Memory and Sense Making

On Wednesday I am off to Orlando to participate in the National Council of Teachers of Mathematics Summer Institute for High School Teachers on Reasoning and Sense Making. I am looking forward to being with a group of teachers who really want their students to understand mathematics. Too often during teacher training I ran across teachers who were more of the "drill and kill" school.

With my experience with myself, my own children (now successful adults,) and the children and young people I have taught, kids don't learn because you force them to memorize something or give them drills to do whatever time and again until it sinks in. Kids learn because they are curious about something and want to find out about it. If they have a reason to learn something that means something to them (and I doubt "to get into college" or "because it's in the standards" are reason enough for most students,) they will want to learn it, and will dig into a topic until it is theirs. They might even ask someone for the answer - or help to find the answer.

I read a short article yesterday about some research that implies that people don't remember as well as they used to because now they can just Google stuff to get answers they don't have to remember. Evidently some people were tested on how well they remembered things (probably a list of unrelated facts) and some were given the opportunity to enter them on a computer. That last group, of course, forgot them immediately. But that doesn't prove the thesis that we remember differently now. The author of the article pointed out that Socrates was just as worried that the new-fangled techniques of writing would ruin people's ability to memorize things - which is probably true, of course. I write things down so that I can go on to investigate other things. In a sense, the written word is an extension of our long-term memory.

During my teacher ed classes I came upon several references comparing the brain to a computer. You know, data comes into short-term memory, but it has to be connected to other information to be transferred to long-term memory. If we just give students facts, or formulas, or steps to solve problems, they may remember them long enough for the unit test, but if they don't have a way to connect those data with something else - something that makes sense to them, and they want to know about - that data we tried to stuff into their heads probably won't be around for the final, or state exams - or life.

I remember a newspaper opinion piece written by a teacher years ago in Denmark, who claimed that a teacher's job is not to fill in the holes in students' brains, but to create the holes in the brains, so that students would go around looking for what they could put into them. Learning, he said, is making holes, not filling them in. Those holes are what students create while they are making sense of their world. And the holes will never get filled. They will be dug deeper, with lots of side channels that connect up with other holes.

This was illustrated beautifully in a very moving film we saw on Saturday, Buck, which is about a guy who spends 9 months out of the year telling people how to train their horses (not break them) at clinics all around the country. Buck likes to say he's not helping people with horse-trouble, he's helping horses with people-trouble.

I kept thinking that he was talking about classroom "management," where teachers are figuring out how to train their students and need help with "student-trouble" while in reality, it's the students (who have to be there, just like the horses had no choice in the matter) who have "teacher-trouble." The movie was about the best movie on education I have seen. I kept wishing I had a notebook, so I could write down all his words of wisdom. So I bought the book that became the movie The Faraway Horses, in hopes that some of those bits of wisdom are stored there.

One of the most telling episodes in the movie was a woman who told about how Buck had changed the way she trained her horse for dressage. Evidently in the bad old days, horses were trained to get into various unnatural positions by harnessing them with torture instruments (there were examples shown in the film.) Finally the horse gave in and did as required to avoid the pain and humiliation of the harness. But the woman had participated in a sheep-herding clinic with Buck, and discovered that all those unusual positions came naturally to a horse when he was using them to herd sheep. The horse found a connection where he needed to be in that position. And then during dressage, he easily moved in the position (probably fondly remembering the weekend herding sheep.)

Are our students being difficult because they don't want to be harnessed to a school desk when it doesn't make sense to them to be there? Are we trying to break them rather than helping them make sense of what we think they should know?

At the NCTM institute, we have each selected a different area to concentrate in, which for me will be Geometry, which I think was my favorite math subject in high school. I taught some Geometry this past year, taking over from another teacher. It was very difficult teaching students to do the proofs of geometry, which is what I liked best, and which is what geometry is all about. I hope that the Institute will help me see how to present geometry so it makes sense to them. Of course it's easy enough to make sense when you're talking about things that can be represented physically, like area and volume, circles and cylinders. But the abstract high-order thinking of proofs seems to have been distracted by low-level memorization of theorems.

I expect to be a better teacher after the Institute - but it is only one of many ways I am trying to make sense of my job as a teacher.

