MasterMath

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Math Jokes

January 21, 2013 by · No Comments · Uncategorized

An infinite crowd of mathematicians entered a bar. The first ordered a pint of ale. The second ordered a half pint. The third ordered a quarter pint.

“I get it,” said the bartender, and poured two pints.

 

Q: What do you get if you divide the circumference of a jack-o-lantern by its diameter?
A: Pumpkin Pi!

 

One evening Rene Descartes went to relax at a local tavern. The tender approached and said, “Ah, good evening Monsieur Descartes! Shall I serve you the usual drink?”. Descartes replied, “I think not.”, and promptly vanished.

 

Algebraic symbols are used when you do not know what you are talking about.

 

Is Math Important?

August 14, 2012 by · No Comments · Math Subjects

Tip 8: Make every effort to ensure that your student is confident that he can learn.

August 11, 2012 by · No Comments · Homeschool Educators Tips

A lot has been written, and I suspect you’ve read a lot about improving the self-esteem and confidence of a student. It’s typically good advice, but I won’t repeat it here. When you compliment your children for effort or success, you are convincing them that their parents think they are good, or smart, or diligent. And that’s important. But it’s more important that the children, themselves, think they are good, smart or diligent. My Mom used to tell me I was smart. That certainly didn’t hurt anything. But it wasn’t until later, after I’d had a few successes in my young life, that I started to think that maybe I wasn’t that stupid after all.

I think you’ll agree that success creates self-confidence. But it’s a little more complicated than that. It has to be success at something that is important and perceived by the child as a challenge. If they have success at drinking a glass of milk, their self-image probably isn’t impacted. But if they are given a challenge that is within their grasp, and they succeed at it, they not only learn the lesson, but they learn they are capable. The lesson was effective and affective!

So what prevents them from always succeeding at challenges that are within their grasps? Very often it is fear of failure. Failure hurts. Failure diminishes their self-confidence. Trust me, they want to be self-confident. But fear often prevents them from making the effort required to succeed.

If you teach your children to understand their fears differently, you can give them the key to unlocking their self-confidence. Here are some tips for

REFRAMING FEAR:

  1. Fear is good! It’s a gift from God. Animals react to fear with a “fight or flight” decision. So do you. Use your brain, and make the right choice.
  2. Everyone experiences fear! Some just handle it better than others.
  3. It is always easier to face fear than to live with it.
  4. Create an Affirmation Mantra you say to yourself before taking on any challenge: “I can handle it!”; “I am brave!”.
  5. Do a positive thinking exercise: have the child hold their arm out horizontally, and while you try to push their arm back against their body, the child says “I am weak; I can’t hold my arm up.” Then do it again, but this time the child says “I am strong; I can hold my arm up.”

Visit www.MasterMath.info for free middle school math lessons, worksheets, and quizzes.

Tip 7: Try creating a Learning Group

July 21, 2012 by · No Comments · Homeschool Educators Tips

Tip 7: Try creating a Learning Group with other home school kids. Lots of times kids can explain things to each other better than an adult can explain it to them.

Cooperative Learning is fundamental to many traditional classrooms. Research has overwhelmingly demonstrated its effectiveness. However, the very nature of homeschooling makes Cooperative Education a challenge to implement: unless you have triplets, your student has no one to form a group with at home.

First, let’s quickly describe Cooperative Learning: students work in groups (typically 2 – 4 members) to complete group tasks. Group members should not be working competitively. The goal is to establish “positive interdependence”. Students learning cooperatively capitalize on one another’s resources and skills (asking one another for information, evaluating one another’s ideas, monitoring one another’s work, etc). The educator’s role is to determine the group’s task, then facilitate group interaction (including the group’s development of social skills). Each group member must have a role to play towards completion of the group’s task (each member has assigned responsibilities, such as scribe, or researcher, or artist). And the task is not completed successfully unless each member can, on completion, explain the results (the educator can pick a member at random and ask them to explain the groups work). The group’s success is not based upon the correct answer. The group’s success is based upon the randomly chosen member’s ability to explain the group’s results. Usually verbal rewards for successful completion of a task are sufficiently motivating.

