Reflections on Liping Ma’s Work

Liping Ma’s book Knowing and teaching elementary mathematics has been very influential in Mathematics Education circles. This is a short summary of the book and my reflections on it.

Introduction

Liping Ma in her work  compares the teaching of mathematics in the American and the Chinese schools. Typically it is found that the American students are out performed by their Chinese counterparts in mathematical exams. This fact would lead us to believe that the Chinese teachers are better `educated’ than the U.S. teachers and the better performance is a straight result of this fact. But when we see at the actual schooling the teachers undergo in the two countries we find a large difference. Whereas the U.S. teachers are typically graduates with 16-18 years of formal schooling, the typical Chinese maths teacher has about only 11-12 years of schooling. So how can a lower `educated’ teacher produce better results than a more educated one? This is sort of the gist of Ma’s work which has been described in the book. The book after exposing the in-competencies of the U.S. teachers also gives the remedies that can lift their performance.

In the course of her work Ma identifies the deeper mathematical and procedural understanding present, called the profound understanding of fundamental mathematics [PUFM] in the Chinese teachers, which is mostly absent in the American teachers. Also the “pedagogical content knowledge” of the Chinese teachers is different and better than that of the U.S. teachers. A teacher with PUFM “is not only aware of the conceptual structure and the basic attitudes of mathematics inherent in elementary mathematics, but is able to teach them to students.” The situation of the two teacher is that the U.S. teachers have a shallow understanding of a large number of mathematical structures including the advanced ones, but the Chinese teachers have a deeper understanding of the elementary concepts involved in mathematics. The point where the PUFM is attained in the Chinese teachers is addressed. this Also the Chinese education system so structured that it allows cooperation and interaction among the junior and senior teachers.

Methodology

The study was conducted by using the interview questions in Teacher Education and Learning to Teach Study [TELT] developed by Deborah Ball. These questions were designed to probe teacher’s knowledge of mathematics in the context of common things that teachers do in course of teaching. The four common topics that were tested for by the TELT were: subtraction, multiplication, division by fractions and the relationship between area and perimeter. Due to these diverse topics in the questionnaire the teachers subject knowledge at both conceptual and procedural levels at the elementary level could be judged quite comprehensively. The teacher’s response to a particular question could be used to judge the level of understanding the teacher has on the given subject topic.

Sample

The sample for this study was composed of two set of teachers. One from the U.S., and another from China. There were 23 U.S. teachers, who were supposed to be above average. Out of these 23, 12 had an experience of 1 year of teaching, and the rest 11 had average teaching experience of 11 years. In China 72 teachers were selected, who came from diverse nature of schools.In these 72, 40 had experience of less than 5 years of teaching, 24 had more than 5 years of teaching experience, and the remaining 8 had taught for more than 18 years average. Each teacher was interviewed for the conceptual and procedural understanding for the four topics mentioned.

We now take a look at the various problems posed to the teachers and their typical responses.

Subtraction with Regrouping

The problem posed to the teachers in this topic was:

Lets spend some time thinking about one particular topic that you may work with when you teach, subtraction and regrouping. Look at these questions:
62
– 49
= 13

How would you approach these problems if you were teaching second grade? What would you say pupils would need to understand or be able to do before they could start learning subtraction with regrouping?

Response

Although this problem appears to be simple and very elementary not all teachers were aware of the conceptual scheme behind subtraction by regrouping. Seventy seven percent of the U.S. teachers and 14% of U.S. teacher had only the procedural knowledge of the topic. The understanding of these teachers was limited to just taking and changing steps. This limitation was evident in their capacity to promote conceptual learning in the class room. Also the various levels of conceptual understanding were also displayed. Whereas the U.S. teachers explained the procedure as regrouping the minuend and told that during the teaching they would point out the “exchanging” aspect underlying the “changing” step. On the other hand the Chinese teachers used subtraction in computations as decomposing a higher value unit, and many of them also used non-standard methods of regrouping and their relations with standard methods.

Also most of the Chinese teachers mentioned that after teaching this to students they would like to have a class discussion, so as to clarify the concepts.

Multidigit Multiplication

The problem posed to the teachers in this topic was:

Some sixth-grade teachers noticed that several of their students were making the same mistake in multiplying large numbers. In trying to calculate:
123
x 645
13

the students were forgetting to “move the numbers” (i.e. the partial products) over each line.}
They were doing this Instead of this
123 123
x 64 x 64
615 615
492 492
738 738
1845 79335

While these teachers agreed that this was a problem, they did not agree on what to do about it. What would you do if you were teaching the sixth grade and you noticed that several of your students were doing this?}

Response

Most of the teachers agreed that this was a genuine problem in students understanding than just careless shifting of digits, meant for addition. But different teachers had different views about the error made by the student. The problem in the students understanding as seen by the teachers were reflections of their own knowledge of the subject matter. For most of the U.S. teachers the knowledge was procedural, so they reflected on them on similar lines when they were asked to. On the other hand the Chinese teachers displayed a conceptual understanding of the multidigit multiplication. The explanation and the algorithm used by the Chinese teachers were thorough and many times novel.

Division by Fractions

The problem posed to the teachers in this topic was:

People seem to have different approaches to solving problems involving division with fractions. How do you solve a problem like this one?

1/(3/4) / 1/2 = ??

Imagine that you are teaching division with fractions. To make this meaningful for kids, sometimes many teachers try to do is relate mathematics to other things. Sometimes they try to come up with real-world situations or story-problems to show the application of some particular piece of content. What would you say would be good story or model for 1/(3/4) / 1/2 ?

