вторник, 8 декабря 2009 г.

Times Tables - The Worst Way to Teach Multiplication

Learning the "multiplication tables" is one of the first traumas that children usually face when learning arithmetic.

Ask ten elementary-school kids to tell you what, say, eight times seven is. Watch as they look up and to their left (or right) and go into, "let's-see" mode. Often you'll hear them say, "Um, ah..." before give you the answer. Generally, there's a lot of hesitation. Only then, do they actually give you the answer. Sometimes it's even correct.

I know, I was one of them. Maybe you were, too. Most children are victimized by the thoughtless, authoritarian, wrong way to teach the "multiplication facts" (what n unimaginative and uninspiring term!)

Why are "the tables" the wrong way to learn? Maybe I can illustrate it best by analogy. Imagine that you wanted your children to learn the names of all their cousins, aunts and uncles. But you never actually let them meet or play with them. You just showed them pictures of them, and told them to memorize their names.

Each day you'd have them recite the names, over and over again. You'd say, "OK, this is a picture of your great-aunt Beatrice. Her husband was your great-uncle Earnie. They had three children, your uncles Harpo, Zeppo, and Gummo. Harpo married your aunt Leonie...yadda, yadda, yadda.

Boring!

But what if you had them all over for the weekend, and you found out Earnie did magic tricks, Beatrice had been a rodeo queen, Zeppo always wore mismatching socks, Harpo played the, well, you know, Gummo picked his nose and wiped it on his tie, and Leonie could sing like an angel?

Well, then you'd have some relationship with them, wouldn't you? The next time you saw Earnie, you'd ask him to show you a trick. You'd ask his daughter Leonie if she could teach you to sing, and you'd stay away from Gummo's tie.

It turns out that you can build relationships with multiplications, as well. And they have relationships with each other. You already know some of them. Like the relationship of nine to ten. Nine is one less than ten, so when you multiply something by nine, just stick a zero at the end of it, and subtract the original number.

Take the example 8*9. Just stick a zero behind the 8 to get 80. Next, subtract 8 from 80, and you've got 72, which is the correct answer to 8 multiplied by 9.

That is the intuitive way for many people to multiply by 9. So why do they make you stare at the nine-times-table in school? It's boring and fosters no sense of the relationship of nine to the other numbers. It turns multiplication into isolated "multiplication facts" (there's that stupid term again).

If you had children multiply by nine with the subtraction method often enough, they'd know the answers in their bones after awhile. It would take less time than it would to memorize the nine-times-tables by rote, and it would have them actively involved with using the numbers. Imagine that!

This may be hard to digest at first, because learning the "multiplication facts" by rote has been ingrained into the school system for decades. Maybe that is why our children are getting worse and worse at this easy, important skill.

If you're a teacher, you're probably fed up with the bad mojo from the policy-makers. You need to get your own mojo working.

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VIP Families Honored for Involvement

"At the first year's Family Involvement Festival, a mother arrived with her children almost two hours late," recalled Anne Thompson. "She was tearful and agitated, as her car had broken down and she'd had to take several busses to reach the event. She was determined to get there, though, for this was the first time in her life that anyone had honored her and she wanted her children to be proud of their parent."

The memory of that parent still inspires Thompson, the director of the office of parental involvement for Miami-Dade County (Florida) Public Schools. Attendees of the annual festival receive awards for their effort and spend a day with their families at a local attraction. Parents may nominate themselves through a simple questionnaire. From the nominations, those who support their children's education are identified as "Very Involved Parents" (VIPs). Then all district schools honor one family in a special way as a "Family of the Year." The program sprang from the need to better define parental involvement in Miami's diverse urban community.

"Because too often only those parents who are able to volunteer regularly or otherwise take an active role in the school are considered involved, many families feel unable to fill this expectation," Thompson told Education World. "By defining involvement in its most profound activities -- supporting learning at home, assuring school attendance, communicating with teachers, and participating in at least some school activities -- we hoped to provide a standard which is understandable and attainable."

The goal was not to ignore those who give their time generously to the schools but to allow the larger community of parents to feel connected and validated. Thompson has seen the impact of the award program on many families.

"The most moving stories have been those from struggling families, many of them recent immigrants, that have been recognized for providing this support and encouragement to their children's success in school," shared Thompson.

The Family Involvement Festival is a district-wide event that brings together Very Involved Parents and their children. At the time, Thompson reports, a luncheon or award ceremony seemed inadequate to embrace the many types of families honored through the program. While individual schools often also recognize their VIPs, it was important to establish a unique event that provides a sense of community.

The initial event took place at a local zoo called Jungle Island. It was a treat for the families, but it proved to be too limited in size to accommodate the potential numbers of attendees. About 3,000 students and parents came to the event. With the assistance of a sponsor, the event was moved to Miami-Dade County Fair in its second year, and the district is likely to continue to use this venue as the festival grows.

