Mathitudes

Thursday, February 19th, 2015

Ever since I heard this story, I’ve been working to change my communication with children about what is important. I think this comic says it better than my soapbox speeches. And you can substitute anything else for math, but I chose math because I hear that all the time.

*If you’re stuck on helping your child with a concept, try khanacademy.org or other sites like mathplayground.com to refresh your skills and make learning fun for both of you.

For more on why this is important, see this Scientific American article titled The Secret to Raising Smart KidsIt has some citations to research showing why this is so important at the bottom of the article.

Also, if I dare mention it, this is why I think Common Core State Standards Mathematical Practice 1 (CCSS MP.1), Make sense of problems and persevere in solving them, is so essential. The way we have gone on historically has led to a lack of perseverance, but changing our values and how we speak about them can turn it around.

Feel free to share, and teachers and presenters, please feel free to use these comics in your work. Let me know if you do and how they came across if you feel like it.

And as always, please comment below!

More Math Apps for iPad: Singapore Math and Common Core

Saturday, July 6th, 2013

It’s been a while since my last post on iPad apps, and in the meantime a lot has happened. For one thing, I have downloaded and tried quite a number of math apps. I’m going to start a round-up of some of the most useful apps as I have time.

number bondsFirst up: exciting news! The Number Bond software, that I lamented being only on Mac or PC for so long, is now ported to iOS. As far as I can tell, having downloaded only the addition/subtraction version, it’s pretty much exactly the same as the computer version.

This has its pros and cons. Pros: the familiar interface, its simplicity, and the fact that it does one thing – it teaches number bonds at different levels. Cons: In light of the outstanding, more powerful software out there, it takes advantage of very few of these features. For example, it is not adaptive, meaning the difficulty does not change with the user’s proficiency. It also does not save user data, something the better educational software is doing (as I’ll discuss later), even emailing it weekly to the parent or teacher if desired. It also has a few bugs to iron out, which I’m sure will happen soon.

So would I recommend it? Yes, as a practice tool for a child at home or as a station in the classroom – but I would love to see it get more developer attention and become more powerful.

Download Number Bonds: Addition & Subtraction to 99

Next up: AL Abacus

For anyone teaching/homeschooling with Singapore Math or a Common Core curriculum, such as Eureka Math, or working with a child with a math learning disability, you will find  that the Slavonic Abacus, or Rekenrek, is incredibly useful for teaching number sense and place value. It breaks down numbers into groups of five and ten, which are easy to manipulate mentally, not least because our hands are right in front of us since we are in the womb, with five fingers each (otherwise known as digits!). While having the concrete manipulative is ideal for sensory feedback, sometimes teachers want to project the abacus to a group, or show a demonstration to a small group. This is where the iPad version, AL Abacus, comes in.

AL Abacus to 100This app is a Slavonic Abacus with two modes. The first is the side with numbers to 100. To access this side, hold the abacus in landscape (horizontal) mode. When all the beads are to the right, it is like pressing “C” (or Clear) on a calculator. To reset all the beads, just tilt the iPad to the left – exactly like on a real abacus. Just slide single or groups of beads to the left to add, subtract, multiply, or divide within 100.

AL Abacus to 1000sThe second side is accessed by turning the iPad to portrait, or vertical, orientation. In this mode, you can work with numbers to 1000, with different columns of beads representing the different place values. This can be a very powerful, easy tool for computing whole numbers through the thousands. To reset the beads, just lift the iPad up, and the beads all fall to the bottom.

Incidentally, this second side was designed by Dr. Joan Cotter, who did her doctoral dissertation using it. Her website, with additional resources, including how to use the AL Abacus, is http://rightstartmath.com/resources/.

This is an almost perfect representation of a physical version of the abacus. There are only two things missing, in my view: the sound of the beads clicking together, which would be great sensory feedback.

Download AL Abacus – Activities for Learning, Inc.

Since this tool is new to many people, here are some other resources besides just the iPad version.

Do you have other ideas or resources for teaching number bonds or using the Rekenrek? Post them in the comments!

New Parent Workshop: Understanding Math Education

Tuesday, May 7th, 2013

Over my time as a math teacher, I’ve met hundreds of parents and teachers who all came to me with the same fundamental need: “I don’t feel good at math or confident enough to help my child (or students).” We rarely hear this from parents about literacy – everyone knows it starts with reading to your child – which speaks to the gap in our culture between literacy and numeracy.

Teaching Singapore Math and training teachers in it for years has deepened my understanding of how math works in ways I would never have believed possible. While previously I was just “good at” math, the subject now reveals its magic to me on a daily basis. I love the “ah-ha!” moments when a previously mystifying concept comes to light in a child’s – or adult’s – mind.

