I am currently 17 year-old and live in Wilayah Persekutuan Kuala Lumpur. I’m a secondary student in Sekolah Menengah Kebangsaan Miharja. I will be sitting for SPM this year. Therefore, this submission is for those who have difficulty in scoring Mathematics especially Paper 2. I always hope to have my own domain and host for blogging. I would give a big thanks to Malaysia Students if my submission is chosen as one of the winner. This submission is also credited to my former teacher Pn. Noraslinda for giving speech on Mathematics in my school this year.

SPM Mathematics Tips

by Bobby Ng for Writing Contest 2008

Brief IntroductionMathematics (is also known as Modern Maths) and Additional Mathematics are categorized as thinking subjects which you take your time thinking rather than memorizing facts. The formula will be given at the front page of the examination paper. Additional Maths is notably 4 times harder than Modern Maths. It’s like if students think Maths is shit, then take Add Maths. If you get 90% marks in Maths, you may have potential to get 40% marks in Add Maths. It’s near to impossible for someone who get A1 in Add Maths fail in Math. Well it’s not important. What I’m going to discuss at here is Mathematics.

SPM MathematicsIn SPM, mathematics is considered as compulsory subject. You must pass this subject in order to get the certificates along with Malay language. Malay language test takes a lot of time and your hand hurts like hell after writing so many words. It’s not simple either. However, the percentage of students fail in Mathematics is higher than Malay Language in real SPM, which is ridiculous. It is told that Mathematics is quite ‘difficult’ among Art students in seminar SPM, which I can't believe my eyes either.

In my opinion, Mathematics is the easiest subject in SPM for Science students. I believe PMR students can even do with their PMR standard knowledge because some questions like volume of solid and area and perimeter of a circle being test in SPM. It’s not being taught in SPM therefore you can only depend on your past knowledge in Form 2. Although the questions are a lot easier than Add Maths, There are still some pupils having difficulties in Maths.

I see some students leave the 'haven't done' answers after they get the formulae to be applied in the questions, which they didn’t really answer the questions. Some of them don’t understand the questions’ needs. Therefore, exercises and guidance from teachers are essential for improvement.

The questions are so direct and mostly the answers will less likely to appear in decimal. You need a little bit of logic compare to Add maths. Besides that, even if you do well in monthly test, you might end up tilting head during SPM examination hall. It’s because monthly tests don’t follow the real format of SPM. Like Intervention 1 for KL state this year, there's no chance in hell this question is coming out in real SPM.

Based on SPM Maths, it consists of 2 papers

Paper 1- 1 ¼ hors- 40 questions- 40 marks

Paper 2- 2 ½ hours- working steps must be done- Section A= 52 marks= 11 questions- Section B= 48 marks= 5 questions (answer 4 of out 5)

Every chapter will be tested in Paper 1. The questions will be tested from Form 1 until Form 5. Since you have already mastered the some basics in PMR, these shouldn’t be a problem. Do past year objective questions will strengthen your basic.

In paper 2, there are only certain chapters that will be tested in SPM maths. That’s why I will concentrate more on paper 2. The whole paper 2 format based on past year questions in random order with brief tips below

Confirmed to be tested every yearPaper 2 (Section A)1) Volume of solids (which was taught in form 2)- most of the formulae given are for this question- make sure the formulae are used correctly- combined solid is sum of volume of the solids- remaining solid is the subtraction of bigger solid and smaller solid

2) Angles of elevation and depression-using trigonometry rule

3) Mathematical reasoning- statement ‘and’ and ‘or’- If p, then q. If q, then p.

4) Simultaneous linear equation- equalize the same unknown and take outExample : 4p - 2q = 15(2p + 4q = 19) x2 (times 2 to make unknown 4p same)- don’t use Add Math method, answers will be different.

5) The straight line- y = mx + c- gradient, gradient….- What is c? c (y-intercept) is the point where the line touches the y-axis.

6) Quadratic expressions and equations- ‘solve the equation’ is to find the unknown- change the equation of the question into this form- factorise by your own or using calculator- must state x = ?, x = ?, there will be 2 answers

7) Matrices- will mostly ask inverse matrix- if you’re not sure about the answer, check if the whole outcome is identical to the inverse matrix in the question.- the answer in a) is related to b)

8) Area and perimeter of circles (same as number 1)

- 2πr (perimeter or circumference) and πr2 (area)- (angle/360 degree) x the formulae above for the area or perimeter of certain part

9) Probability- is more of (number / total number).- the formulae given are plain useless- final answer is never less than 0 or more than 1, 1 > answer > 0

10) Gradient and area under a graph- based on speed/ time graph= distance is area of the graph= rate of change of velocity is gradient of the graph= speed is based on the graph (seldom being asked)- beware of total distance and total speed

Can be varied each year1) Sets (2004 and 2006)- shading based on the questions (intersection or union)- beware of the complement such as A’

2) Graph of functions (2005 and 2007)- the inequalities (upper line is >, lower line is <)- if slanted line, you can imagine it into horizontal straight line. Same concept as above.

