Site logo
Site logo
Math Education

iPad Apps for Education: Part 1 - Stop Math


Share

As an eager tech user as well as a teacher who likes to use any tools that are handy, I am always trying out new ways to engage students. I recently obtained an iPad and have been trying to fill it with the best educational tools possible.

photo 1
Imagine my delight when I found an interactive book app all about math! The book is called Stop Math, by Jeff Weigel. It is set in the future, when time travel is possible. A young boy dislikes math, thinking it’s a torture device for schoolchildren. He decides to find the person who invented it and stop them from inventing it.

photo 3
The book then takes you on an interactive journey back through time, where he meets various characters from history, like Einstein and Newton, all of whom contributed to our current understanding of math.

Even better, on each page, there is an interactive element the child can play with - which they love to do. There are even side journeys where a student can play with an interactive widget to learn, for example, about relativity.

photo 4
My one minor criticism is that the only computation children are asked to do involves a calculator. They are not even given the chance to try to figure out the answer mentally or on paper, but must rely on the calculator in the book until the final calculation, where they are expected to subtract with the algorithm but without the ability to regroup (borrow) on the screen, which is beyond some students.

Other than that, every student I have shown it to, from kindergarteners through middle schoolers, has enjoyed it and learned something. It appeals to any age - I didn’t get too tired of it even after reading it with so many students time and time again - and has a good message about math in the end. I highly recommend it! $3.99 on the iTunes App Store.
Comments

Why Learning Should Be Fun

Or, Why Baby Animals Have It Better Than Schoolchildren


Share

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.
nclb

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.


Comments

Fun With Blocks: Foundational Geometry


Share

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!

Comments

Math Doubles Plus Fun Time


Share
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.

Comments

Make Easy, Low-cost Math Journals


Share

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!
Comments

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


Share



When 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.

However...

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.

Conclusion
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
http://www.dyscalculiaforum.com/


Comments

New Presentations for the Fall


Share

nyscate
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!
Comments

Review: Number Bonds Software for Singapore Math


Share

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.

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.

Pros:
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!

Cons:
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

Comments

NCTM Illuminations 2011


Share

modeldraw
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.
Comments

ISTE 2011: On my way


Share

compare_0
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://www.isteconference.org/ISTE/2011/program/search_results_details.php?sessionid=60744211

If you are a math teacher or homeschooling parent and haven’t seen their free fraction tools yet, please do so at 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.
Comments

Which Singapore Math series should I use?


Share

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.
Pros
  • 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.
Cons:
  • 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.

Overall
: 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.
Pros:
  • 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.
Cons
  • 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. Pros:
  • 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.
Cons:
  • 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: Greatsource.com

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

Video: MSNBC Report on Singapore Math Model Drawing


Share

MSNBC ran a piece on May 3 about third-grade students learning math using Singapore Math. This report outlines the importance of model drawing for problem solving, and of parent understanding to be on board with it.

The report is well done, except it gives the mistaken impression that the only thing that makes Singapore Math unique is the model drawing approach. I used to think that too, but now I know better; developing number bond-based numeracy is at least as essential, as are other elements of the curriculum.

View the video below:

Visit msnbc.com for breaking news, world news, and news about the economy

Comments

Review and Using Khan Academy Tools


Share

I’m so inspired about a new tool to enhance math education. A friend sent me the link to a TED talk (embedded at the bottom of this post) showing the evolution of the Khan Academy into something truly useful for - well, for just about anybody.

I had come across the Khan videos some time ago, and I thought they were useful and well designed to teach more advanced concepts. Since they were not necessarily pertinent to my work, though, I didn’t return to them.

Then I saw this video, and how the Khan Academy has evolved, and I got excited. I set up accounts for several of my tutoring students and asked them to try the site while I checked their previous work, a few minutes of what used to be down time for them. Right there, I have increased the learning efficiency of my tutoring time.

The first student I set up, a fifth-grade girl, got happily into the site right away. When she discovered you could earn badges for different accomplishments, that sold her - and not only that, but she knew that her seven-year-old brother would like the site too.

