Practical and Fun Math Learning Tips

Are you experiencing the “winter blahs” right now in mid-January? Maybe it’s the cold, grey weather … but maybe it’s because you need some great ideas to liven up your Math learning. Sure, there are lots of worksheets and textbooks and workbooks and commercial “learning games” out there–but maybe some practical, fun learning would bring some summer warmth and inspiration into your family learning!

As you explore the posts in this blog, you’ll find lots of practical learning tips–but in case you’re wondering right now what I’m talking about, here are a few examples of Math tips to get you started.

Look around the house and yard, and have your child make up number sentences about things he sees. For example, you might have two piles of jigsaw puzzles sitting on a table, one with 4 puzzles and one with 2 puzzles, so he could make up 4 + 2 = 6. Then you could ask him, “What sentence would you make if I took away two of the puzzles?” If he’s a bit confused, ask him how many there are to start, move two puzzles away, and then he’ll get it: 6 – 2 = 4. Get some magnetic numbers and math signs and he could put the equations on the fridge (or use foam or cardboard ones). Then have him read them out loud. By doing this he is doing hands-on math (feeling and arranging the numbers and signs), speaking (saying the number sentence out loud), responding to questions, and very important, relating the numbers to real things he can see and touch. You can also have him write the equations on a white- or blackboard. Children often do addition in a math book, but often it is really a “theoretical exercise” without really understanding what the equation really means–so this should help to connect the theory with real life around her. Outside, your child can do similar activities, such as adding trees in different yards, subtracting flowers when she picks them for a bouquet, and so on. Children often learn much better with concrete, hands-on, viewable and touchable examples than with “theoretical” pencil-and-paper or textbook/workbook methods. And “talking through” math aloud is also very helpful. If the child can then turn around and “teach” a younger sibling or friend, or even a stuffie or a pet, all the better!

Lego blocks are handy math manipulatives. Use a group of 10 stuck together for “10s” and then smaller groups for each of the single digit numbers–put them together to create the “teens” numbers. To help your child make connection with numerals, put the lego groups with number cards (you can easily make these on bits of paper–and if you have your child make them, all the better!). Have the child count them aloud. Talk about how the “1” in a teen number says “teen” (which sounds like “ten”); and explain that for the teens, we say the single digit number first (fourteen, sixteen, seventeen, eighteen, nineteen)–but some sound a bit different (fifteen [the “fif” sounds like “five”] and thirteen [the “thir” sounds like “three”]). For “twelve” say “two-elve” if she needs a reminder. For “eleven” just say “what comes after ten?”

Singing is a wonderful way to memorize math numbers and facts. You can practice number order by singing this song (and of course you can substitute the child’s favourite animal or object):

One little, two little three little penguins,
Four little, five little six, little penguins,
Seven little, eight little, nine little penguins,
Ten little penguins in a row.
Eleven little, twelve little, thirteen little penguins,
Fourteen little, fifteen little, sixteen little penguins,
Seventeen little, eighteen little, nineteen little penguins,
Twenty penguins in a row.
Twenty little, nineteen little, eighteen little penguins,
Seventeen little, sixteen little, fifteen little penguins,
Fourteen little, thirteen little, twelve little penguins,
Eleven penguins in a row.
Ten little, nine little, eight little penguins,
Seven little, six little five little penguins,
Four little three little, two little penguins,
One little penguin alone.

To help your child learn the “decades” numbers (ten, twenty, thirty, etc.), use dimes and pennies (hopefully, if you’re Canadian, you will still have some pennies kicking around the house, or you can get pretend ones cheaply at the dollar store). Set out pennies in single digit groups in rows, in order from 1 to 9, and have your child count and name each group–and for “10” just use a dime. Then put a dime in front of each of the penny groups, and help your child count/name each group. Then put two dimes in front of a group of pennies and ask what that number would be. Then three dimes in front of a number, and so on.

Use coins to skip-count: Use nickles to skip-count by 5s, dimes to skip-count by 10s, quarters to skip-count by 25s, and loonies ($1 coins) to skip-count by 100s.  Children especially enjoy using coins from their own piggy-bank if they have one; if you child gets coins for birthday gifts, chores, etc., they can save them up in a piggy bank and skip-count them to see how much they have.

While children can learn to tell time (analog) with worksheets or flash cards, there is nothing like telling real time with real clocks. Take every opportunity you can to point out clocks around the house and wherever you go, and have your child figure out the time. Children enjoy “setting clocks”–get an inexpensive clock from a thrift store or dollar store, and allow your child to play with it to set different times, and to set the alarm clock at bedtime or nap time.

On a road trip, use a real map, and figure out the distance for the whole trip, as well as the distance between towns. If the distance for the whole trip is, say, 350 km, and you pass a sign that says there is 125 km to that destination, have your child figure out how far the family has already gone. Road trips are actually a wonderful time to do lots of math–count numbers of big trucks, or red cars, or licence plates from different provinces/states; record mileage and amount of gas bought, and figure out the gas mileage; watch for signs with dates, times, temperatures; and so on. Have the children keep an eye on road speed signs, and an eye on the driver’s speed–kids love to “catch out” the driving speeding–or going too slow!

These are just a few ideas on how to do “real-life math” with your child. Now it’s up to you to think of lots of other ways to make math real and clearly understandable for your child. What are your favourite “real-life math” methods? Why not share them in the comments? Thanks!

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Practical and Fun Language Arts Learning Tips

Are you experiencing the “winter blahs” right now in mid-January? Maybe it’s the cold, grey weather … but maybe it’s because you need some great ideas to liven up your Language Arts learning. Sure, there are lots of worksheets and textbooks and workbooks and commercial “learning games” out there–but maybe some practical, fun learning would bring some summer warmth and inspiration into your family learning!

As you explore the posts in this blog, you’ll find lots of practical learning tips–but in case you’re wondering right now what I’m talking about, here are a few examples of Language Arts tips to get you started.

Is your child having trouble with letters– such as a letter that she often leaves off a word, or letters he often mixes up (m/n; p/d/b; p/q)? A good idea is to point out words on anything–signs, newspaper headlines, cereal boxes, etc.–that have any of these letters, to give your child practice with these letters in a wide variety of “real” uses. Real-life learning is almost always superior to worksheets and such, and its a lot more fun.

Does your child have a hard time thinking of antonyms (opposites)? Instead of drilling lists of antonyms, watch for “real life” opportunities in general conversation to point out opposites, and ideally, have her put them into action. Examples: “The door is SHUT; please OPEN it” or “Put this book on the TOP shelf, and this other book on the BOTTOM shelf” or “Please pick up the ball that’s UNDER the tree and throw it OVER the bush to me.” Using practical, “real” examples like this in daily life will help her develop an understanding of opposites.