Response

As in the previous two cases the U.S. teachers had a very weak knowledge of the subject matter. Only 43% of the U.S. teachers were able to calculate the fraction correctly and none of them showed the understanding of the rationale underlying their calculations. Only one teacher was successful in generating an illustration for the correct representation of the given problem. On the other hand all the Chinese teachers did the computational part correctly, and a few teachers were also able to explain the rationale behind the calculations. Also in addition to this most of the Chinese teachers were able to generate at least one correct representation of the problem. In addition to this the Chinese teachers were able to generate representational problems with a variety of subjects and ideas, which in turn were based on their through understanding of the subject matter.

Division by Fractions

The problem posed to the teachers in this topic was:

Imagine that one of your students comes to the class very excited. She tells you that she has figured out a theory that you never told to the class. She explains that she has discovered the perimeter of a closed figure increases, the area also increases. She shows you a picture to prove what she is doing:

Example of the student:

How would you respond to this student?

Response

In this problem task there were two aspects of the subject matter knowledge which contributed substantially to successful approach; knowledge of topics related to the idea and mathematical attitudes. The absence or presence of attitudes was a major factor in success

The problems given to the teachers are of the elementary, but to understand them and explain them [what Ma is asking] one needs a profound understanding of basic principles that underly these elementary mathematical operations. This very fact is reflected in the response of the Chinese and the U.S. teachers. The same pattern of Chinese teachers outperforming U.S. teachers is repeated in all four topics. The reason for the better performance of the Chinese teachers is their profound understanding of fundamental mathematics or PUFM. We now turn to the topic of PUFM and explore what is meant by it and when it is attained.

PUFM

According to Ma PUFM is “more than a sound conceptual understanding of elementary mathematics — it is the awareness of the conceptual structure and the basic attitudes of mathematics inherent in elementary mathematics and the ability to provide a foundation for that conceptual structure and instill those basic attitudes in students. A profound understanding of mathematics has breadth, depth, and thoroughness. Breadth of understanding is the capacity to connect topic with topics of similar or less conceptual power. Depth of the understanding is the capacity to connect a topic with those of greater conceptual power. Thoroughness is the capacity to connect all these topics.”

The teacher who possesses PUFM has connectedness, knows multiple ways of expressing same thing, revisits and reinforces same ideas and has a longitudinal coherence. We will elaborate on these key ideas of PUFM in brief.

Connectedness: By connectedness being present in a teacher it is meant that there is an intention in the teacher to connect mathematical procedures and concepts. When this is used in teaching it will enable students to learn a unified body of knowledge, instead of learning isolated topics.

Multiple Perspectives: In order to have a flexible understanding of the concepts involved, one must be able to analyze and solve problems in multiple ways, and to provide explanations of various approaches to a problem. A teacher with PUFM will provide multiple ways to solve and understand a given problem, so that the understanding in the students is deeper.

Basic Ideas: The teachers having PUFM display mathematical attitudes and are particularly aware of the powerful and simple concepts of mathematics. By revisiting these ideas again and again they are reinforced. But focusing on this students are not merely encouraged to approach the problems, but are guided to conduct real mathematical activity.

Longitudinal Coherence: By longitudinal coherence in the teachers having PUFM it is meant that the teacher has a complete markup of the syllabus and the content for the various grades of the elementary mathematics. If one does have an idea of what the students have already learnt in the earlier grades, then that knowledge of the students can be used effectively. On the other hand if it is known what the students will be learning in the higher grades, the treatment in the lower grades can be such that it is suitable and effective later.

PUFM – Attainment

Since the presence of PUFM in the Chinese teachers makes them different from their U.S. counterparts, it is essential to have a knowledge of how the PUFM is developed and attained in the Chinese teachers. For this Ma did survey of two additional groups. One was ninth grade students, and the other was that of pre-service teachers. Both groups has conceptual understanding of the four problems. The preservice teachers also showed a concern for teaching and learning, but both groups did not show PUFM. Ma also interviewed the Chinese teachers who had PUFM, and explored their acquisition of mathematical knowledge. The teachers with PUFM mentioned several factors for their acquisition of mathematical knowledge. These factors include:

  • Learning from colleagues
  • Learning mathematics from students.
  • Learning mathematics by doing problems.
  • Teaching
  • Teaching round by round.
  • Studying teaching materials extensively.

The Chinese teachers during the summers and at the beginning of the school terms , studied the Teaching and Learning Framework document thoroughly. The text book to be followed is the most studied by the teachers. The text book is also studied and discussed during the school year. Comparatively little time is devoted to studying teacher’s manuals. So the conclusion of the study is that the Chinese teachers have a base for PUFM from their school education itself. But the PUFM matures and develops during their actual teaching driven by a concern of what to teach and how to teach it. This development of PUFM is well supported by their colleagues and the study materials that they have. Thus the cultural difference in the Chinese and U.S. educational systems also plays a part in this.

Conclusions

One of the most obvious outcomes of this study is the fact that the Chinese elementary teachers are much better equipped conceptually than their U.S. counterparts to teach mathematics at that level. The Chinese teachers show a deeper understanding of the subject matter and have a flexible understanding of the subject. But Ma has attempted to give the plausible explanations for this difference in terms of the PUFM, which is developed and matured in the Chinese teachers, but almost absent in the U.S. teachers. This difference in the respective teachers of the two countries is reflected in the performance of students at any given level. So that if one really wants to improve the mathematics learning for the students, the teachers also need to be well equipped with the knowledge of fundamental and elementary mathematics. The problems of teacher’s knowledge development and that of student learning are thus related.

In China when the perspective teachers are still students, they achieve the mathematical competence. When they attain the teacher learning programs, this mathematical competence is connected to primary concern about teaching and learning school mathematics. The final phase in this is when the teachers actually teach, it is here where they develop teacher’s subject knowledge.  Thus we see that good elementary education of the perspective teachers themselves heralds their growth as teachers with PUFM. Thus in China good teachers at the elementary level, make good students, who in turn can become good teachers themselves, and a cycle is formed. In case of U.S. it seems the opposite is true, poor elementary mathematics education, provided by low-quality teachers hinders likely development of mathematical competence in students at the elementary level. Also most of the teacher education programs in the U.S. focus on How to teach mathematics? rather than on the mathematics itself. After the training the teachers are expected to know how to teach and what to teach, they are also not expected to study anymore. All this leads to formation of a teacher who is bound in the given framework, not being able to develop PUFM as required.

