Monday, November 25, 2013

A Ray of Hope for Education

In the depression and gloom of the current movement of  the private sector take over of public education there's a ray of hope that has to be developed from its quiet, gentle nucleus into a roaring inferno that will  extinguish the darkness that is enveloping our schools.

That ray of hope, a beacon of light, is embodied in the writings of Diane Ravitch and others with  visions of what education should be. In this particular piece she asks why we have to treat schools like sports teams with leagues containing winners and losers. Race to the Top has done much to engender this analogy by implying the education is a competition in which everyone is racing to get to the top.

The interesting thing about that analog, for that's surely  what it must be, is that it implies so many different ways in which some people are better than others. If it is a race it implies there are winners and losers; that not all people can be at the top. Even if everyone could reach the top it wouldn't be the top anymore because 'top' is a relative position implying that those on top are on top of those below those below. If everyone was on top they couldn't be on top because there would be no-one for them to be on top of.  This makes the whole idea of Race to the Top rediculous.

As Ravitch says ' We must think and act differently. If we do, we will not only have better schools, but a better society, where people help one another instead of finding a way to beat out their competitors".

Now the big question is how can we get the private sector to think in that same collaborative way where individual people come before dollars and the profit margin? 

Sunday, November 24, 2013

Dark Days for Education!

One of the good things about the impending Common Core is that it is designed, in theory,  to just  describe a set of standards expected of students at different grade levels in ELA and maths. Unfortunately, that is also one of the really awful things about it. In essence it is open to just about any interpretation including what is happening in New York State where modules. are being prescribed for implementation at each elementary school grade level. If this eloquent presentation is an accurate description of what is happening all is lost and these are dark days indeed for elementary education in New York State.

I cannot imagine what it must be like, to teach these modules where content is dispensed in carefully timed segments regardless of  student understanding and participation. One has to wonder who is in chanrge in Oneonta. Then, of course, there is the corporate control over the curriculum such as that exerted by Pearson and others. SBAC and PARCC, the two approved assessment companies, will make a fortune out of the mandatory assessments associated with the Common Core.   The private sector has probably moved faster than any other aspect of our culture to "make a quick buck" from the implementation of the CCSs. It's not just in public schools where the private sector is taking over. Future teachers are going to be required to complete an electronic portfolio scored by ETS in order to get their teaching licenses. Control over the quality of teachers in the future will pass from the State to the private sector.

Ultimately, the private sector will have direct control of the education of "young consumers". Perhaps schools themselves will be taken over by the private sector. Students from kindergarten on will wear school uniforms with company logos on them; classrooms will be equipped with all the company's latest products, teachers will say "Math class is brought to you today by Walmart". Teachers will be required to drive Fords in schools owned by Ford and wear clothes purchased at Kohls at schools owned by that company. 

Friday, November 22, 2013

Jo Boaler Almost Has it Right

I really like what Jo Boaler has to say about maths education. I was one of the 40,000 who followed her Stanford course this summer on teaching maths. Her research over the years has shed much light on many different aspects of mathematics from the best way to teach to how to get people to open their minds about what maths and maths education are all about.

Sometimes, however, I fear she is guilty of making  over-generalizations in a way similar to those who believe that math should be memorized and learned the way it was 50 years ago.

In a recent article in The Atlantic she  avers that  "Speed doesn't matter, and there's no such thing as a "math person."". While I would agree that the two ideas of a) the need for speed, and b)  only people good at maths can do it, are two misconceptions that plague the real and joyful  study of maths there is difficulty in stating the situation categorically as Boaler does.

Clearly, the argument she gives against the need for speed in problem solving and so on is exactly right but I believe there are times when speed is a good thing such as in recalling facts. Having quick access to certain pieces of information is empowering and makes life in general easier and better. Generally, waiting for your mom to cut your food or for your dad to tie you shoe laces is OK when you are 3 or 4  but not when you are 9 or 10.

