## FAQ: Playful Math for Older Students

My students are so busy that time-consuming math projects are a luxury. How is it possible for older kids to play with mathematics?

Too often, the modern American school math curriculum is a relentless treadmill driving students toward calculus. (Does this happen in other countries, too?)

But that’s definitely not the only way to learn. For most students, it’s not the best way, either.

Here are a few ideas to get your older children playing with math…

## FAQ: I’ve Ruined My Daughter

My daughter is only eleven, but I’m afraid I’ve ruined her chance of getting into college because she is so far behind in math. We’ve tried tutors, but she still has trouble, and standardized testing puts her three years below grade level. She was a late reader, too, so maybe school just isn’t her thing. What else can I do?

Standardized tests are not placement tests. They cannot tell you at what level your daughter should be studying. They aren’t designed that way. The “placement” they give is vague and general, not indicative of her grade level but rather a way of comparing her performance on that particular test with the performance of other students.

There can be many different reasons for a low score. I’ve listed a few of them in my post In Honor of the Standardized Testing Season.

## FAQ: Struggling with Arithmetic

My son can’t stand long division or fractions. We had a lesson on geometry, and he enjoyed that — especially the 3-D shapes. If we can just get past the basics, then we’ll have time for the things he finds interesting. But one workbook page takes so long, and I’m sick of the drama. Should we keep pushing through?

Those upper-elementary arithmetic topics are important. Foundational concepts. Your son needs to master them.

Eventually.

But the daily slog through page after page of workbook arithmetic can wear anyone down.

Many children find it easier to focus on math when it’s built into a game.

Take a look at Colleen King’s Math Playground website. Or try one of the ideas on John Golden’s Math Hombre Games blog page.

Or sometimes a story helps, like my Cookie Factory Guide to Long Division.

### Math Textbook Tips

Games are great for practicing math your child has already learned. But for introducing new concepts, you’ll probably want to follow your textbook.

Still, even with textbook math, there are ways to make the journey less tedious:

• Most children do not need to do every problem on a workbook page, or every page in a section. There is a lot of extra review built into any math program.

• You don’t have to finish a section before you work whatever comes after it. Use sticky bookmarks to keep track of your position in two or three chapters at a time. Do a little bit of the mundane arithmetic practice, and then balance that with some of the more interesting topics your son enjoys.

• As much as possible, do math out loud with a whiteboard for scratch work. Somehow, working with colorful markers makes arithmetic more bearable.

• Set a timer for math, and make the time short enough that he feels the end is in sight. I suggest no more than thirty minutes a day for now. And whenever the timer rings, stop immediately — even if you are in the middle of a problem.

### The Timer Can Be a Life-Saver

Doing math in short sessions helped us avoid the emotional melt-downs my daughter used to have.

Thinking is hard work, and if I asked for too much, she would crash.

Because I sat with her and worked together every problem, I knew what she understood and when we could skip a problem. Or sometimes even jump several pages. Which meant that, even with short lessons, we still got through our book on time.

### Arithmetic Is Like Vegetables

But as I said before, textbooks include a whole lot of repetition.

Too much repetition deadens the brain.

So we also took long breaks from our textbook program. Entire school-year-long breaks, just playing with math. Letting “enrichment” activities be our whole curriculum.

As healthy as vegetables are, you would never limit your son to eating just lima beans and corn.

Similarly, be sure to feed him a varied math diet.

For example, you can follow his interest in geometry beyond the standard school topics.

Explore tessellations, Escher art, and impossible shapes such as the Penrose triangle.

Building Lego scenes is a practical application of 3-D geometry. He might even want to try stop motion animation.

Talk about how math works in real life. Ponder the choices on John Stevens’s “Would You Rather?” blog or try some of the challenges at Andrew Stadel’s Estimation 180 website. Many of these require three-dimensional reasoning.

This post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.

CREDITS: Frustrated Child photo by by Pixabay on Pexels.com. Penrose Lego by Erik Johansson via Flickr (CC BY 2.0). Homework Hands photo by Tamarcus Brown on Unsplash.