What’s the conclusion? 2008 will be ‘Sets’! Wow, I can predict what will come out in this year’s SPM. :D

Paper 2 (Section B) Answer 4 questions1) Graph of functions- Linear functions (less likely to come out as it’s a straight line after plotted)- Quadratic functions (2004 and 2005)- Cubic functions (2007)- Reciprocal functions (2006)= this question is easy because you can detect the type of graph after you plot it.= elastic ruler is recommended= x-axis and y-axis should be stated in the graph

2) Transformation- Translation- Reflection- Rotation- Enlargement ( careful with the word ‘to’ and ‘from’ because it determines the image would be smaller or bigger)= combination of transformation like VT-do T before V. It's some kind of law.

3) Statistic- Histogram ( 2004 and 2005)= x-axis the upper boundary with an additional lower boundary at the front of the graph= y-axis is frequency- Frequency Polygon (2006)= x-axis is midpoint= y-axis is frequency- Ogive (2007)= x-axis is upper boundary= y-axis is cumulative frequency= additional upper boundary should be added to the table= x-axis and y-axis should be stated in the graph

My school hasn’t come to these chapters below, but I will try my best to explain it.4) Plans and elevations-well I’m not sure but what I can see is you must be able to imagine the solid from every side-plan is looked from above-elevation is looked from the side of the solid-the length and the edge (ABCD) should be stated correctly-similar to a chapter of the living skills in PMR

5) Earth as a sphere-no comment because I’m not going to explain something that I’m not sure-latitude is vertical and longitude is horizontal of the sphere-nautical mile

If you concentrate on these chapters and do a lot of past year questions, I’m sure getting A1 in Maths is not a matter for you. Choose the 4 questions that you’re confident in section B paper 2. Do all questions if you think you have much time to spend for taking a nap. Why study more if you know what kind of questions will come out?

Additional Tips1) You know doesn’t mean you can get correct, try to make less careless mistakes in each paper.2) See through the questions word by word as there will be some tricky part in the questions, especially ‘to’ and ‘from’ in enlargement.3) Don’t be sad if you do badly in trial SPM because the odd might come to you in SPM.4) Be sure to study smart, not study hard. Hope this helps.

At the end of Form Three, which is the third year, students are evaluated in the Lower Secondary Assessment (Penilaian Menengah Rendah, PMR). However, PMR is to be abolished by 2016. At the end of Form 5, students are required to take the Sijil Pelajaran Malaysia (SPM) or Malaysian Certificate of Education examination, before graduating from secondary school. The SPM was based on the old British ‘School Certificate’ examination before it became General Certificate of Education 'O' Levels examination, which became the GCSE (General Certificate of Secondary Education). As of 2006, students are given a GCE 'O' Level grade for their English paper in addition to the normal English SPM paper. (Previously, this was reported on result slips as a separate result labelled 1119, which meant students received two grades for their English papers.) This separate grade is given based on the marks of the essay-writing component of the English paper. The essay section of the English paper is remarked under the supervision of officials from British 'O' Levels examination . Although not part of their final certificates, the 'O' Level grade is included on their results slip.

National secondary schools use Malay as the main language of instruction. The only exceptions are Mathematics and Science and languages other than Malay, however this was only implemented in 2003, prior to which all non-language subjects were taught in Malay. The government has decided to abandon the use of English in teaching maths and science and revert to Bahasa Malaysia, starting in 2012.[10]

they will still have to grade that homework when you turn it in, whether it was turned in before or after the break. They will have that much more to grade in a short period of time, so in effect, they don't get a break either. Usually if they are nice, teachers won't give a lot of extra homework over spring break, but they don't want you to totally forget everything you have learned or get out of the habit of doing schoolwork, so they give you a little something to do. Usually this homework is done late Sunday night, before it is due on Monday!

My son had some homework, it was write about what you do over spring break. It was clear, have an intro, body, then conclusion, simple stuff, but I like that she did that for my son. He struggles in writing, reading.

I would say that if your teacher didn't care about your grade, then go party in Cabo, who cares......your parents obviously don't......but my son is in fourth grade and she cares how her students perform, so she assigns temporary assignments to help students improve what they are lacking.

If you are past high school, you should be able to take care of your assignment without whining to mommy, I thought I heard it all from my fourth grader.......:-(

Poor rich guy?

