Eyewitness to Dumbing Down

 

people-316506_1280Uh Oh! We’re in trouble!

We run a educational bookstore business, and we often hire employees to help us. Usually these are college students. Recently we decided to give a simple math test to our potential employees as a way to screen out those who may make costly computation errors when working for us. I was stunned at the ease of the standard industry test form we found: simple division and multiplication, addition and subtraction that required “carrying” (“regrouping”). Nothing very advanced. I know that my 11-year-old could do it easily, as could yours!

The results of giving this test were so alarming to me, that I feel like an eyewitness to the dumbing down of America. One applicant went to college on a scholarship. The very first problem on the math test (simple 2 digit long division) stumped her, and she could go no further. When questioned, she replied, “I always used a calculator in school.” Others who applied for the test did equally as poorly. Some were appalled that we would even ask them to take such a “hard test”.

I can’t help but wonder about the future of our country . . . particularly when compared to the math whizzes of the Asian nations. Do the students in our medical schools have the same problem as my applicants? What will happen when you or I are the one in the ambulance while the medical personnel are trying to calculate the amount of life-saving medication needed? What will happen when they have to calculate the measurements for proper launch of a space shuttle or the runway distance needed when building a new airport? If you can’t do the mental math to estimate the range an answer should fall in, you can make some mighty big mistakes! Sure hope I am not on the operating table when those goofs happen!

Please, Moms, teach your children to do their math by hand. When it is learned to mastery, they may use a calculator, provided there are still basic math practice problems done regularly by hand. Keep them sharp and practiced so they can breeze through a mental calculation in the grocery store to see which bag of apples are the best buy per pound, or be able to estimate to see if a complex answer given by a calculator is right or not.

There are times when we have to use our head. I think we’ve become way too dependent and are not teaching our kids to think instead of relying on electronic devices.

I’m motivated. . . time for some math facts practice at my house!

 

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Egg Carton School

eggcarton1

I am always looking for ways to “fun up” learning, and this one is a hit . All you need is an egg carton to make practicing facts fun. For little ones, you can practice color or number recognition, or beginning letter sounds. Elementary age children can drill their addition facts or times tables, or practice more advanced phonics sounds. Even 12-year-olds think it is fun to do their math facts practice this way.

Simply write the information you want drilled on stickers and place them inside each egg carton cup. Add a token (a nut, penny, marble, button or small stone) and have your child shake, shake, shake! When they open the carton and find the nut, they name the number or say the phonics sound.

If you want to drill math facts, put 2 tokens in the egg carton. Now shake! Open the egg carton and add (or multiply) the 2 numbers that have tokens in their egg cups.

Here are some games to make and play:

Color Recognition for Toddlers

Use markers or tempera paint to color the inside of each egg cup.

Number Recognition

Use numbers 0-11, and one token.

Easy Addition

Use numbers 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 5, 6 and 2 tokens.

Multiple Digit Addition

Use numbers above and 3 tokens, so you will be adding together 3 numbers.

Advanced Addition

Use numbers 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9 and 2 or 3 tokens.

Multiplication

Use numbers 2, 3, 4, 5, 6, 7, 7, 8, 8, 9, 9, 10 and 2 tokens.

Letter Recognition

Use alphabet letters and 1 token, asking your child to say the letter name (not the sound it makes).

Phonics sounds

Start with simple consonants: b, d, f, h, j, k, l, m, n, p, r, s. Next use the rest of the simple consonants and more complex consonants, and later, the phonics units (such as th, sh, wh, qu, ee, ai, ea, eigh, ch, ay, igh, ou).

Scramble some eggs, and take time to play!

 

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Messed up in Math

Question:

Our granddaughter goes to public school and she is struggling so hard with math. The school has really messed her up and is teaching her things backwards. When we try to help her it confuses her. They are teaching her to do math problems from left to right, to do all of her borrowing before she even starts to subtract right to left. She hates math because of it and it is so hard to get to work on her math homework. We tell her how important math is and how she will use it the rest of her life. Do you have any suggestions that would help us?

Answer:

It depends on how much time you can commit to this, but if you are able, the ideal would be to take her out of school during math period. Usually math comes first in the school day, so working with her first thing in the morning, and then taking her to school might be a good option.