So, how can homeschoolers utilize this learning strategy? Well, of course you could find students that live near you and get together once a week. But we live in a digital age, and there is a digital solution. Web Conferencing allows groups to get together over the internet, and see each other, hear each other, see each other’s computer screens. Some charge for use of the platform (www.GoToMeeting.com; www.WebEx.com; www.livemeetingplace.com). Others are free, or inexpensive, but typically less robust (www.yugma.com; www.zoho.com; www.vyew.com).

My website offers Group Lessons, and we use Cooperative Learning strategies (www.MasterMath.info). You can see a recorded Group Lesson by clicking on this link: http://www.youtube.com/watch?v=2iVmP7saNu8.

Tip 6: Kids learn a lot more when they are working hard than when you are working hard

June 25, 2012 by · 1 Comment · Homeschool Educators Tips

You can lead a horse to water, but you can’t make him drink. You can also lead a student to knowledge, but you can’t make him think. So your goal isn’t really to “teach”, it’s to get the student to learn.

I’m sure none of you have this problem, right? Sometimes I discover that I talk too much. Can you believe it? Both in a classroom, and with my son, it was easy to sometimes get up on a platform and give a lecture. I had lots of knowledge to offer my students, and I usually enjoyed offering it. And sometimes that’s OK. But often, I was doing more for myself than for my students. Often, they lost attention, and became unengaged. I was not only wasting time, I was helping to convince some students that education is boring.

The ultimate goal for any student is to become a self-directed learner. All those people at the top of the education world are self-directed learners. They are at the top, so there are not many who can show them the way forward. They need to move forward on their own. That’s true in business, as well. If you are at the top of your field, you are leading, not following, and that’s self-direction. So, instead of answering your student’s question, suggest where he might research the answer on his own. Instead of showing her how to solve a problem, point out a portion of her solution that she might want to think about.

 

Tip 5: As much as possible, make it “real”, not abstract

May 11, 2012 by · No Comments · Homeschool Educators Tips

Human intelligence is based, to a large extent, on our ability to make abstractions. Language is an abstraction. Math is an abstraction. Science is an abstraction. Philosophy is an abstraction. Obviously, the ability to make and understand abstractions is important.

But if you want to understand orange juice, you better understand the orange first. If you want to teach a baby the concept of motherhood, you probably don’t want to start with discussion on reproduction. You want to start with something the baby understands and is interested in: Mama. Then build on that.

All of us learned at a pretty early age that hot things can cause pain to us. But we probably learned that abstraction from a concrete, real example. I’m sure my wife and I explained the abstract concept to our son lots of times: “Don’t touch hot things!” But he learned it one evening while he was helping his mother cook dinner.

This reality is based in motivation. My son at the age of 5 wasn’t greatly motivated by a desire to benefit from his parent’s years of experience. However, he was motivated by his desire to not feel pain.

The Pythagorean Theorem is an amazing, powerful tool. But if you want to teach the Pythagorean Theorem to a young person, which approach do you thing will be more successful (image me illustrating these concepts on the blackboard as I talk):

  1. Here is a triangle. What is the length of the hypotenuse? You can determine the length of the hypotenuse with this formula: the square of the hypotenuse is equal to the sum of the squares of the other two sides. Here, let’s try it.
  2. On a baseball diamond, it’s 90’ from home plate to first base. It’s also 90’ from first base to second base, How far is it directly from second base to home plate? A Greek mathematician, Pythagoras, showed us how to figure this out 2500 years ago: the square of the distance from home plate to 2nd base is equal to the sum of the square of the distance from home to first plus the square of the distance from first to second. Here, let’s try it.

Certainly, as we get older, our ability to quickly associate the abstraction to a concrete example that relates to our lives improves. As a Homeschool Educator, it is your responsibility to gauge where your student stands on that continuum, and adjust the way you introduce new concepts accordingly. It’s an art. But the glassy eyes probably mean something. And the level of enthusiasm also tells you a lot.

How do you come up with good concrete examples of an abstraction? Think about what excites the student. Here are my typical starting points: sports; money; dating; games; family; electronics; their future.