In most cases it is fair. Imagine how the teacher would feel if you joked off the entire vacation, forgot everything you learned the week before, and when you get back to school, she has to teach it all over again. This will set her schedule back all because you did not want to do homework. In high school homework in not the difficult. Wait until you get to college and the homework assignment no longer consist of answering 10 questions at the end of each chapter.

It's fair!

it actually is because:1) it prevents you from forgetting what you have learnt (teacher's hard work isnt wasted)2) come exam time there might be some questions which were there in your assignment.

Not really.Vacations are for teachers and students to relax.My daughter who is in year 7 brought home her reading assignment home by choice because she wants to finish it as they have only 1 week left of this term after the Easter break.

Candidates are graded based on his/her performance relative to the cohort. A grade in one GCE exam subject is a number with an accompanying letter. In descending order, the grades are: A1, A2, B3, B4, C5, C6, D7, E8, and F9. A grade of C6 or better is considered a pass. Those who obtain a pass in one or more subjects are awarded a Singapore-Cambridge General Certificate of Education (Ordinary Level). Candidates whose subject(s) are denoted as 'Absent' - should they be absent from any component(s) for the subject - will not have the subject listed on the certificate; this is likewise for those who obtain a Grade 9, though it will appear on the result slip.

Objective:

SASMO is devoted and dedicated to bringing a love for Mathematics to students.  Unlike most Maths Olympiad Competitions, SASMO caters not only to students in the top 5% but to the top 40% instead. It aims to arouse students’ interest and enthusiasm for mathematical problem solving, develop mathematical intuition, reasoning and logical thinking, as well as creative and critical thinking. In addition, this can help improve the students’ maths grades because they can apply problem-solving strategies learnt during the training to their daily school mathematics. 

Contests and Workshop:

Contest papers will be sent to your school 3 days before the contest date.  After the contest, we will collect the papers from your school.

 This contest promotes mathematical reasoning, logical thinking, critical and creative thinking, and the love for mathematics. 

No traveling is required for the students. The workshops are optional.  Our SASMO coaches will prepare your students to solve interesting problems individually and within their groups. The problem set includes challenging but not too difficult problems so as not to discourage novice problem solvers (see attached examples). Students will be introduced to higher-order thinking strategies and more advanced mathematical ideas to help them solve problems. They will experience the satisfaction, fun and thrill of discovery associated with creative problem solving.

Students can purchase past years contest papers from www.noble-education.com or www.excelleague.com

FORMATContests are taken in the participating school or at our SASMO Maths Olympiad Centres.

The contest consists of 25 non-routine problems.

Each student, working alone, scores 1 point for each correct answer. Thus, a student can score up to 25 points.

Calculators are not permitted.

When a problem introduces a more advanced concept, all necessary definitions are included.

The detailed solution for each problem usually names the strategy required.

Many solutions include follow-up problems and activities.

After the contest, we will collect the score sheets for marking.

TEAMS

Each team is made up of up to 20 students. Schools can have more than one team.

Only teams from schools qualify for the team awards. The team score is the sum of the ten highest individual scores.

AWARDS :i)   INDIVIDUAL

Each participant receives a Certificate of Participation.

The high scorer of each team receives a Top Scorer certificate.

Each of the top 10% of all participants receives a bronze, silver or gold collar pin.

Each student who achieves a perfect score of 25 points receives a Perfect Score Collar Pin.

ii)   TEAM :

Each team in the top 10% of all teams receives a trophy.

The grade level of a team is the highest grade level of any of its members

The test questions are created by the examiners at the University of Cambridge Local Examinations Syndicate, with the exception of the "Mother Tongue" and Social Studies subject. After the examination, completed papers are sent to Cambridge for marking by British teachers and subsequently sent back to Singapore. The exceptions are papers set in Singapore as mentioned above, which would be marked by local teachers. In this case, the personal details of the student are omitted with the use of the Integrated Examination System where barcode labels are used. In this way, the local teachers would not be able to recognise scripts from students of his or her own school as the candidates' names are neither written on the papers nor printed on the labels, preventing the integrity of the examination from being violated

Continue Teaching Science and Mathematics in English

by M. Bakri Musa

In May 2003, five months after the government started the teaching of science and mathematics in English in our schools, the Ministry of Education produced a “study” with the incredulous findings of significant improvement in our students’ achievements! All in five months!

Now five years later, research from the Universiti Pendidikan Sultan Idris (UPSI) showed the very opposite results. What gives?

Both studies were prominently and uncritically reported in our mainstream media. That first study was presumably swallowed whole by our policymakers to justify continuing their policy. Rest assured that this second one too would be used for a similar purpose, as an excuse to jettison that same policy.

Despite many attempts I was unable to get a copy of that first study. Nor have I seen it published in any journal, or find any paper credited to its author, raising questions on the credibility of the “study” and competence of its “researcher.”

