Category: Views on Education
An article I wrote in 2014
I dug up the above article as the same problems that confronted me then are perturbing me now. Is acceleration encouraged and effective? If we have limited time, should we spend it on helping students master basic concepts or giving them difficult problems to solve? What do you think?
Length
Lesson objectives:
For the topic of length, students should be able to:
(1) visualise how long 1 km is
(2) state that 1 m = 100 cm and 1 km = 1000 m
(3) convert from cm to m and cm and vice versa
(4) convert from m to km and m and vice versa
Lesson ideas:
(1) Students measure their heights and their arm spans in m and cm and convert the measurements into cm.
Interesting facts:
– The height of a person is approximately equal to his arm span.
– Using one arm’s length to estimate one metre is not accurate for children. A child’s arm’s length is usually shorter than one metre.
(2) Students measure the length of real life objects (e.g. height of door and length of whiteboard) and convert the measurements from cm to m and cm and vice versa.
(3) To get a sense of how long 1 km is, students can use Google Maps to find the distance between their school and their home. They can also find out the length of Singapore from east to west (50 km) and from north to south (27 km). Students are told that 1 km is 2.5 rounds around a stadium track or 20 laps of an Olympic-sized pool.
Common errors:
(1) Students may think 1 m = 1000 cm, since 1 km = 1000 m.
How to rectify: Tell students that “centi” means 100. For example, century means 100 years.
(2) Students may not understand the concept of 0 as a place holder. For example, when converting 4 km 90 m to m, students may write 490 m instead of 4090 m.
How to rectify: Tell students to write
1 km = 1000 m
4 km = 4000 m
4 km 90 m = 4000 m + 90 m
= 4090 m
Defending Model Drawing and Examining the Reason for Drilling
There was an opinion piece in the Straits Times last Friday entitled “Let’s Kill the Drill Approach in Schools”. While I agree with the general sentiments of the paper – that there is too much drilling in schools and that we should encourage independent thinking, I think the author downplayed the model drawing approach and other heuristics, which I wish to help defend.
Below is an excerpt from the commentary:
Firstly, the average 8 or 9-year-old in Singapore is not expected to solve this problem. According to MOE syllabus, word problems on fractions are introduced to Singaporean students at Primary 4, the year the students turn 10.
Having established that, I would solve the cited problem using both the model drawing approach and algebra.
Model drawing:
The algebraic solution will be:
On the same question, I personally feel that the model drawing approach helps students visualise the problem better. X + y =520 is shown in the diagram, where both bars add up to 520. In the model method, pupils do not need to deal with the abstract representations of x and y, nor do they have to deal with fractions in their calculations. They arrive at 7x = 520 – 30 after drawing the model. In the algebra approach, they only arrive at 7/4 x = 520 – 30 in the fifth line, and face the peril of mixing up operations.
The following is another excerpt from the article:
I fail to see how the model drawing method ‘cuts short the actual thinking required for such types of questions’. In the problem above, students need to know that since 1/4 of the blue marbles were given away, 3/4 of the blue marbles were left, regardless of which method they employ. In the model approach, the calculations are simplified, but that does not mean that the actual thinking is cut short. Students have represented their thinking on fractional parts in the model.
Personally, I am quite an unorthodox teacher and have taught my former primary 6 students to solve problems with algebra, even though it is not within the syllabus. My high progress pupils caught on and were fluent in any method that I introduced. Those in the middle and low ranges struggled more with algebra. I remember once after I had shown an algebraic solution, a helpless student exclaimed that he still did not know what x was and asked where x could be found in the question.
I have come across questions where an algebraic solution might be more efficient, but that is rarely the case for PSLE questions. Some questions set by schools may fall into such a category, and in those cases, my personal view is that the questions are too complex and should not be administered at the primary level.
One last statement from the commentary that I disagree with is:
At the secondary level where mathematics is learnt in a more abstract manner and where the model method has been eradicated, students still attend extensive tuition classes. Thus, it is not the type of problems that is helping the tuition industry flourish. It is more likely the desire to do well at exams.
Many teachers resort to drilling as a result of high-stake exams. By this term, I do not mean only the PSLE. Most bite-sized assessments contribute to a final score which is used for internal streaming purposes, so there are many high-stake exams in a student’s life. Teachers themselves are ranked and this may compel some to use the most convenient way to improve test results – drill.
However, teachers are taught (during teacher training) to include investigations and opportunities for students to self-discover mathematical concepts. The concrete-pictorial-abstract approach which encourages the use of relevant manipulatives is also emphasised during teacher training. Teachers are also trained to teach for relational understanding (understanding the why and how) rather than merely for instrumental understanding (understanding the how).
In addition, teachers are encouraged to teach problem solving strategies, rather than drill students or try to expose students to all kinds of question permutations. A popular problem solving model that is used in schools originates from George Polya, a famous mathematician. Polya suggests that problem solving should be take place in four stages: Understand, plan, do and check. A good mathematics teacher will lead students through these four stages and equip them with sufficient strategies or heuristics, so that students can plan which strategy to use when they have to solve a problem.
If teachers fail to implement what they have been taught, it is most likely due to the pressures of constant assessments and the lack of time and not because of the model drawing approach.
(All opinions are mine and in no way reflect the views of the organisation I work for.)