Math is a basic skill that must be mastered in order to move on with her education. If they are “messing her up” in math, it is pretty important to get her out of that situation, if you cannot work with the teacher to make a change. If not, tell the school you will be taking her out for private instruction in math, and get the textbook they are using and the schedule they are on, so that you keep her up to date. If the math book is faulty, then you’ll want to use Singapore Math or Saxon Math instead. Test her—both companies have free placement tests online—and find out just where she needs to start.

If you can work with the math book, and it is just the teacher that is doing things confusingly, then using the math book will help her transition back into her school class eventually. Focus 10 min. daily on doing math facts, if your granddaughter is not proficient in the basic facts. If you work with her daily on math, you will be very surprised how much more you can accomplish with one-on-one tutoring in the same amount of time the school takes!

If she is feeling resistant, do things to make it fun and help renew her attitude. Math is truly fun, and she needs to feel that enjoyment again.

Here are a few ideas to motivate her:

*Make a chart with bubbles (dime size) that represent a goal (15 min. steady work, 10 problems completed, math facts done for the day, or whatever goal is appropriate) and stick a dime on each bubble when it is earned.

*Let her choose to do evens or odds (problems) for the day, if it feels like she has too many math problems to do.

*Use hands-on items to illustrated the problems, such as Legos, beans, coins, etc. (I taught my daughter to subtract using shampoo bottles while I was taking a shower!)

chalkboard*Work on the chalkboard. It is easier to do math when it is big-sized and involves the fun of writing with chalk, too. You can hastily illustrate story problems to make it even more fun!

*Give her “points” for right answers, with a goal in mind. For example, if she wants a certain item or privilege, she could earn it by diligent effort.

*Use real life math to help her see how useful math skills are. Use receipts to practice rounding off numbers and adding a column, keeping the total hidden to self-check.

*Let her correct her own work using the answer key herself (with you nearby observing). Often this grown-up thing to do will make a child more careful with their work.

*Time her math facts practice with a stopwatch. Saxon has this built into their program and it is truly motivational to keep a graph recording the times, seeing progress more visibly.

wrapup*Use math facts games to make it more fun. I recommend  Math Wrap-Ups, Multiplication Songs, and others.

*Work math problems on a big sized scribble pad with colorful markers.

Best success!

 

 

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Memorizing the Times Tables

My grandson Isaac

My grandson Isaac

Question:

My 11-year-old boy is still trying to memorize his times tables. He’s finally gotten his 5’s and 9’s (and of course 0’s, 1’s and 2’s) but the rest seem to be hard for him. I’m wondering what we can do without spending much.

Answer:

How frustrating for both of you! Math facts are part of that essential knowledge, just like reading, and the quicker they can be learned, the better off for everyone. So, the challenge is to make it both fun and do-able. Making it “do-able” means giving kids the tools to figure out the answer–and make sense of it–rather than just trying to teach rote facts.

1707a-150x150Rather than use flashcards (even Saxon flashcards), I use Math-it and I can’t imagine teaching math-facts without it! (This product is pricey, but very well worth it in my estimation, especially if you have more than one child you will be teaching, as it is non-consumable.) The reason why Math-it is so fabulous is that it actually teaches children how to understand and remember. For example, in teaching the x 9’s, Math-it teaches this method: to find the answer to any number times 9, just count back one and that is the first number of the answer. To find the second digit of the answer, just add the two digits to make the number “9”. That sounded complicated, but if I could show you with Math-it, you’d see how easy it is.

Here’s a chalkboard explanation:

To find the answer for x 9’s,

for any number (for example, “7”)

7 x 9

just count back one from that number

7–down one to–6

and that is the first digit of the answer (6)

So the answer is 6__.

To find out the second digit, just count up to 9.

Start at 6 (the first digit) and then count with your fingers –7–8–9 (that was 3 more fingers).

The number of fingers is the second digit in the answer: 3

So . . .7 x 9 = 63

It works for every number x 9.

Here’s another example:

4 x 9

Count back one from the number 4 and you have the first digit of the answer: 3__

Ask: what number added to the first digit would equal “9”. (3 + ___= 9)

The answer to “6”, which is the second digit.

