Saturday, November 9, 2013

Question about Student Support and Teacher Education

Thanks for your presentation at the Blake School on Monday afternoon.  I was attending with a team of math intervention teachers from our school district in Edina, MN, and we have some questions about differentiation.

1. In Singapore, how do schools provide support for students that are not keeping up with the rest of the class?
2. How do schools support students that are consistently one or two grade levels ahead of their classmates?

Additionally, do most of Singapore’s teachers matriculate from the same university? If so, do you think that is a benefit to math education or a detriment?

I’m looking forward to seeing you again this afternoon in Wayzata!

BanHar responds ...

All Singapore teachers complete their pre-service education from the same university (National Institute of Education NIE). Plus, it ensures consistency but we need to make sure this place provide the best teacher education money can buy. On the down side, the institution faces no competition and unless it has the discipline to improve and innovate despite the lack of competition, it can be the start of a decline. I hope our NIE is of the former. (I used to teach there.)

1. In Grade 1, students who are not on grade level competency receives support in mathematics and English Language - it is a pullout (we call it learning support program in mathematics or LSM). At all other levels, they receive extra support during class (in more difficult cases, there is a learning support teacher in class but that is not the norm). Usually, the teacher will have to take care of these students when the others are doing independent work. In many cases, we will meet with them after school for an hour or so once a week for remedial work. Having said all that, the use of concrete materials is to help every learner, including the struggling ones, learn well.

So we have in-class as well as pullout / separate remedial classes. In some cases we have a learning support teacher ( we call them allied educators, they are not trained teachers but undergo a training program for the job).

2. We provide these students with more challenging problems i.e. the enrichment approach. We do not accelerate them. However, these challenge is also made available to all other students. At upper levels (grades five on wards but sometimes as early as grade three, we track these students i.e. they are put into a separate class and the teachers do more challenging stuff with them, again not accelerating but provide more challenging tasks). For the most advanced they join the so-called gifted education program (GEP) from grade four onwards, where they are challenged with all kinds of things include research and project. From grade seven there are schools that they can go to to enhance their ability / interest e.g. schools of science and mathematics etc. 

Saturday, July 27, 2013

Lesson Study Question

I am currently leading my school's (primary) lesson study efforts. 

I would just like to seek your expert advice on the number of cycles of Lessons Study. Right now, my school currently embarks on two lesson study cycles. Some teachers have actually asked if the second cycle itself can be done not by observing just one teacher, but by taking the improved lesson plan back to their classes and conducting it. 

Would such a practice dilute the essence of lesson study given that there will thus be only one lesson during the first cycle where teachers observe teaching and understanding? 

I would greatly appreciate your expertise and take on this subject matter. 

Brenda, Singapore

You can have teachers taking the lesson and then teaching it to their own classes after the lesson refinement stage. In this case, the team has completed one cycle of the lesson. It is fine. Of course, going into the second cycle offers teachers with another opportunity to observe and talk about the lesson. If the team is motivated and can afford the time, doing a second cycle should offer them new things to see and should enrich the professional learning.


Sunday, June 23, 2013

Pies and Tarts

I am  a parent of a student in the school you gave a seminar. I found a problem in an assessment book which was confusing. Can you please help me to find out a solution to that problem?

I do not understand the way the answer given in the assessment book.
A Parent in Singapore



The Problem
Students with good number sense will know that the number of tarts and pies have to be in certain multiples given that they do not come in halves and quarters in a shop.

The ratio 3 : 2 tells us that tarts are in multiples of 3 (and pies in multiples of two) but as the tarts are packed in boxes of 4's, it must be in a common multiple of 3 and 4 (12). In the same way, the pies come in common multiple of 2 and 3 (6).

The least possible number for this to happen is 36 tarts and 24 pies - 9 boxes of 4 tarts and 8 boxes of pies. These will be $9 x $5 and 8 x $4 or $45 + $32 = $77.

It is also given that if all the tarts and pies are sold then they will bring in $770.

I think you can finish this up now.

This problem is based on ratio (P5), multiples (P4) and some basic multiplication and division (P3) and addition (P1).

This is a challenging P5 or P6 problem.

