October 29th, 2009

Recently, someone was sharing how their child was beginning to struggle with more advanced elementary math. There were problems with keeping the numbers organized and keeping track of the math and the standard ‘use graph paper’ advice was given.

While graph paper may be all that’s needed, in reality, things that are easy for kids aren’t hard to keep track of. Most of the time we take messy math as a sign that kids need help being neater, whereas I would argue that messy math doesn’t matter if kids know what they are doing. By all means, break out the graph paper, but don’t expect it to be a cure all.

Here are some ways, besides graph paper, you can help your child when they hit the wall in math.

1. Avoid frustration. People stop learning when they are frustrated so back off whenever you sense your child is at their limit. This is the most important rule when it comes to helping kids with math.

2.Explain what the real problem is. Many kids begin to self identify as stupid or dumb or not good at math when they ‘hit the wall’. In reality the issue is a lack of study skills and a need to expand their knowledge base. Be sure your child understands this and explain this is probably not the first time they will experience this.

3. Praise hard work and effort instead of results. This encourages kids to keep trying and de-emphasizes getting the right answer which reduces pressure and frustration (see #1).

4. Go back to when your child was successful. Work on math they’ve mastered and carefully observe how their thought process works. Since math so often builds on what came before, there may be some hints as to what went wrong in an earlier skill.  Also, this gets kids back into their comfort zone and back to being successful.

5.Break new skills into smaller pieces or micro steps and do fewer problems, but  do them slowly and frequently. Kids don’t need to do 25 problems to master a math skill, but they do need to see exactly what the steps are and need time to digest the process. Especially for something new that is challenging.

6.Work on math sense/number sense. Beef up math sense by going beyond the usual math facts. For example, most flashcards or math facts drills focus on single digits from 0-10–12 if the flashcard deck is really ambitious. Two digits and up, we often expect kids to just perform the steps of the operation as opposed to showing them (or letting them discover for themselves) the patterns for bigger numbers. So most kids get pretty good at simple math facts, but throw out 188-31 and they really have to stop and think.  Go beyond the usual math facts and drill on double digits and even triple digits with various operations. This builds number sense for bigger numbers and reinforces understanding of place value.

Usually messy handwriting is a problem when kids have weak number sense and/or a poor sense of process. Kids with a strong grasp of fundamentals compensate for sloppy handwriting with their mental math skills and strong number sense.

7. Ask your child to predict the answer to a problem before they solve it.  Their prediction may be (and really should be) a ballpark estimate, which is fine because what we want is a barometer for accuracy. Take 4500-1500 and ask questions like ‘do you think the answer will be less than 2000?’ and ‘what would you estimate the answer to be, just by looking?’ This kind of dialogue will tell you a lot about a child’s math sense or lack thereof. Further, it gets them using their math sense as a compass pointing toward the right answer. Eventually, they will almost instinctively know when an answer seems off.

And if their prediction is waaaaay off, be sure to dissect their thinking and show them where they took a wrong turn.

8.In the same vein as #7, be sure kids have strategies for checking their work and build that into any math work you do with them. Many times, kids aren’t asked to verify their work until later in their academic career and they often resist it because it’s a new step and outside their comfort zone. I have yet to meet a teenager who is thrilled about having to check their work. Most kids actively resist this step because it’s taught later, after the bulk of their math operation skills are learned. Get kids into the habit of checking their work and proving their answers early on to develop good habits for more challenging math.

9.Develop mental math skills to grow the areas of the brain that work on math. Challenge kids to do math in their heads. Ask them to count backwards from 100 by 2s, 3s, 7s etc… Also make a game out of how many numbers they can remember in a row–this will directly increase mental math capacity. Play FBI agent too by setting up a ‘crime scene’ or simply dumping out your purse and seeing how many objects they can remember after only 20-30 seconds. This is a fun exercise and is based on actual skills used in law enforcement (which might ignite their imaginations too!).

10.Engage in activities that stretch complex thinking and problem solving skills. Some examples include the Rush Hour game which I’ve mentioned before (everyone loves that game!). Books such as You’re the Detective are good as well.  Anything that involves a knot of a problem to unravel and requires multi-step strategic thinking. Plus, since it’s not directly math related, kids won’t associate this activity with math, but it builds important logic and pattern recognition skills.

Notice that none of these tips require doing worksheets (or using graph paper!)  and that many of them address underlying more oblique skills. Sometimes the deficits we think are so obvious are really a weakness hidden somewhere else (e.g. logic or pattern recognition). A comprehensive approach, such as in the tips above, will cover all the bases.

Tags: critical thinking, helping kids with math, logic, math sense, math skills, mental math, number sense, problem solving
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September 15th, 2009

As I’ve mentioned, fractions are confusing and are often the first conceptually abstract math kids experience. Kids don’t even need to have learning differences to struggle with fractions, they are confusing all on their own. To complicate things, schools and teachers often do a haphazard job of teaching fractions as well.