Homonyms are words that sound the same but have different spellings and meanings. Many children (and adults!) find it a challenge for her to “sort out the spelling” of homonyms. But using “tricks” (mnemonics) are lots of fun! For example, “meet” has “me” in it so think “meet me”–while “meat” has “eat” in it, so think “I eat meat.” Also, “too” means “also” or “more” so you can say that’s why it has the extra “o” instead of “to.” A “deer” (unlike “dear”) has 2 eyes, which are the two “e”s in the middle. “Piece” (unlike “peace”) has “pie” in it, so think “I’d like a piece of pie.” And so on

Does your child have difficulty with “Mr., Mrs., Ms, Dr., etc.”? Obviously, you can’t easily sound them out. But if you connect these titles/abbreviations with people in your family (or close friends), they take on a strong personal connection and that makes them so much more relevant and easy to remember. Let your child label photos, draw stick people sketches and label them, make name tags and stick them to people (kids love doing this!). With these picture connections and family connections, your child will easily remember these words!

Encourage “practical reading” at home by having your child read recipes when you are cooking, and have him do some of the parts of the recipe that he has read about; when you make a grocery list, make sure you print it clearly, and have him read it to you as you shop together–or give him the list and have him search the shelves and find the products with the matching words; and so on.

Is your child having difficulty reading a newly assigned book or story? Work through it in stages. First, look at any pictures and discuss the title. What do you think the book might be about? Then read it to your child slowly, finger-tracking the words. Then read it again, still tracking the words, and have your child do his best to read along with you (don’t correct or wait, just read smoothly and with appropriate emphasis). Then try reading half of a sentence and have him finish it; then read alternate sentences; then move to alternate paragraphs. Your child will soon be familiar with the content–and be able to not only read the words but read them fluently, with good emphasis. Other useful strategies include choral reading (reading aloud together), taking turns (sentence by sentence or page by page), fading (start by reading chorally, then slowly “fade out” so she is reading by herself–and “fade back in” if she needs help).

Ideally, allow your child to choose his own reading material quite often–that will also provide interest and motivation! Libraries and bookstores and thrift store bookshelves are wonderful places. Spend lots of time together in them, because doing lots of activities, reading, writing, research, etc. on a topic a child is very interested in is a great way to encourage him in developing his literacy skills–even if you aren’t as interested in spiders and other creepy crawlers as he is, and it freaks you out to discover them in his pockets when you’re doing laundry!

Encourage your child to read to her siblings, her pets, her stuffies–and to anything or anyone else who won’t critique or help, but rather will admire her ability–and encourage her to ask them the questions at the end. Children love to be “the teacher” and it’s true: teaching someone what you’ve just learned is one of the best ways to plant that knowledge and skill into long-term memory.

Tongue twisters are a wonderful way to practice sounds. There are fun tongue twister books available (try this one I put together, for example)–but then be sure to make up tongue twisters with your child. It’s so much fun–and they don’t even have to make much sense. Children love “silliness”!

Make up “silly sentences” with rhyming words (and word families)–or make up little rhyming poems. They can be lots of fun to create–together! Children are so creative–get your child involved! Also, search through colourful nursery rhyme books and other poetry books for simple rhymes, limericks, nonsense rhymes–your child will love repeating them after you, even if she can’t read them yet. Finger-track under the words, and she’ll soon start connecting sounds and letters–and soon start spelling, as well.

Here are some things to look for in library books–make it an adventure, encouraging the child himself to get involved in the search: different levels of difficulty on the same topic (of the child’s interest!) but in different picture books, fiction books, non-fiction books, magazines, videos, etc.); entertaining books that have repetition of sight words or other words you want the child to learn (have the child look for books that have words from a list you’re working on–think of book topics that might have those words, or even try using the library subject catalogue);  books with humour or funny twists (kids love books with jokes and riddles in the story–like Joanna Cole’s Clown Arounds series); colourful illustrations which give “hints” as to the “new words”; and books that encourage expressive reading through fun and entertaining dialogue or story line.

And while it’s fun to get a stack of new books from the library every week, if she “loves” a book and wants to read it over and over, encourage her to do so, as it will build fluency–even consider suggesting favourite titles as a birthday or other gift that grandparents and others can give your child. Perhaps a birthday party could have a “theme” related to a favourite book series, and guests could bring books, videos and other items related to that series.

Help your child help make her own “card games.” When a child helps make a product and feels “ownership,” she is more likely to learn and to want to play with it. For example, to learn to put words in correct order, print simple sentence words on little cards (capitalize the first word), and have her move them around until the sentence makes sense. If she puts them together in an unexpected order, have fun with that–even let her make up more “silly sentences” with the cards, and have a good laugh together–and then chat about why it’s important to put words in a sensible order. Includes cards with a period, a question mark, and an exclamation mark for her to choose appropriate punctuation.

Watch for commonly seen words, such as “stop” or “exit.” Point out the words (which your child will very likely be able to “read” simply because she “knows” the “sign” in its context), and emphasize the letter sounds in the word. You can also use containers (“milk”), and can talk about everyday objects in her life (cup, sun, apple, pet, pot, etc.). Another fun way to learn vowel sounds (or consonants) is to use “alphabet cereal” and write simple words, say them — and then eat them! After eating each word, say the sound stretched out as if enjoying the taste of the sound. “c-a-t Cat — [eat] –aaaa!!”

What fun, practical Language Arts ideas do you have to make these grey, chilly winter days an exciting learning time for your children? Be sure to share your ideas in the comments and help out other families, too!

 

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Posted in adventures & explorations, family learning, home learning, homeschooling, learning games, libraries, rhymes | Leave a comment

Distractable–Or Imaginative and Creative?

Today’s post is from a “tutoring lesson report” on a child whose parents had been told was very “distractable.” As the lesson went along, I began to think maybe the child wasn’t really so “distractable” after all. What do you think?

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Today I had M read two short books, Counting Bugs and The Pie that Jack Made. She was able to quite easily sound out a number of fairly hard words–several for which there were no picture hints. Such words included “wiggle, flutter, creep, ground, flower, pumpkin.” I notice that she tries to sound the words out silently in her head, and has difficulty that way, but when she sounds them aloud, she does much better. So try to make sure she sounds aloud! It will help her to focus.

We also worked on skip-counting (without looking at numbers). We said the 10s together once, then M said them herself, and got them all right. Then I explained that the 5s simply go in between the 10s, and that “five” is part of each one (except FIFteen). After once together, and twice more with me fading out more and more, she was able to do 5 to 100 in 5s, without help (and without looking at numbers). Keep practising these at home. I suggest doing it once together, once with you helping quietly when needed, and once by herself. If you do this a couple times a day, she’ll soon have the 5s down pat, and then we can work on the 2s (evens, then odds). You don’t need to make it feel like part of “school work”–it’s something that can be done at odd times, like when driving places in the car, going for walks, even together as a family at the dinner table–and the other kids will then learn theirs, too. Make it a fun family activity. M is very talkative and sociable, and approaching memorization of facts in these ways will be far more effective than writing them out repeatedly ore reading them over and over or filling in worksheets.