Tip 4: Try to tap into their Intrinsic Desire to control their world

April 9, 2012 by · No Comments · Homeschool Educators Tips

Daniel H. Pink wrote a very interesting book titled Drive. In it, he talks about the rise and fall of Motivation 1.0 and 2.0. Motivation 1.0 started at the dawn of man, and was all about survival. Motivation 2.0 started replacing Motivation 1.0 as we as a species learned more about human behavior. It is the carrot and stick style of motivation: reward appropriate behavior and punish inappropriate behavior. I was a Skinnerian Behaviorist as an undergraduate, and I learned how powerful rewards can be in influencing behavior. But they also have limitations and shortcomings. In Pink’s words, rewards for ‘appropriate behavior’ “can extinguish motivation, diminish performance, crush creativity, and crowd out good behavior…They can encourage unethical behavior, create addictions, and foster short-term thinking.” If you know your boss hates it when you chew gum, does that stop you from chewing gum when he’s not around?

Pink says that Motivation 2.0 is being replaced, or at least enhanced by Motivation 3.0. Motivation 2.0 is extrinsic motivation: something outside the individual manipulates the environment to encourage the desired behavior. Motivation 3.0 encourages and fosters intrinsic motivation. Intrinsic motivation, motivation from within the student, arises from a desire to learn a topic due to its inherent interests, for self-fulfillment, enjoyment and to achieve a mastery of the subject.

Think of it this way. At your job, you probably work pretty hard trying to accomplish the company’s goals. There are two types of motivation at work here. Extrinsic motivation, such as a paycheck, certainly has an impact on your behavior. If the boss sees that you are not working hard, you know your paycheck can be affected. At the least, you work hard to make certain the boss thinks you are working hard. But hopefully there are intrinsic motivations at work as well. If your job is to write video math lessons for kids, you hopefully are motivated by your belief that you are, or your desire to be, one of the best video math lesson writers in the world. You have decided that you want the world to see you as a video math lesson writer, and you want them to appreciate your good work. You understand the inherent value of what you are doing, and it makes you feel good when you do a good job.

A couple questions for you. Which is more fun, something you do because you are being paid, or something you choose to do because you have decided that it is part of who you are? Which of these tasks do you do a better job at?

So how do you foster Intrinsic Motivation? Carleton College has a great webpage on motivating students (http://serc.carleton.edu/NAGTWorkshops/affective/motivation.html). Here are some of their recommendations, mixed with some of mine:

  • Make it real. Relate the lesson to the student’s world. Don’t just explain an abstract concept. Show how you and the student can use the concept in your lives.
  • Provide choices. Students can have increased motivation when they have a sense of autonomy. Give the student some options; let them decide when, where or how they plan to master the lessons.
  • Offer role models. “If students can identify with role models they may be more likely to see the relevance in the subject matter.”
  • Establish a sense of belonging. If the student feels that he belongs to a group, or wants to belong to a group, and that group prizes math skills, then the student will want to be good at math.
  • Strategize with the student. If the student is having trouble, help them with the creation of their strategy to overcome the obstacle.
  • Recognize the student’s efforts and successes. Use extrinsic motivation that fosters intrinsic motivation. You are suggesting and reinforcing a self-image you want the student to adopt. “You know, you really have a logical mind.” “Your memory is better than mine.”

Students on their way to self-actualization are becoming autonomous and self-directed. They seek mastery of those things that matter to them. And they have purpose; in Pink’s words, the students seek “to make a contribution and to be a part of a cause greater and more enduring than themselves.” One of our job as educators is to foster self-actualization. It isn’t easy. It won’t happen overnight. But it is certainly one of the greatest gifts you can give your child.

Tip 3: Kids Can Forget – Schedule Regular Review

February 28, 2012 by · No Comments · Homeschool Educators Tips

This is not intended to be an academic discussion, and I’m not the right person to be citing tons of research and scholarly thought. But my undergraduate psychology major, and my experience as a teacher makes this statement seem very true: students forget; and reviewing material previously covered is essential to the student’s retention of that material.

Well, it turns out that research backs this up. Psychologists compared retention between 2 groups: one group studied in one mass session. The other group studied the same amount of time, but the time was distributed over several sessions. The retention of the 2nd group was significantly greater than the 1st group. Re-exposure to the material to be learned reinforced the learning, and led to greater retention.

