Re-Envisioning Maths

This is my favorite bridge in the world. It's the Clifton Suspension Bridge designed and built by Isambard Kingdom Brunel in Bristol and is about three miles from where I spent most of my life before emigrating to the US in 1977. Opened in 1864 it has stood the test of time for 150 years and is a testimony to the quality of the mathematics used by engineer Brunel.

But it has also stood the test of time aesthetically as it is as much a part of the scenery of the gorge as it was when it was built. A whole variety of bridge constructions could have served the purpose of getting people and animals from one side of the bridge to the other but none, I think, would have provided such an harmonious relationship between the acts and interactions of nature and human endeavor. Brunel did this by using the mathematical formulas and relationships available to  him.

In my last post I discussed the depressing outlook described by Elizabeth Green in her NYT article about why Americans Stink at Math. The Common Core may hold out hope for change but unless we can re-envision the way we see maths, especially in the elementary grades, I hold out little hope.

The way we have always taught math, and the way proposed by the Common Core is as a form of functional perseverance in which things have to be learned because "some day you'll need this" or because "somethings just have to be memorized" or "because this is the way math is" . There is no sense of seeing the wholeness or the inter-relatedness of mathematical facts and ideas, the pattern, the artistry and beauty in symmetrical relationships. It's like teaching children to read using only things they need to be able to read in order to function in life; how to read street signs, menus, instruction books, directions, how-to manuals and so on. It's like teaching children to read and write without anything creative; no poetry or story writing, no alliteration activities. We teach math as if we are teaching reading and writing without all the fun, motivational, exciting, adventurous and joyful aspects of those areas of skill development.

Why do we do that? Why does the Common Core not contain any standards related to the aesthetics of math that make the remembering and retention of the myriad facts so much easier?

With a nod to John Tapper it's time we solved for why.

Why Wasn't I Taught Math This Way;

Ever since I started teaching elementary school math education courses some 35 years ago students at both the graduate and undergraduate level have been saying to me "why wasn't I taught math this way?". When I ask them why they ask they usually say something along the lines "it's so easy to understand things the way you teach it".

I've always believed in the importance of understanding what you learn instead of the traditional process of just memorizing disparate bits of information for later recall on tests. To do this, I try to help students see the relationships and patterns between different facts, concepts and ideas. Almost everything in math fits together in some way just like a tapestry or mosaic. It's also much easier to recall remembered facts if they fit into a pattern of related facts; four threes is just one more three than three threes.

So why is it that our public schools do not teach math in a way that students can understand what they are learning. Why Do Americans Stink at Math, a recent article by Elizabeth Green in the NYT, sheds some light on this dilemma. Green suggests that the Japanese approach to change through lesson study is an effective way of bringing about the adoption of more effective classroom pedagogy. She also suggests that parents and members of learning communities need to be patient with the slower rate of change brought about by genuine pedagogical change. She also suggests that this might be difficult in a culture twice stung before by failed attempts to improve math education.

For my own part, I believe  that the study of math at the elementary school level has to be made more motivating for students. The development of  young children's mathematical ideas is critical to the way they will be able to use these ideas to solve problems and enhance their appreciation of the world around them.

Perhaps one day students will stop asking why they were not taught math this way but I fear it will be long after I have stopped trying.       

Evaluation is not Assessment

Every so often something appears on my Facebook page that makes me stop and think, and then think some more. Then there's something that makes me change my thinking or reminds me of something wonderful in Education that we have, perhaps, lost sight of

This letter from a UK primary school headmistress to one of her students is something I just cannot stop thinking about and reminds me of how we used to focus on the whole child in the assessment process and not just test results. 

This letter is so wonderful on so many levels. I can imagine this school Principal knows every student as well as she knows Charlie. She probably also knows every student's strengths and challenges and knows who they are as individuals. I can also imagine that this wonderful example of assessment runs deep in the school, that all the teachers and everyone else in the school shares this same level of caring for the well-being of each and every student.

The letter also implicitly acknowledges that while it's important to hold schools and teachers accountable there is great folly in using test scores as the only form of accountability. Tests, especially those scored externally, thousands of miles away, by people, or more likely machines, that do not know the students who completed them, give us a narrow band of information about a strudents level of knowledge or understanding relative to a specific predetermined piece of content. The soon-to-be-mandatory SBAC tests, for example, cannot distinguish between a student's knowledge and understanding of the test material and the students linguistic of technology skills required for completing the test.

And no matter what the folks at ETS say about the SBACS they are not assessments, they are evaluations and must remain a small part of the assessment process.