Today’s Alphabet story was “A Hot Rod in A Rut.” This story didn’t have any pictures, so I thought it might be a bit challenging for her as I’ve noticed she tends to rely on pictures–not surprising, as she is so artistic. Also, there were a few words in the story she didn’t know the meaning of, so I had to explain those. But the interesting thing I noticed is that when she seemed to be “distracted” (looking off into the distance, smiling to herself, tapping her fingers, etc.) I told her, “Tell me what you’re thinking.” Here is kind of how it went:

Rich had a hot rod. (What’s a hot rod? — It’s a racing car — Oh, well, why is it hot? …–so we discussed that–) It had a lot of mud on it. (Like our car. It’s really, really dirty. You should see it!) Rich got in. Rich got Rob, his chum. (What’s a chum? … so we discussed that, too). Rich and Rob bat the rug. (What does that mean? –I explained– Oh. They’d need to be careful so they don’t get hurt, right?). They mop the top. (Why did they do that? — To clean it — Oh, that would be funny to see them mopping the top of the car!)  Oops, a bug. (A bug? I wonder what kind of a bug it was …) Rich and Rob are in a jam (I explain to her what “in a jam” means — Oh! Wouldn’t it be funny if they were really in a big jar of jam. It would be so sticky. It would be so funny to see that…). It is a job for Bim-Bam. Bim-Bam did it. Rob and Rich are out of the rut. (Is Bim-Bam their friend? Maybe he’s their pet? Do they know him? I guess they must know him if they know his name, right?)

By getting M to speak aloud what she was “thinking” in her “distracted” moments, what it appears to me is that she is less “distracted” and more creative and curious and imaginative. Perhaps when you are working with her, if she seems distracted, ask her to tell you out loud what she is thinking. If it is related to the work at hand, it can’t hurt to discuss it–and you could even encourage her “writing/storytelling” skills by writing down or tape-recording her thoughts. Then rewrite or type the story, but add the ideas she expressed. Finally, have her read it with her ideas included. By having her thoughts added in, she may indeed be more motivated to read it in a more focused manner, and more willing to try “hard words” (since she suggested them!). She might even become motivated to write her own versions of the story or create original stories.

(I also noticed that when M seems to be distracted, she tends to tap her fingers or swing her legs or otherwise move her body. I told her that when she is reading, she is welcome to use body movements to “act out” parts of the story. For example, she could act out batting the mat or mopping the roof of the car. M thought this was great fun–and it really kept her focused on her reading!)

Here’s an example of how you could rewrite the story above, using M’s ideas: Rich had a hot rod racing car. The engine got hot when he drove it fast. It had a lot of mud on, just like our car is really muddy and dirty. Rich got in. Rich got Rob, his chum–his friend, pal, buddy. Rich and Rob batted the rug from the floor of the car. Rich held it and Rob hit it with a stick so the dirt and mud fell off it. They had to be careful so they did not get hurt. They mopped the top of the car. That is a funny way to clean a car, using a mop. Oops, a bug! It was a great big black fly, and it flew straight at the window, so Rich swerved the steering wheel, and the car slid into a rut in the mud at the side of the road. Rich and Rob were in a jam. They were stuck in a muddy rut, and the car was sticking like jam in a big jar of jam. It is a job for Bim-Bam. Bim-Bam is a ram. He is a big man sheep with big curly horns. They know Bim-Bam because he belongs to their neighbour, the farmer. Bim-Bam is their friend.

As you can see, this version introduces lots of new words, while including the words and sounds that are being focused on by the author/publisher. So not only does M continue to work on the “focused” words, but she adds lots of other words that come from her, and it becomes HER story, which will motivate her in many ways.

So maybe M’s problem isn’t so much “distractability” caused by outside factors, but simply strong personal imagination, curiosity, creativity–all things we need to encourage, though of course she also needs to learn to focus.

Note: M’s mom and I have also discussed some other possibilities/solutions related to “distractability” such as rewards for focused work, and withholding of rewards/privileges until required work is completed; providing a less distracting environment, such as making sure the TV is off, curtains are drawn, other children are not in the learning area; alternating short periods of “focused” work with other work that engages her creative, artistic, graphical skills; using “unit studies”–such as her interest in bugs–in which math, science, reading, writing, social studies, art, physical education, etc. are all included, but not presented as “subjects”; and so on.

After having M do all that focused reading, I provided her a break/reward by having her do a couple of “2D” and “3D” geometry worksheets which included drawing shapes and colouring. She enjoyed that.

Then I had her do some subtraction practice. First, she did subtraction using a number line. Then I had her use crayons (as counting manipulatives). She is slowly getting more understanding of the concept of subtraction but does need lots of “hands-on” practice, the more the better for a child who is as active as she is. Use as many different methods as you can think of–the more ways she “sees/experiences” a concept, the better.

M enjoys “game” approaches to learning, as well as graphical approaches, so I’ve given her a couple different things to try:

  • A sequencing worksheet which involves a game. The worksheet gives instructions on how to play the game (which she can play with her siblings; all she needs is a muffin tin and some kind of item to toss–pennies, pebbles, paper clips, something like that). The game is for fun. The “sequencing” is to read the instructions at the top, then play the game, and then put the mixed-up instructions at the bottom in sequence/order.
  • A reading/drawing worksheet. M can read the sentences, and then draw a picture for each one.
  • A “Tic Tac Toe” sentences worksheet/game. Each square in the game has a sentence to read. I have given M two colours of sticky-notes, which can be used to play the game (and reused repeatedly, playing the game over and over until she can read the sentences easily). You can also make up your own “Tic Tac Toe” sentences games for her, just choosing whatever sentences you like.

We went on to read another story, Monkey Business. She inserted her own comments and even did some more “body language” as she read. I jotted down her comments, and then rewrote the story, putting the original author’s name and M’s name as co-authors. M was so excited, as writing stories up to this point has been a big “chore” for her.

 

Want to learn what monkeys like?
They like swinging on branches and eating bananas and sitting and dancing.
Monkeys like to live in groups.
They like hugging and sleeping while they are hugging.
Monkeys like to swing in trees.
Monkeys like to sleep in trees.
They are all sleeping in the trees.
They are snoring. Z-Z-Z-Z
Monkeys like to eat bananas.
This one is eating wide. Yum.
And this one is saying “Yummy.”
Monkeys like to say “Eee-eee!”
Ee-ee-a-a-ah! Eee-ee-ah!
Each one is saying, “Eee! Eee!”
They have wonderful teeth. They are all dancing. This one is doing a ballet dance. He is patting his tummy and rubbing his head.
But monkeys do not like itchy fleas!
This one is scratching him, and this one is scratching him.
This one is scratching his butt!
I am going to scratch them too. [and she started scratching them on the picture]
Oh no! A flea landed on me!
Now I am itchy, too!

M was very excited to be able to read the story with her words–and said she is going to draw a picture of it at home and read the whole story to her sister. Even though it includes some “hard-for-M” words, she was able to figure out most of them herself, since she had created the story.