So 4 x 9 = 36

Screen Shot 2015-05-07 at 9.52.49 PMMath-it teaches reasoning and how to figure out the math facts (addition, times, division, etc.). There are other products that I have used to practice the facts and make them instant recall, once they are learned—products that make practicing fun, such as Wrap-Ups, Making Friends with Numbers, and the Multiplication Songs, but teaching kids how to find the answer, how to reason it out, is the core issue here. Otherwise it is just a bunch of rote facts that slide out of the memory very easily! Once the children learn the “how-to” of figuring out the math facts, I see them using it consistently. And if they are stumped, I find myself saying such things as “remember, any number multiplied by 9: you just count back one and . . . .” Before Math-it, I had no way to help them.

image-1Times Tales is another product that teaches kids memory clues to help them retain those vital math facts.

Here are some money saving ideas to practice with:

1) You can easily make your own drilling flashcards out of index cards to flash and orally quiz your child. Start with just 5 cards to do daily, adding one every few days after he has mastered what he has.

2) Use index cards to make the game of “War” adapted to multiplication facts. Leave the back of the cards blank (or make a marker squiggle on them), and the front of the card would list a times problem to solve, for example:
3 x 7 =
4 x 2 =

Deal out the cards to two players until all the cards are gone. Then both players turn over the top card of their deck exposing the math problem. Both players do the problem in their heads and announce the answer, and who is higher. The highest answer takes both cards and puts them at the bottom of his deck. Play continues until one player has earned all the cards.

image3) Make your own multiplication songs tape by chanting or singing the times tables into a tape recorder (or better yet, have your child do it, from a script). Play this whenever you get in the car, or while he does chores. Repetition will make it stick! ( Multiplication Songs is already done for you.)

I once had a Calculus professor tell me that the reason his students didn’t do well on tests was not remembering difficult Calculus formulas! It was that they had not mastered their math facts to a point of instant recall and made stupid calculation errors as a result. That impressed me! I think learning math facts is like learning phonics. Once you get the building blocks down, you can apply them to challenging formulas (or words), but without mastery, you are always lagging.

To learn and drill multiplication facts: sing “Skip to My Lou,” putting in “6 X 6 is 36, 6 X 4 is 24, 6 X 3 is 18, Skip to my Lou My Darling.” You can point to numbers on a white board, (with the 6 in the middle and all the other numbers around the outside,) pointing to a different number for the other factor each phrase. They get the benefit of music and rhythm to help them learn and remember.

 

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Indispensable Math Facts

Louisa

Math facts! Those stalwart, foundational facts that carry us through our lives, making us able compute things in our head at the grocery store and figure out the cost of a tank of gas. We need them! Our kids need them! Let’s give it our best to teach them to our kids, making their experiences with math much easier.

I heard a Calculus teacher at the university explain that most of the errors he saw on his student’s test papers were not problems in forgetting a math formula. They were simple math fact mistakes that made their answers wrong! Math facts must be learned, and learned to mastery in order for math to be “fun” or “easy” for children.

When should a mom start teaching math facts? I think just as soon as children are able to grasp the concept using hands-on objects. If you set up 2 blocks and add another 2 blocks and your child can conceive of the concept of addition, it’s time!

image-1How? I am not a flashcard fan. I don’t like drill. But I do love math games that make computation part of the play, like Muggins or 24 Game. I like the games that roll dice, and have the player add up the sum (or subtract or times or divide it) and use that number to advance so many spaces.  You can make your own games with just a pair of dice.

Setting the table is great for mental math practice. My kids, as they were growing, used to recite, “We have 9 in our family and Daniel is gone and that makes 8 and Mark is at work and that makes 7 and Emily’s friend is staying for dinner and that makes 8.”

image-2As children progress in learning their math facts, you can play a fun game we made up called “Gotcha”. Each player has a stack of number cards face down in front of them. (You can use Uno cards, or write your own numbers on index cards.) Players both flip a card at the same time, and the first player to say the answer wins both cards. Once the cards are depleted, measure the stacks side by side, and the player with the highest stack wins the game. You can use this to practice addition, subtraction, multiplication or division facts. When I play with my daughter Louisa, I clap my hand down on the table 3 times softly before allowing myself to answer. This evens up our ability level and gives Louisa a chance to answer before I whip her!

