Why Learning Should Be Fun

Monday, December 24th, 2012

Or, Why Baby Animals Have It Better Than Schoolchildren


UPDATE: Pediatricians say not to cut recess! “In order to learn well, children need a period of concentrated academic activity followed by a break that allows them to process information…”

Back in the mid-2000s, when I was a newly-minted teacher launching my career, I interviewed at a number of different schools. One school – where they had us take a test and write an essay in response to a question – was a near miss: the teachers and other hiring team members loved me, but then I interviewed with the principal, who brought up my essay. The essay question had been about how I would approach teaching math. I had written that I would use fun, engaging activities to teach the students through different approaches.

The principal – who was one of the most tense, anxious people I have ever met – proceeded to lecture me about how learning should not be “fun,” and that is everything wrong with education these days. She objected to the point of view expressed in my essay, in spite of the fact that it was based in cutting-edge research about teaching math.

Needless to say, I did not get the job.

Fast forward to this holiday season, when I am an independent teacher, tutor and consultant. Here is the text of one of the notes from a second-grade student:

“Thank you for being my math tuter i am very glad i started again… every seshion i have more fun and every seshion i learn more and more.”

Are learning and fun incompatible? According to this student, no way!

kitten hiding

Last summer, I reluctantly adopted a kitten, Abby. She was a tiny feral thing, crying and crying on the street for her mama. I captured her, brought her home, cleaned her up, vetted her, and tried my darndest to find her a new home. With the abundance of unwanted kittens this year, though, I had no luck.

She shook up my calm, settled home and older pets. And she shows me how much learning happens through play.

Abby will play with absolutely anything new that comes into the house. If I put something on a table or counter, she knocks it off to see what it does. If it’s mobile, she’ll chase it around the floor. If she can fit in it, she will play hide-and-seek-and-attack. If it smells good, she’ll try to eat it.

Why does she do this? She’s developing the skills and abilities she would need as a predator. And what makes it so miraculous is that she has a great time doing it. Her joy is contagious and makes people want to play with her. She has even won the reluctant affection of my cat-aggressive dog.

Watch any baby animal, and you will see the same kind of thing. This is why we love to be around them, and why they are guaranteed Youtube hits.

This is the incredible grace of youth: in learning what we need to survive, every species plays and discovers. Learning is hard work, but it’s fun!

I could list dozens of scholarly articles talking about why play is important to learning, and the different types of learning through play that children need. If you need that sort of thing, here is a place to start (check page five). But the point here is, what are we doing to our children when we structure play right out of their day and make them sit in desks or on the floor, except for maybe 20 minutes of recess?

Does this mean we should throw out all the workbooks? No way. My students love their workbooks. But that’s because the books are not stressful – they are chances to practice what the students have just learned. They are well designed, and if the students doesn’t understand the concept well enough to complete the homework, I tell them to wait so I can help them. Also, workbooks are not the only tools for learning. We use toys, games, iPad apps, manipulatives, and more. The more learning feels like play, the more fun it is, and the more it happens naturally.


And this is a reason I started using National Novel Writing Month in the classroom. When writing starts out as a joyride, it’s a lot more tolerable to slog through those term papers later on.

When we suck the joy out of learning, we are going against everything the planet and all of nature tells us about what works for real learning. Yes, we need to teach students to survive in the real world – but not by turning them into institutionalized drones.

And not by driving the inspired, fun teachers in favor of real learning to seek other careers.

Fun With Blocks: Foundational Geometry

Saturday, September 1st, 2012


In the course of my teaching and tutoring experience, I’ve come across the fact that Americans often fall short of others in geometry1,2. Besides the fact of test scores, I see that in how difficult it is for bright high school students I tutor to grasp certain spatial concepts. In fact, I was recently tutoring one incoming tenth grader, and she was unable to visualize how many cubes were in a stack.

Photo Sep 01, 6 36 27 PM

Recently, I found these foam blocks in packs of 50 for $1.00 at Dollar Tree. I bought a bunch, and they have been so useful for my teaching already. For one thing, I used them to help the tenth grader understand and visualize the geometric/volume concepts I was trying to teach her. Since Singapore Math always teaches from concrete to pictorial to abstract, and she had been missing the concrete experience, I needed to go back to that level to help her visualize what was in the diagrams.

