Tuesday, August 18, 2009
Thursday, July 23, 2009
Saturday, July 18, 2009
Jenny, a teacher in the Philippines
My co-teacher asks me to e-mail you because she attended a conference in Manila, the Philippines in May 2009. What are the different processes in teaching concrete ideas in mathematics? Thank you so much.
Wednesday, July 1, 2009
Ahmad and Mei Ling saved $800 altogether.
A quarter of Ahmad's savings was $65 more than a fifth of Mei Ling's savings.
How much more money than Mei Ling did Ahmad save?
Please explain the answer using model
Tendo, a teacher in Indonesia
Thursday, June 18, 2009
Thursday, June 4, 2009
We have to tell you that this is our first year using your method in Mathematics, and, at the beginning , we had some problems, because of the language (our students don´t speak English at home, they learn it only at school). But now, we have used the book for 4 months, and we think the students, and we, the teachers, have learned a lot from it.
Wednesday, June 3, 2009
Monday, May 25, 2009
Question posted by Paula, a mathematics co-ordinator in Chile
Also in multi-step problems, the students may not have the ability to monitor their thinking. This is metacognition. When we teach word problems, we should model and coach rather than explain. That way, we help them in developing the ability to think through the many steps in a problem.
Monday, May 11, 2009
Friday, May 8, 2009
Monday, April 27, 2009
AB + B = BA
A = ________B = ________
How do you teach a P1 child algebra?
Monday, April 13, 2009
Car A and Car B left Town X for Town Y at the same time. Car A was travelling at an average speed of 80 km/h and Car B was travelling at an average speed of 60 km/h. Car A was leading Car B by 8 km for every 1/6 of the distance from Town X to Town Y. Find the distance between Town X and Town Y. One of my friends solve it like this: 6 units x 8 km = 48 km and 80 km - 60 km = 20 km. 80 : 20 = 4. Hence, the distance from Town X to Town Y = 4 x 48 = 192 km. However, the solution is too difficult for my pupils.
Car A travels 20km more than Car B in an hour. (80-60)
Saturday, April 11, 2009
Friday, April 10, 2009
Thursday, April 9, 2009
88 children took part in a swimming competition. 1/3 of the boys and 3/7 of the girls wore swimming goggles. Altogether 34 children wore swimming goggles. How many girls wore swimming goggles on that day?
Sunday, April 5, 2009
Friday, April 3, 2009
Is there a flaw in the reasoning? Or the problem was not well-posed. Comments?
Wednesday, April 1, 2009
Looking forward to meeting you in the Netherlands,
With kind regards,
Jaap den Hertog
Freudenthal Institute for Mathematics and Science Education
c/o Ank van der Heiden
PO Box 9432 3506 GK Utrecht The Netherlands
T: +31 30 - 263 55 55 F: +31 30 - 266 04 30
Monday, March 23, 2009
Tuesday, March 17, 2009
Students have difficulties with the word remaining. Although most of them can solve it easily using the model method, some cannot understand the remaining part when asked to solve it just by using a number sentence.
Posed by Khai
Friday, March 13, 2009
The ICME-12 congress will be held in Seoul, Korea, on July 8-15, 2012.
The printed version (together with a CD-ROM with all the regular lectures) costs 50 euros (including shipment). The order form is available at the same address.
Personally, I have been to every ICME since Japan (2000). This conference helps one updated about the latest developments in all areas of mathematics education research. It also offers a chance to catch up with overseas collaborators and form new networks. It is a good sounding board for PhD students to get other opinions about their research problem. I have always encouraged my own to do so.
Tendo, a teacher in Indonesia
There are several variations to this task.
1. 2/3 : 1/3
2. 2/3 : 1/6
3. 2/3 : 1/8
4. 2/3 : 5/8
Students have learnt two meanings of divisions in whole numbers. For example 12 : 4 has been modeled by 12 things shared among 4 persons as well as 12 things put into groups of 4. For the latter, we ask "How many 4s are there in 12?"
We can use this meaning of division to teach 2/3 : 1/3. How many 1/3s are there is 2/3? This is obvious. The answer is 2. For 2/3 : 1/6, students need to be able to see that 2/3 = 4/6. Then the answer to how many 1/6s are there in 2/3 becomes obvious.
For 2/3 : 1/8, students know that 2/3 = 16/24 and 1/8 = 3/24.
It is easier to do 2/3 : 1/6 which is the same as 16/24 : 4/24. There are four 4/24s in 16/24.
In 16/24, there are five 3/24s (which is equal to 15/24) and another 1/3 of it. Thus, 2/3 : 1/8 = 5 and a third.
Can you explain 2/3 : 5/8?
Friday, March 6, 2009
Thursday, March 5, 2009
Tia, a teacher from Indonesia
He should not need to. After all we want them to use mental strategies for computations. He has been able to do that. The use of paper and pencil should be a temporary help for children who cannot do it using mental strategies (because their number sense and metacognition are not yet well developed). For example to divide 96 by 8, we want students to see that 96 is 80 and 16. Both 80 and 16 can be divided by 8 mentally to give 10 and 2. hence, 96 divided by 8 is equal to 12. A 12-year-old should not need to use paper and pencil to do a computation such as this. Similarly, to multiplyu 39 and 6, we want children to use the product of 40 and 6 to obtain the product of 39 and 6. The ability to do so tells us that the child is able to make connections between the two and has a strong number sense.
Tuesday, March 3, 2009
Sinta, a teacher in Indonesia
Sinta, a teacher in Indonesia
Friday, February 27, 2009
Why don't you ask your child to try and listen to his reasons. There are different possible answers depend on the relationship that we give to the numbers. This is the case when the blanks are at the end. Although it is good discussion problem, as an examination item it needs to be less ambiguous.
My son managed to solve the problem for me.
List three terms to continue a pattern in each of the following. 5, 6, 14, 32, 64, 115, 191, 299, __, __
This is his explanation but I am not sure of it is correct. Please advise.
Find the difference between each of the above numbers:
Monday, February 23, 2009
Thursday, February 12, 2009
Virgie, a teacher in Manila
The Singapore curriculum attempts to focus on as few ideas as possible so that students develop a strong foundation for mathematics in grade seven and beyond (secondary school). Topics that are not essential will be taught at later grades. For example, while 0.6/3 can be taught as sharing (0.6 is shared equally among three persons), 0.6/0.2 needs to be taught as grouping (How many 0.2s are there in 0.6?). Conceptually, primary students have done both for whole numbers (grade one) and for fractions (2/3 dividied by 4 in grade 5, 2/3 divided by 1/6 in grade six). In the Singapore curriulum, 0.6/3 is taught in grade four. In principle, 0.6/0.2 can be taught in grade six. However, in order not to burden the students with too many things, why not do it a year later? In fact, we are hoping that students are able to extend what they learn in 2/3 divided by 4 to 0.6 divided by 0.2. This is the spirit of Teach Less, Learn More which the Singapore Ministry of Education encourages schools to do in implementing the curriculum. The same explanation goes for division involving mixed numbers.