## FAQ: Forgetting What They Learned

“As we go through each lesson, it seems like my daughter has a good handle on the concepts, but when we get to the test she forgets everything. When I ask her about it, she shrugs and says, ‘I don’t know.’ What do you do when your child completely loses what she has learned?”

Forgetting is the human brain’s natural defense mechanism. It keeps us from being overwhelmed by the abundance of sensory data that bombards us each moment of every day.

Our children’s minds will never work like a computer that can store a program and recall it flawlessly months later.

Sometimes, for my children, a gentle reminder is enough to drag the forgotten concept back out of the dust-bunnies of memory.

Other times, I find that they answer “I don’t know” out of habit, because it’s easier than thinking about the question. And because they’d prefer to be doing something else.

And still other times, I find out they didn’t understand the topic as well as I thought they did when we went through it before.

No matter how we adults try to explain the concepts, some kids want to be answer-getters. They don’t want to do the hard work of thinking a concept through until it makes a connection in their minds. They want to memorize a few steps and crank through the lesson to get it over with.

In all these cases, what helps me the most is conversation.

My children and I always talk about our math. I ask questions like “What do you think? What do you remember? Can you explain the question to me? What are they asking for?”

And, whether the child’s answer is right or wrong, I practice my poker face. Trying not to give anything away, I ask, “How did you figure it out? Can you think of a way to confirm your answer?”

### Talking Math with Your Kids

Not sure how to talk about math with your children?

If you have preschool and elementary-age kids, read Christopher Danielson’s inspiring book and blog:

For middle school and older students, check out Fawn Nguyen’s wonderful collection of Math Talks. Be sure to read the “Teachers” page for tips and talking points:

“You don’t need special skills to do this. If you can read with your kids, then you can talk math with them. You can support and encourage their developing mathematical minds.”

— Christopher Danielson
Talking Math with Your Kids

### Playful Ways to Learn or Review Math

Games are a great way to practice math. Check out these (free!) math games for all ages:

And if you have elementary-age children, here are a few grade-level tips to help them learn (and remember) math concepts:

CREDITS: Girl in field photo by SOURCE Hydration Systems and Sandals technology via Flickr. (CC BY 2.0) Nigerian classroom photo by Doug Linstedt and young girl studying by pan xiaozhen on Unsplash.

This post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.

## FAQ: Homeschool Burnout

“Spring cleaning has made my desk look worse than before. Nobody feels like studying. The kids would rather be outside, and their mom would rather take a nap. If I line everyone up on the curb in the morning, do you think the yellow bus will take them?”

Homeschool burnout — it’s a perennial problem. If you’re suffering from lethargy and can’t face another day of school work, here are some ideas that kept me going long enough to graduate almost-five kids (my “baby” finishes homeschooling this spring!):

(1) Re-read the homeschooling books on your shelves, or get some new ones from the library. Write down your favorite quotes as you read. Try to read about one a month, to help get your enthusiasm back. And then read at least one new homeschooling book per year to help you stay inspired.

(2) Connect with other homeschoolers. Meet with friends for tea, or have a Mom’s Night Out while Dad babysits. Talk about substantive things, like educational philosophy — what you like about homeschooling, and what you’d like to change. Share your dreams for your children. Remind each other why you’re doing this.

(3) Attend support group meetings. I find that after so many years, I let the meetings slide. I think, I already know everything they are going to say. But being with other homeschoolers is encouraging. And if you find out that you can help a new homeschooler with advice, that gives you a boost, too.

(4) Find one or two forums where you can become one of the resident experts, and answer posts as often as you can. As with number 3 above, being able to give advice (and being appreciated for it) can give you the energy to keep on going.

(5) Go to a homeschooling convention, if you get the chance. The speakers are stimulating, and you may find some new book or tool that sparks your imagination.

(6) Do school anyway. It may seem impossible when you’re stuck in the doldrums, but once you get going, you may find it easier. The light of understanding in a child’s eyes can give Mom quite a lift!