I find that students who played with blocks as children have an easier time visualizing and calculating volume. They help develop the spatial sense. I recommended to several families to buy sets of these cubes just for the children to play with.

One thing I appreciate about Singapore Math is that it starts building geometric understanding at an early elementary level. In fact, I use sixth grade textbooks to teach tenth graders concepts that they are missing.

Today, I was working with an incoming first grader in a kindergarten book. We used the cubes as our concrete manipulative to represent the problems we were doing. (Unifix cubes are another great manipulative, but sometimes they can be hard for little hands to pull apart or put together, especially if they have difficulty with fine motor skills.)

At first the child had a hard time understanding the work, but soon she was doing it with fluency and ease. She was able to compare quantities and see how they connected with the pictures in the book. She also loved playing with the lightweight foam cubes and happily stayed occupied while her mother and I spoke. Hopefully she will spend lots of time building things with blocks and build the neural pathways at the same time that will help her succeed in geometry.

Other school supplies I like and find useful are:

Pilot Frixion pen. This writes like a nice rollerball, and it erases with friction – that is, not a regular eraser, but a piece of rubbery plastic at the end of the pen. It erases cleanly, plus there are no little eraser bits to wipe away, or an eraser to replace.

Sharpie Gel Highlighter: These are a little pricey, but they have some good benefits. One of them is total lack of bleed-through on paper. This is especially important when students have to highlight trade paperbacks with thin pages. Children also like the feel of using the highlighter. It can be used for coloring in a pinch, though it may get used up quickly for the price.

Enjoy your school supply shopping!

Math Doubles Plus Fun Time

Monday, May 7th, 2012

kids on board out edit2If you teach math, or want to enrich your children’s understanding of numbers, here is a set of activities that children will enjoy while learning a lot.

You may have heard about Multiple Intelligence Theory. One thing it tells us is that we evolved to have intelligence not only in verbal and mathematical learning, which are the main focuses in our schools, but in a number of different areas. That’s why some of us learn better through music, or nature, or art, or bodily movement.

This activity is a kinesthetic (movement-based) way to teach some important number facts. I’ve found that it increases math fact retention in everyone who plays it. One reason might be because it’s more engaging and fun than paper-and-pencil or verbal learning. Who learns well when they’re bored?

I made this project because I teach using Singapore Math, which is the best way I’ve found to teach math. However, the materials don’t focus on teaching basic facts; these are left to the teacher and/or supplementary programs. So I use lots of different activities and resources for teaching the facts; this is one of them.

Learning Objectives
After playing these games, students will be able to remember their basic addition doubles facts and squares (powers of two).

For this set of activities, you will need:

  • Number mat OR sidewalk chalk
  • (We’ll go into how to make the number mat in another step.)
  • Space
  • Number cards: Download multiplication and/or addition card PDFs

Step 1 Outdoor Number Mats

Outdoor board

If you have access to asphalt, sidewalk chalk, and decent weather, this is a great activity to get your students outdoors and enjoying learning their math facts.

Just draw your chosen number grid according to the layout in the PDF file, and print and cut out the cards. Instructions for playing the games come in step 3.

Step 2 Indoor Number Mat

times board

This step shows you how to make the Indoor Number Mat. This is a versatile tool to have in your classroom; keep it around for bad weather, and your students may even want to pull it out during recess! You may get some great ideas from them for how to use it.

For this project, you will need:

  • Large piece of fabric, Tyvek, or something else convenient (it could be a good way to recycle canvas used for a stage set). I think the minimum size is about 4′ x 5′.
  • Fabric paint or acrylic
  • Duct tape or ribbon

clothThe first thing I did with my fabric was to fold it in half and see how to split it in twelfths. This was easy given the fold lines in my fabric. If you don’t have this, simply fold twice horizontally, and bring two folds to the middle to make your three. (See diagram.)

cloth with tapeNow use your line-making option to “draw” lines along those folds. I used thinnish strips of duct tape for the vertical lines and the remaining fatter strips for the horizontal ones.