We read another Alphabet Story, A Fin in the Fog. M was very interested about what the fin might belong to–a shark? fish? porpoise? She asked why the writer didn’t say, and I told her it is so she can use her imagination. She was pleased and suggested it must be a porpoise. She also did not know what a “hut” might be. I told her it was like a small house or a kind of shed. Then when she read more, she wanted to know what the light at the top would be, so I told her it must be a light-house. She was puzzled, wondering what a lighthouse is. I described it to her, but she asked if I had a picture. As a matter of fact, just a month or so ago, I wrote a short story based on a magazine picture of the Marshall Point Light House in Maine (the lighthouse in the movie, Forrest Gump), so I dug it out, showed her the picture, and read her the story. This led her to more discussion about the Fin in the Fog story as well. As I’ve said already, she may be a bit distractable … but it might well have more to do with curiosity and imagination. Try to allow time to follow her ideas–she’ll be learning so many new things, at the same time as her reading and writing are improving. Use those “teachable moments” to grab her attention; it will help to turn her “distractability” into amazing focus!

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Is your child distractable? Try some of the methods discussed in this report and see if maybe that distractability is really something else–like creatively, curiosity, imagination–and a naturally active child!

 

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Posted in adaptations, learning differences/disabilities, learning styles, reading, special needs | Leave a comment

A Math Tutoring Report With Practical Suggestions

Over the next while, I will be posting samples from actual reports I have made to parents of my tutoring students. Today’s topic is some practical suggestions for a child who is struggling with primary-level math. Hope you’ll find some helpful tips here!

Addition of Double-Digit (or Larger) Numbers

J was sure he wouldn’t be able to add double-digit numbers. So I showed him some practical ways to make it easier. We started with double-digit numbers that don’t require carrying (numbers added don’t add to more than 9 in any column). I emphasized that it is important to line up the numbers carefully so as not to become confused. To help him, we used cm graph paper (the squares are large enough for his handwriting of each number to fit in each square; there are different sizes of graph paper available, so choose a size that fits the child’s handwriting size). Then I had him add–starting with the ones column, then the tens column … and then I put down hundreds … and even thousands and ten thousands columns. He was very impressed that he could successfully add such large numbers! Building confidence is so important. Once he feels very confident with adding this way, we’ll talk about place value, and then introduce carrying.

Using coins

 

J also doesn’t seem to clearly understand how easy it is to add 5 to 10s. For example: 20 + 5 = 25. You can help him practice this at home by using dimes and nickles. For example, have him count 5 dimes and then add a nickle. This usually helps children catch onto this concept easily.

We practised counting coins — pennies, nickels, dimes and quarters. But while J can count them, it is much more difficult for him to try and figure out what coins to use for a given price. But, as with most children, he likes using coins, so this is something you can easily do with him for practice. Just write down a price–or “play store” and have him choose what he’d like to buy for the prices you’ve marked on items (for example, 38 cents or 55 cents), and have him figure out which coins to use. Let him figure out different combinations. For example: for 38 cents he could use 25 + 10 + 3 pennies OR 10 + 10 + 5 + 5 + 5 + 3 pennies. I realize that officially we don’t use pennies anymore in Canada, but we still need to be able to figure out whether to round up or down, so if you have pennies, it’s good to use them … and besides …

Rounding

J also needs practice with rounding in math. Using pennies, nickles and dimes is a great way to practice rounding! For example, 18 cents: dime, nickel, 3 pennies. To round, we want to just end up with dimes. So count the pennies and nickel. That’s “5 or more” so we round up and it becomes 20 cents (2 dimes). But if it was 13 cents (dime, 3 pennies), we can count the pennies and since they are “less than 5” we round down to 10.

Please also note: When rounding, always ask if the number to be rounded is “less than 5” or “5 or more.” Be careful NOT to say, “less than 5 or more than 5” as that leaves out the 5!

Numeral Order

 

J can generally do “> greater than”, “< less than”, and “= equal to”. However, I noticed that he said 7685 = 7865. I asked him to explain it, and he said that both numbers each contained a 7, a 6, an 8, and a 5. He didn’t seem to realize that just because the numbers contain the same digits, doesn’t mean that they are the same numbers if the digits are in a different order. So we talked about that and did some practice. This is something you’ll want to keep an eye on as you work with him. Really emphasize the “ones, tens, hundreds…” Use the graph paper, as discussed above, so he can clearly see the difference. Have him write the digits in different orders and read them aloud. If he is having difficulties reading the numbers, write abbreviations at the top of each column: th (thousands), h (hundreds), t (tens), o (ones).

What Calculation Method Should We Use?

In the workbook you are using with J, a wide variety of methods are presented for doing certain kinds of calculations, for example, double-digit addition. This can be confusing OR it can be helpful (for parents as well as for the student). My feeling is this:

  • First try the simplest/standard method.
  • If your child is having difficulty with the simple method, try one (or more, if needed) of the other methods, until you find one that your child “gets”–and then do lots of practice with that. Once your child understands the overall concept, it is wise to go back and learn the simple/standard method, as the child will no doubt run into it at various points later in math–and in “real life.” Note: You may discover that the method that helps your child understand the concept is different than the method that you think is easiest/most helpful. We all learn in different ways–so you as a parent may very well end up learning some surprising new ways to deal with a concept!
  • If your child “gets” the simple/standard method, but finds the concept very intriguing, encourage “exploration” of some of the other methods. Learning a variety of approaches can actually help to prepare the child for more complex mathematical concepts in future, as well as using them in “real life” applications.

Counting Backwards

J seems to have some difficulty with counting backwards … and especially counting backwards “over decade breaks” (for example: 62, 61, 60, 59, 58). This is a good thing to practice by using “real” learning opportunities. For example, as you walk along a sidewalk, count each square, starting with a number like 33 or 54 or whatever, and count backwards from square to square, making sure to go back into the next “decade.” You can also use things like “100 number charts” (with numbers in rows of 10), and count backwards, pointing at each number as you say it. Or you can use dot-to-dot pictures that go up to at least 50, but start at the end number and draw the dot-to-dot line backward to the beginning, counting aloud from number to number. Or you can use calendars and count backwards from the end of the month (eg 31) to the beginning (1). There are lots of different fun ways to learn to count backwards–just keep your eyes open for ideas!

Writing Numbers Backwards

J tends to write some numbers backwards. As he tends to be a “hands-on” kind of learner, try having him “write” these numbers with his finger on a textured surface (such as a piece of sandpaper or a textured fabric or on a sidewalk) so he can “feel” the number–or he could write in sand, or in finger paints, or in shaving cream. Or have him “trace” magnetic or foam or plastic numbers, first with his eyes open, and then with his eyes closed. Another idea is to have him close his eyes and you can “write” the number on the palm of his hand with your fingertip (or you could “write” it on his back) so he can get the feel of the number. Also, have him “write” it in the air (or on a window or other surface that has condensation on it–kids love this!) with his finger.

Learning Arithmetic Facts

J really needs to learn his number facts, and it would be great if he could learn his “doubles” first, as he can then use them to easily calculate other number facts. Some methods to learn them: Repeat them over and over (aloud and/or written). Say them as you do an activity, such as bouncing or tossing a ball, climbing stairs, jumping on the trampoline, etc. “Sing” or “chant” them. There are CDs available that have songs or chants for number facts, or you can make up your own. There are lots of free number fact apps available for your smartphone, tablet or cell phone–and many of them have a “game” approach which really appeals to lots of children. Of course, there are also flash cards available very inexpensively at dollar stores or thrift stores–or you can use an ordinary deck of cards (just use the number cards) to practice addition, subtraction or multiplication facts; just draw two cards at a time. Dice also work well, as do dominoes.