(7) Try something completely different. If you have always used a textbook program, then set it aside for a month and just read library books. If you have read lots of great literature, then try some hands-on projects, or get out those science experiments you keep putting off, or visit all the museums within a two-hour radius, or… I’m sure you can think of something that has been lingering on your good-intentions list. I never could stand to teach the same old thing every year, and none of my five kids got exactly the same education. Happily, there is always another way to approach any homeschooling topic. How about Gameschooling?

(8) Figure out what your students are able to do on their own, and let them do it. Encourage them to develop as much independence as possible.

(9) Use some of your children’s independent time to learn something new for yourself. Have you always wanted to try painting, or crochet, or woodworking? Be an example of life-long learning.

(10) Start (or join in progress) a group class or co-op. You may be able to trade around with some other families: you teach history and others teach math or cooking, or whatever arrangement fits for you. This is especially helpful for those time-consuming projects that always seem to get put off, like art or science experiments.

(11) Try some of these intensely practical Tips For Coping With Homeschool Burnout.

(12) And are you a Christian homeschooler? Then pray! Your Father knows what you need, and Immanuel is with you always. Try praying your way through 1 Corinthians 13 (or this homeschooling version).

If you have any other ideas for beating the burnout blues, please share!

Homeschooling is not always peaches and cream. If anyone promised you that, they lied. But be assured that it homeschool burnout is not a terminal condition. You will recover your joy in sharing your children’s education.

I learned one thing from every story I’ve ever read: adventures never run smoothly.

And what greater adventure could there be than to introduce your child to all the wonderful things in God’s world?

CREDITS: “Scream” photo (top) by greg westfall via Flickr (CC BY 2.0).

## FAQ: Trouble Finding the Right Math Program

“I can’t find a home school math program my son likes. We’ve tried Singapore Math, Right Start, Saxon, and Math Mammoth. We subscribed to a month of IXL Math to keep him in practice, but he hates that, too. I know I shouldn’t have changed so many times, but this was our first year of homeschooling, and I was trying to please him. But I’m running out of things to try. Do you think Life of Fred might work?”

You’ve tried all those math programs in one year? Many people recommend that new homeschoolers take a few months off to “detox” from the classroom setting, to relax and enjoy the freedom of making their own choices. But your son might want a few months to detox from his homeschool experience.

I suggest you set aside all those books and focus on games and informal math. Try to avoid schoolish lessons until your son starts to enjoy learning for its own sake. The Internet offers an abundance of creative math ideas.

• For example, download the Wuzzit Trouble or DragonBox apps to play with, but don’t make it a homework assignment.
• Or let him choose one of the activities at Gordon Hamilton’s Math Pickle website and explore it for a day or a week or as long as it remains interesting.
• Browse through the Primary Level 1 or Level 2 puzzles and games at the Nrich Mathematics website for more ideas.

Look for more playful math on my blog’s resource pages:

### Explore Big Concepts: Infinity

Math that captures a child’s imagination can make the more tedious work seem bearable. For instance, in the 1920s, mathematician David Hilbert created a story about an imaginary grand hotel with an infinite number of rooms.

### Explore Big Concepts: Fractals

Take a mental trip to infinity by playing with fractals. Cynthia Lanius’s online Fractals Unit for Elementary and Middle School Students offers a child-friendly starting point.

Fractals are self-similar, which means that subsections of the object look like smaller versions of the whole thing.

Most children enjoy exploring the concept of infinity with hands-on fractal patterns, such as this Sierpinski triangle made of tortilla chips. Talk about what you notice and wonder: How does the triangle grow? How many chips will we need for the next stage?

### The Daily Four

If you worry that your son needs to keep practicing traditional arithmetic during his break, try making him a series of Daily Four pages:

• Fold a sheet of plain paper in half both ways, making four quarter sections.
• Write one math problem in each part. Choose them from any of your math books.
• Make sure each problem is different — one addition, one fractions, one multiplication, or whatever — and that none of them are hard enough to cause frustration.
• Don’t worry about an answer sheet. Show him how to use a calculator to check his work.

You can make up a whole week’s worth of these problem sheets at once, with a balanced mix of problems for each day. Your son won’t feel overwhelmed, but you’ll know he’s reviewing his number skills.

