Thursday, August 29, 2013

Math in Singapore is Elitist

I always find it interesting how much faith people tend to put in test scores. School districts will spend hundreds of thousands of dollars, even millions of dollars, on math programs that are shown to produce great test score results. Such a set of scores is the TIMMS (Trends in International Math and Science Study)  report which shows the top five nations as Singapore, Korea, Hong Kong, Chinese Taipei, and Japan. The US comes half way down the "second tier" countries in mathematics.

If everything in each of the each of the 64 participating countries was the same then one could logically compare the results of the test scores and make comparative judgments. Sadly, everything is not the same, in fact, almost nothing is the same. For example, the numeracy system in most Asian countries is much easier to learn and more logically derived than it is in most western cultures (e.g. the word for eleven in most Asian languages is simply ten and one). Children also spend much more time in school in Asian countries than they do in the US; a lot more of GDP is spent on Education in many Asian countries (20% in Singapore) than in the US and formal education has a different cultural value and identity in each country.

It's not like soccer teams playing in the World Cup where the game is exactly the same in every country. The playing field is the same, the number of players is the same and the rules are the same. It's the same with any international sport. Education is different, it is not a sport. 

Interestingly, text book publishers in  the US  have made the most out of this divisive test score reporting by marketing a program in the US called Singapore Math. They cite the incredible successes of the Singapore education system as if everything were equal.  I wonder how teachers and students would perform in Singapore if they were held to the same humanitarian ethics as we value in the US. Singapore's education system is described as elitist and a meritocracy. Children are "streamed" in fourth grade which means they are put into ability groups based on test results. This means that if you don't make it by age 11 you probably never will. We used to call this the 11+ in the UK until it was abolished in1976. Basically, the claims made by the publishers of Singapore Math are based on the education of only part of the population. Teachers in Singapore do not have to spend time with differentiated instruction, RTI and so on.

Worse still, in Singapore children with special needs have no rights to a public education.In fact, they are not even required to attend school.  There are Special Education Schools  that parents may choose to send their children to.  The last words on this website are "The mission of SPED schools is to provide the best possible education and training to children with special needs so as to enable them to function optimally and integrate well into society".

 How can they possibly do this when they have been segregated for their entire education?

Thursday, August 15, 2013

How To Learn Math

For the past week I've been auditing the on-line course by Jo Boaler of Stanford University. The course, How to Learn Math raises so many wonderful  issues about how we need to develop a more user friendly and conceptually-based  way of teaching math; how math needs to be seen as a creative activity and how we need to get away from the idea  that math is a closed set of procedures to be memorized. Now while these are things I have been advocating for for almost my entire professional life there is something in the course that is having a radical influence  on the way I see my role as a teacher of teachers of elementary school math.

This is the idea of fixed versus growth mindset. developed by Dr. Carol Dweck as described in her book Mindset.   This is clearly an  incredibly important issue for helping children become better at math especially those students who, because of our current system of  testing, have pretty much given up on ever achieving anything mathematically. To be told you are a mathematical failure at age 6 and have no hope of changing that is the world of the fixed mindset indeed.

But there's another application of this incredible idea which is to apply it to parents in terms of their attitudes toward math education. Over the years I have engaged in may discussions, arguments and  even confrontations, some even in public forums, with parents who truly believe that the math they learned by rote in school 30 years ago "was good enough for them so it should be good enough for their children". Sadly, the proponent of the fixed mindset are frequently successful businessmen who point to their success as the reason for maintaining the"no pain, no gain" approach to learning mathematics.

If we are to bring about the evolution of math education to a truly conceptual approach we have to do much to bring about a cultural shift in thinking about mathematics education, a task made more difficult by the disaster of the "new math' activities of the early 1970s in the last century. Perhaps the only way to succeed is to show that the methods advocated by Jo Boaler and the rest of us really do improve scores on tests.

Presentism and Time

 As I listened to the interview with Douglas Rushkoff, author of Present Shock, on NPR this morning I was reminded of just why it is so important to continue to teach children about time using an analog clock and not  a digital one. It's probably OK to use both later in life but we ignore the value of teaching  about time using  the analog clock or watch  at out peril; or at least the peril of our children.

                                                          It is the analog clock face that gives children a sense of time. The circle made by the clock face is an analogy
for an hour, or, more indirectly, a day or a night. The fact that a circle has no end point helps children develop the idea that hours pass continuously from one to the next and that time is constant. The digital face also gives us the language of time in a spatial sense with a "quarter past",  "half past" and quarter 'til" or "a quarter to" (as they say in the UK). In addition, the analog clock face gives us a comparative sense of time in terms of elapsed time or how much time is left. Usually, when we check the time, we do so to see how much time has passed or how much time is left; we seldom look at the clock just to see what time it is.

Without any reference to the analog clock face the digital clock face gives us but a fleeting moment in time. It tells us what time it is at the moment we look at the clock face. There is no before or after, no sense of space. It provides us with no clues for making comparisons between two times; we cannot instantly decide how much time there is left. The digital clock face is the essence of "presentism" or, as one speaker on the radio show said, "immediatism".