Also the fact that is commonly believed that elementary mathematics is basic, superficial and commonly understood is denied by this study. The study definitively shows that elementary mathematics is not superficial at all, and anyone who teaches it has to study it in a comprehensive way. So for the attainment of PUFM in the U.S. teachers and to improve the mathematics education their Ma has given some suggestions which need to be implemented.

Ma suggests that the two problems of improving the teacher knowledge and student learning are interdependent, so that they both should be addressed simultaneously. This is a way to enter the cyclic process of development of mathematical competencies in the teachers. In the U.S. there is a lack of interaction between study of mathematics taught and study of how to teach it. The text books should be also read, studied and discussed by the teachers themselves as they will be using it in teaching in the class room. This will enable the U.S. teachers to have clear idea of what to teach and how to teach it thoughtfully. The perspective teachers can develop PUFM at the college level, and this can be used as the entry point in the cycle of developing the mathematical competency in them. Teachers should use text books and teachers manuals in an effective way. For this the teacher should recognize its significance and have time and energy for the careful study of manuals. The class room practice of the Chinese teachers is text book based, but not confined to text books. Again here the emphasis is laid on the teacher’s understanding of the subject matter. A teacher with PUFM will be able to choose materials from a text book and present them in intelligible ways in the class room. To put the conclusions in a compact form we can say that the content knowledge of the teachers makes the difference.

Reflections

The study done by Ma and its results have created a huge following in the U.S. Mathematics Education circles and has been termed as `enlightening’. The study diagnoses the problems in the U.S. treatment of elementary mathematics vis-a-vis Chinese one. In the work Ma glorifies the Chinese teachers and educational system as against `low quality’ American teachers and educational system. As said in the foreword of the book by Shulman the work is cited by the people on both sides of the math wars. This book has done the same thing to the U.S. Mathematics Education circles what the Sputnik in the late 1950’s to the U.S. policies on science education. During that time the Russians who were supposed to be technically inferior to the U.S. suddenly launched the Sputnik, there by creating a wave of disgust in the U.S. This was peaked in the Kennedy’s announcement of sending an American on moon before the 1970’s. The aftermath of this was to create `Scientific Americans’, with efforts directed at creating a scientific base in the U.S. right from the school. Similarly the case of Ma’s study is another expos\’e, this time in terms of elementary mathematics. It might not have mattered so much if the study was performed entirely with U.S. teachers [Have not studies of this kind ever done before?]. But the very fact that the Americans are apparently behind the Chinese is a matter of worry. This is a situation that needs to be rectified. This fame of this book is more about politics and funding about education than about math. So no wonder that all the people involved in Mathematics Education in the U.S. [and others elsewhere following them] are citing Ma’s work for changing the situation. Citing work of which shows the Americans on lower grounds may also be able to get you you funds which otherwise probably you would not have got. Now the guess is that the aim is to create `Mathematical Americans’ this time so as to overcome the Chinese challenge.

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.

Millions of Computers for Millions of Children

Yesterday ( it should be now read “a couple of years back”)while giving a talk, I was asked this rhetorical question (not verbatim, but close):

“What did you say was the sample size of your study?”

“Two. This was a case study.”

“So, considering that the activity that you have designed requires a computer and expeyes (a hardware for collecting data). How can you scale it up to schools which have millions of children?”

It seems that the person who was asking the question, for lack of any other question asked this. In seminars and academic institutes, there are always people like this, who will ask the question for sake of it. Just to make their presence felt. Anyways, it was good for me. I was expecting that this question would be asked. And I was very happy that it was asked.

The short answer that I gave was:

“You give a million computers to a million children!”

one-computer-per-child

Some people thought, this was a rhetoric answer to a rhetoric question, which incidentally was also humorous, as it also generated a lot of laughter, but this was not the case. In this post, I would like to elaborate on the short answer that I gave.

Of course, most of these ideas have come from reading and hearing Seymour Papert (who has recently demised, the article was started before that, but due to my lethargy never seen completion). The memes have been transferred, and now I am trying to make sense and adapt them to my own experience. And I would like to assert again that reading Papert has been an immensely rewarding and enriching experience for me. His are perhaps few books which I do not mind reading again and again. I like his writing style of giving parables to explain points in his arguments because the points he wants to make do not need a backbone of statistics to survive. Here also I will give a hypothetical example (derived from Papert) to explain what I meant.

The technological tools that children are using now mainly in the traditional school system are the pencil and the book. In this case, almost all educationalists would agree that every child would require to have one pencil to write and book for study. Even then there are some children who do use computers, some because their parents have them, some because the school has them, some have both. Now we consider a time 50 years back. Computers were almost non-existent, as we know them now. Computers were one of the most complicated and expensive technological artefacts that humans produced. But the enormous amount of money and efforts were put in the miniaturization of computers. So finally now we have computers that have become devices that we now know. In the last 50 years, the computer technology has grown exponentially, while the prices for the memory and computing power that one gets are falling, their usage.

Consider a classroom of 50 years back. Though there were computers they were something to be wondered about, something like very very expensive toys. The computers were not mature enough that children could handle them. In the classroom, the only available technological artefacts were used. The technology in the classroom was the pencil
and the printed book and a notebook to write with the pencil and of course, there was the blackboard.