For teachers, tutors, parents, etc., a wonderful feature is to sign up as a coach and have your student(s) or child(ren) add you as a coach. I think they can even add more than one coach, so both a teacher and a parent coach the same student, for example.

After only using the site for two days, I can already see the progress my students are making, as well as areas in which they are struggling. This will allow me to focus my next session with them better and help them master the skills they need, as well as move more quickly past the ones they have mastered.

The site design is excellent, with only a few minor glitches. Having looked at many educational websites, I can say that this is a rare find. To set up an account, one needs either a Google or a Facebook account. This can be a hurdle in itself; you have to be 18 or older to have a Google account, so for children, they need to either lie about their birth year or use a parent’s account. I did run into this problem in setting up student accounts, unfortunately. Facebook has its own pitfalls; while the minimum age is lower (though still too high for most of my students), parents often have more objections to their children joining that site than Google. Khan Academy recommends teachers signing up for Google Apps for Education; I haven’t looked into that option yet, but I may do so, if I qualify as a private tutor.

Once the signing-up hurdle is jumped, the sign-in process is easy and smooth. The site design is clear and simple to navigate, though I wish the “Add a Coach” link would be easier to find.

The real gem for me is the Practice interface. When you click the Practice link, you face a constellation of skills, with Addition 1 at the top. As you demonstrate proficiency, you earn a star in that constellation, and the graphic indicates the suggested skills to work on next.

The interface is simple but effective. When you start to practice, the problems show up as images, and you enter the correct answer in a text box. What’s great about it is that it’s Flash-free, meaning it works on iPhones, iPads, etc., making fun math practice freely, and widely, available.

There was another minor technical glitch, though. At first, I was using my little Asus netbook tablet, and I was thrilled to discover the “Show scratch pad” link. This enables a vertical bar on the left of the screen showing tools like a pencil, eraser, etc. that allow you to write on the screen to do your work, like on a note pad. On the tablet, this was awesome, because my students could use the stylus like a pen to work out their answers right on the screen. I thought the iPad would be as good or better for this, but instead, the touch interface interacts only with the browser controls (like scrolling up and down), and I couldn’t make it register any marks. I’m not sure if this is browser-related, a site programming problem, or an issue in the iOS. It would be great if this could be solved. But it would be ideal for a teacher with an interactive whiteboard as well.

To test the system further, I chose a math topic about which I am very rusty. When I clicked on the subject’s button, I saw a problem that stumped me completely. What to do?

In a classroom situation, a shy student might just sit there and be miserable. But in this tool, right below my choices were the friendly words, “Need help?” and a selection of videos that could show me what I needed to know to succeed in this topic. Better still, I didn’t lose any points by watching the videos - though I would if I asked for a hint.

Are the videos perfect? No, but they’re good, and they have the advantage of being easy to watch over and over until you understand the concept. It would be great if he used more of the methodology in Singapore Math to teach the basic concepts, but we can’t have everything at once. Maybe someday.

One criticism of Singapore Math I have heard is that it needs more skills practice. I think this site is one way for a student to get this practice in a low-key, interactive, fun way. It’s also a terrific tool for students and teachers to improve their learning progress, and for anyone who wants to learn.

By the way, math isn’t the only subject addressed on that site, though I think it’s the first and probably the most thoroughly done. The other subjects, including test prep, are worth visiting too.

Comments

Pi Day Pie and Baking Math


Share

And now for something completely different! When I am not exploring math education or writing fiction, I love to make things. This includes everything from cooking to needle felting to making jewelry. So when instructables.com opened their Pi Day pie contest, I had to enter.

Creating my entry required a great deal of calculation, from halving or quartering recipes to guesstimating how long it would take to bake this unique cookie, cake, and ice cream pie. Fortunately, I’ve had lots of experience with estimation, and I couldn’t have hoped for this pie to turn out better. My friends who shared it loved it too.

If you’d like to see the pie and hopefully vote for it, please head on over to this page. There are also lots of other fabulous entries, and you can vote as often as you’d like. Enjoy!

pipie2

Comments

Pi Day Activities!