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Multiplication by Two - How to Practice Multiplying with Playing Cards

If you want to teach a child to multiply by two, one of the easiest ways is to explain that multiplication by two can be accomplished by simply doubling the number. (Keep in mind that the definition is not repeated addition. They are just two similar ways to arrive at the same answer with whole numbers. It doesn't work with fractions, so it is not the definition.)

Instead of showing the child endless multiplication tables and multiplication charts, get out a deck of cards and do the following:

* Remove the Tens, Jacks, Queens and Kings. You won’t need them.

* Take a Two of any other suit (say Spades) and place it face up on the table.

* Take the Ace through Nine of any suit (say diamonds). Shuffle them face down.

* Start turning the cards over one by one, and as you do, say what the product of that number, multiplied by two, is.

* It is important to remember not to say to yourself, “Two times (whatever number you are working on) is...” Try to just say the answer.

If you have trouble with a problem, like say, two times 9, remember, you are just doubling the number. If you have problems with that, you may want to “skip count” to the number.

To “skip count” you just count by twos, and put out a finger for each number you say. So you’d say “two” and put out one finger. Then you’d say “four” and put out another one. By the time you have nine fingers out, you should be up to “eighteen.” That is two times nine.

This is important: Whenever you come to a problem that you don’t immediately know the answer to (like if you have to think about it, or skip count to it), you may think you now know the answer because you have figured it out. Don’t fall into that trap! That’s what hurts many learners most. You must know the answer to simple multiplications in your bones.

So when you get to something like two times nine and have to skip count, stop, look at the cards, see the problem, and say out loud:

“2 times 9 in 18”

“9 times 2 is 18”

“18 is 2 times 9”

“18 is 9 times 2”

“2 times 9 is 18.”

Say that out loud each time you hesitate with the answer. It will definitely help you for the next time. You won’t have to do this often until you will instantly recognize that two times nine is eighteen, any time you see it.

After you have gone through all nine cards, it’s time to do some serious practicing.

* Leaving the Two of Spades face up on the table, take the rest of the cards, except for the Tens, Jacks, Queens and Kings, and shuffle them face down.

* Start turning over cards as before, saying their products. Don’t forget to do , stop, look at the cards, see the problem, and say the combinations of the answers out loud, as above.

* Keep this up until you can go through all of the cards (there will be 35 of them) in less than one minute. This will not take much practice, and you’ll feel great about yourself when you can do it in under a minute.

Learning this way has huge advantages. Once you are great at multiplying by two, try it with three. This method also has the advantage that you don’t have to print out worksheets, and you can carry a deck of cards anywhere. You also will improve your powers of concentration when you learn like this. I have been diagnosed with ADD, and this method worked wonders for me.

Please keep in mind that we are only talking about whole numbers here. "Simply doubling" is not the definition of multiplication by two. There are subtleties involved that are beyond the scope of this article. But in order to learn simple multiplication by two, this method is much preferable to the “multiplication tables.”

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понедельник, 7 декабря 2009 г.

Applying High Expectations To Everyone

Principal Dr. Gerald Gary knew his students could do better -- he just had to convince them and their families. He improved student achievement and changed the school’s culture by setting high expectations for everyone in the building. Included: How high expectations are implemented.

Principal Dr. Gerald Gary knew his students at Jackson School could do better. He just had to convince them and their parents.

Concerned that his students’ parents often had lower expectations for their children than parents in other communities, Gary introduced parents at his school to research about the affect of parent involvement on student achievement. Soon parents began to take more of an interest in what students were learning at school and at home.

After two years of effort, about 80 percent of parents are supportive of measures to raise expectations and implement consequences for infractions, Gary told Education World. Students weren’t the only ones rising to higher expectations; Gary began insisting that all staff members in the building take on more responsibility as part of a culture of high expectations for everyone.

START WITH DATA

Jackson, a K-5 school in Camden, South Carolina, has a high number of students receiving free and reduced-price lunches, an indicator of low-income families. “I found that parents and the community did not have the same expectations for their children as those in other, more affluent schools,” Gary told Education World. “The teachers always had high expectations -- we just needed to elevate them, and then get parents to buy in.”

Gary began holding meetings for parents during which he presented data showing that when parents get involved with their children’s education, achievement increases. He talked about the importance of reading to children at home and checking their homework regularly, noting that these efforts have a positive affect on student performance.

“I showed them data from schools with the same background as ours and how we could get similar results. They [Jackson parents] couldn’t say their children were not doing well because of poverty or because they came from single-parent homes. If you read to them, that levels the playing field.”

“I found that parents and the community did not have the same expectations for their children as those in other, more affluent schools.”

After about a year, the school staff started seeing gradual achievement growth, and now the staff is expanding efforts to get parents involved by offering manipulatives for them to use at home to help children with math concepts. The school holds parent workshops six or seven times a year on topics such as how to help children with reading, math, science; it offers separate groups for parents of K-2 students and those in grades 3-5.

“We’ve reduced class sizes in kindergarten through second grade, so we can reach the goal of reading at grade level by second grade,” Gary told Education World. “I believe if they are not reading at grade level by second grade, it increases their chances of dropping out.”

