Archive for March, 2011


Review and Using Khan Academy Tools

Friday, March 25th, 2011


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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.

Pi Day Pie and Baking Math

Monday, March 21st, 2011


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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

Pi Day Activities!

Tuesday, March 15th, 2011


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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!

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.

Delaware School District Succeeds Using Singapore Math

Saturday, March 12th, 2011


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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.

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

Saturday, March 12th, 2011


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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.

Math Joke #5

Tuesday, March 8th, 2011


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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!)

Math Jokes #3 and #4

Monday, March 7th, 2011


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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!

Common Core State Standards and Singapore Math

Sunday, March 6th, 2011


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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

Why Long Division Makes No Sense

Saturday, March 5th, 2011


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One of my favorite humor bloggers is Allie Brosh, author of Hyperbole and a Half. I’ve been catching up on reading her posts lately, and this one caught my eye tonight: Hyperbole and a Half: Long Division Isn't Real. (If you visit the link, just be forewarned that she uses the f-word once in her post.)

This is how she describes her mom’s attempt to teach her long division in fourth grade, the year Allie was homeschooled. (Her actual post contains an awesome drawing about it too, so visit it if you can):

My mom was like “First, you draw a line with a little hang-y tail!  Then you write the big number inside the little half-box.  Then you write the little number on the outside!  Now, divide the the little number into the littlest part of the big number that is at least as big as the little number.  It probably won’t fit exactly, but that’s okay.  Figure out how many times it fits all the way and write that number on top of the box.  Now, write the number that the little number does fit into underneath the number that it doesn’t fit into and subtract them.  Then draw a line.  Then write your answer under the line.  Then bring the next number in the big number down next to the number you just wrote.  Then hop on one foot and punch yourself in the face while singing Twinkle, Twinkle Little Star… “

Does that sound familiar?

That’s the pitfall of trying to teach the “how” of long division before the student understands the concept.

Teaching students division the Singapore way – by starting with place value disks and understanding what division is, working with the concept, and gradually connecting it with the algorithm, along with learning alternative ways of dividing – has been a life (mind?) saver for my students learning to divide.

Do you have a story about long division?

        
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