Thursday, April 30, 2015

NGSS - A Worthy Vision

So this week I began my long journey into intimacy with the Next Generation Science Standards. The time has come when I have to know them inside out, be familiar with all the nooks and crannies, find out what resources are available and generally make them part of who I am as a math, science and engineering educator.

My journey began a few months ago when I joined a group of HE faculty working with the science folks at the Vermont Agency of Education to find ways of making sure that the implementation of the NGSS in Vermont schools goes as planned in 2016.

Using John Dewey's pedagogical dualism the NGSS present us with a worthy "inspired vision" of how science education should exist at the elementary school level in the context of the elementary school curriculum which includes ELA, math and social studies. It's interesting that the latter discipline is missing from the Venn diagram above.

The other part of Dewey's dualism, of course, is one's "executive means" or ones ability to put into practice one's "inspired vision" of teaching. According to Dewey's theory there must always be proximity between one's vision and one's executive means but one can never truly achieve one's inspired vision. . The two can never be exactly the same because the practical world of the classroom comprises children who are unique.  The relationships between the students in a class is also unique. Our task as teachers is to continually work to get as close to implementing our "inspired vision" through the use of our "executive means" as we possibly can.

This is a grand task that requires a growth mindset by everyone involved.


Saturday, April 18, 2015

Common Core - Yes; SBAC testing - No

I've said this before, probably many many times, but it's worth saying again because things are starting to happen.
The Common Core is great. In mathematics, the CCSSM clearly identify the math that students should be expected to learn in each grade level. What is not good are the Smarter Balance Assessment Consortium standardized, computer-based tests that students are expected to take starting in third grade. Having just watched four third grade teachers and their students suffer through these anachronistic evaluation devices (they are clearly not assessments)  I think it's time for parents and teachers and everyone involved in Education to say enough is enough. American students are still the most tested and the least examined.

More and more people are beginning to boycott the tests or opt out such as these students. There is also a growing body of evidence that suggests that the PISA test scores that consistently show the US at a lower ranking than most would like are not a true reflection of the quality of education in American schools. More and more research, and opinion papers by scholars such as this one in the Guardian, are casting doubt upon the authenticity of comparing tests in cultures that are so different. The most odious interpretation of these international results based on false comparisons is to say that higher test scores in many Asian countries are the result of better teaching. There are so many other factors that contribute to differences in test scores.

Perhaps if all the parents of third grade students were to go on-line and take the sample SBAC test items they would see why such testing is so invalid. 

Friday, April 10, 2015

It's a "Testing-Crazy" World.

So this might turn out to be a bit of a "blog-rant" but the constant testing HAS TO STOP!. The BBC reports today that 4-year-olds are to be tested in the UK in reading, writing and maths. It seems that politicians, in particular, see the only solution to the improvement of education is to do more testing; test infants, test children, test students, test pre-service teachers, test teachers. Why do we never test politicians?

As stated in the Beeb article the primary reason for testing 4-year-olds is to provide a baseline by which the education system can be evaluated. This is basically another cry for teacher testing and yet another example of politicians' lack of confidence in teachers and the teaching profession.

And all this happens, of course, at a time of a general election in the UK when each party needs an extra plank in their platform. Education is  an easy target because it is so easy, through the manipulation of numbers, to show how poorly students in one country such as the UK or US are doing compared to students in another country such as Singapore. The same is beginning to happen in the US as we gear up for the 2016 presidential election. International test score comparisons such as TIMMS and PISA are readily available and provide instant numerical comparisons. The unfortunate thing is that politicians, of course,  fail to mention the fine details such as in Singapore there are special schools where all students with special needs are sent so the scores do not reflect the effort that goes into teaching the whole student population.

Tests, such as the SBACS, currently being administered in Vermont schools, test only what is easy to test. They only provide a brief, momentary, narrow snapshot of what children know and understand. The scores are also heavily swayed by a students ability to master the computer skills required to take the test.

Nobody knows a student as well as the teacher who teachers the student. Nobody who lives 300 miles away can possibly be in a position to truly assess what a student knows and understands. 

Why the Bridges 2 Math Program is So Good

This morning I observed one of my student teachers teaching a lesson on remainders from the Bridges 2 Math Program. As the student teacher struggled with her understanding of the mathematics involved it became incredibly clear to me why the program is so good. The activities are so rich with mathematical opportunity  for what Bob Wright called the mathematization of children's minds.

The third grade activity I was observing involved rolling two die and multiplying the subsequent numbers to get a product. Then, using a neat worksheet, the students had to divide the product by 2,3,4,5, and 6 to see what happens. The demonstration roll the student teacher used was 4 x 4 for 16. Dividing by 2 yielded 8, but 8 what? The children were using tiles to make 2 x 8 arrays vertically. Here the 2 referred to the number of columns and the 8 to the number of rows. So the 8 was 8 rows. She could have shown 8 groups of 2 or 2 groups of 8, demonstrating the commutative property of multiplication. This is only true abstractly as the actual arrangement looks quite different. This is known as psychological non-commutativity.

She then went on to divide 16 by 3 getting 5 R1, then divided it by 4 getting 4 (proving 16 is a square number), then by 5 getting 3R1 (showing the commutative property), and finally by 6 getting 2 R4 .  
The interesting thing about the commutative property in division is if you then give the remainder as a fraction. 16 ÷ 3 would give 5 1/3. 16 ÷ 5 would give 3 1/5. So the question is; what do the fractions represent? 1/3 of what and 1/5 of what? A fraction has no value unless you know the size of the one to which it refers. It depends, of course, on what the referents for the 3 and the 5 are. If you had 16 cookies divided between 3 people, each person would get 5 and 1/3 cookies. If you had 16 cookies and divided them  into groups of 5, 3 1/5 people could get a group of cookies; which makes absolutely no sense at all.  

The neat thing about the Bridges Program 2 activities is that they are so rich with mathematical possibilities.