Tuesday, December 6, 2016

Tests Only Measure Other Tests!

The PISA test results were released this week and once again the US is slipping in math test scores when compared with test results from 60 or so other countries. Of the 35 industrialized countries included the US ranks 31st.

When I was a fourth grade teacher many, many years ago in England we changed from one reading test to another one year without changing anything else; the reading program and the way I taught children to read remained exactly the same. The most incredible thing happened. All my students' reading abilities improved by more than a year. In other words, my fourth graders looked like they were suddenly reading as well as fifth graders. What a remarkably effective teacher I must have been that year. Not really since I did nothing differently. It was because the reading test was clearly easier or standardized differently from the previous one. This was my first experience of tests measuring other tests.  

In fact this very same phenomenon is mentioned at the end of the Hechinger report of the PISA results in these words:

"However, one test released last week —  the 2015 Trends in International Mathematics and Science Study (TIMSS) — showed a surprising gain for the U.S. in 8th grade math.  Historically, PISA and TIMSS tests have shown contradictory results for Eastern European countries and Russia, as they perform much better on TIMSS than on the PISA test. Scholars will need to explain the divergence for the U.S. this past year".

The PISA and TIMMS tests are clearly different and measure different things in maths. It is so easy to point fingers when you see bare test results such as these reported in the media but there are so many other things to consider. 

Take the maths, for example. Maths is not the same the world over. There are vast differences in the math itself before you even start to teach it. In most Asian countries, for example, the numbering system is so much easier for young children to learn than it is in the US. The teen numbers follow  the pattern ten-one, ten-two, ten-three and so on rather than the difficult eleven, twelve, thirteen, etc system we use. Look at which countries are at the top of the PISA table! In some countries such as Singapore children are given vast amounts of homework to do each night and not all children have the opportunity to attend public schools. There are differences in the sizes and cultural diversity of the countries being compared which can all affect score averages on a simple test. 

Like pretty much everything in our lives we can probably do better in maths education but we need to use caution when comparing test scores obtained from students in vastly differing cultures. 





Saturday, December 3, 2016

Maths Is Easier When You Understand It.

I sometimes wonder just what we have to do in maths education to demonstrate that things are more easily remembered, used and developed if the learner understands what she/he is learning. This interesting piece of recently published research supports, for at least the millionth time,  that when students learn conceptual knowledge, along with procedural knowledge of maths, it is much, much, much, more effective. The neat thing about this piece of research is that it is for high school maths which has tended to lag behind the research on this topic at the elementary school level.

Probably the best way to distinguish between the two types of knowledge is the idea of pi. If I were to ask you what pi is you would probably say "3.14 but that's all I can remember". If that's all you know about pi then you have a small piece of procedural knowledge that you can plug into equations to find the area or circumference of a circle. Now, imagine that you have some conceptual knowledge to go with this. For example, knowing that pi is a ratio between the diameter and circumference of a circle would be immensely helpful to learning all sorts of more advanced maths. It would also be helpful for doing things in one's daily life. The fact that pi is a ratio means it is just over three times further around a circle than it is across the middle of that circle. If you think of pi as a fraction, 22/7, then the circumference could be 22 inches, or feet, or miles, and the diameter would be 7 inches, feet, or miles.

If I asked you to count by fives you would probably say, "5, 10, 15, 20, 25" etc assuming that I meant you to start at 0. So try counting by fives again starting at 3. The first few will be tough but you'll soon see the repeating pattern of 3s and 8s. Seeing the pattern is a piece of conceptual knowledge because you are applying your conception of counting by 5s and 10s rather than just parroting the numbers.

We have long known that conceptual knowledge of maths is as crucial to learning maths as procedural knowledge. Jo Boaler, the amazing Stanford professor and founder of YouCubed  was one of the first to demonstrate the importance of conceptual knowledge in a wonderful piece of research when she was at Liverpool University in the UK. She discovered that elementary aged students who were taught conceptual knowledge along with procedural knowledge did much better in high school maths that those who were only taught procedural knowledge at the elementary school, One of the interesting findings of her study, if I remember correctly, was that the conceptual/procedural knowledge taught students didn't. do as well on the end of elementary school maths tests as the procedural knowledge only taught students. The reason: the tests only tested the students' procedural knowledge of maths; a problem we still grapple with today. 

