normal distribution of scores in a test

http://web.cortland.edu/andersmd/stats/normcurv.html

The normal distribution, or bell curve, is most familiar and useful to teachers in describing the frequency of standardized test scores, how many students earned particular scores.

Of course not all test score distributions are normally distributed. They can be skewed, i.e. have a disproportionate number of people who dovery well or very poorly. This would be the case if a test was too easy or too hard for the testing population. However, standardized tests are designed so that the outcome follows a normal distribution curve.

http://teaching.about.com/od/assess/a/Standardized-Testing.htm

6421_Chapter_3_Kurpius_IV_Proof_2

http://ask.cie.org.uk/system/selfservice.controller?CONFIGURATION=1035&PARTITION_ID=1&USERTYPE=1&CMD=VIEW_ARTICLE&ARTICLE_ID=33226

Exams and streaming: Recalibrating our education system

We face the complex challenges that many members (of Parliament) have spoken about passionately, from stress, tuition and exams to streaming … These challenges are complex because there are no easy answers. There are significant tradeoffs among the multiple objectives.

Some changes may benefit one group while another may feel they would lose out. What may seem good in the short term may bring adverse consequences later. Given how the different parts of our system are linked to each other, we cannot simply change one part without affecting another.

We also have to remember that education is always a complex issue because it is tied deeply to our values as a people.

We should be humble enough to learn and adopt the best practices of others. And indeed we have done so, including from Finland – but we cannot borrow wholesale as our context is different.

We will have to challenge our mindsets, and decide on what matters most to each of us. We have to go back to the basics, and ask what we want to see in our children as they grow up, beyond just academic grades.

For a start, much as our system is not perfect, it is studied by many nations all over the world – not only for what we do for our high achievers but also for how we uplift all our students …

Our success so far in equipping Singaporeans to meet the challenges of the future is a deep strength which many nations would love to have. The challenges we are grappling with need to be always viewed in perspective, so that we do not throw the baby out with the bathwater.

But we shall not cease exploring how we can build even better schools, institutions and universities. I am very encouraged by the many voices we have heard at Our Singapore Conversation, including from over 5,000 educators in the first phase. From what we have heard so far… I discern two key areas where we would need more in-depth conversations.

OVER-EMPHASIS ON EXAMS AND GRADES

First, many parents and students feel that our education system is too focused on examinations and grades. This excessive focus has several consequences.

It may come at the expense of the development of well-rounded individuals, including the character and values of the student which ultimately matters most.

It may come at the expense of learning, as students ‘study to the test’ and teachers respond by ‘teaching to the test’, rather than to stimulate curiosity and a love of learning.

Students may choose subjects, and indeed, schools may offer subjects, based on how easy it is to score good grades, rather than on their intrinsic value. The recent debate over literature, which (Nominated MP) Janice Koh brought up, is a case in point.

Other forms of talent – in the arts, sports, music, leadership ability, applied skills using both hands and head, etc – are not sufficiently recognised. We should not just have an exam-based meritocracy. Rather, we should have a talent-centric meritocracy that recognises talent in a wide range of areas.

A major consequence of a single-minded focus on examinations is stress, in particular, stress related to competition and high stake examinations such as the PSLE … Some mothers take leave for an entire year or more to help their children prepare.

Many see entry into top schools as critical to their children’s future, and prepare their children very early – some as early as kindergartens, and even sending them to two kindergartens.

Many compete to get a place in popular primary schools, or spend significantly on tuition … Others worry about their children being streamed into normal streams, and suffer from the stigma associated with it.

Some teachers, who are committed to helping their students succeed, may give a lot of homework, or set tests that are difficult to stretch their students, but often with good intentions. I appreciate the stress that parents, students and educators feel. This is an important issue.

Some are concerned about the effects of competition. Successful students may develop a narrow, competitive mindset.They may come to believe that: “I have succeeded because I have worked hard, so I deserve nothing but the best for myself”.

MERIT IN COMPETITION

While there are concerns about high stake exams, I have also heard other views, and there are others who see merit in the current system.

Many feel the current system sets clear standards. Many students have told me exams challenge them to learn better. Teachers use exams to determine students’ mastery of the different subjects, and tailor their teaching strategies accordingly.

In a public education system, exams provide us with a standardised measure of progression and achievement, and ensure accountability across the system to uphold rigorous standards … It also provides an objective way of determining entry into the next level of education.

In Singapore, exams have helped assure a very high average among our students. That is why our students, even those who score average here, perform so well when they go overseas.

Some countries, such as the United Kingdom, Japan and Korea, and some states in the US that abolished exams or made these easier, are now reversing course. Their experience has been that while removing exams was popular and brought short term relief, over time, insidiously, standards fall.

They are now concerned that their youths are not equipped to compete in the global market place. I should note that the people who suffer the most when educational standards drop in these countries are not the best students but the average students …

As for the stress that comes with high-stake exams, many have observed that some amount of stress is almost unavoidable. While excessive and prolonged stress is bad, a right amount of stress can bring out the best in each of us … Some parents have also said that some amount of competition is necessary – it is a reality of working life, and equipping our students to learn this early in life strengthens them for the future …

The common position is that we all want our children to get ahead in life. And the higher the aspiration, the greater the drive. The question we have to ask is – what exactly will ensure that our children can get ahead and be successful in the face of global competition, and not just relative to other Singaporeans?