Reaching adults hasn’t always been easy, though. I’ve played with the idea of offering online courses, but I haven’t had the blocks of time to devote to setting this up, plus it seems impersonal to me. Professional development courses in schools are expensive and available only to teachers, while many parents long to be able to help their children, especially if they homeschool.

This led to the idea of offering local workshops. We are piloting one at Think on Hudson on May 18 from 2-5 PM. It will be limited to 20 participants, and Garry, the CEO, will be offering free child care and perhaps classes for the children. I am keeping the cost minimal so everyone who wants to can attend.

May is a very busy time, and not everyone will get to attend. Therefore, assuming it goes well, I am planning to offer access to the video of the workshop and the booklet at a discounted price afterwards. If there is enough interest, I may even offer it live via Google Hangout.

Please register here if you are interested. You can also see the Facebook event here. We would love for you to come!

Singapore Math Cheat Sheet: Starting a Child Mid-Year

Wednesday, March 13th, 2013

A teacher recently asked me a question: “What do I do with the student who is strong enough in his math concepts, but he has no idea about Singapore Math approaches like number bonds, and he starts our school late in the year?”

For her and other teachers in the same boat, I’m making this “cheat sheet,” which is targeted at elementary school children who start mid-year in Math in Focus or Primary Mathematics.

1. Number Bonds

Number bonds show the ways in which numbers relate to each other. They can also be thought of as “part-whole” pictures, in which you see two or more parts that make up a whole.

To catch a child up with these, you can try one of several things.

a) Sit with the child and a laminated number bond page, and write number bonds in them. Ask the child to create number sentences (equations) from the number bonds. Then have the child fill in the missing number in a number bond with a part, or the whole, missing.

Example:

number bond graphic

Whole with two parts

Number sentences:

4 + 6 = 10

6 + 4 = 10

10 – 4 = 6

10 – 6 = 4

With practice, the child will realize that all these facts are related, and that subtraction starts with the whole minus one part, while addition is made of two parts forming a whole. I’ve found it can help students who are struggling with subtraction, especially with those problems missing the whole, for example _____ – 7 = 5. Rewriting these as a number bond can assist the child to see that the whole is what is missing, so she needs to add the two parts.

An article that explains number bonds more in depth can be found at Let’s Play Math.

b) Have the child play number bond games. One of the best I have found is called Number Bonds. It is available for both addition/subtraction and multiplication/division. See my review of these games here.

c) Play other games that involve number bonds. Addition War and Subtraction War, which are outlined in this PDF, are both fun games children love. You can customize them to this need by having the student write the problems that turn up on the cards on a laminated number bond sheet with a dry-erase marker, which will show you how much the child understands about number bonds.

2. Model Drawing

Another feature of the Singapore approach to teaching math that is new to many US teachers in model drawing for problem solving. This is a powerful visual approach, and with practice, it becomes much faster than other ways of solving word problems.

A great resource to learn about model drawing is at thesingaporemaths.com. To practice free problems using the model drawing approach, head on over to thinkingblocks.com. There are also videos on that site that explain the approach, and free iPad apps are available for four different types of word problems here.

For a new student when you don’t have much time to give one-on-one attention, set her up on Thinking Blocks to help her understand how to use this.

3. Place value

The Singapore approach places a heavy emphasis on place value. Many other programs do too, but not all, so you may find this lacking in a new student.

Again, considering that teachers may be too busy to spend a lot of one-on-one time with students, I am providing several electronic resources to teach this.

a) NLVM has some good resources for teaching place value. They require Java to run and can be used on a computer or interactive white board, or you can download their app that doesn’t require Java. Here are links to:

b) Here is an Illuminations lesson plan to play a place value card game.

c) A good iPad app for modeling with place value blocks is Number Pieces.

d) If you do have the time, make your own place value chart and use money or place value blocks to represent tens, ones, and other places your student may be learning. This will help a great deal with his number sense.

 

That wraps it up for this article, but if you have other questions, suggestions or issues, please let me know in the comments, and I’ll update the article as needed. Thanks for reading!

 

Pi Day: Pi Music and Classroom Activities

Monday, February 4th, 2013

With March (and spring!) right around the corner, many teachers are already thinking about celebrating Pi Day, or March 14. This is a great day to celebrate how much fun math can be.

I was inspired all over again by this music video using Pi to make music.

 

pi posterIf you would like to make Pi Day fun for your students, there are lots of fun ideas in this lesson plan, available from Teachers Pay Teachers for $1.99.

I also offer a free downloadable Pi Poster showing almost 1,500 digits of pi. My students always love these. Enjoy!

New Presentations for the Fall

Monday, September 26th, 2011


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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!

Review: Number Bonds Software for Singapore Math

Wednesday, September 14th, 2011


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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.

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

What Makes a Good Tutor?