Share

Yesterday was March 14, or 3/14, or Pi Day. It’s a great day to celebrate the circle, and that most extraordinary number, pi.

With my second grade math club, I did several activities on my new teacher download, Pi Day Activities. These included cutting a circle, measuring a circle, and eating pie. We didn’t have enough time to play Pi Tag, though I’m sure we’ll be doing that one week soon!

I also created a poster showing almost 1,500 digits of pie. You can download it for free either from my site or from my TeachersPayTeachers.com link.

Happy Pi Day!
Comments

Delaware School District Succeeds Using Singapore Math


Share

A Delaware school district has successfully implemented Singapore Math, raising enjoyment, understanding, and test scores. This article describes their success. Here is one example:

Mount Pleasant Elementary Principal Joyce Skrobot did not need to be convinced to add Singapore math to the curriculum. Her school piloted the program over the past four years in some second-grade classes, and, on state tests, they outperformed the classes that did not use the math, she said.


"It really establishes a strong foundation of math skills with a lot of repetition," she said. "It's a very concrete approach to teaching."


The district plans to offer parent workshops to explain the differences in the Singapore approach, a key component of long-term success.
Comments

Video: Learning to Calculate With Ten-Frames: Singapore Math


Share

A video demonstrating how ten frames can be used to develop number sense was posted at http://www.youtube.com/watch?v=zQxS5Z3UHKk&feature=player_embedded. (They disabled embedded on external sites, so you will have to click to see it.)

The video shows progression from counting-on with touching, or the concrete stage, to the pictorial stage of being able to look at ten frames and see how many dots are present. Early in the video, it says the child is a kinesthetic learner, which may be true, but touching the objects is a natural early stage for anyone. So touching the objects doesn’t necessarily mean the child is a kinesthetic learner, but they may be at the concrete stage of learning a certain concept.

The clip does a nice job of showing how a teacher can help a student one-on-one (though I would have liked to see the teacher doing more guiding and less instructing), but what about teaching larger groups of children? There are always issues of permission when dealing with groups; however, I think it would help teachers if they could see how to use this in a larger setting. This is something I can model when offering professional development at a school visit.
Comments

Math Joke #5


Share

If you’re going to tell triangle jokes, you should do them in threes, right? So here’s the third one, also original:

Q: Which triangles are the best conversationalists?

A: The acute ones. The others are either too obtuse or always right.

(That one got a laugh today!)
Comments

Math Jokes #3 and #4


Share

I came across this joke tonight in a blog comment.

Q: What did the triangle say to the circle?

A: Your life seems so pointless.


And a bonus original joke that I just made up:

Q: Which triangles are the most likely to get the point?

A: The acute ones. The others ones are just too obtuse.

Let me know if you thought it was funny!
Comments

Common Core State Standards and Singapore Math


Share

In August 2010, Achieve.org produced a report comparing the Common Core State Standards with the Singapore Math syllabus. I found the report interesting, as it showed that there are many similarities between these standards and Singapore’s syllabus, though in some ways, the CCSS document is clearer in its expectations. Also, Singapore uses the British system of O-level and A-level achievement. Their O-level high school curriculum is slightly less rigorous than ours, but their A-level curriculum is more rigorous than our standard high school curriculum.

I drew the conclusion from reading the report that adopting Singapore Math could be a positive step towards aligning to the CCSS.

Achieve is an independent non-profit dedicated to raising academic standards in the US. You can read the full report below.
Comparing the Common Core State Standards and Singapore’s Mathematics Syllabus
Comments

TERC/Investigations: Comparison with Singapore Math


Share

A great article titled Waiting for Supermath came through my inbox today. It includes commentary on a video (below) of a third grader showing how she solves a four-digit addition problem using what she learns at school, or the Investigations curriculum, versus what her mother (a math intervention specialist) teaches at home, the traditional “stacking” algorithm.

What strikes me most about the video is that the first method, using the graphic model, shows what seems to me an overuse of the conceptual level of addition.

One strength of Singapore Math is that it starts with the conceptual level, which is essential, but then it moves to the abstract. In this process, the student starts with concrete representations of a problem, like manipulatives, then to pictorial or graphic representations, and finally to the algorithm, once they have mastered the concept.

