Monday, December 22, 2014

I'm a Math Geek not a Math Nerd

I often joke with my students that I'm a math nerd. I love math; at least the math that we expect young children to learn. But nerd am I no more! After listening to a great program on Vermont Public Radio this morning I now declare myself a Math Geek.

I see the world through maths-tinted glasses. I see how the angles between the branches and twigs on the same trees are similar and how they are different on different trees. I get a kick out of seeing a bunch of cars the same color or a row of buses; in other words, unexpectedly large numbers of things the same. I revel in subitizing and finding number patterns where there really shouldn't be any. From my increasing  understanding of fractals I am beginning to see the mathematical perfection of just about everything and how there really is very little in the world that is random or that does not follow a mathematical pattern of some sort.I even appreciate the land of my fathers differently ever since I saw the coastline measured using fractal mathematics.

So being a Geek is no longer a negative thing. According to the VPR commentary it is "as cool as being a homecoming queen or captain of the football team". The program also introduced me to the grammatically correct act of "verbing" the word geek as in "geeking out the library".

The really cool think about being a math geek is that it gives legitimacy to the idea that math is really cool; something I have believed in for many years. No, I don't mean that adding 29 + 59 is cool (unless you just see it as 30 + 60 - 2) . I mean looking for the next number in the sequence 0,1,1,2,3,5,8 is really cool; thinking about odd and even numbers as partnered numbers and non-partnered numbers; seeing how all circles are just over 3 times their diameter around the circumference; all circles are.

Math is the science of pattern and the art of making sense.

Wednesday, December 17, 2014

Schools as Places of Learning and Safety.

An article in the Burlington Free Press recently started me thinking about something I just cannot seem to stop thinking about. The article described in detail  how the Shelburne community school, built in 1967, was built with an open plan which was closely related to the idea of Open Education.  The words of the  School Board Chairman,  "The open classrooms represent an idea whose time has come and gone," pretty much sum up what the community thinks of the original idea upon which the school was based. It's a somewhat curt dismissal of something that made Vermont quite famous in the 1960s and 70s as schools like Shelburne bought into the progressive education movement known as the Open Classroom. As a graduate student in the 70s I worked with teachers in an Open Classroom school in Arlington Heights, Illinois,  called the Olive School. It was a magical experience where the focus was on helping individual children learn through a variety of exciting and meaningful experiences. I miss it dearly.

Back then, whether one agreed with it or not, we designed school buildings based on how we thought students learned best; a philosophy of education, if you like.

Today, we design school buildings based on ideas of how to keep children  safe.

Interestingly. back in those halcyon days, the architecture of the building could have little effect upon the way some teachers taught. Even in those open classrooms with no walls there were teachers teaching the same way they had for 40 years with desks in rows, lecturing the 6 year olds, and giving them work sheet after work sheet.  

Sadly, as events in Newtown, Connecticut have shown, the architecture of a school cannot stop people intent on killing young children. More recently in Pakistan, even a school built like a fortress can be breached.

It is clearly not the architecture of schools that we need to address but the nature of our society.

Monday, December 8, 2014

Math and Science Education is Not Enough


I've spent my entire professional life teaching math and science education courses and have always been an advocate for the inclusion of those disciplines especially at the elementary school level. During the 42 years since I graduated with my freshly minted teaching license I have seen many changes in the field of education. The disaster that was New Math in the late 1960s and early '70s, the "alphabet" science programs such as SCIS and ESS of the 1970s and 80s. I have also experienced many different trends in education in general from the total integration of all disciplines in the '70s and '80s through the child centered movement of the late '90s and early noughties to the current standards/high stakes testing movement we are currently suffering through.

There have also been subtle changes in how our cultures view children and education in general. I will always remember the times I spent teaching in Mexico where it was so clear that parents and teachers expected children to be children and to make the most of that developmental stage that we all pass through. I was always so impressed that they didn't seem to view children as mini-adults, or childhood as preparation for adulthood.

Today, as this article on the BBC website illustrates not only do some view childhood as preparation for the future but they see it as an economic force for the future. In British Prime Minister David Cameron's words "There's no secret to success in the modern world. If countries are going to win in the global race and children compete and get the best jobs, you need mathematicians and scientists - pure and simple"......"It will take time but it's absolutely vital for the success of our country that we teach maths and science and computing in the modern way, because that will be one of the things that will determine whether we succeed or not," What happened to the idea that children need to be educated in all disciplines if they are to lead  fulfilled and happy lives? To focus on math and science to the exclusion of anything else would not be in the best interests of anyone. 

In the US we are currently going through an interesting time of paradox regarding the teaching of math and science; a time when the need for good math and science teachers is becoming increasingly important and yet a time when pre-service teachers' interest and skills in these subjects seems to be declining.     

Friday, December 5, 2014

The Common Core and the Deficit Model

Last night, in my Math and Diversity graduate course, we had the most wonderful discussion about the deficit model of education.  The topic was briefly mentioned in one of the  four articles assigned, The Myth of the Culture of Poverty by Paul Gorski.

I first encountered the deficit model of education many years ago while reading about the ways in which Native Americans teach their children. Apparently, there was never any sense that their children were "below standard", or were deficit in their learning in any way. The development of  their skills, understandings, attitudes and values was seen as a natural progression through which children passed in an orderly, logical manner. If a child couldn't do something it was because they had yet to learn it or develop the prerequisite skills first.