Addendum

While reading this afternoon I happened upon a note that is so pertinent to this, that I am quoting it here:

When reviewing radioactivity for this book, I was reminded that too often in science resources, authors explain what happens without really explaining why it happens. If you can only describe occurrences,then you really don't understand what's going on, and you end up only memorizing what happens. If you can figure out a mechanism for the occurrences, though, then you can build a lasting understanding of what's going on. Even though scientists often can only describe what happens when they first encounter a phenomenon, the ultimate goal is a mechanism for the phenomenon and the resultant understanding. You can compare this to mathematics, in which there are rules to follow. Only when you understand the reasoning behind the rules do you understand math.

William C. Robertson, in More Chemistry Basics, p 109 (my italics)

The wisdom of experience

I've been having a few talks with friends about the difficulties of getting a job now that I have my credential. Although I have had a few interviews, someone else (younger) seems to get the job each time. I have been charitable and figured that the younger person is probably more qualified than I am. Perhaps she majored in a subject that I have "only" learned through enormous amounts of reading, discussion, email exchanges and a few courses. Perhaps she has more science teaching experience. Perhaps she has actual science laboratory work experience. I can't beat that.

But recently one of my young fellow students got a job for which I felt I was the more qualified. I was teaching the subjects this last spring to students very much like the ones at this particular school, and had selected the same chemistry book that is being used there. I read incessantly about science pedagogy and love going to professional development courses.

As I was teaching this spring, I tentatively introduced the "when I was your age, we didn't have calculators/ computers/ know about DNA..." comment to see how the kids reacted. It turns out they loved it. They also loved that I could be teaching and suddenly come up with some example from my past that just fit the topic perfectly. I have close to 50 years of life experience more than my young fellow students that has not been spent knitting (at least not most of the time.) I taught, I started an environmentally based business, using a lot of chemistry, was a technical writer, learning how to explain things clearly. In fact, most of my career has been about motivating people (to learn German grammar, to treat our world respectfully and sustainably, to use some piece of software efficiently...) Some of my other older new-teacher friends have been engineers, lawyers, economists, business owners - all with fantastic stories to tell.

In the really old days, the elder members of a tribe were called upon as teachers of the young, because people recognized their wisdom. Elderly people in some cultures were revered greatly for their wisdom. In others they were considered doddering fools - maybe because they couldn't hear well, or see well, so they couldn't hear the question properly, or negotiate their surroundings agilely - or maybe they were senile (although I doubt they got old enough for Alzheimer's back then, although they might have gotten mercury or lead or antimony poisoning.)

People my age are often of good health and mind, and they aren't going to take time off to have babies or have to pick up a sick child from school. They may have older parents who need some help, or a spouse who needs surgery. But my spouse cooks all the meals when I'm working!

I've been told about a principal who said that he didn't think an "old fogeys" (like me) would hang around very long - like more than 5 years. Statistics show that young people, unfortunately don't either. I figure I'll teach until I don't like it any more, or until my health deteriorates. Who knows how long that will be. (I sure don't like the idea of sitting around knitting and reading books the rest of my life!) Another told a colleague that she was not going to hire any more baby-boomers (for some unknown reason.)

Of course there are a lot of teachers even younger than I am who no longer enjoy teaching and do not renew their skills and content knowledge. Some of them aren't very far out of college, in fact.

I was enticed to teach by an organization called EnCorps Teachers, who are recruiting experienced people to teach science, math and engineering. I have spent 2 1/2 years studying and practicing to become a good teacher, and run up a bill of close to $60,000 at a private school of education. I'm not quitting any time soon! And neither are my other older fellow students. We have a lot to share and we enjoy kids. We want to give a little back.

Summer Reading

I've had lots of time to read this summer (also to knit and to swim.) I thought someone might be interested in the great books I've found.I am a member of a number of email lists which have asked about summer reading ideas, and I jumped at the chance when I read about books that seemed useful.

For new teachers (like me!)