Note: P5 = Grade 5
Skeleton of the Solution

Monday, April 8, 2013

About Functions

Can you guide me how to solve Question 7b?

This is from iGCSE past examination paper. I could not even start.

Given that f(x) = 10^x.
(a) Calculate f(0.5).
(b) Write down the value of f^-1(1).

Usman

f^-1(x) is the inverse of function f.
Given that function f(x) = 10^x
So, f(1) = 10^1 = 10
f(2) = 10^2 = (10)(10) = 100 and so on
I think you can figure out 10^(0.5) ... it is the square root of ten, isn't it?

Let's get to 7(b), which is the one you wanted help in.

First you need to know the meaning of inverse of a function.
If a function is 2x (doubling a number) then its inverse is (1/2)x i.e. halving the number.

Given that f(x) = 10^x, the second part is asking you what is the value of x when f(x) = 1.
The answer is x = 0 because 10^0 = 1.

(Note: I use ^ to mean to the power of)

You may want to review the idea of inverse function.

Friday, February 1, 2013

About Range


I am a fourth grade teacher and we are currently working with mean, median, mode and range.  I received a parent email asking to clarify the definition of range.  Her email is as follows:

“ A question came up during homework on the definition of range. Apparently the kids' textbook says that the "range is the difference between the least number and the greatest number".  Range = greatest value - least value. That is not the correct definition. Range is the least number to the greatest. For example, if the test scores in one class range are between 90 to 100, and another class between 60-70. The textbook definition would say the range for scores in both classes is 10, which obvious does not make sense. (I think their textbook is defining what is known as the span of the data but that is rarely used.) A number of parents were puzzled about it but we don't know if this needs to be corrected or at this level the textbook definition should stand. Would you please clarify.”

Am I correct that finding the range does require students to subtract the greatest from the least amount in the data set?  I am not sure how to respond to her question.

Jillian, New York

Definition of Range: 
There are many places one can check on the definition - wikipedia quoted reliable mathematics / statistics textbooks. This is another source for a definition.

You can send the parent some of these links. 

We are often interested about the 'average' in a data set as well how the data distributes itself around the average. Examples of average include mean and median. examples of a measure of this distribution includes range and standard deviation.

Range is the size of the smallest interval that contains all the data and tells us about statistical dispersion.

I tried checking what the parent referred to as "span of the data" but could not find any entry on the internet. Apparently, it is not a conventional term. Range is a more conventional term to describe the idea under discussion. 






Tuesday, January 22, 2013

Question on Division Bar Model

Trish from Hawaii asked a question about setting up the bar model in a division type word problem.



Of course it is not necessary to solve every problem using the bar model.

Saturday, May 26, 2012

Spiral Curriculum

Good day Dr. Yeap! I attended the seminar last May 21-24 at SM Megall (see photo). Thank you for sharing your expertise and time with us. I just want to ask you about spiral progression. How do you apply it in Math? Can you give an example? Cely
Singapore mathematics curriculum emphasizes the spiral approach based on Jerome Bruner's explanation on spiral curriculum. The idea of the spiral curriculum, according to Bruner - 'A curriculum as it develops should revisit this basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them.' Most people will not miss the idea of 'repeatedly' but may miss the subtle notion of 'building upon them' and 'until the student has grasped the full formal apparatus' of the target concept. In Singapore curriculum, addition is taught four times in Grade 1 (this is a core idea and they are new to it) - addition with 10, within 20, within 40 and within 100. Students get to revisit the idea of addition repeatedly but each time building on the strategies that they already had. When they add with 10, they count all and count on, perhaps with the use of concrete objects and drawings. Later, in addition within 20, they learn to make ten before adding, effectively acquiring the notion of place value. Later they progress to more formal approaches such as adding ones and adding tens in the formal algorithm. Thus, it is not mere review of materials. It involves extension. In a similar way, multiplication of whole numbers is taught in grades one through four; addition and subtraction of fractions is taught in grades two through five; area of plane figures is taught in grades three through seven; solving equations is taught in grades seven through nine. As a result, in Singapore, Algebra is taught across grade levels in high school (grades seven through twelve). Thus, we do not have the practice of teaching Algebra, Geometry etc separately. They are all under the subject of mathematics. There is geometry in all grade levels.