But in the video, the girl starts out solving the problem with what could be drawings of base 10 blocks - and way too many of them. This is keeping her stuck at the concrete stage and leads to inefficiency and inaccuracy in her calculations.

It also strikes me, as the video points out in the end, that this method of teaching creates the myth that larger numbers are harder to calculate. Is this what we want to perpetuate in our students? I know if I had, I wouldn’t have had a group of second and third graders who decided, on their own, to learn 50 or more digits of pi.

One other note: I did use Investigations for one year in a middle school classroom. That was the year that some parents and I convinced the administration to finally adopt a curriculum that made sense. And what did they choose? Singapore Math!

Watch the video:

Comments

US vs. Korean Education


Share

President Obama would like to know how South Korea has risen up to have one of the fastest-growing economies and best-educated workers in just over a generation. Rather than look to a magic fix, The Lost Seoul addresses some cultural differences between South Korea and the US in this blog post. One important difference he mentions is attitude. If you ask an American student if he or she is good at math, you will usually get a straightforward answer. If you ask a South Korean student the same thing, he or she won’t know how to answer. The question doesn’t compute.

The Lost Seoul suggests that the reason for this is because in the US, we equate math ability with genetic tendency - you inherit it from your parents - which is self-limiting for those who have parents who don’t believe they are good in math. And if they don’t think they are good in math, Americans won’t pursue it past high school. But in South Korea, math is just something they do, probably more like reading in the US. Adults in the US don’t stop reading after high school just because they might not have been the best or fastest at it in school. It’s part of life, in everything from sports or fashion magazines to professional journals. I found the post interesting and informative, and I recommend checking it out.
Comments

Book Review: You Can Count on Monsters


Share

Today in my Math Mavens program, we opened the book You Can Count on Monsters by Richard Evan Schwartz for the first time. This is a book I bought because I heard glowing reviews of it on NPR.

The concept of the book is teaching prime and composite numbers through colorful, geometrical monsters. It is written for any age, from preschool on up, and my students really appreciated it. They had a lot of fun looking at the monsters, spotting the prime monsters hidden inside the composite monsters, and describing what they saw. For example, one said the 20 monster looked like “two innocent two-monsters held in custody by evil nacho chips.”

For fans of Singapore Math or number bonds in general, you will also appreciate how each number is represented with a number of dots, the numeral, and a multiplication number bond for composite numbers. All in all, it makes a powerful set of connections for students between numbers, images and fun.

The book covers numbers 1 through 100, with an introductory section that explains factoring, prime and composite numbers, and how the book is designed, all with colorful images and not too wordy. A section in the back has a further exploration of prime numbers. A wonderful enrichment for any math education!

To see inside or order the book on Amazon, click below:



Comments

Will Scardale continue to succeed despite budget issues?


Share

Scarsdale, NY is a model district in terms of scores and success. They attribute this success to five building blocks in their curriculum: Singapore Math, inquiry approaches to science and social studies, fluency in information technology, and creative arts. Yet they are having to cut teachers and programs due to budget constraints. They contrast this to China, which funded five educators to visit their district.

Will Scarsdale have to cut back on their successful programs? Meetings of the Scarsdale Forum are happening during February. Read more at this Patch article.
Comments

Fostering Creativity in Math


Share

We hear plenty of talk about teaching and reinforcing basic skills in math. Yes, these are very important, but computation skills aren’t what lead to breakthroughs and new discoveries; new ways of thinking do, right?

This young woman exemplifies real creativity in mathematical thinking. I find this so inspiring. Investigating mathematical principles through art: what a concept!

Comments

Singapore Math Summer Programs in New York


Share

Singapore Math summer programs come to Westchester, NY! Do you have children who would benefit from a summer experience learning math in the proven Singapore Math way? Send them to the brand new program offered this summer by experienced Singapore Math teacher, instructor and trainer Susan Midlarsky. Not only will they learn a lot, but it will be fun! Find out more at singaporemathny.com. Register early - space is limited!
Comments

Delaware School Achieves Success With Singapore Math Adoption


Share

An article published by the Rodel Foundation of Delaware describes how Kuumba Academy took a serious approach to remediating the problem of poor math achievement. They adopted a Singapore Math curriculum, and with it, they gave their teachers “intensive, on-going professional development to deepen teachers’ understanding of math instruction at the elementary level.” The school also implemented parent workshops and a “Bring Your Parent to School Day,” which would help parents and guardians understand the sometimes very different approaches Singapore Math takes.

