them engaged with things they'd probably never thought about before. Rather than just giving them techniques." -Ken Robinson

It's not hugely original, but it's nice to get confirmation of things we believe from outside sources. He touches on engagement several times in the Q&A, and I do believe that's the central issue in teaching, and I love to ponder what is the key for math. Going to more and more of these reading conferences, I am insanely jealous of the teachers who talk about the book that turned a student on to reading. Problems don't seem to have the same effect.



Jumat, 07 Agustus 2009

Math Teachers at Play 13

The new carnival is up at Blog, She Wrote. The Money Games are there, as well as the generally nice idea of runnign a store for money practice at the Pumpkin Patch. I like some of the puzzles at Critical Thinking Puzzles. The card trick that's linked really makes you think about how much information there is in arrangement.

Selasa, 04 Agustus 2009

Money Games

Here are my two favorite money games. Change for the Better is based on a James Ernest design. He's the genius behind Cheapass Games (don't be put off by the name), and the game this is based on, Fight, he used to have on his business card. It really has some non-trivial strategy and thinking to it. Later I made the connection - or one of my preservice teachers did - with Smart, the excellent poem by Shel Silverstein. The other game I think I invented, Make It Take It. The idea was from a group of teachers who wanted students to be forced to find non-standard combinations of coins, instead of always taking 27 pennies, for example. That suggested a dwindling resource game to me. It's poissible to combine both with some visual representations of money, which is a nice support for struggling students. The handout is here, if you like worksheets or some of the representation support.

Smart
by Shel Silverstein

My dad gave me one dollar bill
'Cause I'm his smartest son,
And I swapped it for two shiny quarters
'Cause two is more than one!

And then I took the quarters
And traded them to Lou
For three dimes -- I guess he don't know
That three is more than two!

Just then, along came old blind Bates
And just 'cause he can't see
He gave me four nickels for my three dimes,
And four is more than three!

And I took the nickels to Hiram Coombs
Down at the seed-feed store,
And the fool gave me five pennies for them,
And five is more than four!

And then I went and showed my dad,
And he got red in the cheeks
And closed his eyes and shook his head--
Too proud of me to speak!

Change for the Better

Materials: Each player needs 1 quarter, 2 dimes, 3 nickels, and 4 pennies.

Rules: Play in groups of 2 to 6. Each player takes a turn. On their turn they put in one coin. They can take out a combination of coins that is less than the value of what they put in. For example, if you put in a dime (10¢) you can take back up to 9¢ – if it is there. Play continues until only one person has money left.

Instruction: Beginning players should just concentrate on the moves of the game. After students have gained some experience with the game, they can try recording their games to translate to symbolic representation. The data collected can then be examined for patterns.



Make It, Take It
a money game for 2 players or teams

Materials: Play coins or coin pictures or cards, amount cards. Record sheet if desired.

Play: Put the coins in the center. Shuffle the amount cards and make a stack. Players each turn over an amount card, and the player with the smaller amount goes first. On subsequent turns, players turn over an amount card, and see if they can make that amount with the coins. If they can, they take the coins. If they can not, it’s the other player’s turn. Play until all coins are gone, or both players in a row can’t make their amounts. The winner is the player with the biggest total value of coins they collected.

Variations:
Recommended starting amounts – 4 quarters, 6 dimes, 8 nickels, 10 pennies. Other amounts can be used. Teachers can add amount cards for more complicated amounts.
Players can roll two dice to determine the amount. (Note the dice variation requires more pennies.) Advanced play allows people to make change with the coins they’ve collected. For example, trading a dime from the center with two nickels they have taken before.
Players can use dollar value charts to keep a running total.

Example:
Bill and Keenya have been playing for a few turns.
Bill turns over 12 cents and takes two nickels and two pennies.
Keenya turns over 25 cents, but there are no quarters left. She takes five nickels.
Bill turns over 50 cents and can not make it.
Keenya turns over 6 cents and takes a nickel and a penny.
Bill turns over …

Instruction:
As with most games, it is recommended to play a game with teacher vs. the whole class to launch the game. Emphasize the variation in ways to make an amount by soliciting other possibilities from the students. Ask questions like “what card would be good to turn over next?” or “what card would leave me with no possibilities?” If someone is stuck, encourage good sportsmanship in helping them figure out a way to make the total. If that doesn’t seem to be working, or you are worried about their ability to make the amounts, students can play in a team of two vs. another team of two.

Many students will try a place value approach first, taking dimes and pennies. This will rapidly run them out of one or the other, forcing them to find other amounts. The amount cards concentrate on values that can be made with one, two or three coins, though several can be made with many more coins.

In summary, the teacher may wish to have students share their strategy for figuring their total at the end of the game. It is important to summarize by having students describe how they knew if they could make an amount or not. Another interesting discussion to start is if there is a strategy for better ways to play the game – is there an advantage to using fewer or more coins to make your moves?