Thursday, October 13, 2016

Cursive and Art History sadly axed.

This week we seem to have lost two aspects of education that contribute significantly to our civilized society. In the US it has been determined, by those who wrote the Common Core Standards, that cursive writing will no longer be a required part of the elementary school curriculum. The reason, apparently, is because of a) the time it takes to teach it and b) the prevalence of technology as a form of communication.

I find this second reason particularly irksome and bewildering. I remember when calculators first entered the elementary school classroom and all the students said they would no longer have to learn their math facts.Luckily, we did not fall for this strategy since we knew that fact recall, with understanding of course,  is an important part of being mathematically literate.

Te remarkable thing about the technology argument for removing cursive is that you could use the same argument for removing all instruction in writing from the elementary school curriculum since more and more electronic devices can convert speech into the written form. Even now, texting has auto-correct meaning that spelling is already a dying art.

On the other side of the Atlantic in the UK the History of Art  has been discontinued as an A-level subject of study. Remarkably, this was the reason given for the decision "In a letter to teachers, the board said it was struggling to recruit "sufficient experienced examiners" to mark and award specialist topics".

Sometimes, the decisions made by those who are, presumably, paid to know best are quite baffling..

Sunday, September 18, 2016

Retirement and Contributing

It's bad enough that Michelle van Etten  was billed at the NRC 2016 as employing 100,00 workers when she actually employs none. But when she said in her speech that her husband home-schools her children to "protect them from Common Core" I found myself once again temporarily  lost for words. If only a different term other than "Common Core" had been used to describe the essential elements of what children can explore and learn about as they grow up. The individual words "common" and "core" by themselves have such negative connotations; when you put them together they become a recipe for disaster.

But, I'm now retired and so feel no desperate need to raise such issues as part of my life mission to help everyone fall in love with the study of maths. Like many of us in the field of math education I have lost faith, a little, in the ability of our culture to embrace a conceptual and meaningful approach to the teaching and study of maths. So I will do what I can in whatever small way my failing health will allow me to do.

It's been quite a ride since I made the decision to retire two years ago. For some strange reason I did not want to still be working past my 70th birthday which happens on a few months time. Lat October I had a Pacemaker installed then had a major heart attack at the end of December. Things did not look good and I was given as little as 2 months to live. I went through a lot of soul searching as I recovered at home unable to work. I resolved the effects of the ultimate loss by confirming that I will not be here to deal with what happens after my death. I am at incredible peace with this realization.

Last May, I qualified, just, for a new aortic valve through the TAVR process. It was an incredible experience and has potentially increased my life span by several  years.That is, if I now manage to successfully negotiate a carotid artery stent insertion next Friday.. I knew I would need this procedure after I lost the sight in my right eye last Sunday morning after a mini stroke caused by something letting loose from the blockage that needs stenting.

So, a terribly self indulgent blog post but if it helps someone else deal with the same things I am going through than it is worth it. I am truly thankful for every new day in my life. I can continue to contribute.  .  

Wednesday, May 18, 2016

The Power of Undergraduate Education

It's been a difficult week cleaning out my office and consigning the tangible elements of my career to the recycle bin. The task of deciding which books to keep, which to pass along to colleagues and which to throw away is not an easy one. I probably have close to 500 books on my shelves dating back to my undergraduate days in the late 60s and early 70s.

Deciding what to do with each book was absolutely impossible until I came up with an effective plan. Each book would be judged as follows. The books I would save and take home would be the ones that had impacted my professional life, my thinking and educational values the most. The second category would be those books that my colleagues or replacement might want. The third group comprised those destined for the recycle bin while the fourth and last group were the books my daughter wanted.