To the credit of its authors, this later paper is freely available on the Internet, all 153 pages of it. Its lead author is an emeritus professor, a title reserved for retired accomplished scholars, with a dean and deputy dean as his coauthors. Despite its impressive authorship, this study is deeply flawed in its design and conclusions. It does however, expose many weaknesses in the implementation of the policy, in particular the lack of teachers fluent in English.

Embarrassingly Flawed Study

The most glaring deficiency of this second study is its lack of any control group. This is basic in any research design. As the English language policy applies to all schools, you obviously cannot find a control group among current students. You can however find historical control groups by using the test scores of earlier comparable pupils who had been taught and tested in Malay.

With some ingenuity we could still have concurrent control groups, for example, Malaysian pupils attending English schools like Alice School and International School. Another would be adults fluent in English, or even the teachers. If those adults and students in English schools did equally poorly, then clearly the test is not reliable.

When I look at the test questions, it is not only the teachers who are deficient in English, so too are the test makers! Some of the questions are convoluted and would challenge even those fluent in English.

The second flaw is that there is minimal statistical analysis of the data. The pupils were tested and the results simply collated in pages and pages of raw data presented in dull, repetitive and uninformative tables. The authors must be graphically-challenged; they seem to have not heard of pie charts or bar diagrams.

There is also no attempt in delineating the roles of the many variables the researchers have included, like teachers’ English fluency, parents’ educational levels, and pupils’ geographic background (urban versus rural). To do that the data would have to be subjected to more sophisticated statistical analyses, beyond the simple analysis of variance used by the authors. Thus we do not know whether those students’ test scores could be correlated with their parents’ educational levels (a well-acknowledged factor) or teachers’ fluency in English.

There are numerous conclusions based on just simplistic summations of the data, with such statements as X percent of Malay students finding the study of science “easy” compared to Y percent of Chinese or Indians feeling likewise, or R percent of Malay students scoring high versus S percent of their

Chinese counterparts. It seems that Malaysian academics, like their politicians, cannot escape the race trap.

These studies were conducted in January, February and July. Even the dumbest students knew that those were not the examination months. They knew those tests “don’t count;” thus skewing the results. The only way to make them take the test seriously would be to incorporate it into their regular examinations.

Besides, in January and February those students had just returned from their long end-of-year holidays during which considerable attrition of knowledge occurred. The difference between the racial groups may have nothing to do with academics but on such extraneous matters as how fast they settle down to their studies.

Of the 27 references cited, there is surprisingly no article from refereed journals. Most (14) are government-sponsored surveys, press releases, and newspaper articles, unusual for a scholarly paper. There are a few books cited, with the most recent published in 2002. There is considerable lag time between what is written in books versus the current state of knowledge. For that you would need journals and attend symposia.

Consequently the researchers’ review on bilingual education is dated. Contrary to their conclusion, it is now accepted that exposing children at a young age to bilingual education confers significant linguistic, cognitive and other advantages. The authors’ recommendation that pupils be taught only in their mother tongue and learn a second language later at a much older age is not supported by modern research.

Studies using functional MRIs (imaging studies) of the brain show that children who are bilingual at an earlier age use their brain more efficiently as compared to those who acquire those skills as adults. For example, when asked to translate between the two languages, “native” bilingual speakers use only one part of their brain while those who are bilingual as an adult use two.Other cognitive advantages to “native” bilingual speakers include the ability to grasp abstract concepts faster, precisely the intellectual skill helpful in learning mathematics and higher-level science. The higher scores for non-Malays may well be the consequence of their earlier and more extensive exposure to bilingualism than Malays.

Revealing Findings

The study nonetheless reveals many useful findings. I fear however, that these nuggets of information would be lost by those who care only for the study’s unjustified conclusion to discontinue the present policy and revert to teaching science and mathematics in Malay. That would be a retrogressive step.

This study is only a snapshot; it does not enlighten us as to trend. It could be that the results would continue to improve. It is thus presumptuous for the

authors to make a sweeping policy recommendation based only a limited snapshot study, and a poorly-designed one at that.

UPSI in its previous incarnation as Sultan Idris Teachers’ College was a hotbed of Malay nationalism. This study is less an academic research and more political polemic camouflaged as a pseudo-scientific study to justify its authors’ nationalist bias. Their data and methodology just do not support their conclusion.

The study found that fewer than 15 percent of the teachers were fluent in English, and that most teach using a combination of both languages. That is putting it politely. In reality they use bastardized or “pidgin” English. If those teachers lack English language skills, how could they teach any subject in that language? The fault here is not with the policy, rather its implementation. We should first train the teachers.

In its naivety the government spent over RM3 billion to equip these teachers with computers, LCDs and “teaching modules” to help them in the classroom. Many of those computers are now conveniently “stolen,” plugged with viruses, or simply left to gather dust as those teachers lack the skills to use them effectively.