Wait, you might be thinking we are in a digital age technology by default means computers, be it in your smart-phone, laptop or a desktop or at least a projector for god’s sake. But here I would like you to think about somethings which are very deeply embedded in our cultural psyche. The very fact that many things which we take for granted are
all technologies. For example, the writing instruments that you have to be it a pencil or a chalk are all technologies. But most of us don’t think of them as such because they are so common and most of us have had our experience with them. The mystery is lost. As the Arthur C. Clarke once said about technology and magic as his Third Law:

Any sufficiently advanced technology is indistinguishable from magic.

So deeply embedded this image is that we define it as the normal for our learners to be able to use this technology. Rather the entire edifice of our educational system rests on it. For example, your educational achievement is more or less based on the fact how much you can “write” in a limited time, from memory. And this we call assessment, examination and the like. Also the written text, from the time of Gutenberg, has more
or less complete hold over our intellectual activities. The text formed the basis of our discourse and analysis of the world. Why do children use to write with a pencil on piece of paper in order to learn. The drill typically starts with the children trying to
recreate elegant fonts in some shape or form which is decipherable for the teacher. You have to write “A” 500 times to get it right, ok? How would you write words when you cannot write alphabets? How would write sentences when you cannot write words? How will you write examinations if you cannot write sentences?

Is it the only way in which we can learn language? If we observe this in detail we see that only reason we ask them to write “a” 500 times in a notebook is because it comes from an era when there was no other technology to write. And this is the same learner who can converse well and answer questions, but yet we need them to write it down with their hands. It was the only possible solution. And generations of humans were trained using this method. So much so that most of us still think this is the only method for education. Any deviation from hand-written text is seen as a abomination. But typing on a computer provides us, and especially, young learners with cognitive offloading of immense task of holding a writing instrument and shaping an alphabet, a word, a sentence out of it. Children learn to type much much faster than they learn to write with a pen. And what is even more important is that the written text is in electronic form, which can be revised and shared with their peers and teachers. In hand written text there is no question of revision, the original takes too much effort to produce so there is no question of revising it.

one-pencil-per-child

Considering the amount of cognitive load the child has to undergo to produce decipherable alphabets, words and sentences in order to “write”, a thing which he can perfectly do orally, are the results worth the effort? Are there any studies which show that this is an efficient method? Yet is used everywhere without exceptions and we accept it meekly without challenge because this is how it was done in the past and someone in the past must have had good reason to use this hence, we should also use this. Papert calls this as “QWERTY Phenomena”. Somethings just get culturally embedded because the are
suited for an bygone era, the are like relics in the current era. And writing with pencil and paper is just one of them.

Now consider the question that was asked at the beginning of the post. Replace the computer with a pencil. The question then becomes,

“So, considering that the activity that you have designed requires a
pencil and a notebook. How can you scale it up to schools which have
millions of children?”

one-pencil-per-1000-child-cyan

Suddenly question seems rather bizzare and at the same time sotrivial. Of course you might say but the pencil and notebook is so much cheaper than the computer. Yes. It. Is. But if you consider that a well designed laptop like OLPC, can serve a learners for 5-6 years and can remain with them through the schooling years. Then calculations show the investment that we seek is rather modest. In general when something becomes more
common, it also becomes cheaper. Mobile phones provide an excellent proof for this argument. And it is not happening in some first world country but in our own. What has promoted a rapid growth in the number of mobile users? How do tariff plans compare
from 15 years back to now? How come something which was something exclusive for the rich and the famous, just a few years back, is now so common? It is hard to find a person without a phone these days. Even people who do not have access to electricity have a
phone, they get it charged from some place else. Now if some sociologist would have done some study regarding usefulness of mobile phones for communication, perhaps 20 years earlier, they might have had some statistics to show, but critics would have said,

“but the cost is too prohibitive; this is perhaps ok for a case study you seriously
think all (or most) of the people can have this; and people who cannot
read and write will be able to use this; people do not have
electricity and food to eat and you want to give them mobile phone?”

But look at where we are, because people found contextual and personal value in using a mobile, it became their personal assistant in communicating with others, an inherent human trait, they got it. With proliferation of the mobiles, the cost of hardware came down, the cost of tariffs came down, almost everyone could afford one now.

It is sensationalist to compare a pencil and laptop in terms of cost, but when you consider the kinds of learning that can happen over a computer there is simple no match. They are not different in degree but in kind. Note that I have used “can happen” instead of will happen. This is for a reason, a laptop can be used in a variety of ways in learning. Some of the ways can be subversive, disruptive of the traditional education system, and redefine radically the ways our children learn. But in most cases its subversion is tamed and is made submissive to the existing educational system. And computers are made to do what a teacher or a textbook will do in a traditional context. So it is blunted and made part of a system which the computer has the potential to alter radically.

Some people then cite “research studies” done with “computers”. These studies will typically groups “with” computers and “without” computers. Some tasks are given and then there are pre and post tests. They are looking at the submissive action set in a highly conservative educational system. Even if such studies show the use of computers in a positive light, all these studies are missing the point. They are just flogging a dead horse. The point that computers when used in the right way, the constructionist way, can change the way we learn in a fundamental way. There are many studies which “prove” the counter-point. That computers don’t improve “learning”. Typically children will have limited access both in terms of time and sharing it with more people. One computer shared by three people, one hour in a week. Even then children learn, with computers if
used correctly. Continuing with out example of the pencil, consider this: one pencil shared among three children, once a week! Seems absurd isn’t it? But this is what typically happens in the schools, children are not allowed to develop a personal relationship with one of the most powerful learning ideas that they can have access to. Access is limited and in most cases uninformed involving trivialisation of the learning ideas that can redefine learning.

one-computer-per-1000-child

Politics Science Education or Science Education Politics or Science Politics Education

I am rather not sure what should be the exact title of this
post. Apart from the two options above it could have been any other
combination of these three words. Because I would be talking about all
three of them in interdependent manner.