One minor incorrect point the article states is that Singapore Math uses math sprints to strengthen math skills. Sprints were developed by Yoram Sagher, a US professor, to supplement math fact practice in the Singapore Math curriculum. Using them can help, although they are not the only effective math skills practice approach.

Adopting the Singapore Math curriculum, along with training teachers well and using sprints, led to a complete turnaround in the school’s math test results. As the article states:

Since Kuumba began its partnership with the Vision Network, the school has seen phenomenal growth in math scores. Not only are students no longer falling behind, they are exceeding state performance in many grades in math. In just 3 years, Kuumba went from 49% of students meeting the standard school-wide to 87% proficient, as measured by the DSTP.

Comments

Math Joke Animation


Share

It snowed today - a lot - canceling all my plans and making it a perfect day to get things done at home. So I created the short movie below. I hope you enjoy it as much as I enjoyed making it! This one was taken - and highly modified - from a joke told in Math Jokes 4 Mathy Folks.







Comments

Lateral surface area of a cylinder


Share

How do you explain the concept behind the formula for the lateral surface area of a cylinder, which is 2Πrh? I ran into this question when tutoring a student to prepare for the New York State Integrated Algebra Regents exam. (For some reason, this exam contains a lot of geometry.) The lateral surface area is the area of the cylinder’s surface that does not include the circular ends.
cylindersa


If you look at the cylinder, it resembles a can. If you imagine it is a can of something, the lateral surface area is what the label covers.

So to show the concept behind the formula, we took a can of organic garbanzo beans out of the kitchen cabinet. Fortunately, it had a label that was easy to peel off.

First we measured the width of the label. Next we measured the diameter of the can (the 2r, or twice the radius), and multiplied it by Π. Comparing the two widths, the rectangular label width pretty much matched the formula for the circumference, or a little over three times the diameter exactly! And since the label is a rectangle, to get the area, we multiplied the length by the height.

So we discovered, by this exploration, that the width of the label is equal to the circumference of the circular top. Therefore the formula made sense to the student, and we had fun making it concrete. If she doesn’t remember the formula on the test, I’m sure she’ll be able to access the concept to recreate the formula at the point - and that will demonstrate true understanding.

Comments

Does our math education impact how we value math (or don't)?


Share

The author of Social Media for Trainers and I have been having an interesting debate about the place of higher math education in schools. I had read her book and found it useful, so I looked up her Facebook page. There, under the heading, “Stop teaching math,” she placed a link on her Facebook page to the blog article titled “The Case Against Math.” Of course I found this provocative and clicked over to read the article.

While I agree with the thesis of the article - that the way we teach math and value it as a proxy for measuring intelligence is not useful, and that it should be changed - I do not think we should reduce or eliminate it as a requirement in education. Instead, I agree for the most part with how the article’s author puts it:

“If we must teach math, teach it  as if math was just one aspect of the larger concepts and questions that are the main thrust of education: critical thinking, problem solving, communication, empathy, and creativity. If we must teach math, teach it through music, art, science, technology, history, cooking, construction, engineering etc. because math as an abstract system is useful to very few of our students. If we must teach math, focus less on the answers and the algorithms for specific types of problems and focus more on the questions and the processes of problems.”

I do think that teaching math in an integrated way is best, but I also see merit in teaching math as a subject unto itself, as long as it’s taught in ways that make sense. The process of teaching through problem solving and from conceptual to abstract allows math to make sense to all students I’ve encountered, and problem solving therefore becomes a fun challenge, not a chore.