One of the best books I found about classroom management is K. Cushman's Fires in the Bathroom, which is advice by high school students for new well-meaning teachers, who don't always get it right.
 Learning Outside The Lines: Two Ivy League Students with Learning Disabilities and ADHD Give You the Tools for Academic Success and Educational Revolution is a completely different book - written by 2 students with ADHD who finally figured out how to get their life together to graduate from college. It is a real eye-opener for teachers.
Along the same line is one of the books that is waiting for me: Fair Isn't Always Equal, which I am looking forward to reading.
I was taking a class this summer about teaching  students who are gifted and/or have a learning disability. One of the books I read for my paper was When Gifted Kids Don't Have All the Answers: How to Meet Their Social and Emotional Needs. It helped explain a lot about the problems low achieving but smart kids are having in school.
Since I just got myself a Kindle, I decided to read a couple of books on it. The Accidental Teacher by Eric Mandel tells his story of trying to teach English with no credential and little support. Teaching Outside the Box: How to Grab Your Students By Their Brains by LouAnne Johnson.
Unfortunately most of these books are by English teachers, which is often a different kind of teaching. (I guess English teachers like to write more than math teachers!) So I am very happy to have found Coach G's Teaching Tips, since he is a math teacher.

More books!

I've also been reading about chemistry, biology, physics and math, so I guess there will be at least one more summer reading blog coming up.

Credentialed Teacher!

Hurrah! I received this email today:

Congratulations, the Commission on Teacher Credentialing issued you the following document on 7/20/2011

Preliminary Single Subject Teaching Credential ...
Issuance Date: 07/18/2011 Expiration Date: 08/01/2016
Authorized Subjects:
Mathematics (Examination), Science: Biological Sciences (Examination), Science: Chemistry (Examination), Science: Physics (Examination)

This has taken me since December 2008, when I took the first test, and has been a struggle to get the required field work, since there were so few open jobs. All of this has been documented here in my blog.

But I still am looking for the job where I will be facilitating students' learning and understanding. Same job market.

Process Oriented Guided Inquiry Learning (POGIL)

I spent a fascinating 3 days this week on the University of Redlands campus this week learning about Process Oriented Guided Inquiry Learning (POGIL), a relatively new way to teach science (and other subjects) where students in 3-4 person cooperative learning groups figure out the concepts they are to learn using directed work sheets, rather than a teacher-based PowerPoint lecture. Those who have used the system report dramatic improvements in student learning, and particular, in student retention.

The system was initially used in chemistry classes at Franklin and Marshall College in Lancaster, PA, where several of the boys from my high school graduating class in York, PA, got their training as engineers. Because of the great results, the idea spread to many other colleges and universities, where it has been used successfully in a variety of college courses. The original copied "activities" have now been published as work books, that the college students buy. High school teachers soon discovered the method and started using the college materials in AP classes. This started the High School POGIL Initiative (HSYPI) . You can find sample lessons in both biology and chemistry through that link. Very inexpensive workbooks for these subjects will be available in January (unfortunately.)

A POGIL lesson is carried out in 3-4 student groups, where each student has a role: Manager, PR (the only group member who may ask the teacher questions,) Recorder, Quality Control (consensus builder,) and possibly Process Analyst (who looks at the group's dynamics.) These groups are often kept together for a longer period of time, as they learn to work together.

A POGIL lesson is based on the Learning Cycle: Exploration, Concept Invention/Term Introduction, and Application, which all refer to a model, which can be a diagram, a demonstration or even a video.

1. Exploration involves very direct questions to the model, to make sure the students understand the details of the model. These might include questions as basic, "What does the dotted line represent," but go on to more detailed understanding of the model.
2. Concept Invention helps students derive the concept to be learned in the lesson based on their exploration.
3. Term Introduction gives students a name for the concept. Up to this point, they are exploring and thinking about connections. They may already have invented a term for the concept, but this step introduces the term in a new question.
4. Application gives the students an opportunity to use the new concepts and terms in a broader, often more open-ended question.
5. The Learning Cycle may start again in the same activity with a new Model, Exploration, Concept Invention and Application. 

The students learning is guided by a worksheet with the model and questions that start as Direct in the Exploration phase, then Convergent (using the material gleaned from the direct questions to the model - which have a correct answer) in both the Concept Invention and Application phases, and then the open-ended Divergent questions for more advanced applications. Divergent questions go further, and do not have a correct answer (although there may be incorrect answers!)

As you can see, this is a sort of guided discovery learning. There are also labs created according to this system. In particular, POGIL labs are used for exploration and content invention. They come before any lecture on a topic, rather than afterwards.