In my tutoring, I’ve seen textbooks completely ignore essential fraction concepts. The book will teach fractions step-by-step right up to that critical point and then gloss over major concepts like equivalents, reducing and borrowing in subtraction (which for fractions is different than ‘normal’ subtraction’).  In addition, having corresponded with several math teachers, there are teachers who are coasting and phoning it in due to burnout or other issues. I once asked a math teacher to explain the math theory for cross canceling in fractions* only to be met with silence followed by a grudging “I’ll have to look that up.”  It’s no wonder kids are confused!

So what can you do to help? Buy a set of these fraction cards. They are only $7.99 and you will get lots of use out of them.

When I first introduce these cards to my students, I have them sort and find all the equivalents to familiarize themselves with the deck and to help them relate a picture to the numerical fraction. This is great for visual learners and will really help them ’see’ fraction relationships.

Depending on how they’ve sorted the deck, I then go through and point on that 2/6 is the same as 1/3 using the pictures so that they realize there’s more than one equivalent for each fraction.

Then we play Fraction War which requires the student to determine which fraction is larger. Fraction War helps solidify fraction relationships in their mind. From there, we graduate to fraction rummy. Rummy in of itself is not a terribly exciting game for me, but the fraction cards really make me (and my students) think.

For advanced students (i.e. those that consistently beat me in Fraction Rummy), I split the deck into 2 piles and we draw a card from each to create a random addition, subtraction, multiplication or division problem–whichever operation we decide to work on. Sometimes we end up with an unsolvable problem, which throws students and really works their critical thinking skills.

That’s several fraction games for kids for less than $10. Plus,the fact that it’s a game eliminates tension and worksheet angst.

*By the way, I’m still looking for an answer to that question so…if you happen to know, please leave a comment!

Tags: fraction games for kids, fun fraction games, learning fractions, math homework help, teach fractions
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September 11th, 2009

If you think maybe your child is struggling with math, but aren’t sure, here are some guidelines on identifying math learning disabilities.

Signs of Math Learning Disability By Age (adapted from the book The Mislabeled Child):

-Children are unable to (or late) count 4 objects by the age of four and understand the quantity of four.

-Children are unable to count 15 objects and understand the quantity of 15 by the age of 5.

-Children still struggle to read and write three digit numbers at the age of 8.

-Children can’t do simple multiplication and division by the age of 9.

-Children can’t perform basic math operations (multiplication, division, add, subtract) by the age of 12.

Non Age Specific Signs of Math Learning Disabilities (if any one of these is present, your child likely has a learning difference):

-Poor handwriting that contributes to errors. For example, a 3 is written to where it looks like a 5 which skews the entire math problem.

-Inability to tell when number is bigger than another along with reversals while reading numbers. E.g. 15 instead of 51. Or seeing 6 instead of 9. Or can’t tell the difference between the greater than or less than signs. Or often mixes up the + and x operators. Or can’t spot errors in their work. Basically, numbers are just one big blind spot.

-Poor memory. We call it ‘teflon head’ at our house. Information just bounces off, whether it’s remembering to put dirty dishes in the sink or how to divide fractions, the result is the same; a stubborn inability to accept and retain new information no matter how often it is repeated or explained or screamed at the top of mom’s lungs. Kids with learning disabilities don’t know their times tables and often can’t remember that 4+3 =7, they have to count it out every time, like they’ve never seen it before in their lives.

-Creative workarounds that are inefficient and often incorrect. Some kids will take 8 x8 and just go 8+8+8+8+8+8+8+8+8+8 and still get the wrong answer because their brains can’t keep track of so many numbers. If you check what I wrote, you’ll see 9 eights instead of 8–this kind of error is common.

However, I like to take the presence of creative workarounds as a positive sign because it means the child is still trying–kids who have given up don’t bother and are harder to help. Also, it demonstrates rudimentary critical thinking and problem solving skills. So I’m always happy to see convoluted pretzel math. Ideally, though, we want to get these kids up-to-speed on their math facts and well grounded in the basics of math theory.

-Inability to organize math operations and sequence steps correctly.  These are the kids who take 2/3 x 3/4 and try to divide.  They can’t orient themselves to the problem solving sequence and don’t know the first step from the middle step from the last step. Math is a maze and they are lost in the middle with the Failure Monster ready to eat them alive.

As a child, I exhibited all of these traits and it wasn’t until I became an adult that I mastered basic math. So there is hope! All is not lost!

If your child fits one or more of the descriptions above, please contact their teacher as soon as possible to request a learning disability assessment and tutoring. Do not wait because the longer you wait, the worse the math disconnect gets. While you’re wading your way through the school bureaucracy, invest in some math games and fun activities for use at home. See the links in the side bar for some math resources suggestions.