As I mentioned on the Facebook page, I once had a friend who was working as a carpenter. He asked for my help in figuring out how long a piece of wood needed to be to complete an attic renovation project. I showed him how to solve the problem using the Pythagorean theorem. This was before I became a teacher, but he told me that if he had had teachers like me in high school, he probably would not have left school, as this was useful stuff to know.

The author’s response was to ask 3,000 Twitter followers for examples of using advanced math in their everyday lives. She received one tweet about a problem similar to the carpentry one, and one about helping a child with trigonometry homework.

This doesn’t surprise me if the vast majority of her followers are Americans. I would love to know, though, if we would get a different response from people raised in other countries, especially those in countries that have consistently scored highly in math. If no studies have been done on this, I would like to study it myself. Does how we are raised to think of math affect how we use it (or don’t) in our daily lives, or is the subject objectively useless to all but scientists and engineers and taught only as a carry-over from ancient times? What do you think?

UPDATE: I discussed this topic today with a student of mine who is “unschooled” and started fifth-grade Singapore math with me when she was 15 years old. Two and a half years later, she is at high school Algebra level. Her main interest is fashion design, and she’s been attending high school fashion design classes for a couple of years. She told me that she was pleased to put her fraction knowledge to use in her sewing class last spring. That’s only one story; do you have your own?
Comments

New Multiplication Activity Available - Free!


Share

For my educator friends and colleagues, I have added a new multiplication chart lesson plan, complete with reproducible handouts, to TeachersPayTeachers.com. It is free to download and use. It can be used in a classroom, in a homeschooling setting, or in a special needs or remedial context.

The lesson is aligned to the Common Core Standards and includes objectives, materials, and descriptions of procedures, follow-ups and adaptations. Please let me know if you find it useful, and if you do, please add a rating to the TeachersPayTeachers site.

Download the lesson plan here.
Comments

Math Meaning for Adults


Share

The more I travel and meet people, the more I find that most adults in the US have difficulty with math. I read a comment by a woman from Eastern Europe who found that while she was a mediocre math student in her home country, she was miles ahead of American students when she moved here. She couldn’t understand why, with all the time and finance poured into math education here, including an average of 1.5 hours per day of math class, her children were progressing in math far less well than she had when growing up.

I think part of the reason is that we have a couple of generations of adults who just don’t have a strong grasp of math concepts, especially when it comes to basic number sense. Various adults have approached me and asked if I would teach a math class so at least they wouldn’t pass on their own math phobias to their children, and maybe they could even help their children with their homework and learning. The latest of these I met were a couple of lovely older women in Oklahoma who were staying at the same hotel as I for an agriculture convention.

Reaching these adults presents a challenge because of the distance. Attending a teacher workshop would be overkill and too expensive. So I came up with the idea, what about an online course offering math fundamentals for adults? I think it could benefit a lot of people.

What do you think? Do you, or anyone you know, think you or they might benefit from it? If you were to take such a course, what would you want to be part of it? Let me know!
Comments

Core Knowledge vs. Singapore Math


Share

About two weeks ago, a post titled “Singapore Math Is ‘Our Dirty Little Secret’” appeared on the Core Knowledge blog. It criticized the New York Times article about Singapore Math that appeared on October 1. Apparently, the author believes that the poor state of math education in the US is due to what he calls “reform math.” This ignores an entire generation of math-phobic adults who learned math through “traditional” methods, and most likely instigated the reform movement due to their dissatisfaction with those methods.

While the curricula based purely on constructivist approaches have their limitations, the idea that Singapore Math is a traditional approach is mistaken. It’s better than traditional approaches.

Below are the comments I wrote on the blog:

As a long-time Singapore Math educator and trainer, I have to disagree with a few points in this post. Overall, it seems to be advocating a "traditional" approach to math, the same approach that has led to poor US performance in math and science in the last few decades and an epidemic of math phobia among American adults. This "traditional" approach has also led to one of the main reasons elementary math education suffers these days: too many educators had poor math education and don't understand the concepts themselves, so they have no idea how to teach it to the children. They are afraid of the subject, so how can they be successful in teaching their students? If they were taught algorithms with no idea of the workings behind them, they cannot pass an understanding of the workings on to their students.

