Archive for October, 2010

Core Knowledge vs. Singapore Math

Monday, October 18th, 2010


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.

NCTM Baltimore: Final Report

Saturday, October 16th, 2010


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!

Math Jokes

Thursday, October 14th, 2010


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!

NCTM Baltimore: Day 1

Wednesday, October 13th, 2010


I’m on my way to participate in the NCTM Regional conference in Baltimore, Maryland. My presentation is first thing tomorrow morning, and it will be on the topic of Singapore Math model drawing. The session is 75 minutes long, enough for a taste of several types of model drawing. Hopefully the participants will come away with some understanding of the power of model drawing and will be able to put it to use.

If you are there, come by and see me after the presentation, from 11:00 AM on, at booth 614, with SDE!

The Daily Riff: Singapore Math Articles

Wednesday, October 13th, 2010


Bill Jackson, the Scarsdale Singapore Math coach who is making waves nationwide, wrote an interesting series for The Daily Riff. The first article lays out how he got interested in Singapore Math. Here is a quote from his experience working with Japanese math teachers:

When I began working with the Japanese teachers, I soon realized three important reasons why they were such good math teachers:

(1) They had a high level of math content knowledge. In fact, I felt that their first grade teachers knew more about math than I did as an 8th grade teacher!

(2) They used thin, lightweight paperback textbooks that were much more focused and coherent than our heavy hard cover books.

(3) They continually worked to improve their teaching throughout their careers by conducting lesson study.

The next article describes a lesson that uses problem solving and model drawing to bridge children’s thinking from concrete to pictorial to abstract. I really like the way he describes the differences in approach between Singaporean lessons and traditional American textbooks:

Problem solving and mathematical thinking are two big ideas behind Singapore math. To understand this better, let’s look at an example that many American elementary students struggle with, long division. As noted in part one of this blog, word problems are often the last thing on the page in U.S. mathematics textbooks. Often times teachers never even get to these problems or if they do, usually only the advanced students have the opportunity to tackle them while struggling students continue to practice procedures. The third grade Primary Mathematics textbook, however, introduces long division with a word problem. The description below is one way how the concept of long division might be introduced in Singapore math.

After a brief warm up with multiplication and division flash cards, the teacher introduces a problem by saying, “Our friend Meihua has some toy soldiers. She wants to put them equally in some tents.” (Note that no numbers are mentioned and there is no question asked yet.) The teacher then asks the students to try to imagine the situation and discuss what it means to put the soldiers in tents equally. Students share examples such as, “If she has 15 soldiers and 3 tents, she could put 5 soldiers in each tent,” and “If there were 10 soldiers and 5 tents she could put 2 soldiers in each tent.”

I highly recommend a visit to these articles; he has much of value to say about teaching math.

Teach Show on A&E: Educational

Sunday, October 10th, 2010


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?

Comment: A Slower Approach to Math

Friday, October 8th, 2010


Following on from last Friday’s New York Times article, the NY Times blogs ran a brief follow-up article titled, “A Slower Approach to Math,” with the opportunity to add your own comments to it. There were some pretty interesting thoughts there, which inspired me to add the following comment:

As a teacher experienced in teaching Singapore Math and training other teachers to use it, I am constantly learning about the state of education around our country, especially in math.

I see Singapore Math has many strengths as a curriculum and approach, and more of these are being adopted into our schools, as well as into other curricula. The model drawing approach to problem solving, for example, is a powerful tool that is obvious when you know it, but takes a while to understand and apply.

Without adequate training and development, however, Singapore Math cannot be a panacea for schools that are failing to teach math well. Much more needs to happen there, from teaching the methods to making more time for math in the classroom, as others have noted.

But we are dealing with a double deficit: a generation of teachers who have been impacted by poor math teaching when they were growing up, so they feel inadequate in that area. Not everyone, of course, but those who are confident and able in math tend to be in the minority. How do we solve this problem?

In addition, I too had trouble recognizing the curriculum in the beginning of this article about Singapore Math. Maybe what the writer was referring to, in terms of “slowness,” was the time the curriculum spends on mastering the number bonds for each number. That is, knowing all the different numbers that can be used to make seven (5+2, 3+4, 6+1, 7+0) becomes a powerful tool later to be able to compose and decompose numbers at will, allowing strong mastery of math facts and the basis for number sense.

Finally, @Learningcoach, forgive me, but I found your video difficult to take. First of all, the ability to recall multiplication facts is a useful skill and should be practiced, but to make that a priority in first grade may do more harm than good. The boy in the video seemed stressed to me. To ensure success for everyone, even those who find memorizing math facts difficult, we need to take the stress out, or why will they even want to continue to learn math? Enough challenge to keep them at the edge of their comfort zone is important for learning, but not outright stress. And from what I understand, they do drills like that in Asian countries anyway, so I doubt we will get ahead of Singapore that way.

What will help us to rise up in the ranks is to combine the mathematical skills other countries have achieved with the unique assets of our country, the creative and independent thinking and innovation we prize so highly.

Math and Baseball

Friday, October 8th, 2010


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 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!

NaNoWriMo: Our virtual classroom is up and running!

Friday, October 8th, 2010


Good news! The virtual classroom for our awesome YWP program is up and running. As soon as participants are fully signed up, they will receive login information.

I have received a number of inquiries about the location of the program. The answer is: it’s up to us! Some people are north, some are south, some are middle… we will make it work, even if I travel a couple of times a week. Carpooling can help too.

Remember, if you want to facilitate this, we would love your help. Let us know if you have good meeting places, and what dates and times work for your family.

Math & Science Professional Development Grants

Wednesday, October 6th, 2010


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!


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