Tuesday, March 15th, 2011


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I recently watched a video of a teacher helping a student master tens and ones using ten frames and unifix cubes. While the video showed some of the ways Singapore Math teaches number sense well, a few things about the teaching style struck me. These are pertinent to tutoring because it was a one-on-one situation.
 
One thing that stood out was that the teacher sometimes gave the answer to the student before the student had a chance to think. This is a mistake that is so easy to make; the tutor knows the answer, and the child doesn’t, so why not tell the student what the answer is? That will help them learn, right?

The thing is, any good teacher or tutor knows that the best learning happens when the child discovers something for him or herself. For most people, if they know the answer, it’s hard to hold themselves back from giving it to the child. But the best teachers guide or lead children to making their own discoveries. If children are moving in the wrong direction, a good tutor guides them toward successful results. This requires a knowledge of why students are making the mistake they are making.

For example, say I’m checking some pre-algebra homework. The problem the student has to solve is 3x + 4 = 73. The student’s answer is x = 25-2/3. From my experience working with students, I will know that the student performed all steps correctly except for adding 4 to 73 instead of subtracting it. Depending on the pattern that shows up with other problems, it could be a fluke, or it could point to the need to review the concept of positive and negative integers, or how to solve an equation with a variable. If it’s the latter, we may need to go back to the concrete stage of learning and work our way back up to the abstract (equation) level. Throughout the process, I will not give the child the answers, but will ask them to justify their answers each step of the way. That way, they are more likely to catch their own mistakes and correct faulty thinking.

Being a good tutor requires more than just mastery of a subject. It requires an understanding of how the subject works, how students learn, what kinds of mistakes they might make and what those mean in terms of review. Most of all, it means being able to guide students toward their own voyages of discovery and learning.

Teach Show on A&E: Educational

Sunday, October 10th, 2010


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A new reality show called Teach premiered on A&E on October 1. It follows Tony Danza as he enters the teaching profession as a high school literature teacher, with no prior teacher training.

I was fully prepared to dislike this program, as the preview indicated it would be another feel-good show about a former actor getting a chance to make a difference in young people’s lives. Why, I thought, aren’t they featuring an excellent non-celebrity teacher? But I was pleasantly surprised.

Teaching is a hard profession. It’s even harder if you want to be good or excellent at it. The show does a good job of portraying the real struggles that real teachers face: students who don’t understand what you are teaching, guardians who are in your face about their children’s needs, the demands of a curriculum and needing to differentiate your instruction to meet very diverse learning styles, administrators who bring you into their office for “the talk” about problems in your teaching, and more. It’s enough to bring even the strongest to tears, and I was glad to see the show doesn’t gloss over the pain and struggle of that first year of feeling so inadequate.

Tony’s tears and statements that “I’m not sure I can do this” are feelings I’m sure every teacher can relate to. In once scene, a special needs teacher told Mr. Danza that 100 teachers in their district had already dropped out of teaching in the first week, and she was glad he wasn’t one of them.

Danza clearly has a good heart and wants to do well by the students. However, experienced teachers will cringe at many of the novice mistakes he makes, ones that could have been avoided had he attended a good teacher training program and had an experienced mentor. For example, when he wants to talk to a girl about her poor performance, he does so in class, in front of her peers (and the camera), and he does so too long. Talk about embarrassing – no wonder the girl shuts down and escapes as soon as she can! Tony, you have to keep it real but light, and never in front of the friends. Avoid embarrassment and shame above all.

Another major misstep is how he handles special needs requests. The coach and administration try to push him into allowing students to go to the resource room on request by explaining the legality question. If the students request to work in the resource room, they have to be allowed to go. Danza doesn’t understand and instead keeps trying to build their self esteem, viewing them as lazy and able to achieve more if they only try.

The legality argument does nothing to convince Danza. The only thing that works is a special meeting to explain special needs. Towards the end, Tony is handed a piece of paper to complete. The page has text with mixed-up and backwards letters, as well as some non-words. When he is told that this is how some students see the text he is giving them, the penny finally drops, and he sees how wrong he has been.

If you would like to see this for yourself, there is a good introduction from the University of Essex that includes several reading comprehension tests simulating different types of dyslexia. I remember my special needs classes and how simulating life with a learning difference enlightened me before I ever entered a teaching situation. Without that kind of experience or training, teachers can do more harm than good, as the show demonstrates.

So is it a good idea to feature a reality show about a celebrity-turned-teacher? In this case, I think it is. Danza is personable, comfortable with the camera, able to be honest in front of others and on camera, and has the name to draw watchers. I can only hope that seeing some of his difficulties may show some of the non-educators who create education policy what teaching is actually like. Of course, they would probably think they would do a much better job. Who doesn’t, until they are tested?

        
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