Engineering on a shoestring

 In my last entry I described the joy of using the Lego Wedo and Mindstorms sets to teach elementary school engineering skills as defined in the Next Generation Science and Engineering Standards .

 

However, you don't need to go to the expense of purchasing the Lego kits to teach perfectly good elementary school engineering skills.

 By way of introducing the concept of engineering in the elementary school we first distinguished it from science. This can be most easily done by looking at the origin of the questions or curiosities one might have when studying a situation.

 In science the questions or inquiry arise from the natural world;  how are rocks forms, what causes the seasons, what affects the time of a pendulum swing, how is  paper made?

 In engineering the questions or inquiry arise from how we use our scientific knowledge and understanding to solve problems, resolve issues or make life better.

 This implies that the study of science comes first. We can then use our new-found knowledge and understanding and make it more relevant and meaningful by applying it to an engineering situation.

 During GED695 we studied the science of a swinging pendulum and then used this knowledge to design a pendulum that swung once every second. Since all good engineering solutions need to be presented each group of students timed their pendulum to see who had made the most accurate one.

 

The prize went to Theresa and Monique; their pendulum swung precisely 30 times in 30 seconds exactly. 

 We also used a copy of the Sunday Free Press (free the following Monday) to construct the tallest towers we could that supported a small washer.

 Trisha,

 Kate,

Ashley and Julie built an incredibly elegant one from floor to ceiling.

 Everyone, however, was successful in building a tower and realizing a great sense of achievement.

The capital outlay for these two engineering classes? $0

Engineering with Legos

At around 9:30 on the morning of July 8 I introduced the 13 students in my GED695 Teaching K - 8 Science and Engineering class to the world of Lego-based engineering. Nine of them chose the K - 5 Lego Wedo sets and 4 chose the 5 - 8 Lego Mindstorms. None of the students had ever seen these particular Lego kits before, most were nervous, a little anxious and wondering how on earth they would ever master building a Lego model and then programming it with their computer.

  

By 10:30 they were all proudly demonstrating how they had built and programmedeither the "Dancing Birds" Wedo model . By 12:30 they had all built and presented a model of their choice including those working with the more complex Mindstorm kits. They were amazed with their success and empowered by what they had achieved.
   

As a learning tool it is quite remarkable how Lego has scaffolded the task of building and programming a model built of Lego bricks that provides students with a learning experience they most likely have never never experienced before. To use a computer to control something attached to it externally by coding is an amazingly empowering activity. The coding process uses images and so is not language dependent (traditional language that is) so it's a great activity of students who are linguistically challenged or who are English Learners. 

The really neat thing about this experience was that three of the graduate students in the class brought their own children to take part in the activities

A real pioneer in the development of the engineering part of the elementary school curriculum is the Boston Museum of Science and Engineering and their Engineering is Elementary program.

K - 8 Science and Engineering

Every so often, as a teacher, you have a class of students that is quite unlike any other.There is something about the individual students, as well as the group as a whole, that makes one want to teach for ever. There's nothing quite like the feeling that you have been a part of creating a learning community where every individual  is genuinely interested in learning; the creation of a learning community that is supportive, challenging of ideas, enthusiastic about exploring new experiences and ideas, diligent yet with a genuine sense of caring for each individual in the class.

The class of fourth grade students I taught in 1975/6 was like this and I still remember almost all 34 of them. So too was the group of graduate students who comprised my teaching K - 8 Science and Engineering course this past two weeks. Meeting for three and a half hours a day, the course was an intense exploration of what it means to teach K - 8 science and engineering in a time of great change as we transition to the Next Generation Science Standards. We explored a variety of hands-on, minds-on science activities  involving pendulums, water drops, oil spills, finger prints and so on into which everyone threw themselves with great enthusiasm. We also explore the K - 8 engineering curriculum by building Lego Wedo and Mindstorm sets and programming them to do all sorts of wonderful actions.

For the theoretical background to the course I used Wynne Harlan's brilliant book, Primary Science; Taking the Plunge. This is such a wonderful book for inspiring students to teach science form a constructivist point of view; the way science and engineering should be taught,

The course concluded with a visit to the ECHO science center where we were introduced to ways in which the facilities at the Center could be integrated into a science unit through a field trip. So into the course were the students that they have agreed to meet at the ECHO center later this  week to complete their exploration of the resources available at the Center.

I feel so grateful to have been a part of this wonderful experience. Thank you to all those studets who took part in the course.