If someone tells you that education is or should be independent of politics they, I would say they are very naive in their view about society. Education in general and formalised education in particular, which is supported and implemented by state is about political ideology that we want our next generation to have. One of the Marxian critique of state formalised education is that it keeps the current hierarchical structures untouched in its approach and thus sustains them. Now when we come to science education we get a bit more involved about ideas.

Science by itself was at one point of time assumed to be value-neutral. This line of though can be seen in the essays that some of us wrote in the schools with titles like “Science: good or bad”. Typically the line of argument in such is that by itself science is neither good or bad, but how we put it to use is what determines whether it is good or bad. Examples to substantiate the arguments typically involve some horrific incidents like the atomic bomb on one hand and life saving drugs on the other hand. But by itself, science is not about good or bad values. It is assumed to be neutral in that sense (there are other notions of value-neutrality of science which we will consider later). Scientific thought and its products are considered above petty issues of society and indiduals, it seemed to be an quest for eternal truth. No one questioned the processes or products of science which were assumed to be the most noble, rational, logical and superior way of doing things. But this pretty picture about scientific enterprise was broken by Thomas Kuhn. What we were looking at so far is the “normative” idea of science. That is we create some ideals about science and work under the assumption that this is how actual science is or ought to be. What Kuhn in his seminal work titled The Structure of Scientific Revolution was to challenge such a normative view, instead he did a historical analysis of how science is actually done ans gave us a “descriptive” picture about science, which was based on historical facts. Keeping up the name of the book, it actually revolutionised the way we look at science.

Now keeping in mind this disctinction between “normative” and “descriptive” views is very important. This is not only true for science but also for all other forms of human endeavours. People often tend to confuse or combine the two or many times are not even aware of the difference.

After Kuhn’s groundbreaking work entire new view about science its processes and products emerged. Various aspects of the scientific enterprise which were initially thought about outside purview of science or not affecting science came in to spotlight. Science was dissected and deconstructed from various points of view. Over the next few decades these ideas emerged into full fledged disciplies on their own. Some very valid criticisms of the scientific enterprise were developed and agreed upon. For example, the idea that there exists “the scientific method” was serisously looked into and was found to be too naive. A modified view was adopted in this regard and most of philosophers of science agreed that this is too restrictive a view. Added to this the post-modernist views about science may seem strange and bizzare at times to the uninitiated. This led to what many call as the “science-wars” between scientific realists and postmodernists. The scientific realists who believe that the world described by science is the real world as it is, independent of what it might be. So in this view it implies that there is objective truth in science and the world it describes is real. This view also implies that there is something like “scientific method” and it role in creating true knowledge about the world is paramount. On the other hand postmodernist critics don’t necessarily agree with this view of the world. For example they question the very idea of objectivity of the scientific world-view. Deriving their own meaning into writings of Kuhn (which he didn’t agree to) they claimed that science itself is a social construct and has nothing to do with the real world. The apparent supremacy of “scientific-method” in creating knowledge or presenting us about the world-views is questioned. The entire scientific enterprise from processes to products was deciphered from dimensions of gender, sexual orientation, race and class. Now, when you are teaching about science to learners there should be an awareness about these issues. Some of the issues are usually overlooked or have a logical positivist nature in them. Many philosophers lament that though considerable change has happened in ideas regarding scientific enterprise especially in philosophy of science, it seems corresponding ideas in science education are not up to date. And this can be seen when you look at the science textbook with a critical focus.

With this background I will go into the reasons that made me write this post and the peculiar multi-title. It seems for post-modernists and some others that learning about politics of science is more important than learning science itself. And they feel this is the neutral view and there is nothing political about it. They look at science as an hierarchical enterprise where gender, class and race play the decisive role, hence everyone should know about it. I am not against sharing the fact with learners of science that there are other world-views, what I am against is to share only a peculiar world view which is shaped completely by one’s ideology and politcal stance rather than by actual contents. Many of the people don’t actually know science, yet they feel that they are fully justified to criticise it. And most of these people would fall on the left side of the political spectrum (at least that is what their self-image is). But the way I see it is that these same people are no different from the right-wingers who burn books without reading them. The pomos may think of themselves as intellectually superior to the tilak-sporting people but they are not. Such is the state of intellectuals that they feel threatened by exclusion of certain articles or inclusion of certain other ones in reading courses. They then use all their might to restore the “balance”. At the same time they also tell us only they have some esoteric knowledge about these issues which people like me cannot have. And no matter what I do I will never be able to do what they can. Perhaps they have super powers which I don’t know about, perhaps in their subjective world view the pigs can fly and this fact can be proven by using other methods than the scientific ones. Last point I want to make in this is inspite of all the criticims of science and its products it doesn’t stop these people from refraining use of these products and technologies! This is hypocrisy, they will curse the phone or the computer if it doesn’t work, what they perhaps don’t realise is that it might be working just that the pomos are not able to see it in their worldview.

Main purpose of the educational sector

The main purpose of the health sector is not to provide other sectors with workers in good health. By the same token, the main purpose of the educational sector is not to prepare students to take up an occupation in some other sector of the economy. In all human societies, health and education have an intrinsic value: the ability to enjoy years of good health, like the ability to acquire knowledge and culture, is one of the fundamental purposes of civilization.