The only beneficiaries of that program were UMNO operatives who secured those lucrative contracts. Had the government spent those precious funds to hire new teachers fluent in English, our students would have been better served, and the policy more effectively implemented.

This study missed a splendid opportunity to find out what those students, parents and teachers felt about the policy. It was as if those researchers and their field workers (undergraduates in education and thus our future teachers) were interested only in administering those tests, collecting their data, and then getting back to campus.

Surely those parents and teachers had something to say on the policy. What do the teachers feel about the billions spent on computers? Are they eager to learn and teach in English or do they harbor nationalist sentiments and resent the policy? Those surveys would have helped considerably towards implementing the policy better.

A Better Way

I support the teaching of science and mathematics in English. I go further and would have half the subjects in our national schools be taught in English, including Islamic Studies. The objective should be to produce thoroughly or “native” bilingual graduates, able to read, write and even dream in Malay and English. That is the only way to make our graduates competitive.

I put forth my ideas on achieving this in my earlier (2003) book, An Education System Worthy of Malaysia. I would start small, restricting the program to our residential schools where the students are smarter, teachers better, and

facilities superior. Work out the kinks there first, only then expand the program.

I would also convert some teachers’ colleges into exclusively English-medium institutions to train future teachers of English, science, and mathematics.

In rural areas where the level of English in the schools and community is low, I would bring back the old English-medium schools, but modifying it significantly with pupils taught exclusively in English for the first four years (“total immersion”). Malay would be introduced only in Year V, and only as one subject.

Since Malay would not be taught in the first few years and only a limited subject later on, admission to such schools would be restricted only to those with already near-native fluency in Malay or whose habitual language is Malay. Further, such schools would be set up only where the background level of Malay in the community is high, essentially only in the kampongs.

If we were to do otherwise, as having such schools in the cities where the level of English in the community is high and Malay low, those graduates would not be fluent in our national language, as during colonial days. It would not be in the national interest to repeat that mistake. Besides, the problem of our students’ deficiency in English is most acute in rural areas. Thus it makes sense to establish English-medium schools there.

There are many challenges to the policy of teaching science and mathematics in English. One thing is certain. We will never resolve them if we listen to ambitious politicians playing to the gallery or rely on less-than-rigorous “researches.”

Since 1992, the difference in mathematics achievement among the different ethnic schools has caused concern to various parties, including the Ministry of Education. Some common themes that appeared in the local news media reflect this concern. For example, "Maths help from Chinese schools" (The Star, 21 January, 1992); "Ministry studying Chinese approach to mathematics" (New Strait Times, 21 January 1992); "Teaching maths the Chinese way" (The Star, 3 September, 1992) and lately "Success of Chinese students in science, maths to be studied" (Business Times, 2 September 1999). Indirectly, these titles reflect the eagerness of the Ministry of Education to upgrade the mathematics achievement of the Malay medium schools. There is also an assumption that Chinese medium school pupils perform better in mathematics because the Chinese medium schools have something "special" in teaching mathematics. But, is this a fact or an illusion?

Even the Prime Minister himself has advocated the need for government school authorities to emulate the commitment of the Chinese schools in education. The Malay medium schools are asked to adopt the teaching approach of the Chinese medium school. Some ministers even suggest the possibility of 'importing' mathematics teachers from Chinese schools to the Malay schools (The Star, 21 January, 1992). However, this proposal is yet to be tried out. Of course, this issue is not that simple. As has been stressed by Stigler & Barnes (1988) and Bishop (1988), mathematics is a form of culturally transmitted knowledge. So, the success in mathematics learning among these schools may have been related to the school culture and its

related community culture. Thus, can culture be "imported" from one school to another, by just exchanging the mathematics teachers?

In response to the above concern, there are still not many studies carried out to investigate the possible factors of the differences in mathematics achievement. Perhaps as recognised by Yong and colleauges (1997) that " this is due in part to the reason that cultural influences are difficult to study as much of it appear tacit, implicit and hidden from awareness" (p. 6). However, there are a limited number of exploratory studies that aimed to fill this gap.

Below are three studies (Lim & Chan, 1993; Munirah & Lim, 1996; Yong et al., 1997) that have been carried out in Malaysia with regard to cross-cultural comparisons on mathematics learning. I shall briefly describe each study before I make a critical discussion of all of them.