8739

Multiplication Songs

When I teach times tables, I always start with the “9’s”. They are the easiest! Here are two tricks to get you started:

Hand Me the 9’s

Hold your hands out in front of you. Now look at the math problem: let’s say it is “9 x 4″. Bend your 4th finger and take a look. Starting on your left hand, how many fingers do you see before the bent finger? “3”. How many fingers remain after the bent finger? “6”. The answer to the problem “9 x 4″ is “36”. For the problem “9 x 6″, you would bend down your 6th finger, and see the answer: 5 fingers before the bent down finger, and 4 fingers after = 54. Try it with a few numbers and you’ll get actually see the answer in your fingers.

Magic Digits

Another trick for learning the “9 times facts” is the realization that all “9 times” problems have an answer in which the digits add up to 9. Look at the “9 times” answers below:

9 x 2 = 18

9 x 3 = 27

9 x 4 = 36

9 x 5 = 45

. . . and so forth. Do you see that in every answer, adding the two digits will equal “9”. In “9 x 3 = 27″, adding the digits of the answer (“2 + 7″) will equal “9”.

To get the first digit of the answer, just look at the number being multiplied by “9”. In the case of “9 x 3″, look at the “3”. Now count back by one. “3” counts back to “2”. That is the first digit of the answer. Write down “2”. Now, to get the second digit of the answer, you just have to find the number that adds up to “9”. In this case, “2” plus “7” makes “9”, so you have figured out both digits of the answer!

Here are my top choices for ways to make learning those indispensable math facts fun!

image-2

#1 Math It
Game-like format, great memory clues to help those math facts stick!

 

9041

#2 Math Wrap-Ups
Wonderful for practicing math facts. Fun and unique!

 

image

#3 Multiplication Songs

Stick in it when you drive somewhere and your kids will be signing their times tables before you know it!

 

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Times Tables Fun

timestablesfun1

Mastering the math facts is one of the journeys and victories of childhood. The sooner they are learned to the “automatic-response” stage, the better! All math that follows requires the basic addition and mulitiplication facts. One mathematics professor at the university said that most of the problems his Calculus students misssed on tests were due to math fact errors, not because they didn’t know the formulas!

In our homeschool, we have enjoyed this simple game for a quick review of the multiplication facts along with fun and smiles. Here’s how to make a quick and simple version for immediate play!

Get a stack of blank 3 x 5 index cards (or cut cardstock into cards). Get either two different colors of index cards, or white index cards and use 2 colored markers (red and blue are good). If you use colored ink and white cards, put a little sticker, or make a star or happy face or squiggle on the back of each card in the same ink color, so they are easy to sort into stacks.

On the first color of cards (or on a white card using red marker), write up the “answer” cards, one number to a card:
6
9
12
15
16
18
20
21
24
25
27
28
30
32
35
36
40
42
45
48
49
56
63
64
72
81

timestablesfun2

On a different color of index cards, or In blue marker, write up the “problem cards”, one problem to a card:
3 x 2=
3 x 3=
3 x 4=
3 x 5=
3 x 6=
3 x 7=
3 x 8=
3 x 9=
4 x 4=
4 x 5=
4 x 6=
4 x 7=
4 x 8=
4 x 9=
5 x 5=
5 x 6=
5 x 7=
5 x 8=
5 x 9=
6 x 6=
6 x 7=
6 x 8=
6 x 9=
7 x 7=
7 x 8=
7 x 9=
8 x 8=
8 x 9=
9 x 9=

To play the game, set the 2 stacks of card face down in the center of the table. Each player takes 7 “answer “cards and lays them face up before him. Then the first player takes one “problem” card from the stack and turns it face up. If he has the answer to the problem amongst his 7 answer cards, they make a set, and the player draws an “answer” card to replace the one he used. Then he draws again from the “problem” stack and tries to make sets as long as he can continue. If he can no longer answer the problem with one of his answer cards, he discards the problem to the face-up discard stack. The next player may draw from either the discard stack or the face down stack, and make sets as long as he is able to continue. The winner is the one with the most cards once the problem stack is gone.

You can customize (and shorten) this game by just working on the “3’s”, for example, or just on the one’s that need extra practice. This game can also be made up in an addition facts version for younger siblings wanting to play too.

A quick game is just right to start math studies each day, and makes every happier, and smarter!

 

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