Is there a standard template to answer Sect C Maths?

Very frequently, parents and students ask me if students would be penalized if they did not follow a certain “template” type answer taught in schools.

As an example, here is a question posted to me.
Posted by Anonymous 28 Mar 2008 PM 01:28 :

Mr Song
Wish to seek your opinion on the use of equivalent ratio to solve
this problem. This method may be more suitable for weaker students , but it’s
longer
Before After
B:G B:G
5:3 5:4
25:15 30:24As there is an
increase of 5 boys and 9 girls
30-25 =5 boys
24-15 =9 girls
At first
there are 15 girls
Will students be penalised if they use this method.

The Maths Question that is referred to can found here: http://road-to-psle.blogspot.com/2008/01/mgs-paya-lebar-pri-school-p6-math-ca1_21.html

Before I proceed to comment whether a student will be penalized, let me share with you my personal experience, when I was a teacher in school. I have taught China Nationals in schools and they worked out their sums very differently. Usually they score 100%. So, do I penalize them for using a different way of working their sums?

Mathematically, they are correct. The only difference is that most Singapore students use a step-by-step approach.

If the working is mathematically correct, I mark them correct. I don’t penalize them. After all, how can you wrong a working and the answer if it is right?

However, as much as I am tempted to tell students and parents that it is OK to use their own method, provided the working is mathematically correct, I would not say it publicly. The reason is that I do not want to undo what the teachers in schools have taught their students.

The “standard template” working taught in schools works brilliantly for the average and weaker students. Those who are strong in Maths will of course be able to see that the question can be approached in different ways.

If I were to give an opinion in a public blog, that it is OK to use a method other than the “standard template” working, I may be undoing all the hard work teachers in schools are doing to help the average and weaker students.

All I can say is that when I was teaching and marking exam papers in schools, I have never penalized students who gave me mathematically correct working that leads to a mathematically correct answer. However, I have stopped teaching in schools since 2002 and that of course, means that I have also stopped marking exam papers.

Since I will not be the one who will be marking exam papers, I may actually be the wrong person to ask if a student would be penalized, if he used a non-standard template working.

The best person to ask is still your own teacher.

I hope that answers the question posted by “Anonymous”.

Obsession with calculators

Since the introduction of the use of calculators at P5 this year, I find that many students (and some parents) are only too eager to know how that impacts exam papers. As of Mar 2008, I have not really noticed any significant difference in exam papers – at least not enough to cause any student or parent concern.

I feel that the “over-concern” on how calculators will affect exam papers and eventually the PSLE 2009 next year, detracts students from the real objective – ie the need to do well for the PSLE 2009 Math Paper next year. With or without calculators, students are expected to be able to solve PSLE Maths questions with respect to Fractions, Decimals etc. As such, a preoccupation with calculators or how exam papers will be set because of calculators, in my opinion, is a needless distraction.

I have noticed that some students have the idea that since calculators are allowed, mental multiplication tables are now redundant. That is a fatal mistake. Without mental multiplication tables, students will be slowed down in deciphering lowest common multiples – a crucial skill needed in solving addition and subtraction of fractions.

It must also be remembered some schools allow calculators only in some sections. That also looks to be the likely format for the PSLE Maths 2009 Paper. If a student is too dependent on calculators, he may be slowed down in the sections where calculators are not allowed.

The correct attitude towards calculators should be that it is introduced at P5 so that when the student uses calculators in secondary school, he would be familiar with all the functions that comes with calculators. The attitude should never be that the calculator is introduced so as to lighten the burden of calculation for PSLE Maths.

As for whether Maths questions will be set differently because of the introduction of calculators, I feel that is a non-issue.

If there is no difference on how PSLE Maths Paper is set, the worry and concern on the part of students and parents is unproductive.

If there is a difference on how the PSLE Maths Paper is set, a strong foundation in Maths and a strong foundation in mental multiplication tables, would render any difference negligible.

The only ones who need to worry are those who have not built their Maths foundation topics (like Fractions, Decimals, conversion of units etc) and their mental multiplication tables.

My advice is to drop the unnecessary concern (ie how the introduction of calculators will affect Maths exam papers) and concentrate on the real goal – ie to do well for the Maths Exam Paper itself.

PC School P6 CA1 Revision 3 2008 Math Q2

The total amount of water in Tank A and Tank B is 11 litres. Tank A had 3 litres of water more than Tank B. After pouring out an equal amount of water from both tanks, the amount of water in Tank B is 2/5 that of Tank A. How much water had been poured from Tank B?