Study 1: A case study comparing the learning of mathematics among Malay pupils in Primary National schools [SK] and Primary National Type schools (Chinese) [SRJKC]

Study 1 was carried out by Lim Soo Kheng and Chan Toe Boi of the Specialist Teachers’ Training College of Malaysia in 1993. Their study aimed to compare the teaching strategies, learning facilities, amount of exercises given, and mathematics achievement of Malay pupils between two types of primary schools, the Primary National schools [SK] and Primary National Type schools (Chinese) [SRJKC]. Their study is interesting because unlike other cross-cultural studies, they were only interested in observing pupils from one ethnic group, the Malay pupils who were studying mathematics in the different ethnic schools.

Their sample consisted of 41 Year Six Malay pupils from eight SRJKC schools and another 41 Year Six Malay pupils from one SK school. As noted in the background section of this paper, for the whole country, there are only about 10% of the Malay pupils studying in the SRJKC schools. Perhaps this might be the reason that the sample of this study has to be collected from 8 SRJKC schools. However, it was not known why the other sample was not collected from an equal number of SK schools, instead of just one SK school. The question is, "can we assume that this one SK school is representative of all other SK schools?" Similarly in the discussion of results, it was not reported clearly that the observation of mathematics lesson was made in only one SRJKC school or all the eight schools. These are some weak or doubtful points of Study 1.

The study used an obervation checklist, a facilities checklist, a survey form and three mathematics achievement tests to collect data. Some observed differences between the two types of schools are highlighted below:

Explanation of concepts/skills

In the SRJKC school, 64% of the 30 minute mathematics lesson was spent on explaining concepts or skills. But in the SK school, only 43% of the time was used for the same reason.

Reinforcement activities

Two types of reinforcement activities were carried out in the SRJKC schools: group competition and solving problems on the chalkboard. The learning atmosphere was found to be more lively as nearly half of the pupils in class took part in these activities while the other

half observed or checked the answers. Pupils from the SK school were given exercises to do individually in class while the teacher walked around to help those who needed help.

Besides these differences, Lim and Chan also observed some similar activities that have been carried out by both types of schools.

Teaching aids

The use of teaching aids to explain mathematical concepts was not frequently used by both types of schools.

School facilities

In terms of school facilities, both types of schools were found to have set up "the mathematics corner" and the "the mathematics teacher committee". The mathematics corner was a small space on the notice board at the back of the classroom. In most cases, they found that only some charts were displayed on it. Meanwhile, the mathematics teacher committee was set up among the mathematics teachers to plan and discuss annual activities and teaching problems. Their planned activities include tuition classes and mathematics quizzes and competitions.

Mathematics achievement

Lim and Chan used three tests to determine the mathematics achievement of the Malay pupils. Test 1 aims to test the understanding of basic concepts, Test 2 the computational skills and Test 3 the ability to solve word problems. Their results show that the Malay pupils of the SK school performed better in Test 1 and Test 3, whereas the Malay pupils of the SRJKC school did better in Test 2. Perhaps this is not a surprise because to understand the mathematical concepts (Test 1) or to solve word problems (Test 3), one needs a mastery of language used. As most Malay pupils from the Chinese medium school (55%) failed their Chinese language in mid-year examination, this shows that they are weak in the language used as the medium of instruction. Thus this may explain their low performance in the two tests too.

Nevertheless, this is a very interesting finding because it highlights the important role of language factor in mathematics learning. Although the Chinese medium schools appear to have better teaching strategies and better learning environments, this is still not enough to help their Malay pupils who are weak in their non-mother-tongue language, the Chinese language.

However, it was observed that the Malay pupils from the Chinese medium school performed much better in Test 2 (testing computational skills). Acccording to the researchers, the better performance in Test 2 may have been attributed by the strong emphasis of drill and practices given by the SRJKC school. Is this the possible reason?

Study 2: Primary mathematics learning and teaching in Chinese and Malay schools

Munirah & Lim (1996) compared mathematics teaching in two different ethnic schools – one Chinese primary (SRJKC) and one Malay primary school (SK). Both schools are located at

the same region, just opposite each other. The methods used include observation of mathematics classes (one from each standard) and interviews with the headmaster, mathematics teachers and some pupils of the respective schools.

They observed differences in both headmasters’ and teachers’ approach to teaching and learning mathematics, particularly in the aspects of homework, learning of multiplication tables and tuition classes. Teachers from the Chinese primary school gave comparatively more mathematics exercises (a difference of 10-40 more questions in one thirty minute lesson) than the Malay primary school. Learning and memorisation of multiplication tables started much earlier in the Chinese primary school (from Standard Two) as compared to the Malay primary school (from Standard Five). Although headmasters of both schools used tuition classes as a means to improve their students’ mathematics achievement, the Chinese primary school headmaster regarded tuition classes as remedial classes for students who have difficulty in mathematics. Thus, tuition classes in Chinese primary school might start as early as Standard Four. Meanwhile, the headmaster of the Malay primary school seemed to hold a different aim for having tuition classes. As it was aimed to increase the number of students who would achieve higher grades in examinations, the tuition classes were given to pupils of Standard Six and of high ability groups only. These results suggest that there are cultural differences in both the headmaster and teachers’ preferences and choices for teaching mathematics between the different ethnic schools.