Next, paint the numbers according to the layout inside the boxes in the Grids PDF.
cloth numbers
I chose to use the full length of my fabric and use the top half for squares, leaving the bottom half for addition doubles. I needed to do this partly because I was in a hurry at first and painted just by squeezing acrylic paint directly onto the fabric, so it bled through to the other side. I had planned to use the other side for something else, but that’s no longer possible. If you are more careful, though, or use fabric paint, you can use one side of a smaller piece for the addition and the other side for multiplication.

If you are using a fabric board, I recommend the children play on it with their shoes off.add board

Step 3 Games to Play

class on in board
There are so many possible games to play with these boards. Here are a few I discovered on the first day I tried them with my students.

Doubles Fun Plus or Times Jump
Note: The idea for the addition doubles jump game comes from Adrian Bruce, an Australian teacher with an awesome website, but all extensions, photos, files, and multiplication-related activities are mine.

1. Children line up.
2. Cards are shuffled. Each child picks a card and tries to solve the problem. If successful, child jumps to the number on the board.
3. Card is returned to the bottom of the pile, and another children gets to try.
4. Play continues until all children have been on the board and have had a chance to solve at least two problems.
marcel jumping
If you are working with a small group of children just learning these facts, have them retry problems they missed until they know them automatically. Not over and over again in a row so that it’s boring, but they won’t mind doing another problem and repeating one they missed a few times because they are having too much fun, in my experience.

Doubles Fun Around the World Hopscotch
rubyonboardThe idea of this game is to say the equations in order (e.g. “3 x 3 is 9, 4 x 4 is 16, etc.”) while hopping on the successive solutions. Teacher should model how to do this.

I think it’s important in this game that the student says the full equation aloud. This reinforces the equation in their automatic systems. I noticed that directly after the game, my students were using what they had practiced to solve problems.

For young children, once they have practiced with the equations, have them try counting by twos and jumping on the numbers in order.

Discussion Time
This isn’t a game, but an important part of developing the students’ metacognition (higher-level thinking) about these computations. Ask:

  • What do you notice?
  • How can these facts help us figure out a problem?
  • For example, if we know what 7 x 7 is, how can we use that to figure out 7 x 8?
  • Do you notice any patterns?
  • Where are the doubles the same in addition and multiplication, and where are they different?
  • With young children, explore odd and even numbers on the addition mat, and then flip it over and have them identify odd and even numbers on the multiplication mat.

Allow the children to explore the concepts. It will make math a lot more meaningful to them.

This project was originally published on Instructables.com. It is all my original work.

Make Easy, Low-cost Math Journals

Monday, November 28th, 2011


Math journals

Like many teachers, I am always looking for ways to economize while giving my students the highest-quality educational experience possible. Math journals are part of this experience in my classes. Rather than buying commercial journals, though, I make my own quickly and inexpensively.

If you’d like to learn how to do the same, please visit this link that tells you how to do it, and also gives a few tips about using math journals in your classroom. If you have other ideas about how to use math journals, please leave them in the comments below.

Thanks for reading!

Book Review: The Absolute Value of Mike (and Dyscalculia)

Sunday, October 23rd, 2011


absolutemikeWhen I saw this book at the library, I was drawn directly to it. Why? For one thing, my post on dyscalculia and teaching math is one of my most popular posts ever. For another, I am always seeking good children’s books with mathematics themes to enhance my teaching or recommend to students. Finally, given that the theme of dyscalculia is such a hot topic, I thought I might be able to learn more about it, as I have done with books about people on the autistic spectrum, such as The Curious Incident of the Dog in the Night-Time.

So it was with great eagerness that I devoured this book. And it is with mixed feelings that I write this review. Therefore, I thought it would be best to write it in two parts, the first about its literary value, and the second about its value in understanding what dyscalculia means.

Part 1: Literary Value
This book has a lot going for it. For one thing, the characters are all unique and unconventional. While some other reviewers have criticized them as being too strange, I liked them because such people do exist, and reading about characters like these portrayed in positive ways can help promote tolerance and understanding.