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What practical math tips have worked well with your child/ren? Why not share them with us in the comments?  Thank you!

 

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A Sample First Tutoring Session Report

Do you wonder what kinds of things might happen in a first tutoring session, and what kind of a report you might receive from the tutor? Here is an example of an actual report from an initial tutoring session with one of my students, whom I would be helping with math. B was an 8-year-old student, homeschooling through a DL (Distributed Learning) school. He had been struggling with math, and his parents had decided to see if some tutoring could help him. He was nervous at first, but by the end of this first session, both he and his dad were excited about their upcoming math tutoring lessons!

Greetings!

So nice to meet B and family. I had fun! Hope you did, too 🙂 It was good to have B’s dad sitting in for this session, so he can see the methods I’ll be using, and can use them with B whenever they fit with the math in the workbook he is using at home.

Goals of our Tutoring Sessions

As this was B’s first day, my goal was to find out what B already knows in math, and what “gaps” (like missing ladder rungs or missing jigsaw puzzle pieces) he might have that we can fill in, which will make more advanced work much easier.

Getting to Know My Student

B told me he really likes cursive writing and art. He also showed me some work he is doing in his math workbook at home, and he said he likes when there are pictures, but not work without pictures. This suggests that he is a “graphic” learner, and we can take advantage of that to help him with his math. Also, he’s a pretty active, “physical” boy, so we’ll take that into account too, and use methods that include “active” learning.

Exploring My Student’s Skills and Needs

I used a workbook of math skill builders for grades 1-2 math with B, starting out with very simple work and lots of pictures, etc., to make him feel comfortable and confident. Here are some things I found out:

  • he is able to count well
  • he is able to tell what numbers “come after” but struggles with what numbers “come before”
  • he needs help with ordinal numbers (first, second, third, etc.)
  • he can “skip count” easily by 5s and 10s, and by 2s up to 10 (but then has trouble with teens and beyond). He really struggles with counting by 3s.
  • he knows quite a lot of his basic addition facts, and for facts he doesn’t know automatically, he knows to start with the larger digit and “count up.” His preferred method is “counting up” in his head (rather than finger counting or other similar methods).
  • he struggles with basic subtraction facts.
  • he is fine with “greater than” and “less than” (aka “more” or “less”)
  • he understands “tens” and “ones” for double-digit numbers.
  • he is able to measure with inches and centimeters, though he may be a bit confused about which is which.
  • he is able to add three numbers (single digits).
  • he was nervous about trying to add double digit and triple digit numbers, but once I explained about 1s, 10s, 100s, 1000s columns (place value), he had no trouble to add larger numbers (without carrying). I also introduced very simple single digit + double digit adding with one “carry,” and I think he’s really starting to “get it.”

Word Problems:

We did some “word problems.” B was able to read the word problems, more or less (he seems to have a bit of trouble with reading more complex words, but that could have been because of nervousness in today’s first lesson). He also wanted to solve the problems “in his head” and was hesitant to say the equations before giving the answer. It is really important that he expresses the equation, as word problems start to become more complex in grade 3 math, and he needs to be able to work them out “step by step.” I went over a couple of tips with him:

  • circle or underline the key numbers in the problem.
  • also, circle or underline the “keywords” in the problem, so he knows what kind of problem it is. For example, “in all” is a signal to add; “how many are left?” is a signal to subtract.

Tricks and Games Can Make Learning Math Fun

For the items he was having trouble with, I introduced a variety of “tricks.” I think Dad had even more fun learning the tricks than B did 🙂 He said he wished math was this much fun when he was in school.  Now that he knows the tricks, he can use them with B whenever appropriate work comes up in the workbook.

I also mentioned that I have a wide variety of math games, and we will use them during lesson times, when Brett needs a fun break. He is also welcome to borrow games he likes to play at home.

Here are some of the “tricks” I taught today:

  • Subtraction is just “backwards adding.” So if B learns his addition facts, the subtraction facts will be easy.
  • In fact, B only needs to learn half of the addition facts, because addition is commutative, which means, for example: 3+5 is the same as 5+3.
  • Once B has learned one fact such as 5+3=8, he has actually learned 4 facts that are in the number family of (3,5,8): 3+5=8, 5+3=8, 8-3=5, 8-5=3
  • I noticed that for addition facts (and subtraction facts) that B has not memorized, he was trying to “count add” them in his head–and it took him a long time. It is good he already knows to start with the larger number. While we ideally want him to be able to do the facts automatically (memorized), it may help him to learn them by using more “hands on” methods for practice. Some people are afraid their children will spend the rest of their life “finger counting,” but actually, using physical methods can be a very helpful way to learn facts, especially if the child is taught to use a variety of methods, so he doesn’t end up just using one and making it a habit. Some methods I will be introducing to him are:
    • draw sketches.
    • use a number line.
    • finger counting or counting with objects such as pieces of macaroni.
    • “touch math” … which I introduced today. This combines both “physical” (touching) and “graphical” (dots) which appear to be ways that Brett learns more easily. I have given Dad a sheet with the “touch dots” for the digits 1 to 9, and I showed Brett (and had him practice) adding using the dots. To start with, he can put the dots on the smaller number (for example, with 8+5, he can put dots on the 5), and then use his finger, or a pointer such as a pencil, and count: 8…9, 10, 11, 12, 13. After awhile, he’ll be able to stop drawing the dots and just use the finger/pointer … and before long, he’ll know the facts.

Doubles are Handy!

I recommend that you practice the “doubles” facts with B, as once he’s really comfortable with them, he can quickly and easily use them to do all kinds of “tricks” for other facts. The doubles he needs to practice are: 1+1=2, 2+2=4, 3+3=6, 4+4=8, 5+5=10, 6+6=12, 7+7=14, 8+8=16, 9+9=18, 10+10=20

Most children don’t have much trouble learning doubles. If B is having difficulty, here are some suggestions:

  • have him repeat them as a “chant.” The rhythm makes it easy to remember.
  • have him clap or tap his feet or tap a tabletop (or drum) as he chants them.
  • make it physical. As he says the facts, have him jump up (or down) stairs; or make a “hopscotch” on the sidewalk with chalk and have him jump from square to square as he says the facts; or bounce a ball (or toss it back and forth) as he says the facts; or call out the facts as he jumps on a trampoline; etc.

