I discovered this great video on education on YouTube while looking for the cartoon that follows. I've seen others by this group RSA. It's a look at education - why, for whom, etc. - and creativity. Are we educating creativity out of our students?

Here's the cartoon I saw on Facebook. I can't figure out what the original is.

We're theoretically supposed to be providing diversified teaching, but it's hard with a classroom filled to the window-sills. But politicians evidently don't want students to be creative.

I once had a student who knew exactly how long 5 cm was. A teacher had had each student find 5 centimeters somewhere on their hands. Connecting up to prior knowledge?
2 cm is a good deal more than half an inch, though, more than 3/4 inch. I think they need more practice working with rulers!
Here's another reason to learn math. American Chopper vs The Metric System:
(another reason to learn the metric system)

When I was a "pupil" in elementary school, we had a subject called "arithmetic." We learned to add, subtract, multiply, do fractions, percentages and convert from inches to rods, and similar activities. Sometime we had word problems. For some reason, this subject interested me. Or maybe it was science that interested me, and science needs math.
In high school we had 2 years of Algebra, Plane, Solid and Analytic Geometry and then Trigonometry, which I looked forward to, because Dad was an engineer and loved to survey things, which involved trig. None of this was called mathematics, as far as I can remember. That was something I would learn in college.
College came, along with math. Suddenly I was expected to understand very abstract thinking, which I had no training for. It took me a week to understand the necessary predecessor of Calculus: Limits, which is hard to comprehend, now that I know what they are. I expect we were given the definition in all its glory,

DEFINITION: The statement has the following precise definition.
Given any real number , there exists another real number so that

Now there are all sorts of ways to ensure that limits and other math concepts make sense, for example this new tool in the NCTM Illuminations collection of lesson plans and activities: Illuminations: Interactive Calculus Tool. Why are teachers still befuddling their students with definitions and procedures to be memorized instead of helping them reason their way to a point where math actually can make sense?
There are far more students taking Algebra and Geometry now than when I went to school. I guess we were somehow motivated to learn it because it was required for college, and those who took it were planning to go to college (about 40% of my suburban high school class. Far fewer from the inner city high school.)
Research has shown that all (i.e. most) students can learn Algebra and Geometry, and many schools are now requiring the 4 years of math in high school that we "college prep" students had back in the late 50's. But I don't think they are motivated in the same way we were.
The National Council of Teachers of Mathematics (NCTM) has been on to this for many years (even before I went to school.) In his closing words at the summer Institute on Reasoning and Sense Making, NCTM 's president Michael Shaughnessy offered several quotes about using reasoning in math instruction, that went back to 1830, which he included in the latest edition of the NCTM newsletter Summing Up:as Reasoning and Sense Making—Expanding Our NCTM Initiative. For example

Continued emphasis must be placed on the development of processes and principles in the solution of concrete problems, rather than on the acquisition of mere facility or skill in manipulation. The excessive emphasis now commonly placed on manipulation is one of the many obstacles to intelligent progress. —MAA, Reorganization of Mathematics in Secondary Education, 1923

and

Students should be encouraged to question, experiment, estimate, explore, and suggest explanations. Problem solving, which is essentially a creative activity, cannot be built exclusively on routines, recipes, and formulas. —An Agenda for Action, NCTM, 1980, p. 4

Why was I not learning "the development of processes and principles" back in the 50's? Why are math teachers still teaching "routines, recipes and formulas"?

The NCTM is trying once again to get teachers to help students learn to reason with math so that it makes sense, with conferences like the one I attended and several series of books to encourage teachers to go beyond their textbooks. That this is important is obvious when you inspect the standard mass-produced textbooks, which thrive on steps, "recipes and formulas," with a picture added every once in a while to try to have it make sense. For example, Glencoe Mathematics, Algebra I (which I just happen to have on hand) introduces Polynomials this way:

Why It's Important
Operations with polynomials...form the foundation for solving equations that involve polynomials[!] In addition, polynomials are used to model many real-word situations. In Lesson 8-6 you will learn how to find the distance that runners on a curved track should be staggered. (This is accompanied by a picture of a track race.)

Fortunately, 45 states and the DC have adopted the Common CoreState Standards. As you can see, most of the Standards for Mathematical Practice in the CCSS explicitly refer to reasoning and sense-making as part of mathematics instruction:

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

We can look forward hopefully to future textbooks that take these to heart, and help teachers facilitate students' reasoning, rather than require that students memorize steps and procedures that won't even help them pass the current state tests! In the meantime, I hope that math teachers use the many resources provided by the NCTM, such as these in the Illuminations site and the Focus in High School Mathematics: Reasoning and Sense Making books.
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I've finally caught my breath after returning from a fantastic 3-day Institute in Orlando about motivating students to learn mathematics through Reasoning and Sense Making (the link goes to a page with handouts from the many presenters.) What a wonderful experience being together with about 700 other math teachers from all over the country (including Puerto Rico and the Virgin Islands - but only one other person from my neck-of-the-woods) who are also concerned about the state of math instruction these days.