I wonder what effects  "presentism" is having on children's ability to learn how to tell time?

Wednesday, August 7, 2013

Vermont Math Scores

While the recent disclosure of the lack of growth in math scores in Vermont is depressing by far the most depressing situation is the fact that we are still using these  NCLB measures to evaluate student performance and, ultimately, schools and teachers  The way the AYP, annual yearly progress, targets are set up is almost like saying the average height of children must increase by a half inch each year. When we know what children are developmentally capable of learning and understanding at each stage of their lives why do people think we can constantly increase that natural development without changing something else.

There are, no doubt, places where the quality of teaching mathematics could be improved but to set "standards" so high that only half the population achieves them suggests that either the standards have to be reviewed or the method of evaluation has to be changed.

What is of much greater importance right now in math education, the "something else" I refer to above,  is to get students to enjoy, like and be captivated by mathematics. Part of the reasons why more students do not do well in mathematics is because they find it so deathly dull and irrelevant. The tests focus on memorization and recall and do not always test those things in math that are most important and meaningful in the lives of young children..

Our culture in general also has a terrible time with math. Many people are not afraid to say "I'm  no good at math" but no-one would say publicly that they cannot read. A recent news item about T-shirts being sold at The Children's Place store just adds to the way math is portrayed as being un-cool and not something to be enjoyed and valued by young people.

For the past few posts I have been suggesting that there are ways of making way captivating while at the same time maintaining the rigor and precision called for in the Common Core Standards. We have to do something before it is too late.

Monday, August 5, 2013

Math is NOT for Checkbook Balancing

I've lost track of the number of times I've been told that math is for balancing your checkbook, not that I was counting, of course. It is probably testament to the dire methods of teaching math that our fore fathers and mothers suffered through that math is now consigned to this anachronistic task. Anachronistic because most people today have instant access to their bank accounts through cell phones and so on so the need to "balance" the bank account using basic arithmetic no longer exists.

Saying that we need math to balance a bank account is like saying that we need to be able to read and write so that we can write checks drawn upon that bank account. If t his were true there would be no creative writing activities, no poetry., no language exercises in school that helped children play with language and learn all the wonders of alliteration, onomatopoeia and so on.

Hmmmm, that would make the English language arts just like math at the elementary school level wouldn't it!

Math is the wondrous study of all things quantitative and relational in this world and a good many other things too. The study of math by young children should should include exciting topics such as the numerical relationships in the Fibonacci sequence, the way multiplication facts are related to addition facts, the patterns made by fractions are the symmetry in the place value system we all use.

We need to captivate young children's attention in math just like we use exciting stories to fire their imaginations and motivate them to read on the English language arts.

Sunday, August 4, 2013

A New Math Identity

The identity property of addition is 0 while the identity property of multiplication is 1. There are many other ways of defining identity mathematically but a new line of research in math education is revealing a completely different math identity.  I am currently reading a very interesting book in which the authors describe ways in which students identify themselves with math. The book, The Impact of Identity in K - 8 Mathematics by Aguirre, Mayfield-Ingram and Martin, brings a long-needed focus to the way students, and teachers, see themselves in the context of mathematics.

The authors raise interesting questions about how students see themselves in the context of math in relation to how they see themselves in other activities. Frequently students will have very positive identities in all sorts of things related to sport, art, music, language and so on but when it comes to math their self esteem plummets. This is  particularly true of students with diverse needs such as those who have special needs, come from disadvantaged homes, or are English language learners.

Since we live in a time when fewer and fewer students are choosing to enroll in  math courses in high school or college or, indeed,  follow math-based careers we have to do something to change these negative identities to positive ones at an early age so that students find math interesting rather than boring and irrelevant.

In recent posts I have been sharing the way I think math needs to be made more user friendly by relating it to art, and real life while at the same time maintaining the same standards of academic rigor as those required in the fields of the English language arts. In other words, we need to find ways that captivate students interests so that they see math as interesting and relevant as well as stimulating and challenging. 

Friday, August 2, 2013

Maths is the Science of Pattern

So here's the latest in the penny fractals I've been making on the wall outside my office. This one shows the development of the Koch curve through four iterations. If the thin line of pennies at the top is 1 (one) or 3/3 then the next one down is 4/3 (count the "sides" = 4 over the horizontal space =3. Each successive one is 4/3 of the previous one so the next one is 16/9 and the next one is 64/27.

There are so many interesting relationships between numerical patterns. Look at this neat relationship between the Sierpinski triangle and Pascall's triangle. If you color all the even numbers one coler and all the odd numbers another color you get a Sierpinski triangle. There's also a relationship between Fibonacci numbers and Pascall's triangle. If you add the diagonal numbers in Pascall's triangle you get the Fibonacci sequence.

Wouldn't it be wonderful if young children could learn these magical mathematical relationships in elementary school rather than learning math as a disjointed unrelated group of rules and facts. It would be much easier for them to remember their addition, multiplication and subtraction facts if they saw the relationships between them.