When I teach my workshops, one of the things I see is when I demonstrate one of the basic four operations on whole numbers - addition, subtraction, multiplication and division - with number disks on a place value chart, many of the participants have an "Aha!" moment. So that's how it works, they realize. And once they have this understanding and practice it, teaching it to the students - and being able to be flexible enough in their approaches to reach all students - becomes a reachable goal.

This use of place value disks is an example of the concrete stage of concrete > pictorial > abstract that Singapore Math is based upon. The textbooks are full of diagrams that show the place value chart being used in this way, but those diagrams are meant to illustrate what the students have already done with the place value charts and disks, which then builds into understanding of the algorithm and how it works. And yes, this is part of the process of learning from conceptual understanding to algorithm built into the curriculum. Manipulatives can be very powerful, and I find them necessary for most students. There are always the few who will understand no matter what, but those are not the students we need to help.

I had used the textbooks and workbooks for a few years, even with training, without understanding this pedagogy, and was somewhat successful - just because I understand math myself. But when I became equipped with the deeper understandings mentioned above, I became a much better math teacher, able to differentiate and address different learning needs.

Regarding the model-drawing books, the cynical comment about them in this post is misplaced. Some teachers may use the steps for model drawing as a rote formula, but that's not how they are intended. If you have never learned how to do model drawing, you need some kind of instruction. Then after that, the steps are just there to remind you until they are internalized and personalized.

I have taught several model-drawing workshops in which participants (mostly high school teachers) have said the most valuable part of the workshop for them was the step, "Write your answer statement first." This is a sentence with a blank for the answer, reworded from the question in the problem. It serves the purpose of refocusing the student at the end of the problem when they need to find which of the many calculations they may have worked is actually the answer to the problem. The Singapore workbook problems are set up this way, but without instruction, children may miss out on this step. I know I did!

I agree that the purely constructivist math approaches leave a lot to be desired, but the idea that Singapore Math has no constructivist elements is incorrect. I think that if it is taught well, it strikes a good balance between constructivist and elementary knowledge in such a way that children can master the math knowledge they need to succeed – and I have seen this success in my own students over the years.

Comments

NCTM Baltimore: Final Report


Share

My first trip to NCTM is over, and I’m glad I went. Although the setup had a few glitches, like an LCD projector that didn’t want to project from my laptop, my presentation on problem solving using model drawing went well, with close to 180 participants. Many of them came back to the booth, interested in further learning, and some bought books and materials or inquired about future opportunities to develop this skill. I’m really pleased about this, because it means more children may be better equipped to enjoy and understand math.

The booth was busy the whole day, and I demonstrated model drawing with word problems a number of times. That was fun and always drew attention. It’s great to see that “Aha!” moment when teachers see what a powerful tool model drawing is to visualize a word problem. I even used model drawing today in a tutoring session with a high school student who was studying for the PSAT. We were going over some of the problems about which she had questions, and I showed her how to model a problem involving ratios. Using the model drawing method made the answer visually obvious.

It was also great to spend time with team members and colleagues, as well as to meet new people. I hope some of the new contacts will develop into lasting relationships.

If you were a participant in my workshop, I do plan to post the answer key to the model drawing questions here shortly. Check back; they should be here by Monday. Thank you!
Comments

Math Jokes


Share

After a long day of arriving and helping to set up the SDE booth, I had a little time to look around the NCTM bookstore. (NCTM, in case you don’t know, is the National Council of Teachers of Mathematics and the host of this conference.) There were some interesting books, but the one I just HAD to buy was Math Jokes 4 Mathy Folks by G. Patrick Vennebush. How could I resist? It shows what a math geek I am that I was laughing out loud while reading some of the jokes. This will be a great resource for any of the math presentations and/or classes I give.

While I don’t feel good about reproducing any of the contents of the book on my blog, I can share a joke told by a wonderful woman I met tonight.

Q: What did the zero say to the eight?
A: Nice belt!

Check the book out here:



Besides doing the presentation tomorrow, I am really looking forward to meeting Greg Tang, my favorite author of math-themed picture books. He will be stopping by the SDE booth (#614) at 11:30 tomorrow. If I’d known before I left home, I’d have brought my copies of his books to be autographed!