Or download some of the Corbettmaths 5-a-Day practice sheets for him. Some problems may seem too easy while others require concepts he hasn’t studied yet. Easy review won’t hurt anything, but do let him skip the problems that feel too hard.

CREDITS: “Rock Surfer Boy” by Ken Bosma and “Boy” by Isengardt via Flickr. (CC BY 2.0) Hotel Infinity video by Tova Brown.

This post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.

## FAQ: He Won’t Stop Finger-Counting

“My oldest son has somehow developed the horrid habit of counting on his fingers. We worked on the math facts all summer. He knows the answers in simple form, such as 9 + 4, but if it’s in a bigger problem like 249 + 54, he counts up to add or counts down to subtract, all using fingers. My younger children have no problem with mental math, but he can’t seem to get it. Are there any tips or tricks to stop this?”

Counting on fingers is not a horrid habit, it is a crutch. Please think for a moment about the purpose of crutches. The blasted things are an uncomfortable nuisance, but there are times when you can’t get anywhere without them. And if you need them, it does you no good for a friend to insist you should crawl along on your own.

That is how your son feels right now about his fingers. He is struggling with something his younger siblings find easy, and he can tell that you are frustrated. His confidence is broken, in a cast, and needs time for healing. So he falls back on what he knows he can do, counting up the answer.

Think positive: this means he still believes that math ought to make sense — that to understand what he is doing is more important than to guess at an answer. You want him to value sense-making, because otherwise he will try to memorize his way through middle school and high school math. That is the road to disaster.

“Schools spend a lot of time working with young children to get these facts memorized, but many children aren’t ready for that task yet. They’ll count on their fingers, and may be reprimanded for it.
“What happens when a person becomes embarrassed about counting on their fingers? If they still want to think, they’ll hide it. That’s the better option. The worse option that way too many students choose? They start guessing. When math becomes too incomprehensible, or not living up to someone else’s expectations becomes too painful, many students give up on math, and then they just guess.
“We count on our fingers as part of a thinking process. Perhaps the thing I want to figure can be memorized. But if I haven’t memorized it yet myself, the most efficient way to figure it will likely involve fingers.

—Sue VanHattum
Philosophy

### The Problem of Transfer

What you describe is called the problem of transfer, and it is one of the huge, unsolved problems of education.

We can train someone to do a simple, limited task such as answering flash cards. But how do we get that knowledge to sink in, to become part of the mind, so they can use it in all sorts of different situations?

No one has figured that out.

There is no easy solution. It requires patience, and providing a variety of experiences, and patience, and pointing out connections, and asking the student to think of connections, and lots more patience.

### Some Things to Try

It might help to do fewer math problems in a day, so you can take time to work more deeply on each one. Talk together about the different ways you might solve it. Make it a challenge: “Can we think of three different ways to do it?”

In math, there is never just one way to get a solution. Thinking about alternatives will help your son develop that transfer of skills.

Or pick up some workbooks that target mental math methods. The Mental Math workbook series by Jack Hope and Barbara and Robert Reys will help him master the techniques your younger kids learned without effort. It may still take him longer to do a calculation than what you are used to with the other children, but these books will give him a boost in recognizing the types of mental tools he can use.

Here are a few of my previous blog posts that include mental math tips:

Or perhaps encourage him to keep using his fingers, but to switch to a more efficient system, such as Chisenbop. According to math education expert Jo Boaler, research shows that finger-counting supports mathematical understanding.

### Mental Math: A Battle Worth Fighting

Jumping into mental math is hard for an older child who wasn’t taught that way. I believe it’s a battle worth fighting, because those mental math techniques build understanding of the fundamental properties of numbers.

But the main goal is for him to recognize his options and build flexibility, not to do each calculation as fast as possible.

And be sure he no longer needs those crutches before you try to take them away.

CREDITS: “Stryde Walking To School on his New Crutches” by Jim Larrison and “Silhouette of a boy” by TimOve via Flickr. (CC BY 2.0)

This post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.