Working



The above is a model drawn to help students solve the Maths question. Further working and the answer will not be given, as the school that gave the question above, has not given the working and answer to its students yet.

Word gymnastics, mind bender or P6 Maths?

It appears that Primary schools are now trying to outdo each other – in the field of Mathematics. Section C P6 Maths set by schools appears to get tougher, wordier and more complex. I got a call from a student on Sunday night to help her solve the Maths problem below. She couldn’t solve it over the weekend.

The question below is about Fractions. However, note how the question was set. For a 12 year old, it takes a clear mind and a strong comprehension of the English language to be able to understand what is asked.

Question:
There were some mangoes at a fruit stall. In the morning, the number of mangoes sold was 2/5 of the number of mangoes left. In the afternoon, another 22 mangoes were sold. The total number of mangoes sold was 3 less than 9/14 of the number of mangoes the fruit stall had at first. How many mangoes were there at first?

Click on image below to enlarge


The above model is to help my students solve the question. I am not giving the rest of the solution or the answer, because the school that gave the question above, has not given its students the working or answer yet.

As such, I do not feel it is right to give a "free handout" to students under my care.

Red Swastika School P5 CA1 2008 Math Paper 2 (Q15)

The figure below is made up of five identical rectangles. If the toal area of the figure is 540 square cm, find the perimeter of one rectangle.



Solution

Area of 1 rectangle ----- 540 square cm divided by 5 = 108 square cm



Length of rectangle is 3 times breadth rectangle, therefore, we can divide 1 rectangle into 3 equal parts as shown above.

The area of 1 square above ----- 108 square cm divided by 3 = 36 square cm

The side of this 1 unit square has to be 6 cm (6 x 6 = 36)

Since 1 side of the square is 6 cm, the length of 1 rectangle is -----
6 cm x 3 = 18 cm

The perimeter of 1 rectangle is therefore,

18 cm + 6 cm + 18 cm + 6 cm = 48 cm

Answer: The perimeter of one rectangle is 48 cm.

Red Swastika School P5 CA1 2008 Math Paper 2 (Q13)

In a Maths quiz, each pupil had to answer 20 questions. 5 points were given for each correct answer and 2 points were taken away from each wrong answer. Mirabel answered all questions and scored 79 points. How many questions did she answer correctly?

Solution



Right answer ----- plus 5 points

Wrong answer ----- deduct 2 points

Difference between right and wrong ----- 7 points

Assuming that Mirabel had all 20 questions right, she would have -----

20 questions x 5 points = 100 points

However, she had only 79 points, which means -----

100 points – 79 points = 21 points

She “lost” 21 points.

7 “lost points” ----- 1 (question wrong)

1 “lost point” ----- 1/7

21 “lost points” ----- 1/7 x 21 = 3 (questions wrong)

If she had 3 questions wrong, it means she had -----

20 – 3 = 17

Answer: She answered 17 questions correctly.

Is CCA for students’ development of students or for teachers’ career advancement?

An article from the Straits Times forum, dated 3 March 2008, Don't run schools like a business , highlights how CCA is being used for the glory of the school rather than for the development of the students.

Ms Lee, the writer, laments the fact that CCA is now used as a yardstick to measure how well a school does. She cites the example of how a particular CCA was withdrawn because it was not winning enough awards and glory for the school.

Left unsaid, but implicated, is that teachers and staff, who are from the unnamed school, are seeking personal glory. I believe that this example is not isolated. It will indeed be sad if the education system is used by the staff to enhance their career advancement, at the expense of students.

Excerpts from the link above:

IT APPEARS to me that, increasingly, Singapore schools are being managed more like businesses than as institutions of learning.

I graduated from a neighbourhood secondary school six years ago. The place held many beautiful memories for me, especially of the years I spent taking up gymnastics as my co-curricular activity (CCA).

However, the system has changed. Two years back, my CCA girls' team was disbanded.

This was a sport that the school had nurtured for over 40 years, and which had benefited various cohorts of students over the years.

This was the CCA that had shaped me, and taught me to face challenges with courage, take failures as lessons, and conquer difficulties with perseverance.

I was saddened by the school's decision to terminate this CCA, but what was more disappointing was the reason given: 'We are not winning enough awards for the school, and we are simply not bringing glory to the school.'