Another strength is the plot, which compelled me to keep reading. I found it gripping, moving, and believable in its own world. It was also well written, which is only to be expected from a National Book Award winner. I enjoyed the story tremendously.


Part 2: Representation of Dyscalculia
First of all, a disclaimer: I am not an expert in dyscalculia. I have done some reading, and I have worked in math for many years with a variety of students, some of whom struggle with math due to poor math teaching or different learning styles, and a few who genuinely could not work with numbers. Some had parents who hired me as a private tutor precisely because they had such a struggle with math.

That being said, I do understand some things about dyscalculia. I know that it can result in the inability to have number sense, to know how to do some calculations one day and forget the next, perhaps to have no sense of time or money, poor sense of direction, and/or not much working memory. You can read more about it in my entry titled “Dyscalculia and Teaching Math.

Therefore, I expected to see at least one of these struggles shown in the main character. Instead, Mike was able to multiply and divide large numbers in his head. For example, on p. 229:
Good luck getting twenty dollars in one week! Even I could do the math – that was almost three thousand a day.”
Mike was able to keep appointments on time, manipulated numbers in his head, and while he got lost in a new town a few times, who doesn’t? The inability to read maps does not necessarily imply dyscalculia, and he always managed to find his way in the end.

The central conflict of the story is Mike’s relationship with his father, who is a genius in the math and sciences, and who wants his son to succeed in these too. However, the father has a great deal of trouble empathizing, relating to his son, understanding people in general, and being able to converse outside of his own areas of expertise. In short, Erskine has done a beautiful job of characterizing a man with a recognizably typical autistic spectrum disorder, without ever naming it. Mike’s great-aunt Moo even describes oddities in the father’s childhood behavior to confirm to us that these strange behaviors aren’t only due to grief from Mike’s mother’s death, or some other lifetime trauma.

Rather than dyscalculia, Erskine has characterized a boy who can manage the basics of math, but for whom advanced math holds no interest or appeal. That is true for a much larger segment of the population than those with dyscalculia! If the character did have dyscalculia, I wish she would have done as excellent a job in showing it in the character as she did with the father’s autistic behaviors. Granted, dyscalculia isn’t as well understood or “popular,” but I really think the book would have benefitted from an expert’s review before publication. I think marketing it as a book that addresses the topic of dyscalculia is misleading and could lead to a lot of popular misdiagnosis or self diagnosis.

Recommended Resources:
Since I can’t recommend this book for learning about dyscalculia, here are a few resources I can recommend. Please add yours below in the comments. Also, if you disagree with my assessment, I would love to hear your point of view; I want to learn as much as I can about this topic.

My Thirteenth Winter: A Memoir

New Presentations for the Fall

Monday, September 26th, 2011



As the fall gets into high gear, I will be getting on the road again. If you’re in New York, try to attend NYSCATE this year and register for my session on Singapore Math on Sunday, November 20. If you can come on Saturday, I will be giving a three-hour workshop on NaNoWriMo in the classroom, which will be fun and hands on.

I will also be offering six Singapore Math full-day workshops this fall, starting in October and ending in December. The schedule and links to register for those, and for the conference, are at the bottom of my Professional Development page. If you come, be sure to tell me you saw this website, and you will receive a special little gift!

Review: Number Bonds Software for Singapore Math

Wednesday, September 14th, 2011


Number bonds software

Crystal Springs Books recently produced a new software program for number bonds practice. This concept is foundational to Singapore Math. Number bonds can be used for everything from addition and subtraction to understanding fractions, and Singapore Math makes great use of them in its teaching.

The software, intended for grades K-2, is a simple Flash-based program. The CD comes with installers for both Mac OS and Windows. The program is small and snappy, even on older or slower computers; I have tried it on a first-generation Macbook Pro as well as two netbooks. I have used the software with young students and demonstrated it in front of a group of teachers, and this is what we found.