Once he’s learned the doubles facts, here are some fun tricks (which I showed B today):

  • for numbers that are one apart: example: 6+7 : double the smaller number and add one: 6+7= 6+6+1= 12+1=13 or 7+8=7+7+1= 14+1 = 15
  • for numbers that are two apart: example: 6+8 : think of the “inbetween number” and double it: for example: 6+8 = 7+7 = 14 or 7+9 = 8+8 = 16

Learning the 9s Facts Are Easy With These Tricks:

Another set of tricks are the “9s” tricks. There are several fun 9s tricks, for addition, subtraction, multiplication and division. Here are some tricks I showed him today:

  • to add 9 to another single digit number, the answer will always be a “teen” and the digit in the 1s column will be one less than the other number: for example: 9+5=___ The answer is a “teen” and the number in the one column will be (5-1) = 4. So the answer is “4 teen” = 14.
  • an alternative is to change the 9 to a 10, add the other number, and then subtract 1 … but I find the extra steps can be confusing for some students. If you want to try it, it would work like this: 9+5=____ (9+1)+5= (10+5)-1 = 15-1 = 14.
  • to subtract 9 from a “teen” number, the answer is 1 more than the other number in the ones column. So, for example, 17-9=___ The number in the ones column is 7 so the answer is (7+1)=8. Another example: 15-9=___ The answer is (5-1)=4.

 

Some Recommendations to the Parents

Don’t try to teach all these things at once. Just watch for opportunities to use the different methods as suitable work comes up in his workbook.

Also, it is very helpful indeed to watch for opportunities in “real life” situations, to do addition and subtraction. For example, when you are taking a road trip, get a map that shows distances between towns and have him add up the distance from one town to another. Or if you are baking an apple pie and doubling the recipe, and it calls for 8 apples, ask him what 8+8 is and ask him to count out that many from the apple box. Or if you are having a plate of cookies for supper, and there are 8 cookies to start with, just casually ask him how many will be left after everyone in the family has had one–and if there will be enough for everyone to have a second cookie. These kinds of “real life” experiences come up all the time; just keep an eye out for them, and use them in a casual way. His little sister will also love the game, and it will get her started on math facts without any formal teaching.

Oh! One more thing. If you want to practice “number facts” in some of the ways I’ve suggested, it works much better to just do 10 minutes or so daily, rather than 30 minutes twice a week or 60 minutes once a week. Frequent, short practice sections move short-term memory into long-term more efficiently.

Let Me Know How I Can Help

For future lessons, if you want me to help B with any particular pages in his workbook, just let me know what you want me to cover. Or if you notice he’s having trouble with something, just let me know.

And don’t worry–my first report is always long as it covers all the things I’ve noticed, and lots of explanations. In future, reports generally will be shorter!

Do You Have Any Questions About Initial Tutoring Sessions?

If you do, please feel free to ask them in the comments section, and I’ll do my best to answer them–or you can contact me directly, if you prefer, by email.

You can also find out more by reading the following posts:

You can also find out lots more about tutoring by checking out the links at the Tutoring Topics page and all links to all kinds of specific learning tips on the Home Education Tips page.

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Spelling Memorization Tips

The other day I read an article in which the author said allowing children to just spell “the way it sounds” to them will work out just fine. The children’s spelling, she assured her readers, will gradually become more and more “correct,” until someday they’ll all be great spellers!

Well… that might work for some children, especially if they love to read and tend to “just pick up” the accepted spellings. But for other children, spelling needs to be taught very carefully through step-by-step phonics teaching and through learning spelling “rules.” And then, unfortunately, many words in English, including a large proportion of “sight words” (aka frequently used words), don’t even follow the rules, and this means memorization.

Again, some children can memorize spellings quickly and easily by repeating the word a few times (spoken and/or and written). But memorization is much more difficult for other children. This post will provide you with lots and lots of ways to help your child (and maybe you, too, mom or dad or other significant adults) memorize those difficult words. Every person learns a bit differently, so try out these different (and often entertaining) approaches. We’ll start with some traditional “writing” approaches–and then on to more adventuresome alternatives!

A Variety of Worksheet Type Approaches:

Use these suggestions to create worksheets and discussions that are made especially for your child’s personal spelling challenges:

  • Go over spelling “rules” and “sounds” together orally
  • Draw little sketches to go with spelling words. It can be especially helpful for children to make their own little sketches; the connection (association) is often very helpful, and the sketches don’t even have to be particularly accurate. Sometimes they can just be a funny shape or even a sketch of an “opposite.” Each sketch will give children a “hanger” for the word.
  • Practice handwriting. Trace the word; fill in letter shape boxes (even have the children make their own); copy the word; then write without looking.
  • Make a list of rhyming words that are in the same word family as the word being learned.
  • Create a story using spelling list words. The children use their list to fill in the blanks, either “in context” of the story, or you can create a little sketch under each blank as a hint. Then encourage the children to create their own stories with the list words (and their own little sketches for the words). Silly stories are good as they are fun and memorable
  • Create word pyramids. On the top row, write the first letter; on the second row write the first two letters; on the third row the first three letters, and so on.
  • Use the letter (or combination of letters/blends or spelling rule) being studied in words other than the list words. If the children can come up with some of those words (or find them in a dictionary–a rhyming dictionary can be helpful for this), all the better.
  • Write the list words in one list. In a list beside the first one, write (in mixed up order) a rhyming word for each list word. Have the child match them. In the beginning, use words that follow the same pattern (eg. pane/mane); then try using other patterns that make the same sound (eg. pane/gain); and finally, try homonyms (eg. pane/pain).
  • Create funny sentences that contain the list words (if the child can make the sentences up, all the better).
  • Use compound words with the desired sound/letter combination. For example, if the word is “rain,” use “rainfall.” This is a great way to introduce syllables.
  • Find and circle (or underline or highlight) list words and other similar words in a story, news article, etc.
  • Put the list words in alphabetical order.
  • Discuss different sounds for a letter or letter combination (for example, “long a” can be written with magic e (age), two vowels walking (pain, say), and “eigh” (eight, weigh).
  • If you’re doing multiple ways of spelling a certain sound, as in the “long a” example–or if you have a single spelling that has different sounds for the same letter combination (eg: oo –> book, zoo), first sort the list words, then think of and list more words for each sound category.
  • Create a word search or a crossword puzzle; if children create their own puzzle it can be even more effective, especially crossword puzzles.
  • Create a chart (for example, list words that start with a vowel in one column and with a consonant in another column; or divide the list words into columns by long and short vowels, or by different vowels).
  • Sort the words into sound categories by writing the words on small cards or slips of paper, then sort them. Encourage the children to make their own cards.
  • Write a series of list words run together and have the child separate them.
  • Scramble the letters in the list words and have the child write them in the correct order.

Lots of Different Kinds of Spelling Tips:

Put aside the paper and pencil and start a spelling adventure!