Study 3: Basic number concepts acquisition in mathematics learning: An exploratory cross-cultural study

Unlike the above two studies, which relate mathematics achievement to mathematics learning in general, Study 3 focused only on the acquisition of basic number concepts. It was a group project headed by Dr Yoong Suan and his colleagues in 1996-97. The main aim of the study was to investigate the acquisition of basic number concepts among the Malaysian Primary One students of different ethnic and cultural backgrounds. The sample included 152 Primary One students, distributed as shown in Table 2.

Table 2: Distribution of sample by school type and ethnicity

Ethnic group

  School stream (medium) Row total

SK (Malay)

(3 schools)

SJK (Chinese)

(3 schools)

SJK (Tamil)

(2 schools)

Malay Count

Row %

Col %

30

55.6

68.2

14

22.2

31.8

-

-

-

44

28.9

Chinese Count

Row %

9

16.7

32

50.8

-

-

41

27.0

Col % 22.0 78.0 -

Indian Count

Row %

Col %

15

27.8

22.4

17

27.0

25.4

35

100.0

52.2

67

44.1

  Col total

Col %

54

35.5

63

41.4

35

23.0

152

100.0

Source: Yong et al, 1997, p.12

The main instrument used in this study was the Basic Number Concepts Test (BNC), developed by the research team in collaboration with three experienced primary school mathematics teachers. These three teachers, one each from each type of school, conducted the clinical testing to their pupils in the respective language media.

The BNC test consisted of 8 dimensions:

1. General counting 2. Skip counting 3. Concrete counting 4. Comparing quantities 5. Word-symbol representation 6. Place value concept 7. Basic number concepts achievement 8. Counting time up to 50

Highlights of main findings

1. By means of school mathematics test scores, the results show that there were more high mathematics ability students among the Malay sample than among the Chinese and Indian sample. It follows that there were more high mathematics ability students among the SK school than the other two types of schools.

2. The results of the overall BNC test show that students in the Chinese medium schools (SRJKC) performed significantly better than students in the Malay medium schools (SK), even though the Malay and Indian students scored significantly better than the Chinese students. This is interesting because it shows that school stream by medium of instruction may be a more important factor for mathematics achievement than ethnicity.

3. Comparing the different sub-dimensions of the BNC Test, the results suggest that students in the Chinese medium schools (SRJKC) performed significantly better than students in the Malay medium school in Counting Time to 50, Skip counting, word symbol representation and the acquisition of place value concepts.

4. The Malay students in the Chinese medium school performed significantly better than their counterparts in the Malay medium schools on the overall BNC Test, Counting time to 50, General Counting and word-symbol representation. The trends were similar for both high and low mathematics ability students of the Malay medium schools.

5. The Indian students in the Tamil medium schools (SRJKT) performed consistently better than their counterparts in either the Chinese medium or the Malay medium schools in terms of Skip counting, Concrete counting and Compare quantity. However, it was noted that the sample of Indian students in this study was over-represented by the high mathematics ability students and the Tamil medium schools were also mono-ethnic. Therefore caution is needed in comparing the results with other medium schools.

In general, the findings of this study suggest that there may be a strong Chinese cultural advantage in counting skills and basic number concepts acquisition. Yong et al (1997) propose that this advantage may have been related to the simpler and consistent number system of the Chinese language, as compared with that in the Malay or Tamil language. However, this claim is yet to be confirmed by further research. Although there is some evidence to show that some Malay students from the Chinese medium schools tended to use the Chinese number-naming system in their mental or oral computation even at higher grades.

Another interesting aspect of the finding is the importance of language in counting and basic concepts acquisition. The results of this study show that the low mathematics ability students who entered a school stream whose instructional medium was other than their mother tongue performed badly. This may be partly due to their poor mastery of the language. This problem was found to be universal for all the ethnic groups.

What can we learn from these studies?

Although all the above three studies are still exploratory in nature and their findings are far from conclusive, there are at least two significant issues that can be drawn out. Firstly, language seems to play a significant role in mathematics learning. As pointed out by Yong et al (1997), the Chinese language seems to have a cultural advantage over the other two languages, Malay and Tamil, particularly in terms of its simpler and consistent number-naming system. It follows that any student--Chinese, Malay or Indian--who is trained to use this numbering system may be able to count faster and memorise the number system faster than his counterparts who use other languages.