Krug, D.; Davis, T.B.; Glover, J.A. (1990). Massed versus distributed repeated reading: A case of forgetting helping recall? Journal of Educational Psychology, 82, 366–71

 

Some homeschool educators, and many students, aren’t fond of quizzes, tests and exams. But testing is an important part of the learning process. Studying for a test reinforces the student’s learning of the concepts, and will improve their retention. Material re-studied several times, first for a quiz, next for a test, and finally for an exam, has been carved much deeper into the brain’s neural networks.

Adding regular Quizzes, Tests and Exams to your student’s curriculum creates natural review periods, and increases retention of the material that’s been studied.

Tip 2: Try to Make Learning Fun

February 9, 2012 by · 1 Comment · Homeschool Educators Tips

Learning Should be Hard Fun!

 When you are learning to play a sport, or a musical instrument, there is almost always two parts: 1) You need to practice; and 2) then, you get to demonstrate what you’ve learned, in a game or a recital (GAME). Knowing there will be a GAME makes the practice a lot easier to endure. The GAME is the “fun thing” that motivates you to practice hard.

Learning a subject like math certainly requires a lot of practice. But you can help motivate your student to practice harder if they know that there will be a chance to demonstrate their new skills in a fun way.

Quizzes and Exams aren’t usually considered to be GAMES by the students. They’re not fun, and they are stressful. Testing is necessary to assess learning. But it’s usually not a great motivator or reward for hard work.

Consider ending each lesson with an activity that allows the student to demonstrate what they’ve learned. And be certain that you are there, as the audience or a participant. When they do well, applaud. When they don’t do so well, give them a “Good Try”.

Here are some ideas for post-practice GAMES:

  1. Race your student: Print two copies of the worksheet; you do yours while the student does his. The first one to get the entire worksheet 90% correct wins!
  2. Take it outdoors: If your student is studying Geometry, have him show you how he can calculate the area of your driveway.
  3. “I need your help”: “What percentage of this grocery bill was spent on vegetables, what percentage on meat?” “I want to build a vegetable garden in the back yard. How many feet of fencing do I need? How much seed will I need?”
  4. Change a game: Play your favorite game with the student, but change it so that you have to answer questions on the lesson before each move. If they like to play checkers, play checkers with them. But before they move, they have to tell you what the square root of 16 is.
  5. PC Game Time: There are lots of good websites with great educational games students can play as a reward, and as practice. Here are a few math sites that I like. I’ve checked these out, and find them useful and appropriate for middle school math students. But you should check them out and use your own judgment. And this will be a better GAME if you spend the time watching them demonstrate their skills, rather than just turning them loose.
    1. http://www.greenleecds.com/mathdownloads.html
    2. http://www.squidoo.com/math-games-r-fun#module42012012
    3. http://www.ixl.com/promo?partner=google&phrase=IXL%20-%20Branded%20-%20Ohio&gclid=CNDA1unymqwCFY5Y7AodmElaIQ
    4. http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.NUMB
    5. http://www.ezschool.com/Grades6-12.html
    6. http://www.aaamath.com/
    7. http://www.coolmath-games.com/

Tip # 1: Don’t teach until the concept is “covered”, teach until the concept is “mastered”.

January 17, 2012 by · 4 Comments · Homeschool Educators Tips

Homeschool educators have a big advantage over their counterparts in public or private schools.
The P or P teachers are given a calendar and a curriculum at the beginning of the year, and told to fit the curriculum into the calendar. They know that they can only allocate a certain amount of time to teaching any one concept, or they won’t finish the entire curriculum. And they can’t be very flexible with their schedule, because soon the bell will ring, and the student has to move to a different subject. Consequently, some kids learn the lesson quickly, and sit thru many more boring hours than they need on the concepts. And others don’t get it, and just when they get close, it’s time to move on to the next concept. The teacher has “COVERED” the concept, but have all the kids “MASTERED” it?
Your students have the ability to spend just the right amount of time on the concept, so that they learn it, and then move on before they get bored. But this requires a lot from you, the teacher. Be certain you have a good Assessment (Quiz or Test) of the concept. Have your student “show their work” and explain the concept to you. Keep them on that concept until they demonstrate to you with Assessments that they understand it enough to move on. If math is easy, and history a challenge, schedule more time for history, and less time for math.
Learning “scaffolds” upon itself. The next concept to be learned assumes an understanding of the previous concepts. If a student leaves one concept before she has mastered it, she will have problems with later concepts.