  • Make associations between the spelling of the word and a picture or object. I’ve already suggested drawing little sketches. But you can use other sensory associations. For example, if learning to spell the name of a food, tasting it, smelling it and feeling it while practising the spelling can be very effective. Likewise, if learning a “sound” word (like “whistle”) listen to the sound and/or make the sound while learning the spelling.-
  • Practice in a variety of ways: flash cards, books that contain the word in context, writing the word in the context of a practical kind of writing rather than a regular spelling assignment (eg an email or letter to a friend or grandparent), etc.
  • Play games that strengthen vocabulary and word retrieval: Scrabble, Spill and Spell, Boggle, hangman, crosswords and word searches.
  • Play dice games like Snakes and Ladders–but before taking a turn you have to spell a word. Start with the easiest ones and work toward harder ones. If you spell it incorrectly, you can only move 1 place or half the places indicated on the dice. (Avoid having to miss a turn or other similar “punishment”).
  • Visualize: create a mind’s eye picture. Imagine some particularly memorable aspect of the word. Concentrate on getting a “flash” of that element. For example, if learning to spell “shoelace,” have the child close her eyes and picture a particularly bright, colourful, shiny shoelace on a favourite pair of shoes or boots. Then have her close her eyes and visualize the spelling of the word. Then even try to visualize them together.
  • Association is very helpful in memorizing any sequence of data (including spelling). For example, you are memorizing a list of spelling words: “banana, gloves, guitar, flashlight, midnight” (they don’t even need to have much in common). As you practice each word, visualize it or draw a sketch. Then link those pictures (and spelling) together. Imagine putting the gloves on your banana-sticky hands before you play your new guitar by flashlight at midnight. Use any kind of pictures and any linking story that pops into your mind. Crazy and fun is memorable!
  • Use a variety of writing tools when drawing or writing. Try pencil crayons, markers, sidewalk chalk, paints, black/white boards, or “write” with fingertips on textured surfaces (fabric, sand, finger paints, shaving cream, sandpaper, etc.).
  • Study the word for 15 to 20 seconds. Don’t just read the letters themselves, but look at the shape of the word, the shapes of the letters. Discuss them–think of it as an adventure with the word. Close eyes and recall as much as possible. Then open eyes and take in more detail. Close eyes and add new observations to the original mental picture. Repeat until you can’t come up with any more details. Then write the word with eyes closed (on a large sheet of paper or a whiteboard, etc.), drawing the “word picture” from your mind.
  • Write the word with different kinds of letters–eg. manuscript, cursive, different fonts (you can also do this typing on a word processor like Word), different sizes of letters, uppercase, lowercase, different colours, highlighted with different colours.
  • You can even “decorate” difficult-to-remember letters and letter combinations. For example, for the word “between,” in order to remember the “ee” long vowel combination, the child could sketch little eyes in the circles of the “e” letters, and emphasize the “smiley” bottom part of the letters in order to make an emogi funny face to put the “ee” into his memory.
  • Say or sing the word; set up a beat (tap, bounce a ball); say a syllable (or letter) for each beat.
  • Set up a pattern for the word: listen to a helper spell it aloud, spell it aloud yourself, write it in the air with giant imaginary letters, close eyes and visualize it, write it on paper, type it on the computer, write it in a sentence…. Figure out a pattern that works well for you.
  • Make up catchy rhymes or songs of the material to be memorized (or search a poetry or songbook for poetry/lyrics that repeat that word’s spelling sound or pattern–children’s poetry and songs like Mother Goose are especially good).
  • Have a family discussion related to the word. Talk about what it means, how it is spelled, any spelling rules, similar words–and how the word is used in practical ways.  Then find it used on cereal boxes, how-to instructions, recipes, newspaper articles, etc.
  • Have a helper spell a list word (start with the simplest one). The child repeats it. Then the helper spells that word and the next easiest one, and the child repeats both. See how far you can go with this. If a word is very difficult, start with one letter, then add a second, then a third, and so on. Or do it by syllables and/or by vowel combinations, consonant blends, etc.
  • Use repetitive, rhythmic physical actions/activities while doing spelling practice. For example: spell the word while playing hopscotch, climbing stairs, jumping on a trampoline, bouncing a ball, skipping with a jump rope, playing catch with a friend.
  • When using the word in writing assignments or practical writing, don’t be afraid to whisper or speak the spelling aloud; use the sketch you developed; close your eyes and visualize, etc. These associations and actions will bring the word back to your memory.
  • Make up funny acronyms of words you need to remember. For example, for “because”: Bunnies Eat Carrots And Usually See Everything.
  • Use a puppet. Have the puppet repeat or act out the spelling of the word, use it in a sentence, etc.
  • Teach someone else how to spell the word in as many ways as possible. Teaching a newly learned fact or concept is one of the best ways to retain it.
  • On small cards or slips of paper, make a collection of individual letters, vowel combinations, consonant blends, etc. (Make at least 2 or 3 each of the frequently used ones). Spread them out on the table or floor. Instead of writing the words, find the correct letters/combinations and put them together side by side. Then have a helper remove one or two important letters (without the child looking) and say what letters were removed.
  • Create a “bingo” game, but use spelling words instead of numbers or letters.
  • Act out the word with gestures or role-playing.
  • Play charades and similar traditional parlour games (use your spelling list words) with family and friends. Personal interaction can add greatly to memorization.
  • Spell the word(s) with another person. Take turns adding letters until the word is complete.

Long-term memory strategies:

  •  “Store” new words in memory categories with words you already know how to spell, that have similar attributes.
  • Use rote drill. But do short daily practice sessions (10 minutes or so) for 6 days in a row, then take a day off. Then practice the same word list again a week later, then a month later, then 6 months later. This is much more effective than long sessions a couple times a week.
  • For rule-based learning (as in spelling), combine practice and discussion. Give examples of words which follow the rules, and similar words which break that same rule. The learner identifies which is the “broken rule word” and which is the “rule word” and then explains the rule.
  • Have the helper spell the word to the child (either written or spoken). The child decides whether the helper spelled the word correctly or incorrectly (the helper decides which way to go before spelling it, but doesn’t tell the child). If the helper spelled it incorrectly, the child tells what the helper did wrong (for example, what rule was broken, or what letter is missing or should have been used instead), and asks the helper to try again. Is the helper correct now?
  • Knowledge is often best consolidated right before sleep. Read, practice or review material for 5 to 10 minutes before dozing off–then immediately go to sleep. The brain will continue to “practice.” Do a little “test” the next morning.

More Memorization Tips–for Math Facts, Tests, and More:

For lots more great memorization ideas–for spelling and all kinds of other memorization needs–I have developed 3 booklets with “Memory and Learning Strategies.” One is a general overview, the second is specific tips and tricks (from which the above ideas are drawn) and the third is for use with classrooms or groups of learners. You can get them here for just $2 each!

There are also lots of other great spelling tips in this blog (for FREE, of course). You can find links to a list of them in the “Tips to Tutor Your Child at Home–Reading” section of the Home Education Tips page.

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Ways to Relax and Overcome Math Anxiety

What Can We Do About our Child’s Math Anxiety?

I often have parents sign up their children for math tutoring due to concerns over the child’s math anxiety–which of course has a negative effect on math learning. Today I’ll share some of the advice I’ve given in these situations to parents and children

Take a Break!