After three days of sorting, one spent with my daughter Marie, I have pretty well consigned every book to one of the groups described above. The pile of books that have touched my life the most are almost all books that I read as an undergraduate student. Books by Bruner, Dewey, Peters, DeBono, Whitehead to name a few. Looking back it seems remarkable that so few have had the same deep influence on educational values and core ideas as these great masters. Carol Dweck and Jo Boaler have been great influences along the way but it was these great writers who introduced me to the wonders of teaching in my undergraduate education who had he most profound affect on the way I think about teaching and teachers education.

The second group of books contain books all about teaching math, science and engineering; books that contain great ideas and activities for helping children at the K - 6 level learn to enjoy and succeed mathematically and scientifically.

By far the largest selection of books have filled a very large recycling bin to overflowing and contain books of several types. There are the what I would call the "fleeting fad" type of book while others are earlier editions of current books. Many were sent t me by publishers hoping  I would adopt the for my courses.

Undergraduate education today is promoted aggressively as a route to a better job, career preparation
and a pathway to fame and fortune in some instances. But the true value of undergraduate education is teaching students to be constructive and free thinkers; to develop cognitive and social values and a sense of who one is as an individual. Regardless of where I have worked in different parts of the world, the things I learned as an undergraduate have remained as the fundamental core of my beliefs.

 

Thursday, May 12, 2016

When You can't Hear the Song for the Singer

There's a line in my current favorite song, Black Muddy River,  that goes "When you can't hear the song for the singer". The song, written by Robert Hunter,  is sung by Bruce Hornsby, a quite unassuming "pop star" by current standards. His piano playing is quite remarkable and, although he didn't write the song, I find myself listening to the words and instrumentation intently. I hear every nuance in his voice, every note and cadence in the instrumental accompaniment. This is not always true. When I listen to Prince, or watch Celtic Women video I am preoccupied by the performance and the performer and not the song  With Prince it is his entire aura of who he is and what he stands for. His facial expressions and gyrations. I just can't hear the song for the singer. With the Celtic Women videos the sheer size and over production of the performance overtakes the actual words and their meaning. It's as if the song becomes a vehicle for everything else going on so you can;t really listen to it. The beauty of the Celtic women performers, the striking makeup on the drummers and the outside locations at castles and other notable venues.

I find  so much of educational "innovation" and "advancement" to be like this. You cant grasp or come to terms with what is being said because of who is presenting it. Much of current research is presented through emotional contexts based on  individual's unique experiences. It becomes difficult to grasp a theory of some sort that can become food for thought and reflection. Angela Lee Duckworth's Ted talk on the concept of grit in the classroom is a classic example. There are many others who shout about bullying, and dress codes, and all sorts of peripheral things that have little bearing on what education is all about.

The same is true inn the current political arena where the participants themselves become the object of the vote and not the idea and theories for which they stand. For example it's virtually impossible to determine exactly what Donald Trump stands for because his persona and delivery style far outweigh
what he really means.We seem to be becoming a nation of performers who know how to perform but but who's performances completely obscure the songs they are trying to sing..     

Monday, May 9, 2016

Testing is not the way to Improve Education

It's absolutely remarkable watching the British Government's current attempts to destroy on of the best education systems in the world. Having already backed down on their lunatic plans to turn every school in the country into an "Academy", they now have come out with a standardized reading tests that appears to have the potential to destroy every student's self confidence according to this TES article  The  incredible pressure put on young children through this relentless regime of testing by a government that has minimal educational expertise  outlined in this BBC article is  absolutely staggering.  There was even a protest by parents who kept their children home for the day because of the testing. And all the time the British Government is clamoring for more and more rigor Finland lets children play more and still outscores the UK in global tests.  In fact there are so many articles on the dissatisfaction of the over-testing of children and other government mismanagement of education issues in the UK that there is almost an entire BBC webpage devoted to articles about it.

  Thankfully in many States such as New York the "Opt-out" movement  is growing as people come to realize there is little benefit to children from constantly testing them. Assess, yes, test, no.

So why do Governments feel the need to test so much. In he case of the UK there is a terrible lack of trust of teachers on the part of the national government. They see education as "economic investment" and global competition first as opposed to helping children become the best they can be by whatever yardstick success as a human is measured. This is an incredibly complex issue, of course, but you simply cannot raise standards by raising the difficulty level of tests.