Newtown: what have we learned?

As the one-year anniversary of the Newtown tragedy approaches one cannot help but think that we have done little to improve the quality of school life in a way that will help avoid the replication  of such terrible events.
Since that fateful day almost 200 children have been killed by guns and yet nothing significant has been done to curb the sale and possession of fire arms.

There has been a raft of misguided strategies such as those identified here  where people and organizations have grasped at straws in order to try to protect those who are most vulnerable. Some of the suggestions have seemed pathetically comical such as throwing erasers and cans of soup at gunmen or having bullet-proof white boards available. At one point I even thought I might have to include instructions on how to use a gun in my math education courses when arming teachers was being suggested.

In this article, the piece I find most hopeful is the section on what steps should be taken to help prevent such tragedies. Interestingly, these suggested steps are based on extensive research and give hope that there might be a solution since it appears sadly, that our culture is too dependent upon guns to give them up. According to the article schools should develop a strong emotional climate based on listening, trust and caring; reduce bullying and remove the code of silence. In other words, we need to create school environments that are sensitive to students who are having difficulty; an environment in which it's alright to seek or offer help to an individual.

This sounds like a wonderful set of goals and yet do we really value these attributes in our places of learning. Recent trends in Education would suggest we don't. What seems to be more important is creating climates of competition in and between schools where many schools are identified as failures based on a narrow set of test scores. "Race to the Top" even implies that life in schools is a competition where only a certain number pf participants can succeed. In the UK there are even "League Tables" where schools are compared based on student test scores. Not surprisingly there is a clear correlation between those schools that do well and those where the students' parents have higher incomes.

A competitive climate of success and failure will not encourage an environment of trust, caring and sensitivity researchers suggest is the key to making our schools safer places for students and teachers. We owe it too our children, our students to be better than this.   

ELL and Math resources

Here's a really neat Powerpoint  resource I came across recently that looks at teaching math to English learners from a different perspective; that of the TESL person as opposed that of me, the math person. 

There is an absolute wealth of information in this presentation especially the linguistic identification of the different types of words used in math.

And here is another really good account from the Virginia Department of Education that also gives some historical background to the theories involved in teaching math to English learners.

Finally here's a book that I probably should have read some time ago but have only just discovered.
It is the CALLA handbook. The book describes the development and implementation of the Cognitive Academic Language Learning Approach to teaching English learners.

K-5 Math Teaching Resources

The Common Core has done one thing if it has done nothing else and that is to stimulate growth in the educational section o the public sector.  A Google search of "Common Core math" yields "36,200,000 hits in 23 seconds". Many, many of these are publishing company's attempts to cash in on the need for new materials to meet the demands of the soon-to-be required Common Core math (at least in those states that have signed up).

Over the past year or so I have been bombarded with websites offering all kinds of things usually promising to make my job easier ( I wish they would promise to make it better) Every-so-often I poke around on my own looking for something I can use i my courses and recommend to colleagues. Here's one that I find quite amazing because it is so simple and  straight forward and the math is absolutely wonderful. The work-cards and images for arrays are terrific and are so much better than the rectangles one so often sees that I find confuse arrays with area.

How many eggs are there? A student who understands the concept of the array as multiplication will say 4 x 6 while the student who doesn't will count them one ob one.

Here is the K-5 Math Teaching Resources; it really is worth a visit. I wish I knew who the authors were though.   

Recognition of Math and English Learners

It was such an honor to receive the 2013 Balomenos award as the math educator for New England  at the recent ATMNE conference in Killington. (That's Mary Calder, VCTM president presenting the award). It was a recognition that teaching math to students who are English Learners requires something different, that we need to stop and think a little more carefully about what we are doing. We are now beginning to recognise that there are significant differences between the math students learn in other countries and the math they learn when they arrive in US classrooms.

Differences can exist in so many different ways from the simple algorithmic procedures we use to the complexity or simplicity, as is so often the case, of the counting or number  systems being used. There are also so may other ways that the quantitative aspects of a culture can differ. The strangeness of our measuring system must drive English learners used to the metric system absolutely crazy. Imagine trying to estimate distance in kilometers, or weight in kilos or length in centimeters?. What is your hand span in centimeters? Now measure it to see how close you are. Try the same thing in inches and I bet you are more accurate.

