Las Vegas Lessons

Latest: The slides for the keynote lecture for National Conference for Singapore Math Strategies are already available at www.singaporemathz4kidz.blogspot.com Other slides will be available at math.nie.edu.sg/T3 soon.

Riviera Hotel and Casino will be my classroom for four days. I will be teaching classes at the National Conference on Singapore Math Strategies for Grades K-6 with five other American teacher trainers. Several teachers are also sharing their experiences with the participants. I was told that there are 800+ participants from all but four states in the US with California having more than 100 representatives. There are also about 10 international participants from places as diverse as the Uganda, Mexico and the Philippines.

On Monday, I kicked the conference off with a keynote session with Char Forsten. The session is titled Singapore Math: Where East Meet West. I gave the audience the context in which mathematics is taught in Singapore. In particular, I touched on the emphasis on challenging problems in the PSLE, and the fact that most schools have their own problem-solving programme to supplement textbooks which focus on developing strong basics. I also spoke on high parental expectations and LSP and Foundation Mathematics as safety nets to make sure every student get help so that they do not fall too far behind. Many Singapore teachers conduct remedial programme in one form or another - some schools have structured remedial while others do them as and when the need arises. Finally, I touched on teacher education, before they enter the teaching service and when they are in service. I raised the point that perhaps it is possible for teachers to acquire pedagogical content knowledge and content knowledge by working through the student textbook.

Over the four days, I taught classes on a variety of topics ranging from word problems to visualization to lesson study and more. The participants were enthusiatic and appreciative despite the relatively large class size. On the first day, all the three classes I taught (visualization, questioning technique and challenging word problems) had about 200 people.

I will write about these classes. I will upload the slides for the keynote lecture as well as for the different classes at mathz4kidz.com and at math.nie.edu.sg/T3.

Other than this blog where I talk about the lessons I teach, you may go to http://www.singaporemathz4kidz.blogspot.com/ for general discussion on Singapore Math. There is a video gallery here. http://www.askyeapbanhar.com/ is where I post responses to questions I receive through e-mails. If you are interested in lesson study, go to http://www.singaporelessonstudy.blogspot.com/

Some Lesson Ideas for AYG2009

There is a sample lesson plan on incorporating scoring in diving mathematics lessons. See http://www.adrianbruce.com/maths/diving/diving_math_lesson.htm I think scoring in diving is especially useful for Primary 4 topic on operations involving decimals and Primary 5 topic on average.

NSM101 Lesson on Probability

I taught this lesson in Manila to a group of high school teachers using the New Syllabus Mathematics. The problem posed is to find the probability of drawing two cards with the same number, one from a stack of cards labelled 1 to 4 and another from another stack of cards, also labelled 1 to 4. Using the responses from eight groups, we were able to solve this problem that involved combined events using the knowledge of basic probability of single event. The responses included the use of listing, tree diagrams and table. I was quite satisfied we managed to use the responses to explain the multiplication rule.

Education in the US

Secretary of Education Arne Duncan

Last week I went to Berkeley County, West Virginia, to begin an open, honest conversation about education reform.I wanted to hear ideas about how we can accomplish President Obama's goal of providing every child in America a complete and competitive education, from cradle through career.As we prepare for the reauthorization of No Child Left Behind, I want to hear from classroom teachers and other educators, parents and students, business people and citizens. What's working, and what's not? What do we need to do that we're not doing, and what do we need to stop doing - or do differently?

In the coming weeks, I will ask questions here. Topics will include raising standards, strengthening teacher quality, using data to improve learning, and turning around low-performing schools. I will be reading what you say. So will others here at the U.S. Department of Education.Today, I want to start with a simple set of questions: Many states in America are independently considering adopting internationally-benchmarked, college and career-ready standards. Is raising standards a good idea? How should we go about it?

Let the conversation begin!

Arne Duncan

Art & Mathematics

Another interesting problems we solve at the Ateneo Summer Institute is the one in which the teachers created interesting pictures like rat, cat and flowers on geoboard. Later, I asked the teachers to predict which of the picture occupies the largest area. Interestingly, in both groups, teachers suggested counting 'dots left over' as an indicator of area. We later tested this theory by finding the area by counting squares.

Some of the pictures were easily dealt with because they were made up of squares and half-squares. Others were more challenging. I hope the teachers got the idea of how to sequence discussion in students' creation in a way they are kept challenged all the time. We moved from cases which were easy to find the area to cases which demanded more visualization.

Ateneo Summer Institute

This is the second year I am teaching this course for early grades teachers (kindergarten to third grade). In today's session, we explore why we teach mathematics. We did a problem that also includes drills-and-practice based on subtraction. Typically subtraction algorithm is done in grades one to three all over the world. I hope the teachers were able to understand that if all the child is able to do is to do subtraction then we have failed. The teachers told me a a cheap calculator cost about 50 pesos retail, that's a little more than USD1. I am sure the wholesale price is even lower. The teachers agreed that a 50-peso calculator can do subtraction rather well. So, if a drill-and-practice exercise enable childrent o do subtraction perfectly then they are just as valuable as a 50-peso calculator. i tried to convey the message that helping children develop thinking and other human competencies are equally important, if not more improtant than developing the ability to perform the subtraction algorithm. A teacher said the activity took more time. I hope we will see that the time invested (50 minutes) is well-spent. In fact, I argue that this is necessary. Unless a task is an extended one, the thinking involved is not very deep and, hence, not significant.

In case you are not in the class today, the problem was to use one set of digit tiles (0 to 9) to make two 4-digit numbers such that the difference is as small as possible. In both classes, we had 25 as the smallest possible difference. The teachers were impressive and were able to make some connections - such as the thousands digits are consecutive. In the end, they found three possible solutions 4xxx - 3xxx = 25, 5xxx-4xxx = 25 and 6xxx - 5xxx = 25. Try it and let me know what other insights you manage to have.

A teacher asked how teachers can formulate such problems. A short answer is to attend courses like these as well as to lookt hem up in books and on the internet. A long answer is to change our beliefs what mathematics teaching is all about. Once that happens, all the tasks we create or choose will have features that allows students to develop good thinking abilities and habits.

Division of Fractions

I have just completed nine periods of mathematics lesson on this unit with a class of primary five students who struggle with mathematics. I am teaching dividing fraction a/b by a whole number c which is often done using the invert-and-multiply method. Instead of using this method which I believe contribute to these students' difficulties with mathematics, I use an alternate method which based on simple reasoning ... if 4 divided by 4 is 1 then 4 fifths divided by 4 is 1 fifth. In cases when this is not obvious such as 2/3 divided by 4 we talked about changing 2/3 into 4/6. 4 sixths divided by 6 was then "easy beezy" as one student put it. It gave the students plenty of chance to revise equivalent fraction, which is fundamental to operations involving fractions.

I particularly enjoyed the third lesson when I gave each pair of students a fraction. If they thought that their fraction has the same value as the one I put up, they put it next to mine. In other words the board was filled with equivalent fractions which the students can then use to do various division.