More Math Apps for iPad: Singapore Math and Common Core

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!

Normal vs. Abnormal


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I was at the Westchester County Airport this morning, in the women’s room, when a woman and I started a conversation over soap. The topic soon changed to bathroom decor, which we discussed for a few minutes before wishing each other well.

Then the woman walked out, and I was able to see her gait. It was quite lopsided, and she walked with the aid of a cane. I had noticed that she had mostly been using one side of her face to talk, but now I could see the extent of the asymmetry of her body.

After seeing this, I found myself wondering why. A stroke, some kind of palsy, something else? Then I stopped myself. Why was I focusing on this? The woman clearly wasn’t; she didn’t even use the handicapped stall, though she would have been most entitled to use this spacious stall.

This thought process led me to think about education in general, and how much focus there can be on what is “wrong” with a student, to the point that all we can see are the “problems.” Many educators have written about the issues around labeling, and I think this is what is at the core of the matter: that instead of a whole human being who may be encountering some challenges, children end up being viewed – and often viewing themselves – through the lens of a diagnostic label.

But those closest to them know they are so much more than that label. The families that have cared for the children since infancy and have seen their serious, funny and talented sides need to know that the teachers of their precious children will be seen as the whole people they are.

It’s hard for teachers to do this when under the tremendous pressures of time, curriculum, large class sizes, behavior issues, and most of all, performance on standardized tests. It is also normal for our brains to observe, analyze, and try to understand things we encounter that are outside our typical experience.

If we want children to succeed, though, we need to override this urge to focus on what is “abnormal” and bring humanity back into the classroom as the main driving force behind what we do.

Teach Show on A&E: Educational


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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?

Dyscalculia and Teaching Math


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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.

13thwinterIf 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. 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.