Gary also set goals for students above the minimum standard. He decided students needed to surpass the target point on the state’s Measure of Academic Progress (MAP), which is used in the fall to determine students’ expected academic growth. “I said we need to exceed target growth if the kids are going to succeed -- so now we look at the target as the mid-point.”

BRING ON THE INCENTIVES

More incentives also were introduced to encourage student achievement and better behavior. Jackson now uses the Positive Behavioral Interventions and Supports (PBIS) discipline approach, which stresses rewards for positive outcomes. Students who score in the highest range on the state tests, for example, have the chance to earn a Wii. Smaller prizes are available for other high-scoring students.

“It has improved all aspects of behavior,” Gary said of PBIS. “We probably have between 50 and 60 percent fewer referrals than we did two years ago. We look at rewarding the good as opposed to focusing on the negative.”

HIGH EXPECTATIONS FOR ALL

Besides pushing students harder, Gary made it clear to his staff members that they also had to step up their game. In the past, there were some students who put their heads down on their desks and refused to do any work. “I said students won’t be allowed to sleep in class or say they can’t do it,” Gary said. “They have to put forth the effort or the parents are contacted.”

“I said we need to exceed target growth if the kids are going to succeed -- so now we look at the target as the mid-point.”

Other staff members are required to take on more responsibility as well. “We hold bus drivers accountable,” said Gary. “If someone writes a kid up every day, we want to see what he or she has done to change situation.”

And if a custodian complains that a particular classroom is extremely messy every day, that custodian has to talk to the classroom teacher about what he or she needs to do to facilitate cleaning. “Teachers have to know they have to do basic cleanup so custodians can do their job,” he said. “It’s helping everyone understand their roles and holding everyone accountable.”

Initially, there was some difficulty getting people to buy in to the idea. “Part of the fear was that not everyone was going to be accountable, so you can’t let anyone get away with not doing what they are supposed to do,” Gary noted. “You have to hold everyone accountable.”

His advice for other administrators looking to engage the community in school reform -- break out the data. “Take people to a successful school with a similar population and see if you can adapt it [the school’s operation] for your building.”

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Multiplication - Do you I have to show the work?

Teachers have uttered the mantra of "you must show the work!" since any of us can remember. But is there any good reason for it?

The only reason that would make sense is to find out if the child understood the problem.

But if a child can consistently get the right answers to multiplication, or other math equations, what good reason would there be for him or her having to show work? Does the teacher think the child doesn't know how to do the problem? That would be crazy, because the child clearly just did the problem!

In English class, when they ask a pupil to read a paragraph, and s/he does it well, do they say, "Okay, now write an essay on how you knew how to read that?"

How nuts would it be to ask a kid in gym class how they ran that mile, or else the running wouldn't count?

What if, in history or social-studies class, students were required not only tell you who won the Battle at Gettysburg, but prove it, with archeological facts. It might be a nice exercise once, but for every question?

"Hey, Picasso, put down that brush and write a 300 word essay about why you put two eyes on the same side of that woman's head. If you can't, I'm afraid we'll just have to rip it up and do it again right, won't we?"

No wonder Einstein said, "Education is what remains after one has forgotten everything he learned in school."

All too often, the wonderful experience that should be school is turned into a learner's nightmare because of ill-thought-out pedagogical dogma.

Schools seldom take into account that different students have different learning styles. Misguided efforts like the "No Child Left Behind" act (what a cynically sinister misnomer!) would have you believe that there's one thing to learn, one way to learn it, and one way to test it. (Maybe more than the name is sinister!)

People who do not understand people who are "different" have a hard time reaching them. The loss is on both sides.

Learning the Multiplication Tables - Skip counting by two and three

If your child or student is learning to multiply, a good way to have them start out is learn skip counting.

Skip counting is simply counting by a whole number other than one. It's counting by twos, threes, fours, etc. For example, skip counting by twos is the same thing as reciting the two-times tables.

So what are the benefits of using playing cards to learn skip counting compared to staring at multiplication worksheets?

* Well, for one thing, it's not boring!

* For another, if you are actually counting objects, you have the tactile experience of feeling what you are counting.

* And there's the fact that you are saying the numbers (for a reason - after all you are actually counting something.)

* So with skip counting, you get the trifecta of seeing, feeling and hearing. You experience the numbers in three ways.

* And it can be fun. If you teach your child to count, say, playing cards by twos, not only will s/he count the cards faster, but s/he will lock in the two-times tables in his/her head

without having to stare at boring worksheets, watch or do any of those typical dumbing-down activities like watch cartoons teach them math, sing inane songs, or listen to baby-rhymes.

* One of the advantages of using normal playing cards (not flash-cards or cards from some contrived kiddie-math games) is that playing cards can remain life-long friends. They are objects that exist in the adult world, so your child will not have that feeling in the back of his/her mind that they are being pandered to.

Children can sense when their minds are being respected. When you teach them with methods that respect and foster their thinking abilities, instead of talking down to them, you are doing them one of the biggest favors you can do. You are also doing one for yourself, too.

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пятница, 4 декабря 2009 г.