The program comes with four different games, ranging from very basic to more advanced. In the first game, Pond Bonds, children must move frogs to the appropriate lily pad to form correct number bonds. In the second game, Bird Bonds, the purpose is to move the appropriate bird to the right hole in the birdhouse. In this one, each bird is labeled with a number. The third game, Which Number, shows number bonds with one of the numbers missing; students must click on the correct number to complete the bond. The final game, Which Bond, gives students a number at the top of the screen, with two number bonds below. The student must click on the correct question mark where the top number should go.

The games follow the progression of Concrete > Pictorial > Abstract, which is known to lead to student success. Picking up a kicking frog and dropping it on the lily pad, or hearing it splash in the water, triggers concrete sensory feedback, especially when used with a touch screen or interactive white board. Moving birds with numbers on them starts to combine the concrete with the abstract, and the shapes of the holes in the birdhouse mirror the shapes of the number bonds in the next levels. The final two levels use the pictorial and abstract levels to good effect.

The software has several options for customization. For each game, you can set a numerical range, a time limit, and a number of players. Be aware, though, that if you go with the defaults, it may be a recipe for failure; the time limit is set to lowest, and the numbers are set to the highest range, meaning even a very fast adult can’t get a very high score. I wish the defaults had been reversed. On the other hand, if you need to move students quickly through stations, the fast pace can be good. The fastest time may not allow adequate time for learning, though. Once you set the settings for a game, they stay that way until you change them.

One area where this software is lacking is educational feedback for the player. On the early games, if you miss a question, you can go back and try again, but you don’t receive any clues about what went wrong. On the higher games, if you miss one, too bad; you can’t even try again. I would like to see some sort of helpful feedback when mistakes are made.

When you have one player set, the score for the player is displayed at the end of the game. For more players, the others have to sit through each entire set until the scores are displayed at the end. I think more interactive game play would be nice. There is no way to save scores in the software, either. I would recommend that teachers create individual score sheets for students to keep track of their scores and how they improve over time, so they compete against themselves, not against others.

Since the software is Flash-based, it cannot run on iOS devices. I hope they develop a version for that platform soon.

UPDATE: As of March 2013, an iOS version is available! Read the review here.

Conclusion: Highly Recommended
Number Bonds is a simple, inexpensive software package that can provide extra addition and subtraction practice in the classroom or at home. Children find it fun and engaging, and it provides good composing and decomposing practice, as well as mental addition and subtraction. I would use it for a wider age range of children; it can be helpful for differentiating, like with more advanced preschoolers and upper elementary students who need foundational number bond practice. It would be nice if the software had a few more features, but I’m sure those features would take away from the software’s speedy response on older hardware. For best results, it should be run on a touch device, so it would be great if it could be installed on iOS or Android in the future.

Not expensive
Site license available
Small and fast
Good educational design (concrete > pictorial > abstract)
Fun for children
Range of levels and challenges
Compatible with a wide range of desktops and laptops
Singapore math-based!

Not enough feedback on mistakes
Can’t save score data
Settings need to be reset when first played
Not a true multiplayer game
Needs teacher introduction to be most effective (not stand-alone)
Teachers need training to make the most of it, but program-based help is minimal

NCTM Illuminations 2011

Wednesday, September 7th, 2011



This summer I gave a three-hour workshop on Singapore Math model drawing at the NCTM Illuminations Institute in Reston, VA. This was a fun workshop with a great group of people, and we accomplished a lot of model drawing practice and understanding.

I was pleased to see recently that the workshop received a couple of mentions on the web. One is on the thinkfinity site, which is run by Verizon and which I first joined after attending ISTE 2011. The other is from one of the participants, who wrote a blog post mentioning it.

If you are interested in seeing what I can offer your school, please be sure to contact me.

ISTE 2011: On my way

Monday, June 27th, 2011



ISTE 2011 is up and running, and it’s huge! Look for me there with Conceptua Math at booth 2852 on Wednesday morning before and after our session. I will also be presenting with Arjan Khalsa, the CEO and founder, at this session:
http://conceptuamath.com. The tools are extremely intuitive and valuable, work great with a white board or tablet (but not iPads), and have helped many children understand how fractions work. They are also very compatible with Singapore Math.

Which Singapore Math series should I use?