via Thomas Piketty’s Capital in the 21st Century

Gandhi on Textbooks

M. K. Gandhi

Harijan Vol VII, No. 31 pg. 1, 9 September 1939

Text Books

The craze for ever-changing text books is hardly a healthy sign from
the educational standpoint. If text books are treated as a vehicle for
education, the living word of the teacher has very little value. A
teacher who teaches from text books does not impart originality to his
pupils. He himself becomes a slave of the text books and has no
opportunity or occasion to be original. It therefore seems that the
less text books there are the better it is for the teacher and his
pupils. Text books seem to have become an article of commerce. Authors
and publishers who make writing and publishing a means of making money
are interested in frequent change of text books. In many cases
teachers and examiners are themselves authors of text books. It is
naturally to their interest to have their books sold. The selection
board is again naturally composed of such people. And so the vicious
circle becomes complete. And it becomes very difficult for parents to
find money for new books every year. It is a pathetic sight to see
boys and girls going to school loaded with books which they are ill
able to carry. The whole system requires to be thoroughly
examined. The commercial spirit needs to be entirely eliminated and
the question approached in the interest of the scholars. It will then
probably be found that 75 per cent of the text books will have to be
consigned to scrap-heap. If I had it my way, I would have books
largely as aids to teachers rather than for the scholars. Such
textbooks as are found to be absolutely necessary for the scholars
should circulate among them for a number of years os that the cost can
be easily borne by middle class families. The first step in this
direction is perhaps for the State to won and organize the printing
and publishing of text books. This will act as an automatic check on
their unnecessary multiplication.

Equity Over Excellence

There is an interesting piece in The Atlantic by Sergey Ivanov on the education system in Finland. Though the article is written from a viewpoint of an American, there are a lot of take home points for everyone and particularly for India. In this post I am trying to make sense of this article from an Indian standpoint. Through out the post if you just insert India for America (which I have done at places), it at once catches. For the problems Indians are facing are also the problems of the Americans, as we have more or less tried to follow their model of education. The basic theme that underlies the article
is this:

The Scandinavian country is an education superpower because 
 it values equality more than excellence.

To many in the Indian context who believe that excellence must be given priority over equity this might be surprising. Surprising because it undermines a basic premise in their logic: that to excel in science and technology the only way is to promote excellence. In India there have been two distinct approaches to education, there is a clear stratification of the students based on standardized tests, and it is these tests which filter out students. But as the Finnish experience shows us that this need not be the case.

The newly found fame for Finland’s educational system comes after excellence of their students in the PISA scores since 2000. This seems paradoxical when we learn more about the educational system. The tried and trusted formulae of instructionism and rote-learning, which many people swear by, have almost no place there. The Finnish educational system seems like an educational philosophers utopian materialized in the real world.

To understand why it is working, the way it is, Indians will have to give away their long cherished beliefs about educational system. This would make the government more accountable towards education of the people. This is not just cosmetic school reform, but a revamping of the complete educational philosophy with which we are running the show.

One of the most intriguing (at least for me) things to notice is:

“Oh,” he mentioned at one point, “and there are no private schools in
Finland.”

This notion may seem difficult for an American (Indian?) to digest, but it’s true. Only a small number of independent schools exist in Finland, and even they are all publicly financed. None is allowed to charge tuition fees. There are no private universities, either. This means that practically every person in Finland attends public school, whether for pre-K or a Ph.D.

(emphasis added)

Now, this is interesting. What can we say about India? In fact over the years there has been general trend that we are seeing, that the number of private schools is increasing. And then there are branded schools which are spreading their networks across the country. Not to tell that they charge really hefty fees, and are meant for the elite. And so is the case with the colleges, each professional degree has a price tag, only people who can afford it, get those degrees. The haves not, the non-elites, who are mostly from the deprived classes, remain with almost no education. The government keeps on talking about reaching out to people, and by allowing the private schools colleges to exist, it is actually preventing people from joining in. Another aspect about this is that since there are alternatives to the government schools, the government schools themselves have no pressure to perform. And as any intelligent parents will tell you, it is better to put your child in a private school than a government one. Most of the parents who are in a financial position to put their children in private schools, do so.

How many parents do you know who have enrolled their children in government schools, even when they can afford private schools?

There was yet another interesting piece If You Send Your Kid to Private School, You Are a Bad Person in which the author makes a case that it is parents who are driving the change of declining government schools. If the educated parents make a sustained effort of challenging and helping government schools to improve, they will surely improve. The parents adopt the path of least effort, and send their children to private schools, which are supposed to be better. This automatically creates a class divide without asking.

Even among the private schools there is an hierarchy. There are international schools, convent schools etc. So the social stratification that exists, is just reflected in the school system. Seen from this perspective, one can understand why are the government schools neglected. They are neglected because the people who are influential and who are amongst the rich and powerful are never affected by the dismal state of the government schools. They have an alternate avenue for their children where these schools never come into picture.

There is another thing that is striking in the Indian system, that is of the coaching classes. I do not know if they are present in Finland or even anywhere in the world. But in India, the coaching classes have a complete parallel system of cracking the educational system. The amount money that the coaching classes do attract must be comparable to the amount Government of India spends on education. This is another avenue where the class divide comes in. Only people with enough finances can afford to send their children to the best coaching classes. But the more fundamental question to ask is:

Why do coaching classes exist in the first place?

The answer to this question is not easy and it related closely to the way in which Indians look at education and its practices. The coaching classes exist because there is a demand for them. And what do coaching classes achieve. Most of the coaching classes are aimed at helping students crack some standardized test or the other. But why do you need standardized tests? Some of the rhetorical questions that one might ask against this question are:

From his (Sasi’s) point of view, Americans (Indians) are consistently obsessed
with certain questions:

+ How can you keep track of students’ performance if you don’t test
them constantly?
+ How can you improve teaching if you have no accountability for bad
teachers or merit pay for good teachers?
+ How do you foster competition and engage the private sector?
+ How do you provide school choice?