Again, to say there is no such thing as a "math person" seems to overstate what we really believe. There are clearly some people who will always be better at maths than others in just the same way some people will excel in sports or art or as musicians. I guess I still have to  agree with Howard Gardner that some people have a propensity for being able to think in certain ways while others may not. What I think is the heart of Boaler's assertion is Carol Dweck's idea of fixed versus growth mindset. In other words, so many, many people end up believing they are not good at math because they couldn't solve problems quickly, couldn't remember facts and were made to feel foolish by uncaring teachers resulting in a lifelong belief  that they were not good at math.  No-one should ever say again "I'm no good at math".

When we teach young children maths we should be sensitive to the way we respond to their efforts and accomplishments in maths class. We should encourage them to take time to think through what they are doing and to use what they know and understand.  We should encourage them to do the best they can but recognize a situation where, for one reason or another, a student might need extra help in the form of a different example, method or strategy to understand a particular idea or develop a particular skill, Everyone should have the opportunity to become the best "maths person" they can be. 


Thursday, November 21, 2013

Math Apps for iPAD2s

Finding good APPs for the iPAD2s in your classrom can be a time consuming business, and expensive too if you pay for them. One way to reduce the amount of time and download them with a greater degree of certainty is to use a reveiw center like this one at Ed Shelf. It has a whole bunch of features that add to it's value such as being able to make "collections" of your favorite Apps which you can then post for other to share.

This strategy significantly increases the sense of trust one can have that the "likes" and recommendations are not being posted by those who might profit from increased sales. The site is also recommended by the IT folks at St. Mike's and one that they all use.

More and more schools are investing in iPAD2carts so that more students have access to this neat learning tool. There's a new Mac Lab

Wednesday, November 20, 2013

Math and English Learners

This past weekend I gave a presentation on teaching math to English Learners at the NNETESOL conference at the University of Southern Maine campus in Gorham, Maine. Titled My Math Counts Too, the presentation focused on selected issues related to teaching math to students who are English language learners or English Learners (ELS) as they are now referred to. I have made several presentations at this conference over the years and they are always well attended. I have the sense that there is a great need for more research/information/support and so on for teaching math to students who are English learners. Quite often the math ELs have learned is quite different from that in the US classroom which can present quite a challenge. For example, the new CCMSs require that all students be taught the standard algorithms. Many EL student will, however, have spent many years learning algorithms
that are quite different from those defined as 'standard' in US classrooms!   

I always begin these presentations by addressing some of the assumptions we tend to make when teaching math to English learners. For example, we tend to think that math is the same the world over but there are so many differences between the math of different cultures that we really cannot make this assumption. The procedures and strategies students are taught as well as the mathematics of the culture can all be significantly different. It can also be assumed that a student's difficulty in math can be attributed to a lack of English competency but if the student has never had the opportunity to learn math no amount of instruction in English is going to make any difference to the student's math skills and understanding.

Next fall I will be offering a course titled Math and Diversity which will include a section on teaching math to English learners. Offered through the Graduate Education Program at St. Michael's College the course will focus on this and three other strands; teaching math to students with special needs, students in poverty and students with math disabilities.    

Early Chidlhood math

Here's a really useful and interesting resource a friend in Early Childhood Education recently sent me. It's research-based and has a wealth of ideas and suggestions for teaching math to preschoolers and kindergartners. The really neat thing, however, is the suggestion that we need to make math an integral part of children's lives in the sense that they see things through a mathematical lens from a very early age.

I have a feeling this is similar to the idea of mathematization developed by Bob Wright in the Math Recovery materials. As we know, manipulative materials are essential lfor helping children develop all sorts of mathematical and quantitative relationships but it's the student's ability to use these skills and apply these concepts abstractly that enables them to think mathematically.

The paper also suggests that children gain experiences in a variety of math topics such as measurement and geometry in addition to fundamental ideas of number. I wonder what the effects of the increased use of iPADs and other tech-based learning tools will have on the development of student's mathematical ideas?

Math TED talks

Tracy Watterson reminded me today of the wonderful Arthur Benjamin TED talk about the magic of Fibonacci numbers.So I did a quick search to find all the TED talks about math. and started watching them (one of the joys of being on sabbatical). So far I've watched The Math and Magic of Origami which shows how Origamists eventually turned to math to develop rules and new origami projects. This was quite amazing in terms of the mathematical laws and rules that govern origami. I've also watched the Benjamin one of the Fibonacci numbers which really brings them to life beyond their usual natural occurrence.