Tuesday, May 17th, 2011


Singapore Math is a rising trend in math education in schools and with homeschoolers, for the simple reason that it works. As an experienced Singapore Math teacher and trainer, I often get the question, “Which Singapore Math series should I use?” This question is posed by both teachers and homeschooling parents, and as more series enter the market, the choice becomes more challenging. In this article, I will present the pros and cons of each current series as I see them. Please feel free to contribute your views in the comments below.

Singapore Math, US Edition, published by Marshall-Cavendish:

This edition has been around the longest in the US. The main difference from the curriculum Singapore was using until recently is that this edition includes some additional problems using US measurements (feet, miles, pounds, etc.). This is the series that Singaporean students used when they scored highest on the TIMSS (international) test.

  • Short, focused textbooks and workbooks.
  • Clear graphics.
  • Emphasis on mental math.
  • Clear sequence from one book to the next.
  • Follows the best of the Singaporean teaching model.
  • Fits the Common Core State Standards well (see this article).
  • Decent Homeschooling Guide, from what I hear.


  • The measurement units don’t follow the Singaporean teaching model; that is, they don’t thoroughly teach one type of measurement before moving on to the next, rather mixing US and metric together. This can cause confusion in students.
  • For American teachers, teacher’s manual may be inadequate without further training.
  • Doesn’t come with assessments; I used the Practices and Reviews in the textbook for this.
  • Needs supplementation with math facts practice.
  • Children going from this edition to public school may be missing some subjects, but stronger in others.
  • Must be ordered online; shipping is high.

: This is my preferred series despite its shortcomings, which can be easily overcome with a little knowhow and creativity.
Buy here: SingaporeMath.com, Inc.

Singapore Math, Standards Edition, published by Marshall-Cavendish:

This edition was created to meet the California learning standards. It is more colorful than the US Edition and covers slightly different topics each year. A comparison chart showing the scope and sequence of the two is available here. This series has been approved by the California State Board of Education.

  • Designed like the US Edition, with most of the same pros.
  • Thorough Teacher’s Guide.
  • Comes with Assessments.
  • Decent Homeschooling Guide, from what I hear.


  • One of the strengths of the Singapore Math curriculum is its focus on mastery of fewer subjects per year. This edition repeats the mistake of many US-designed curricula by putting in too many subjects per year so there is less time for each.
  • Must be ordered online; shipping is high.

Overall: Recommended if the child is in California or the state has similar standards to meet.
Buy here: SingaporeMath.com, Inc.

Math in Focus
, distributed by Houghton Mifflin Harcourt:

This series is new to the US market, and Houghton Mifflin has Americanized it, with the typical large-sized teacher guides, a variety of student books, and manipulatives, packaged in typical school bundles. I have seen the company at trade shows and looked at the materials there, and have requested samples, but none have been forthcoming, so I have not been able to test them out until now. I just discovered the online sampling website they provide, but it’s slow, and I can’t try it out with my students. So while I have been able to see the series to some extent, this review is less in depth than others.


  • Easiest for US public school teachers to adapt to, with explicit guides and scripts.
  • Flows better to the middle school/high school Singapore curricula.
  • Wide variety of differentiation options.


  • Expensive.
  • Scores in Singapore went down after they implemented this program.
  • Less emphasis on mental math.
  • Books are larger with more complicated/busier graphics, potentially distracting from the learning process. I like the drawings, but combining them with photos can be confusing.

Overall: Recommended for teachers who don’t have prior experience using Singapore Math. For those who do, I need more experience with this program to recommend it or not, but I would stick with the US Edition for now. Homeschooling parents are better off with one of the series from singaporemath.com.
Buy here: Houghton Mifflin Harcourt

Singapore Math Practice
, published by Frank Schaffer Publications:

This series appeared in bookstores a year or two ago, and I made a beeline to it with interest. I put it down almost immediately, though. It appears to capitalize on the popularity of Singapore Math without a thorough understanding of its best principles and practices.

  • Readily available in bookstores
  • May provide extra practice in addition to using one of the other series, but use with caution.


  • Promotes the use of calculators too early, a big no-no in my book.
  • Problems have mistakes and are not well designed.

Buy here: Amazon.com or in bookstores like Barnes & Noble


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