Really? Does that sound too easy? How is a child supposed to learn if you back off the pressure? Here are some thoughts:

  • If you are stuck on a math assignment, leave the math work, and go do something totally different. When you come back, you’ll often find that the difficult question is now reasonably easy. By leaving the work for a while, your brain will subconsciously keep working on the problem, but more important, by doing something totally different, you will relax and de-stress, and come back to the problem with a fresh outlook and much less anxiety.
  • When a child finds math difficult and becomes anxious, I would suggest doing only a few minutes at a time, then take a brain break (doing some short activity that is fun and relaxing, or some activity that you need to do anyway, that doesn’t take “brain work,” such as going for a walk around the block, doing some stretches or  exercises, tidying up, drawing a picture or coloring, having a snack, or taking a shower. Then come back to the work and repeat the procedure.
  • Try doing “math” for no more than 25 minutes at a time, then take a 5 to 10 minute break before returning to it. If still feeling stressed, shorten the time to 15 minutes math and a 5 minute break. Even though it may seem that the math homework time is being stretched out, you will actually be able to do the work more quickly and accurately while you are doing it, and you will feel much more relaxed and less stressed and will retain the information better.
  • If you have reached the point of feeling really stressed, take a longer break, such as 30 minutes or an hour, or even until the next morning (but don’t put it off much longer than that), and do something that really distracts your mind from the math. Then you can return for a fresh start. You may need to review the work you have already done, but that will only take a few minutes and your brain will quickly get into gear for the math again.
  • Sadly, one can’t usually get up and go do something else during an exam, but at least in the exam, you can still do the “easy” questions first, and they will often jog your mind for the tough questions. Even in an exam situation, you can close your eyes, stretch, rest your head on the desk for a couple minutes, draw a couple doodles, hum your favourite song in your mind, or whatever helps you relax. You might also ask the teacher to divide the test into sections and only give the child one section at a time, starting with the easiest. This will allow the child to get up and take a break before returning to do more since the child hasn’t yet seen the rest of the test and thus won’t have a chance to sneak off and get help or check the textbook.

Keep it Simple!

Some textbooks and/or curriculums and/or classroom teachers offer a variety of approaches to a particular concept. While this can be very helpful as it provides for different learning styles and background experience, and also allows children who are especially creative or independent learners to do lots of exploration, it can be frustrating for a child who is already anxious about math. My feeling is this: – try the simplest/standard method. – if the child is having difficulty with the simple method, try one or more of the other methods, find one that the child “gets” and do

My feeling is this: Try the method you think will be easiest for your child to handle–based on your knowledge of how your child learns best, in math of course but also in other subject areas. You may need to experiment a little. Try one method and watch carefully for how your child responds. If the child catches on quickly, great. If not, take a break to allow your child to relax, then try another method. Do this until you find one that the child “gets” and then do lots of practice with it.

Then, when the child understands and is comfortable with that approach, you can experiment with other approaches, especially if the child now finds the concept interesting or intriguing and wants to explore it. Note: It is wise to have your child at least learn the “standard” (most commonly used) method, as in the future, it will no doubt come up as a basic foundation for more advanced math, and will also come up in real life math.

Create Word Problems From the Start

It is also wise to introduce word problems right from the start. Even when introducing such basics as counting and simple math facts, think of them in terms of experiences in real life so that the concept makes clear, concrete sense to the child rather than being some difficult, hazy theory to which the child can’t relate. Furthermore, as math becomes more difficult, more and more word problems will be introduced, so by using them right from the start, the child will be comfortable with them. Even before the child can read, you can easily create word problems and discuss them with your child. Just relate them to your child’s own experience. For example: “If I gave you 3 cookies for dessert, and you ate two of them, how many would you have left for a snack later? … Hmm… How can we figure that out? Should we add or subtract? Why should we subtract? What method could we use? Finger counting? Use our ruler for a number line? Draw a picture? …”

If you are using written word problems, together circle or underline the key numbers/facts in the problem, Also circle or underline the “key words” in the problem, and discuss what kind of problem it is. For example, the phrase “in all” is a signal to add; “how many are left?” is a signal to subtract. If in doubt, draw little pictures to illustrate the problem–or even get some cookies and make it a real life situation–a very effective way to learn!

Encourage your child to create his own word problems, and guide you through them, too! Teaching something just learned is one of the most effective ways to ensure the learning will “stick” and it also shows you whether or not the child has really understood the process.

Also Create Equations From the Start

Once you’ve discussed a word problem, turn it into an equation. This approach can be much more effective than simply giving the child a list of equations to solve. When the child creates the equation (based on the word problem), his understanding and use of math will be much more effective. He also wanted to solve the problems “in his head” and was hesitant to say the equations before giving the answer. It is really important that he expresses the equation, as word problems start to become more complex in grade 3 math, and he needs to be able to work them out “step by step.” I went over a couple of things with him: – circle or underline the key numbers in the problem – also circle or underline the ”

Sometimes a child who is anxious will want to solve the problem “in her head” and be hesitant to say the equation before giving the answer. It is really important that she expresses the equation out loud, and also writes it down–even if she can’t read or write yet, she could write it as little sketches and you could introduce plus (+), minus (-) and equal (=) signs. Using as many senses as possible will really help the child learn. Also, as word problems start to become more complex in later math, she needs to be able to work them out “step by step” and starting right away, in the early stages, will make that easier and less stressful. If your child is already anxious and stressful, go back to the simplest arithmetic concepts and review them, using these methods, creating a new, strong foundation (it might also demonstrate some “gaps” in the child’s learning which you can resolve before moving on).

Math Fact Learning Suggestions

Some children can memorize and quickly write down the facts on a timed quiz, but when it comes to putting them into practical use in an equation or word problem, they find it difficult to remember the facts, as they are now working through a multiple-step process, which is more complicated. Other children have great difficulty just memorizing the facts, not to mention actually using them in practical ways.

It is important for children to practice basic math facts and concepts in equations and word problems rather than just in timed quizzes or flashcards. In fact, time quizzes can be very stressful for many children. I personally think timed quizzes should be reserved for children who enjoy them and who find memorization and repetition easy.

For other children, there are a variety of ways to help them learn the basics without so much stress. Some examples:

  • use of different sense methods such as “finger writing” on a textured surface;
  • close eyes and “picturing” the facts or spelling in the mind;
  • say the entire fact aloud (not just the answer);
  • listen to mom or someone else say the full fact aloud;
  • draw little sketches to go with facts being struggled with;
  • create entertaining/funny stories that involve the fact

Oh! One more thing. If you want to practice “number facts” in some of the ways I’ve suggested, it works much better to just do 10 minutes or so daily, rather than 30 minutes twice a week or 60 minutes once a week. Frequent, short practice sections move short term memory into long-term more efficiently. For lots more ideas on how to learn math facts (and concepts, too), check out my Easy to Learn math booklets.

And Don’t Forget Real-Life Math! It’s so Important!

It is very helpful indeed to watch for opportunities in “real life” situations, to do addition and subtraction (and then more advanced math, of course). For example:

  • when you are taking a road trip, get a map that shows distances between towns and add up the distance from one town to another.
  • if you are baking an apple pie and doubling the recipe, and it calls for 8 apples, ask what 8+8 (or 2×8) is, then ask your child to count out that many from the apple box.
  • if you are having a plate of cookies for supper, and there are 8 cookies to start with, just casually ask how many will be left after everyone in the family has had one–and if there will be enough for everyone to have a second cookie.

These kinds of “real life” experiences come up all the time; just keep an eye out for them, and use them in a casual way. Include the whole family in these math activities. Make them like a game. Older family members will enjoy it, and younger siblings will also love these games and they will get started on math without any formal teaching!

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