Comments

Math and Baseball


Share

Are you looking for ideas about how to engage students in math, or show them how it applies to the real world? Here is a fun one for sports lovers. John Roach at msnbc.com recently published an article called “The Math and Science of Baseball.” It outlines various ways in which math and science have been applied to the sport.

We all know about batting averages, but did you know scientists have analyzed everything from how likely it is that the best team will win with the current number of games vs. the ideal number of games per season, that mathematical models judging fielding ability have been created, and that statisticians have studied managerial style in relation to different types of teams?

Also, do you know which is faster, a head-first or a feet-first slide into base? Check out the article to find out - and maybe include some of these fascinating facts in your next math class!
Comments

Math & Science Professional Development Grants


Share

Teachers of grades 3-5, are you interested in a grant for professional development in science and math? Parents and students of a 3-5 grade teacher, are you interested in helping your teacher have a great opportunity to learn more math and science? The Mickelson Exxon-Mobile Teachers Academy is accepting applications through October 31. Be sure to apply soon!
Comments

Dyscalculia and Teaching Math


Share

Imagine trying to pay for a doughnut and not knowing if a $10 bill is enough.

Imagine not knowing which is more, 5 or 4.

Imagine never having a sense of time, so you are always early or late for things. Or someone gives you an hour to complete a task, and you have no idea how long that is or how to pace yourself.

Imagine never being able to retain the difference between left and right.

Imagine being in high school and understanding the concepts of algebra, but being unable to do basic addition and subtraction, let alone the higher operations.

Imagine being gifted in many, many academic areas, but having such difficulty in these areas that you “average out” so your school system never qualifies you for either the gifted programs or the special needs support you so badly need.

Imagine taking a summer job cleaning hotel rooms and being repeatedly reprimanded because you can’t keep all the steps in your head, forgetting the towels one time, the soaps another, dusting the counters yet another time.

Imagine that most of your teachers don’t understand, say thoughtless and clueless things about your disability, and some even try to block you from getting the special services and supports that you need.

Imagine the stress and anxiety that comes from not understanding what is wrong with you, why you can’t get the simplest things that come to all your peers so easily.

If you take the time to imagine all this, you might get a glimpse of the feelings conveyed by Samantha Abeel in her memoir, My Thirteenth Winter. I just finished rereading it, because I wanted to remind myself about what it is like for a person with dyscalculia.

This disability, unlike dyslexia, is one that I had never been trained in during my teacher education, though current research suggests in might be related to dyslexia. I think it is one of the lesser-understood disabilities, at least by the general population. Reading this memoir helped me become a better and more sensitive teacher, but it also raises some questions: how best to support people with this disability? After all, it makes living a regular life very challenging, between having to handle money (a big one) to using directions to get somewhere (though GPS can help) to being able to manage your time.

I have thought about Singapore Math in relation to this. In a session with Dr. Yeap Ban Har this summer, he mentioned that being able to do mental math and compute with number sense should be able to be done by all students without calculators, but that those with disabilities who can understand the concepts but cannot compute should be able to use calculators.

Part of the answer might be to look at multiple intelligence theory and use the student’s own strengths. Samantha Abeel is very strong in her visual and literary abilities. For her, a program that teaches math facts through poems, stories, and/or pictures might have been helpful, as it would use different brain pathways to help her retain these facts. One promising resource is here; please share others in the comments if you have any suggestions. I also had some success making multiplication table music CDs with a couple of math classes, and they seemed to help my students with learning differences the most.

Another interesting project with some research to back it up is a software program for young children that incorporates a game to teach basic number sense. It is a Java-based game, so it starts up slowly on my computer, and it’s not super-polished or professional looking, but the pedagogy looks solid. The game is called The Number Race. The full published research article about its effectiveness is at this site. In summary, the students who used it had some improvement in kindergarten, but it did not hold over time. A one-shot deal is not good enough; they need repeated help and practice.

If you would like to add anything about dyscalculia and how to help students who have it, please do so in the comments below. Thanks for reading.
Comments