## FAQ: Trouble with Worksheets

“Worksheet problems make my daughter’s brain freeze. Even simple things such as “2 + ___ = 2″ confuse her. What can I do?”

Can your daughter do math if you put away the worksheet and ask her a real-life problem: “I have a lunch sack. I put two cookies into the sack, and then I give it to you. When you look into the sack, you see two cookies there. Can you tell me what was in the sack at the beginning, before I put my cookies in?”

Or can she solve problems when the answer isn’t zero? Could she figure out how many you started with if she saw four cookies when she looked in the sack?

The idea of having a number for “nothing” can seem strange to young children.

### Worksheet Calculations Are Not Math

Can your daughter think mathematically, without calculations?

The symbols on the worksheet are not math. They are just one way of recording how we think about number relationships, and not a very natural way for children. Mathematics is a way of thinking — paying attention to the relationship between ideas and reasoning out connections between them. Encourage your daughter to notice these relationships and wonder about them.

Try watching Christopher Danielson’s video “One is one … or is it?” together, and then see how many different examples of “one” she can find around the house.

### The Power of Story

Many kids at this age have a hard time with abstract number math — then their brains will grow up, and they’ll be able to do it. Development varies from one child to another.

When I do worksheets with young children, I turn each equation into a little story. Like the “cookies in a lunch sack” story above.

Sometimes we use blocks or other manipulatives to count on, but often the mental picture of a story is enough. Having something solid to imagine helps the child reason out the relationships between the numbers and symbols.

CREDITS: Carl Vilhelm Holsøe ‘Interior with a mother reading aloud to her daughter’ 19th Century. Image from Plum Leaves via Flickr. (CC BY 2.0)

This post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.

## FAQ: Lifelong Learning for Parents

“I’m so tired of being ignorant about math. I can memorize rules and do calculations, but if I miss a step the numbers make no sense at all, and I can’t spot what went wrong. Another struggle I have is keeping everything organized in my mind. When I learn a new concept or strategy, I easily forget it. My son is only a toddler now, but as he grows up, I don’t want to burden him with my own failures. Where should I start?”

As a first step, convince yourself that math is interesting enough to learn on its own merits, because parental guilt will only carry you so far. Start with Steven Strogatz’s “Elements of Math” series from The New York Times, or pick up his book The Joy of x.

As a next step, reassure yourself that elementary math is hard to understand, so it’s not strange that you get confused or don’t know how to explain a topic. Get Liping Ma’s Knowing and Teaching Elementary Mathematics from the library or order a used copy of the first edition. Ma examines what it means to understand math and to clearly explain it to others.

Don’t rush through the book as if it were a novel. There are four open-ended questions, each at the beginning of a chapter, after which several possible answers are analyzed. When you read one of these questions, close the book. Think about how you would answer it yourself. Write out a few notes, explaining your thoughts as clearly as you can. Only then, after you have decided what you would have said, read the rest of that section.

Don’t worry if you can’t understand everything in the book. Come back to it again in a couple of years. You’ll be surprised how much more you learn.

### Books for Parents and Teachers

To build up your own understanding of elementary arithmetic, the Kitchen Table Math series by Chris Wright offers explanations and activities you can try with your children.

If you want more detailed guidance in understanding and explaining each stage of elementary mathematics, you can pick up a textbook designed for teachers in training. I like the Parker & Baldridge Elementary Mathematics for Teachers books and the Teaching Student-Centered Mathematics: Developmentally Appropriate Instruction series. The two series are completely different, but they complement each other well. Check out the sample chapters from the publishers’ websites to see which one you prefer.

Discover more great books on my Living Math Books for Parents and Other Teachers page.

### Focus on Relationships

As you learn, focus on how the math concepts relate to each other. Then the more you learn, the easier you will find it to connect things in your mind and to grasp new ideas.

You might want to keep a math journal about the things you are learning. When you write something down, that helps you remember it, even if you never look back at the journal. But if your mind goes blank and you think, “I know I studied that,” the journal gives you a quick way to review. Make it even easier to flip back through by writing the topic you are studying in the top margin of each page.