You can find a few worksheets on the website. Unfortunately the many activities that have been developed in Bio and Chem for high school will not be available until January. At least the workbooks then will be very affordable. (The current college workbooks cost about $35.)

A lot of teachers are creating lessons for their own use, and sharing them on the site, and elsewhere. The main way to create your own lessons is to turn the book lesson around. Start with the examples as models. Then turn the introductory material into concept invention and term introduction questions. But easiest for a beginner of course is to find existing materials. I googled POGIL and found several sites where teachers have made their lesson activities available.

As soon as I find out what I will be teaching (which depends, of course, on which school hires me to teach which subject that I soon have a credential for: Math, Bio, Chem or Physics) I will be working on finding or creating appropriate POGIL lessons. From what I can see, the students are active all the time, so there is little time for them to cause classroom management issues. Even the smart kids will be working well in their groups (for which there are always a few extension questions.)

In a couple weeks I'll be off to Orlando to learn more about Reasoning and Sense-making in math, which is a less structured concept with the same aim - to facilitate the students' owning their learning, so they have little need to memorize factoids that don't necessarily make sense.

Discovery Learning

Comics were great on science education today.
Even the New York Times was in on it with a A solution for saving the space program

Doonsbury on teaching biology in Texas

Doonesbury was great today.

Summer Vacation?

There are those who envy teachers their long summer "vacation." I am using mine to

• Apply for jobs
• Finish the last course for my credential, including a research paper
• Attend two different summer institutes, one on teaching science and one on teaching math
• Read many books and journals to provide more background for teaching science and math, particularly historical information and pedagogical strategies
• Read a couple of novels
• Swim
• Share the cooking with my husband, who did ALL the cooking last spring!

On my NSTA chemistry list, there has been a discussion about how to tackle those envious acquaintances. One person (K Gorski) wrote this:

Before you can address the "summers off" thing, people have to understand the commitment during the school year. When I served as one of the '07-'08 Albert Einstein Distinguished Educator Fellows in DC, we were asked by our supervisors (program directors and managers of many of the federal agencies) to give a presentation that was a "shop floor perspective." Some of my colleagues came up with an analogy that was brilliant - we had virtually every individual with their jaws dropped, and saying omg I never thought about it like that.... we have continued to use it, with the appropriate tweak for the audience - and it seems to be successful.

We told them:

• Imagine that it is Monday, and you have 6 meetings, back to back. You are organizing and leading each meeting and must prepare the visuals and handouts. Assume you'll have about 30 people in each one.
• If they say you teach multiple sections of the same class; note that it's really a different meeting because they have a slightly different focus and you need to prepare for that focus.
• On Tuesday, it's the same thing: 6 different meetings, back to back and you are in charge. Same for Wednesday, Thursday, Friday.
• At each meeting, the participants will turn in their proposals/plans/what have you that you must read, review, and comment on before the next day.
• During your lunch hour (and if you are lucky enough to have a "free" period), you use that time to answer voice mail,email, and other office memos that have come in.
• Note that you are expected to keep up with current research in your field (so you can prepare for those meetings).
• And that you are on several other committees for which you must attend meetings.

We asked them if they could do all this in a 9-5 workday, and not take work home with them, or work on the weekend.  I think we added something about differentiation and special needs. It was very powerful.

As you can see, we did not even broach much of the detail - and it still left our audience amazed at what we do. We never got antagonistic, we never whined or complained, we just said - here's the data in your terms.

There's a great video "What Teachers Make" which should be taken out and shown at least once a year - for yourself if no one else. 

The Future of Public Education?

Cartoon by Steve Breen, San Diego Union Tribune, 7-3-11, seen in today's Daily Bulletin.

What worries me most about teaching is trying to have contact with all 40 students squeezed into a single classroom. There is no room for a computer area, no room for a group to go off by themselves. No way to have the whole class standing at the whiteboard doing problems.

And how do I know when a student is having a really bad day if he's sitting with his head down, or being particularly disruptive? I want all of my students to have the opportunity to learn, and there will be 200 different versions of high school students in my classes.

I am very willing to differentiate my teaching, but how do you know who needs what when you have 200 students?