I usually find myself agreeing with the speakers especially those like Dan Meyers who insists that we really do need to do something to make math more captivating for students of all ages. But, occasionally I do find disagreement with the ideas being presented. One such TED talk is the one given by Conrad Wolfram entitled Teaching Kids real Math with Computers. His fundamental idea is that we have to "stop teaching calculating and start teaching math". His fundamental error is that he defines "basics" of maths as calculating using paper. This is an error that is so frequently made by people who would have us teach the way we taught fifty years ago. He completely ignores the idea of numeracy and the fundamental understanding of place value and base ten which comprise the real "basics".

After you watch the Wolfram TEDtalk read this article by Karen Fuson about standard algorithms in the CCMS. She makes a good case for "calculating". The real question then becomes:  "What is the standard algorithm?" especially if you are and English Language Learner.

If you have a favorite math TED write about it on this blog.

PS The Ken Robinson TED talks on Creativity in Education are also really good.

Are Standard Algorithms for All Students?

x 25
  Every so often I get asked to interview students who are enigmas in the classroom; students who are difficult for teachers to understand; students who, perhaps, do things slightly differently. When this happens I use one of the several Interactive math Interviews I have developed over the past ten years. designed to engage the student in a conversation with a purpose, the interviews provide a framework or jumping-off point from which the student's thinking can be thoroughly explored. 

As an aside, I recently came across this study at Florida State University  in which the researchers found out, after using up a 2.9 million dollar grant, that;

         "When early elementary math teachers ask students to explain their problem-solving strategies
         and then tailor instruction to address specific gaps in their understanding, students learn
         significantly more than those taught using a more traditional approach. This was the conclusion
         of a yearlong study of nearly 5,000 kindergarten and first-grade students conducted by
         researchers at Florida State University".

To me, this seems like studying whether it's raining or not but watching people week after week to see if there's relationship between  umbrella use and inclement weather. WHY WOULD TEACHERS NOT ASK STUDENTS TO EXPLAIN THEIR PROBLEM SOLVING STRATEGIES? Clearly, I'm not the only one amazed by this somewhat banal finding.

But to return to the remarkable 3rd grader. When asked to solve the problem above he said; "Hmmmm, four 25s are 100 so 40 are 1000". All in his head but was getting a bit confused so I suggested he write it down which he did. He then said "so, twelve 25s are 300 which leaves just one 25 which mans the answer is 1325". I was pretty impressed.

I probably should have given him one with "un-nice" numbers to see what he would do but I ran out of time. My hunch is that he would have worked out a similar way of doing it using his incredible understanding of number. The real question is; Should he have to learn how to do the Standard Algorithm since he will most likely be tested on it in the upcoming SBACS? 

What do you think?


Tuesday, November 12, 2013


The time has just passed 14:15:16 on 11/12/13. These three numbers are probably three of the most interesting numbers we have in our numerical series. Eleven  has a really interesting history and basically means one left over after ten in several different ancient languages. One can see the lev - left connection. Similarly twelve also has a similar connection with two and lev being sort of smashed together to make twelve. Then thirteen is the first number to adopt the teen suffix although for some obscure reason it is not threeteen which would make things easier for many to pronounce. Like fiveteen it probably got contracted to make things a little easier to say.

This is all good and well, or well and good, unless you happen to be a person who grew up with a wonderfully logical numbering system like most people who live in Asia where things tend to go ten-one, ten-two, ten-three and so on. How much better it would have been had we had the foresight to change things around a bit to make it easier for our young people learning to count. Oneteen, twoteen, threeteen, fourteen etc would have been so much easier.

Two of these numbers have also been embellished with all sorts of wonderful extras. Twelve even has its own name; dozen, and thirteen is famous for its triskaidekaphobia label. Thirteen is also a baker's dozen, a phrase which has a checkered and often gruesome set of possible origins. 

And remember this date means nothing in the UK where it is written 12 - 11 - 13. Their 11-12-13 will be the upcoming December 11!!!!!!!.