When you run into a new vocabulary word, draw a Frayer Model Chart and fill in all the sections. The Frayer Model provides a way to organize information about a new vocabulary word or math concept.

And if you read something that’s particularly helpful, you may want to turn to the back page of your journal and start a quick-reference section.

### Always Ask Why!

Find a fellow-learner to encourage you on your journey. Bouncing ideas off a friend is a great way to learn. You might want to join the parents and teachers who are learning math together at the Living Math Forum.

And here is the most important piece of advice I can offer. Your slogan must be the one used by the Chinese teachers Liping Ma interviewed: “Know how, and also know why.”

Always ask why the rules you learn in math work. Don’t stop asking until you find someone who can explain it in a way that makes sense to you. When you struggle with a concept and conquer it, it will make you free. You don’t have to be afraid of it anymore.

Know how, and also know why.

This post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.

## Let’s Play Math FAQs: Introduction

I’ll let you in on a secret about teaching: there is no place in the world where it rolls along smoothly without problems. Only in articles and books can that happen.

—Dr. Ruth Beechick
You Can Teach Your Child Successfully

Learning math is an adventure into the unknown. The ideas we adults take for granted are a wild, unexplored country to our children. Like any traveler in a strange land, they will stumble over rocky places and meet with unexpected detours.

Whenever I visit a parenting forum, I feel compassion for the families who are struggling with math. No other school subject elicits such depths of frustration and despair:

• I’ve explained until I’m hoarse, and she still doesn’t get it. Help!! I want to pull my hair out.
• My child is not a mathy person at all. Now he’s convinced that he’s “dumb.”
• She says she can’t do it. She says she hates math. She says she can’t think. She hits her head and pounds her fists in frustration. I am so tired of fighting over math Every. Single. Day.
• The problem is not him … It’s me. I am a failure at math.
• I am sooooo struggling to teach my daughter math. Please, does anybody else deal with this? I will try anything!

### Yes, There IS Hope!

Solving the problems of math education is not easy. Situations have built up over years, so they will take time to resolve.

But children are resilient, so improvement may not take as long as you fear.

No matter how much your family has struggled, there is hope. If children can get over the “I’m no good at math” mental block, they can learn all of elementary arithmetic in one school year of determined study.

Does that seem unbelievable? Consider Daniel Greenberg’s experience:

### Math as a Second Language

If math feels like a strange and dangerous wilderness to your children, you may need an experienced guide to lead you through the rough spots. For arithmetic, try Herb Gross’s Math as a Second Language webpages:

For upper-level math topics, explore Murray Bourne’s Interactive Mathematics pages or take a look at Kalid Azad’s Better Explained site:

### About the Let’s Play Math FAQ Series

The questions in this blog post series will be based on actual forum discussions, though I always change the details, removing anything that might identify the families involved.

We’ll look at a variety of struggles with math, such as:

• Lifelong Learning for Parents
• Primary Level Problems
• Middle Grade Mishaps
• The Agonies of Algebra
• Gaps and Standardized Testing

The questions will cover a wide range of common frustrations that resonate with anyone who has tried to explain an abstract idea to a confused child. Some questions apply specifically to homeschool math, yet non-homeschooling families can use many of the resources I recommend to supplement their children’s schoolwork or to keep skills sharp over the summer.

### Special Cases

In my FAQ post answers, I will assume you are working with children of normal intelligence, facing the mental strengths and weaknesses that are common to us all. The human brain is not designed for working with abstraction, so most people find math difficult.

But some face additional hardship because their minds are unable to process numbers and related concepts. If you suspect one or more of your children may struggle with a learning disability, please have them tested and get advice from someone who can help you learn to deal with their special circumstances.

Auditory or vision problems, undiagnosed food allergies, and a family crisis or other emotional strain may also affect a child’s concentration. Sometimes, the best way to help your children learn math is to let it go and deal with other issues first.

To be continued . . .

This post is an excerpt from my book Let’s Play Math: How Families Can Learn Math Together—and Enjoy It, as are many of the articles in my Let’s Play Math FAQ series.