The answers Finland provides seem to run counter to just about everything America’s (India’s) school reformers are trying to do. For example the introduction of CCE or Continuous and Comprehensive Examination introduced as part of NCF 2005 is one such reform. Similarly we have incentives in forms of awards for best teachers, and of course the best students get rewards like getting admission to the best colleges. Their parents are proud, schools are proud, and their coaching classes are also proud. This can be seen by the number of advertisements the coaching classes put up. But all the exams like IIT-JEE, AIEEE, Medical Exams, Olympiads, etc. are standardized tests. These are the parameters of excellence in the country. Similar tests are also found in the US, like GRE, TOEFL, SAT etc. One would assume the standardized tests in Finland would be of very great quality, but in reality they don’t exist there.

For starters, Finland has no standardized tests. The only exception is what’s called the National Matriculation Exam, which everyone takes at the end of a voluntary upper-secondary school, roughly the equivalent of American high school.

The very idea of standardized tests emerged in the shadow of the Second World War. The mass recruitment of troops required a mass approach, which resulted in production of tests. In his book The Tyranny of Testing physicist Banesh Hoffman, criticises the standardized tests that were prevalent in the US, and takes to task the leading makers of these tests on the fundamental premise of their objectivity. Similarly one can, question the fundamentals of the standardized tests in the country.

Can any standardized test be really objective?

Personally, I do not think so. None of the standardized tests, take into account multiple factors that a student has skills in. These tests make the process of filtering students easier for the administrators. But do they help students at all (except for getting admission to a desired institute)? Do they really test the understanding of the subject matter? Do they take into account various social factors that is part of the mileu of the students? As Banesh Hoffman says the only thing objective about these tests is that once, the students fills in the answer sheet, the grading is objective. But why is that the teachers who are actually teaching the students cannot test them? Why do we need standardized tests to test the students?

And here comes in the idea of academic flexibility in the schools. In India even most university department do not have academic flexibility. There is a central committee which decides, what is to be taught and a committee sets a test with which we grade the students. This creates a definite goal in form of “completing the syllabus” for the teachers. This is a malice which pervades the educational system of India from primary schools to university departments. The teachers are in a race to reach the finish line of the syllabus, because if they do not, the students might face questions which they were not taught.

Though the teacher is the representative of the entire educational system in the classroom, they are nothing more than, to use a term by Krishna Kumar, “meek dictators” in the classroom. The real dictators are adminitrators and decision makers sitting at the top of the educational system. This perhaps is a colonial mentality which has been deeply embodied in the Indian psyche. But in Finland what happens:

Instead, the public school system’s teachers are trained to assess children in classrooms using independent tests they create themselves. All children receive a report card at the end of each semester, but these reports are based on individualized grading by each teacher. Periodically, the Ministry of Education tracks national progress by testing a few sample groups across a range of different schools.

People say that then the teachers cannot be trusted that they will grade their students correctly. So how will they be held accountable?

As for accountability of teachers and administrators, Sahlberg shrugs. “There’s no word for accountability in Finnish,” he later told
an audience at the Teachers College of Columbia University. “Accountability is something that is left when responsibility has been subtracted.”

For Sahlberg what matters is that in Finland all teachers and administrators are given prestige, decent pay, and a lot of responsibility. A master’s degree is required to enter the profession, and teacher training programs are among the most selective professional schools in the country. If a teacher is bad, it is the principal’s responsibility to notice and deal with it.

This is where the responsibility of the Government comes in. Goverment slowly is trying to distance itself from its role in providing education to all its citizens. But if teachers are themselves left unsatisfied both monetarily and ideologically??, what results one can
expect. In this way the Government is indirectly encouraging the private schools and coaching classes, and thus making the class divide even more striking.

And while Americans (Indians) love to talk about competition, Sahlberg points out that nothing makes Finns more uncomfortable. In his book Sahlberg quotes a line from Finnish writer named Samuli Paronen: “Real winners do not compete.” It’s hard to think of a more un-American (Indian) idea, but when it comes to education, Finland’s success shows that the Finnish attitude might have merits. There are no lists of best schools or teachers in Finland. The main driver of education policy is not competition between teachers and between schools, but cooperation.

Compare this with the Indian attitude. Competition seems to be the key to everything and especially education. Where does collaboration of
cooperation enter in Indian educational scenario?

Finally, in Finland, school choice is noticeably not a priority, nor is engaging the private sector at all. Which brings us back to the silence after Sahlberg’s comment at the Dwight School that schools like Dwight don’t exist in Finland.

“Here in America (India), parents can choose to take their kids to private schools. It’s the same idea of a marketplace that applies to, say, shops. Schools are a shop and parents can buy what ever they want. In Finland parents can also choose. But the options are all the same.”

And in India there are coaching classes which prepare students to get into better coaching classes. With both private schools and the coaching class industry around the education and related services have been commercialised to furthest extent possible. This just works in the favour of the already existing class divide. Parents do choose best for their children, and thus do perpetuate the divide as they have no other choices.

Decades ago, when the Finnish school system was badly in need of reform, the goal of the program that Finland instituted, resulting in so much success today, was never excellence. It was equity.

This is the state of the educational system in India now. And with the over emphasis on the excellence part which addresses a small set of mostly elite students, the goal should be creating equal opportunities for equity. The idea of equity in the academic circles is unfortunately equated with that of sub-standard or below average. There are people who will tell you, that “Look, there are bright students, and they need special coaching.” The government has to spend the money of bright students, so as to make the country excel in education. This is done at the expense of the average students. One may ask the question, how in the first place do you know a student is bright? The answer comes from scores of the standardized tests, which are the root cause of many problems that the educational system in India is facing now. If one is serious about changing the educational scenario in the country this has to be addressed. Though there are champions of the standardized tests, in India as in the US of Amerika, they are the ones whose existence is based on such tests. Without these tests their existence becomes meaningless. It will certainly increase the workload of lot many people a lot many times. But the problems of magnitude of changing educational system in India is no mean problem and will require solutions of these magnitudes.

Since the 1980s, the main driver of Finnish education policy has been the idea that every child should have exactly the same opportunity to
learn, regardless of family background, income, or geographic location.