However, one needs to master a language well enough to understand the mathematical concepts and skills, to understand and solve mathematical problems that are posed in words. Thus, we observed that the Malay pupils who learn mathematics in a language which is not their mother tongue such as Chinese, may face difficulty in understanding the problem and thus do not do well in mathematics tests that involved word problems. Similarly, Chinese pupils from the Malay medium schools were not found to perform better than the Malay students of the same schools. Instead the Malay pupils from the Malay medium schools were found to perform significantly better than their Chinese counterparts in the acquisition of Basic Number concepts. Does this suggest that it is better to teach or learn mathematics in the pupil’s mother tongue language?

Secondly, findings from the above three studies strongly suggest that there are differences in teaching approaches that were adopted by the different medium schools. Chinese medium

schools seem to favour more "lively learning atmosphere in class"; "plenty of drills and practices"; "more homework", "more tuition" as well as "more competition and quizzes". Consequently, pupils of the Chinese medium schools tend to perform better in computational skills and counting of number, as well as memorisation of multiplication tables. Even the Malay pupils from the Chinese medium schools were found to perform better than their counterparts in other medium schools with regard to computational skills.

Indirectly, all these findings seem to point to the direction that ethnicity may not be an important factor that determines a student’s achievement in mathematics. Language and teaching approaches that are adopted by a school may be more important than ethnicity. Implicitly, this means it is not that Chinese students are better than Malay students in mathematics, but it is the language and the mathematics learning culture that matter most.

In fact, it is the whole culture that supports successful mathematics learning. We know that culture can be a dubious term that encompasses many things from ideology to technology (White, 1959). In general, the word ‘culture’ can be taken as "a system of shared knowledge and belief that shapes human perceptions and generates social behaviours…"(Bennet, 1990, p.47). In other words, one shares similar models of perceiving, believing, doing, evaluating and interpreting within the same cultural group. Thus, culture is learned and not inherited (Hofstede, 1997). Thus, we see that it is not the issue that one culture or ethnic group might be fundamentally better at mathematics teaching, learning and achievement than another, but the different cultural practices, beliefs and values that might have helped to improve mathematics learning.

Suggestions for further study

However, there are much more to be explored and researched further if we are to look into the impact of culture on mathematics learning. One derives one’s culture from one’s social environment. Consequently, understanding our own and other cultures may help us "to clarify why we behave in certain ways, how we perceive reality, what we believe to be true, what we build and create, what we accept as good and desirable, and so on." (Bennet, 1990, p.47)

Therefore, to look into the impact of culture on mathematics learning, I suggest that further studies need to look at the following aspects:

1. As suggested by Bishop (1988), there are 6 activities that have been found to be universal in every culture. These are counting, measuring, playing, locating, designing and explaining. Therefore further research may study the other 5 activities, to see whether there are cultural differences even within Malaysian culture.

2. According to Hofstede (1997), values are the deepest manifestation of culture. Values are broad tendencies about how one ought to behave or prefer certain states of affairs over others. Thus, we need to study the different social and cultural values that have been manifested in the process of the teaching and learning of mathematics. These values include:(i) values that are manifested in goals and objectives of mathematics curriculum/education; (ii) values that are inherent in mathematics as a subject or discipline of study;(iii) values that underpin a mathematics teacher’s decision making and philosophy of teaching, such as preferences or criteria for making decisions during mathematics teaching (iv) values that influence teachers’ and students’ behaviours and attitudes

towards mathematics, such as attributes or qualities of a successful mathematics learner;(v) values that are hidden behind unwritten rules or curricula (decided implicitly by all members of the school and its social community).

3. All of these studies have sampled primary school pupils. Further studies therefore need to look into whether cultural differences that are rooted in primary school may be brought up to secondary and higher learning, too.

In fact, this list is by no mean exhausive.

Conclusion

Although there are not yet enough studies to make a substantial claim, a review of these studies suggest that it is not ethnicity that determines better performance in mathematics learning. Indeed, ethnic differences may bring about cultural differences in terms of language, practices, ritual, attitudes, values and beliefs. Perhaps these are the factors that give rise to different ways of teaching and learning approaches towards mathematics, and consequently might have resulted in differences in mathematics achievement.

It is true that all these constructs are so subtle and tacit that most of the time it is difficult for us to distinguish them. This may be one of the reasons that there are so few studies trying to untangle this mess. However, if we can show that ethnicity is not the causal factor, then we can argue that mathematics ability is neither inborn nor inherited. This also implies that we can improve mathematics achievement by ‘adopting’ some cultural beliefs, values, attitudinal changes of other cultural groups, even to the extent of ‘modifying’ disadvantages in language factor by adopting some new sign and symbols in language. This is not impossible if we strive hard enough. Of course, it is not easy to ‘change’ one’s culture or to ‘adopt’ others’ cultures. After all, culture can be learned and it is not inherited (Hofstede, 1997).