SOCIAL MOBILITY AND INCLUSION

The second area is that of opportunities, social mobility and inclusion. Some parents are concerned that without tuition, their children cannot cope, or cannot do well enough to excel. Others whose children are doing well want them to do even better, and procure all sorts of tuition and enrichment classes to help them advance.

Some are concerned that in some schools, students tend to come from similar social-economic backgrounds and have similar academic abilities. Without the opportunity to interact with students from different backgrounds and academic abilities, our students may not develop empathy, and our society may lose its cohesiveness.

But some have also cautioned that if we mix up our students too much, it will be harder to cater to the learning needs of different groups. We will lose our peaks of excellence and also fail to support those who may fall behind without different approaches …

RETURN TO FUNDAMENTALS

I have been thinking long and hard about these issues, and have had many sessions with our educators on this. Before we change our major policies, we must get back to fundamentals: First, re-affirm the basic goals of education, and second, the fundamental strategy of how we will achieve these goals.

In the spirit of Our Singapore Conversation, allow me to highlight a few ideas for discussion.

On the basic goals of education …. We must first and foremost provide opportunities for every child to actualise his or her full potential, to be the best that he or she can be. To achieve this, we must:

• Develop a love for learning, stimulate a lively curiosity about the world around us, an urge to explore and discover;

• Develop well rounded individuals of integrity and sound character, with strong social emotional maturity;

• Build a strong foundation, especially in self confidence, literacy and numeracy, analytical and inventive thinking, communication skills and other 21st century competencies, so as to prepare Singaporeans to be lifelong learners, and succeed in a more globally competitive environment; and

• Develop the abilities and interests in each child, so that he or she may go on in life to pursue these interests with passion, realise his or her aspirations, and have a fulfilling career.

Second, nurture in each child a sense of responsibility to his fellow human beings, and a sense of commitment and loyalty to Singapore and to fellow Singaporeans, so that he can contribute to taking Singapore forward.

RETHINK APPROACHES

To realise these goals, we have to re-think the fundamental approaches in tandem with changes in policy.

First, we have to see education as a lifelong journey, not a destination. It is an exciting journey of continual learning, discovery and mastery, not a competitive sprint.

This means learning the right things at the right time. For instance, the early years are about building the disposition for learning and discovery.

We have to do what is developmentally appropriate at different stages of their education. Seeking to hothouse our children when they are in kindergarten and preparing them in advance for primary school generates stress, and then, boredom when they enter primary school.

Second, each child is different – in interests, aptitude and rate of development. Ideally, our system must allow each to learn at their own pace, customised to their different learning styles. Everyone must be encouraged to put in effort.

Third, we must develop students with a Singapore Heartbeat, with empathy for others, a regard for the common good, and a shared sense of responsibility for Singapore’s well-being and future.

PSLE AND STREAMING

In the next phase of Our Singapore Conversation, we can discuss the various policy options. For example, the PSLE serves as an objective benchmark for secondary school posting today. So important questions that we need to discuss include:

How do we maintain our rigorous standards and accountability and whether we can allocate all secondary school places without an objective benchmark like the PSLE?

Are there alternative posting systems that are still objective, but can minimise the current over-emphasis on academic results, and enhance social inclusion?

To what extent should choice or proximity to school be a consideration in secondary school posting, as some have suggested?

Mr Gan Thiam Poh’s suggestion about PSLE cut-off points is something that we can consider further. Ms Denise Phua spoke about a through train model from pre-school to secondary school.

As another example, streaming at the secondary level allows us to tailor instruction to the abilities and learning styles of our students. But some have questioned if we should re-think whether streaming is absolutely necessary.

Important questions to discuss in the next phase of Our Singapore Conversation include:

Can we ensure that every child can learn at his or her own pace, if there is no streaming?

Will our schools be even less diverse if we did not have students from the various academic streams?

Can we replicate what we have done at the primary level, such as subject-based banding, at the secondary level?

BE THOUGHTFUL ABOUT CHANGES

Whatever we do, we must be deliberate and thoughtful about what we need to change, how fast we can change, and how far we can sustain these changes.

We must have the resources to sustain any change. I have been watching the debates on resourcing education in various countries. Countries that have started with a big bang now have to make painful changes to cut back.

Education is a long-term endeavour, and always a work in progress. We should not rush into anything as the results, whether good or bad, are evident only many years down the road …

It is also critical for us not to see our education system in isolation. … Education alone cannot give us a good life, and we need to be clear what a good life is. If a good life is simply about getting ahead of others, and achieving the 5Cs (Cash, Condominium, Cars, Credit Card, and Country Club), the competitive pressure in the workplace will define how we as parents and teachers view education.

Then, no amount of changes in the education system can alter the reality of each of us chasing after material and positional goods. We cannot have broader definitions of success in education without our society accepting broader definitions of success in life. In many respects, the education system reflects societal norms and expectations.

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