Tags: learning disability in math, math learning disabilities, math learning disablity, math resources
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September 2nd, 2009

One of the more interesting dichotomies that strikes me about our culture is how biased educational activities are toward reading. For example, we have a ‘My Baby Can Read’ program that teaches young toddlers to read, but there is no similar product claiming to produce the next Einstein. In our culture, the path to genius is paved with letters, numbers need not apply.

This is wrong. Very wrong. It means that math literacy is left to the fates and a child’s own innate ability. And then everyone wonders why Johnny can’t do Algebra and why Jane doesn’t know a hypotenuse from a Manolo Blahnik. Like reading and language, acquisition of math literacy starts in infancy. It begins with pattern recognition. First knowing the routines of the day and week, then being able to put together puzzles or predict which color bead should come next on that necklace you’ll be receiving for Mother’s Day. Then counting followed by skip counting (which is often neglected until elementary school).

Most parents don’t spend any time on pattern recognition and counting*, which  undermines their child’s future math literacy.  However, you’d better believe they are reading a bed time story and singing the ABC song until they think their heads will explode. Reading is the Holy Grail of education. It gets almost all the attention and emphasis.

I see this all the time in the families I work with. They either ignore reading and math altogether, or only focus on reading–it’s patently obvious.  The times I give my students math tricks specifically to demonstrate over dinner, it never happens. Math is almost as bad a word as Voldemort in the Harry Potter books.  How many people know who Voldemort is versus how many can properly add fractions?  The fractions don’t even stand a chance.

So my proposal is this; Make math a family activity. Something that is discussed over dinner. Do story problems together. Play games. Learn about the history of mathematics together.Challenge your kids to make up their own math games and then play them.** Balance the checkbook. Whatever, just don’t ignore the numbers.

Here are a few resources for math games and activities:

25 Super Cool Math Boardgames is an inexpensive book I use often with my students. It contains versatile games covering basic math concepts including fractions and decimals.

40 Fabulous Math Mysteries for Kids is another inexpensive book that would be an ideal post-dinner activity for the whole family.

Fraction Cards are great for reinforcing basic fraction concepts over a friendly game of fraction rummy. It’s not as simple as it looks and my students can always be suckered into learning with a game.

Contig is available online and is a logic game that involves basic math operations. This is an easy way to reinforce basic math such as multiplication facts.

*In our culture, we, typically, make sure our kids can count and then don’t bother with it again.

**Although I will warn you that kids very often concoct much more intricate and difficult math problems than adults would choose. Also making up games not only keeps kids busy, it also works logic skills which are vital to math literacy.

Tags: math games, math is for families, math literacy, pattern recognition, preschool math, reading bias
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August 27th, 2009

Here are links to some articles on another site that I wrote before I started this webpage.

How to Develop Math Literacy in Preschool Kids is full of ideas for parents of toddlers. Math literacy starts at birth and should be nurtured with the same attention to detail given to reading. At this age, math should be play based which makes it guaranteed fun for parents and kids alike.

How to Help Kids Understand Fractions is full of ideas on ways to teach fractions. Fractions are a huge problem area in math. Kids consistently struggle with fractions. I call fractions ‘tricksy’ because one addition problem may also use multiplication and division.  I think fractions are one of the first times kids are faced with multi-operation problems and figuring out when to do what becomes overwhelming.

How to Get Kids’ Minds Ready to Go Back to School You’ve got the clothes and the new backpack stuffed with school supplies, but is your child ready for school? This article helps kids strengthen their mental muscles and ensures they start the school year off with a bang.

How to Help Learning Disabled Kids With Math. It’s critical that parents, tutors, and teachers understand learning disabilities. You can show a learning disabled kid what to do a million times, but if the lesson isn’t in a format they can absorb, you’re better off trying to learn how to catch bullets with your teeth–it would be easier and a more productive use of your time.

Learning disabled kids are wired differently and those differences need to be accommodated in order for them to learn. The most important part of this article is: “Every time you push a learning disabled kid to the point of frustration, you completely alienate them from the learning process. Helping learning disabled kids with math is not just about the math, it’s about their emotions and psychological scripts too.”

Tags: back to school, fractions, learning disabled kids and math, math literacy, tutors
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July 30th, 2009

I’m a math tutor working with learning disabled kids struggling with math literacy.  I started this blog because I’ve had a rough time finding good online resources to supplement the workbooks we use.

As for finding a math tutor, why not start with yourself? Good tutors are hard to find and they are expensive, so why not try helping your child yourself first?

You won’t be alone, this blog will feature ideas and worksheets to help you cover basic math topics thoroughly and, more importantly, in an enjoyable way.

Tags: find a math tutor, math for learning disabled kids
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