Why I Am Still A Teacher
About twenty years ago, I had to decide between a place in Accountancy at NTU and a teaching scholarship to read Psychology in NUS. The first offer came first and the logistics had been settled. I was to live in one of the newest halls in NTU and had looked through the orientation activities to decide which ones to attend. Finally, when the scholarship offer came, I gave up the place in NTU and enrolled in the Faculty of Arts and Social Sciences instead. Some people thought I was foolish to give up the much coveted place in Accountancy. Nevertheless, that decision led me to become a teacher and I am still enjoying the job very much. 🙂
Here are three reasons for my still being in the profession:
1) When I see former students growing up and excelling, I feel very happy for them.
Sometime last year, I met one of my former students for tea. He was quite a precocious boy in primary school and I remember using up all the discipline strategies I had learnt on him as he was very talkative in class. When we met, I found out that he was excelling in his area of study and had even picked up violin playing and wushu. He also courteously offered to buy me a drink. Recently, I had a chat with one of his prospective employers and was very heartened to hear that the student was well-regarded.
A few years ago, I received a call from the mother of another student. The mother was very pleased that her son had got into Medicine and thanked me for guiding her son in primary school! That call made my day and the elation has stayed till this day.
When one of my former students was named a President’s Scholar two or three years ago, I felt so proud of him. Another student was featured in the newspapers for being the first Malay student to graduate with a Bachelor of Music at the Yong Siew Toh Conservatory. I still remember the Teachers’ Day song she composed as a primary school student and felt privileged that I was ever her music teacher in school. Heh. One other student owns a business and he is only in his early twenties. He just became a proud father and I am glad to see pictures of his blissful family on Facebook now and then. I was also happy to hear about the student who gathered his friends to bake cookies in order to raise funds for the victims of a calamity.
I was most pleased when I managed to contact a student who used to be quite errant in the past. I found out that he is now working hard to support his mother and siblings. Upon connecting with me, the student said that he was grateful to me. I also found out that he had sought out the then discipline master of the school to apologise for his misbehaviour (this part is hearsay, so I am not sure of the accuracy). It is hard to explain the joy I felt when I saw how sensible he is.
Many others are doing well in their chosen paths and I wish them all the best as they continue with their pursuits.
2) Teachers can make a (positive or negative!) difference to the lives of their students.
The teacher who made the greatest impact in my life was my form teacher in secondary three and four. She was always encouraging and when I did not do well in one exam, she tried to find out if anything was wrong instead of chiding me. She also took time to know each and every one of her students. She scheduled to meet us individually at the staff lounge and during our meetings, she would ask us how we were coping and was also concerned about our families. That inspired me to spend time with my students during recess when I became a teacher.
When I first became a teacher, one of my pupils invited me to his house during a festival. He gave me a time range to be there, so I assumed I could pop by anytime within the range. When I arrived at his house in the late afternoon, his grandma told me that he had been waiting for me all day and got more and more disappointed when I did not turn up. I felt so sorry, but that incident reminded me how important teachers were to students. I guess it was particularly so for this boy since his family background was challenging. I was more sensitive to students’ needs after that incident.
I am also aware that our words and actions to our students could make a long-lasting impact on them. Although I try to say positive words and give wise advice, I know I have not always succeeded and I am truly sorry to students who have been negatively affected by my words. I am depending on God’s wisdom to say the right things at the right time out of love.
Thank God that I did get affirmation from my students now and then:
3) The role of a teacher is very versatile. It is never boring.
We do not just teach, but we serve as counsellors, event planners, tour guides, first aiders, janitors, security guards, interior designs, directors and more. Students’ personalities differ and we have to constantly think of new ways to engage them.
I remember fondly how a primary six class took on my challenge of writing an email to the Principal asking for permission to raise funds for victims of an earthquake. I was teaching situational writing and wanted the students to have an authentic context for writing. When the Principal did give her approval for the fund raising, the students took off independently. Some boys were talented in drawing comics and they printed their own comic booklets and sold them at 50 cents a booklet. I remember that the booklets were sold out! The girls made more delicate craft. They raised slightly more than $1000 in two days. I was glad to be part of this meaningful event.
I have also enjoyed directing a musical based on the Five Loaves and Two Fishes story, leading worship during chapel, leading my first school in singing National Day songs, coming up with math trails at the Esplanade, Botanic Gardens and Labrador Park with my colleagues, accompanying students on overseas trips to Japan and Perth, praying for students before exams and the list goes on and on. In my earlier years, I also enjoyed teaching music. Some of my classes were taught how to play Ode to Joy in three parts on the recorder and during my wedding, about sixty pupils turned up and gave a beautiful rendition of the piece whilst I was signing on the marriage register.
Sure, there were many nights when I had to stay up late to mark pupils’ work or to prepare lessons. Some weekends were also burned and my closest companion was my red pen. Holidays seemed to fly by and before we knew it, school was starting again. However, the fulfilment gained from the job outweighs the exhaustion and that is why I am still an educator.
I had fun writing this post and reminiscing the past. I dedicate this post to all my wonderful students who have made teaching worthwhile and fulfilling, as well as to all my friends who are teachers.
Happy Teachers’ Day to the teachers and God bless you!
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