In the Indian scenario this seems to have been forgotten. And one of the main reasons for this is the presence of private schools and coaching classes where parents can shop for education.

Education has been seen first and foremost not as a way to produce star performers, but as an instrument to even out social inequality.

This particular quote is exactly opposite of what the Indian
educational system does by promoting academic excellence over equity.
And this also relates to the qualities that Indians cherish. If good
education is equated with chances of making good money, then we know
where we are wrong. With private schools and coaching classes the
education of a student becomes a balance sheet, which will be brought
to green from red by the money that student will make after
completing education.

In the Finnish view, as Sahlberg describes it, this means that schools should be healthy, safe environments for children. This starts with
the basics. Finland offers all pupils free school meals, easy access to health care, psychological counseling, and individualized student
guidance.

In case of India we have seen implementation of the mid-day meal scheme. But does it extend to the other domains?

In fact, since academic excellence wasn’t a particular priority on the Finnish to-do list, when Finland’s students scored so high on the
first PISA survey in 2001, many Finns thought the results must be a mistake. But subsequent PISA tests confirmed that Finland — unlike,
say, very similar countries such as Norway — was producing academic excellence through its particular policy focus on equity.

And with so much emphasis on coming on top of the class in India, we are getting what we are sowing. Surveys will tell you that students,
including even those from the best private schools in the country do fail in simple evaluation. But is this unexpected? If the entire
focus of the educational system is to pass standardized tests, why should we expect our students to be better in something else?

That this point is almost always ignored or brushed aside in the U.S. (India) seems especially poignant at the moment, after the financial crisis and Occupy Wall Street movement have brought the problems of inequality in America into such sharp focus. The chasm between those who can afford $35,000 in tuition per child per year — or even just the price of a house in a good public school district — and the other “99 percent” is painfully plain to see.

Though India is yet to undergo Occupy BSE protests, it is not long before this happens.

Some people may point out that Finland is a developed nation. It is much more homogeneous as compared to India. Here it might become more complicated than in the US, but the central argument should hold through.

Yet Sahlberg doesn’t think that questions of size or homogeneity should give Americans (Indians) reason to dismiss the Finnish example. Finland is a relatively homogeneous country — as of 2010, just 4.6 percent of Finnish residents had been born in another country, compared with 12.7 percent in the United States. But the number of foreign-born residents in Finland doubled during the decade leading up to 2010, and the country didn’t lose its edge in education. Immigrants tended to concentrate in certain areas, causing some schools to become much more mixed than others, yet there has not been much change in the remarkable lack of variation between Finnish schools in the PISA surveys across the same period.

The social conditions in India do not match those in Finland. We have many factors like, caste and religion, which do strongly affect our educational policies in practice, if not in theory. So is this comparison valid? But comparing Finland with an country whose demographics are similar, namely Norway, we find different results. Which shows it is the educational policy which determines the outcome, and not the demographics.

Like Finland, Norway is small and not especially diverse overall, but unlike Finland it has taken an approach to education that is more American than Finnish. The result? Mediocre performance in the PISA survey. Educational policy, Abrams suggests, is probably more important to the success of a country’s school system than the nation’s size or ethnic makeup.

And time and again it is said that India does not have enough money to spend on its enormous population. Looking at the amount of GDP that is spent on education India ranks spends 3.1% of GDP on education (2006), while the US spends 5.5% (2007) and Finland 5.9% (2007). A more updated list shows this hasn’t changed much in the intervening years. A look at the graph below from the World Bank Data on these matters makes the picture clear. Though Norway spends more than Finland on education, the results are poor. So if we assume that this is the control then it clearly shows it is not the amount of money you spend or your socio-economic status of the people that matter. What matters most is the way in which you have planned for education and its spending.

gdp-educationPeople tell you that most problems in Indian education system will go away if we have enough teachers! But why are not there enough teachers one may ask? Isn’t it funny that in a country which has second largest population in the world, we do not have enough government teachers? It is surely not a problem of human resources, but of will, both political and social. We do not want to spend more on education, and yet we expect the things to be better. And somehow government is willing to spend on private partners for education, a sort of outsourcing if you want. And with more and more Public Private Partnerships for education, government is just abdicating its responsibility, in the field of education as in other fields.

Finland’s experience suggests that to win at that game, a country has to prepare not just some of its population well, but all of its population well, for the new economy. To possess some of the best schools in the world might still not be good enough if there are children being left behind.

Problem in India is manifold.

“Finland’s dream was that we want to have a good public education for every child regardless of where they go to school or what kind of families they come from, and many even in Finland said it couldn’t be done.”

Clearly, many were wrong. It is possible to create equality. And perhaps even more important — as a challenge to the American (Indian) way of thinking about education reform — Finland’s experience shows that it is possible to achieve excellence by focusing not on competition, but on cooperation, and not on choice, but on equity.

(emphasis added)

The problem facing education in America (India) isn’t the ethnic diversity of the population but the economic inequality of society, and this is precisely the problem that Finnish education reform addressed. More equity at home might just be what America (India) needs to be more competitive abroad.

Most of us think that utopian ideas are not practicable. The talk about equity in education is essentially seen with that attitude. But the Finland example has just shown us that this is possible. Though it is definitely not to say that we blindly follow that model. But it seems that utopian things are possible, just that we will have to give up on long cherished notions of what we consider excellence as.

Cram, don’t think

The message from 15 years of education in my country – first at a top-notch school and then at one of the best known colleges in India – was:

Facts are more important than thought and imagination; that it’s more important to know the answers than think critically; that exams are more important than knowledge itself. Some may say that in college the majority of us chose the convenient way out and they are right.Our system of education, even at the undergraduate level, does not encourage us – in fact, gives us every opportunity not to think independently, critically, creatively or analytically.

via The Hindu