Several years later, I was deep in conversation with Rick Marcotte, a beloved principal in a South Burlington elementary school when he began talking all about the concept of "yet". His whole outlook on the way children learned was based on the idea that if a child couldn't do something or understand something it was because they hadn't learned it yet. In other words he saw only the positives in children, the jewels of their passions and what they knew and could do; he didn't see them as deficit based on some arbitrary grade level standard designed to make all students conform to what someone thinks a 10-year-old should be like.

Our current obsession with testing and with identifying standards at each grade level that all students must achieve is destroying our education system in a way that is turning student away from the joy of learning.As so-called standards are raised, with terms like "high stakes testing", "race to the top" and so on, more and more students will fall by the wayside because they will see themselves as deficit failures, not good enough, sub-par, below standard, incomplete human beings.

How wonderful, in contrast, to celebrate the jewels inside each student, to build upon what they know and understand, think and believe, to allow them to pursue their passions within the epistemological structure of the academic subjects studied in school. That structure exists in the form of the Common Core if we strip away the grade level standards and expectations. The learning sequences and structures  exist so that we know what students need to know or develop an understanding of next, based on what they already know and  understand.

Here are two interesting articles that give one a sense of what it might be like if we were to abandon the deficit model of learning. This article, Ditching the Deficit Model, describes building on students strengths and interests, while this one, Discarding the Deficit Model, focuses on the application of the term to teaching minorities and children with special needs, an area where the application of the deficit model has caused the greatest grief.        

Wednesday, November 12, 2014

Traditional Math Just Doesn't Work Anymore

I recently fell into an illuminating conversation with an old friend about math and math education. He was telling me how his daughter is homeschooling his grand-daughter and how much his grand daughter loves math and science. As the conversation continued he told me how his daughter was teaching her child traditional math and "how well" it was working out. He went on to say how he didn't think these new methods of math instruction helped at all and wondered why schools were not using the same methods to teach math his daughter was using and that he had learned 50 years ago..

I then shared with my old friend how I had had an unusual experience in my undergraduate math education course yesterday when one of the students had asked me why young children need to know why there are 180 degrees in a straight line. "Can't you just tell them?" the undergraduate student had asked. "I know there are 180 degrees in a straight line and that's been fine for me", she continued.

A little taken aback I then asked the student how she would explain to a young child how there were 180 degrees in a straight line when there was no angle to measure. She didn't say anything.

So, with my old friend watching I then tore the three corners off a paper triangle and lined them up so that they made a straight line by putting the three points together. There, I said, 180 degrees in the three corners of a triangle and a straight line. Seeing  a somewhat disbelieving glint in his eye I then took a 360 degree rotating protractor and rotated it through 180 degrees saying that degrees are a measure of rotation about a point; in this case the point where the three corners of the triangle come together. Here's a nice demonstration of the concept that angles are measures of rotation.

After a few seconds of thought he said "Hmmmm, why wasn't I taught math this way?" I wonder if he will say anything to his daughter.

The persistent  perception of math as a process of telling and memorization seems such an enigma in this day and age.

Sunday, November 2, 2014

Why a Rigorous Math Curriculum?

Why oh why did the maths education community have to choose the word "rigorous"? The greatest problem about choosing a word like this is that "rigorous" has so many different meanings. In an incredibly informative NCTM Summing Up statement, Linda Gojak, NCTM president describes how many different ways there are of defining the word rigorous. The problem with having such a loose word is that it can be interpreted in so many ways depending on a particular individual's agenda. For example, there are myopic people like Angela Lee Duckworth who have taken the word to mean "grit" and are advocating that all children develop the type of rigor that is all consuming and totally at odds with theories of child development. Clearly some people will do anything to make a name for themselves and get to deliver a TED talk, even if it is the worst one I have ever watched.

How much better it would have been to use a word like "interesting' or "relevant" or "meaningful" or even "inspiring" to describe a math curriculum. Why does maths have to be rigorous for kindergarten children? It's like requiring them to engage in rigorous play, or rigorous reading. It's like asking fifth graders to engage in rigorous creative writing, or rigorous music or P.E. lessons.

Why can learning not be a natural process through which we hold children to achievable standards through activities they find rich in interest, relevance and motivation.  Why can maths not be inspiring, wonderful, relevant, meaningful, and simply interesting?

How many adults would classify the pursuit of their adult lives as rigorous? 

Thursday, October 30, 2014

Homework Hotline's dismal math.


  I wasn't feeling at all well today and so I stayed home. When I do this I invariably watch Homework Hotline on Mountain Lake Public Television. This is never a good idea because every time I have watched it the math teachers solving the math problems called in by students have tended to solve math problems using rote learning strategies devoid of any conceptual knowledge and completely separated from the real worldin which math problems occur.

Today, in the Halloween edition with the teachers dressed in costume, one of the math problems called in by one of the students was this. If a table is 1.75 meters long and 1 meter wide and a chair is 39 cms wide, how many chairs will fit around the table.

So, the math teacher, Sir Lancelot I think he was dressed as, solved the problem by  adding all the sides of the table together, then divided this total by the width of the chair. The total of the 4 sides was 5.5 meters. When he had divided 550cm by 39cm he got 14.1. Correctly ignoring the .1 he said 14 chairs will fit around the table

Although this answer is mathemtically correct it makes absolutely no sense in reality. To fit 14 chairs around the table you would have to fit 2 1/2 chairs at each end and 4 1/2 chairs along each side. The correct, realistic answer should be 12; 2 at each end and 4 along each side; a solution arrived at by dividing the width of a chair into the length of each side of the table. This would leave space between each chair and not require 2 of the chairs to be cut in half.

This is an example of why we, as a nation, struggle to teach math effectively. So often the math of the classroom, especially in middle and high schools, bears no relation to the math required in the real world.