The numbers inherent in unique cultures are also very different. Our lives are defined by numbers and quantitative relationships whether we like it or not. House numbers, SSNs, clothes sizes (we are different sizes in different countries), numbers of States, shires counties or Provinces, stripes or patterns on flags and so on. Every country has a mathematical profile that affects the individuals who live there.

Then there are differences in the math education. The recent PISA test results show several Asian countries at the top with the US and UK fairly well down the charts. I always find such comparisons fairly futile and frustrating since there are so many difference that are not considered. In Shanghai, for example, which came top, there are reports of students working under incredible pressure, studying 15 hours a day and all weekend, There are also reports that teachers get a lot of time during the day for professional development and I am sure there are many other reasons why the differences in scores exist.

So when we are teaching math to English learners we should never dismiss their math difficulties as the result of their limited English. There are so many other reasons why they might be having difficulty. It could also be that they are not having difficulties in math at all; just difficulties communicating what they know but we should never make this assumption. We owe it to our students who are English learner to find out about their math, the math  they know and understand.   

English Learners and Counting

As I continue to interview students who are English learners it is so interesting to observe different things which when put together create a more solid understanding of the issues EL students face when learning maths in US schools.

The difficulty English learners have in hearing the difference in the pronunciation between the teen numbers (fifteen) and the decade numbers (fifty) is well documented. The 'n' phoneme at the end of a word is rare and quite difficult to say in some languages and therefor is very difficult for some people used to speaking those languages to hear.

I remember discovering this several years ago working with a group of Somali students who kept saying "twenty" after they had counted by tens to ninety. Yesterday I was interviewing a third grader form Burma and he almost made the same error catching himself at the last moment. The student has a wonderful cheerful disposition and immediately said "teen is 1 and ty is 0" as if it was something he had been taught to help him differentiate between the two. I must follow up to see if this is in fact true.

The other thing I am noticing is that many of the English learners I am working with find it very difficult to skip count by 2s an 5s. Even when they have an excellent grasp of place value up to reading, writing and modeling 4-digit numbers they still have considerable difficulty skip counting.
This apparent lack of a sense of pattern in number could be quite an issue. This is something I will begin to watch for more closely.

Edshelf; A Great Resource

The world of iPAD Apps is truly bewildering but here's a great resource with what appear to be genuine reviews and collections sorted by topic. It's called Edshelf and is free but you have to sign up. It also looks as if it is free from the fine-print that can get you into trouble if you leave a negative comment of a product. Here's the math manipulatives page
which gives you a sense of how usefuol people are finding each of the different Apps.

There's information about sources of funding for purchasing iPADs such as this Apple information and  and here is the US Department of Education funding site. There are also many YouTube videos featuring iPAD math Apps.

Math Triangle of Meaning

I've been on sabbatical this semester researching ways to help students who are English Learners learn math in US classrooms. Part of the project has involved interviewing both adults and children who have settled in the US having grown  up in other countries, just like I did. This week I have interviewed a couple of third graders who were born in Burma and came to the US via Thailand.

Both students spoke English well so communication was not an issue. In the first interview the student did something quite remarkable in that it was so exactly in line with a particular theory I use in my math education courses. It is always so neat when this happens because it reconfirms the value of a theory-based education. When we can make an observation and relate it directly to a particular theory, or piece of a theory, as teachers we are in such a better position to know where to go next in the instructional process.

The particular observation happened as I was interviewing the student on his understanding of basic numeracy; more specifically being able to read, write and understand 3 and 4 digit numbers. The triangle of meaning is a piece of theory that identifies the  three component of a piece of math understanding; the idea, the word and the symbol. For example 5 is "five" and *****. Put one of these at each  corner of a triangle and there are 6 relationships (e.g hold up five fingers and ask how many, hold up 5 fingers and ask student to show the correct numeral). Students may  frequently have some of the relationships but not all 6.

Yesterday the student kept reading 4 digit number incorrectly. For 4,582 he would say "forty-five thousand and eighty two". So I asked him to write numbers such as 4,275. He did this correctly every time. I then asked him to read back to me the numbers he had correctly written and he read them incorrectly using tens of thousands as in the example above.

He could model the numbers using base ten blocks and he could write them when given them orally  but he could not read them even when he had written them. The important lesson here is to remember that just because a student can write a number doesn't mean to say she/he can read it, or knows what it means.