Funny thing is, there has been concern about the way mathematics has been taught in this country since way back in 1833, when a guy name Colburn wrote about using the Pelozzi method for teaching arithmetic. He complained that arithmetic was all drill and memorization, not reasoning. Sound familiar? The NCTM president Mike Shaughnessy went through a long list of early quotes, including 1923, 1935 and more recently since the '80s. I hope he'll upload his PowerPoint, because I'd love to have those quotes!

I mostly followed the sessions about Geometry, since I couldn't figure out last winter how to get students interested in doing proofs, which is what I think is the fun part of geometry. It turns out that kids are turned off by having to prove the obvious, when we ask them to prove things like vertical angles as congruent.

Michael Battista, in his presentation, The Role of Proof in Geometry, said that proof in Geometry is a caricature, since we are teaching the form of proof, rather than the content. We start too low to teach the method of proof at a point where it just doesn't make any sense to prove things. Kids experience that as busy work, which just doesn't make sense! We should start where it takes some thinking, reasoning, struggling, to figure out how to get from the given to what is to be proved. When the students have figured it out and can explain it - that is when they will be open to learning how to do formal proofs. The proof is just a final written justification of the work they have already done. No mathematician would start writing the proof before having reasoned his way to a solution. We shouldn't expect our students to do so either. Proof is a personal sense making, he said, where we go from saying what is "true" to "why" it is true. We are explaining our reasoning to others. Students move through 5 levels of geometric understanding, he said (known as the van Hiele levels:)

A visual, holistic examination of the shape

A description of the parts and their relationships

The interrelating properties (like vertical angles and the properties of parallel lines)

Conceptual proofs (explaining verbally)

Formal proof.

We have been trying to get students at level 2 to write formal proofs. They need to work with geometric shapes a while to get to level 4. At that point we can introduce formal proofs.

Battista has written a lot about using the software Geometer's Sketchpad to help students reason about geometry so that it makes sense, and has contributed to several books published by the NCTM. The man behind Sketchpad, Michael Serra, honored us with a wonderful collection of Investigations in Geometry from his textbook Discovering Geometry. We had a nice break in all the talk working in groups to figure out a variety of geometric problems. I worked with Origamics problems, developed by Kazuo Haga. (I just ordered the book. What a fun way to work with geometric reasoning!)

Jeffery Wanko provided a fun session, Developing Proof Readiness with New Logic Puzzles. He uploaded his materials to the Institute website, so you can enjoy them, too: Presentation (PDF)and Handout (PDF).We started with puzzles and their solutions, which we studied to figure out the rules. Then we did a big one together (this was a whole roomful of Sudoku addicts, of course,) and worked individually and in pairs to solve some smaller ones. He provide several pages of puzzles, which gave me something to do besides reading on the long plane trip back home! He recommended the Japanese puzzle magazine, Nikoli.com. Students can become ready for writing formal proofs through talking about puzzles like these with each other, getting to at least levels 3 and 4 listed above.

All that confirmed my previous experience that geometry is fun. I hope I can inspire my students the same way!

I will try to find time to write more about my experiences at the Institute in another blog. Besides swimming every day,of course, the most valuable part of the Institute was the many discussions with teachers from all over the country with many different school experiences.

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.

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.

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.

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.

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.

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.

Concept Invention helps students derive the concept to be learned in the lesson based on their exploration.

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.

Application gives the students an opportunity to use the new concepts and terms in a broader, often more open-ended question.

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.

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.

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?

I am doing a "review of literature" for my very last paper for my MA, which is supposed to be about teaching math to gifted students - or those who have learning difficulties, like Dyscalculia, which I'd never heard about before.
I am getting very tired of review of literature, because almost every promising article or book I look at turns out to have a lot of quotes from other people. So do I have to track down the original, or is it safe to quote the reviewer?

At the same time, I am applying for a job, the reward for all this hard work, and I've already had 3 interviews, which is encouraging. Two of these went well (although I haven't heard back from them yet.)

The third was with the principal of the high school. He asked me how I would teach his 9th and 10th graders Algebra I so they got it (I'm sort of assuming that most have been there at least once before!) so I told him that I've become very interested in Reasoning and Sense-making, which the NCTM is focusing on in many ways, including a summer institute in Orlando I will be attending when this class is done. The principal raised his eye-brows at those words. He seems to believe that kids learn best with the good old-fashioned "drill and kill" that got me dismissed from my student teaching position (when I wouldn't go along with it!) As expected, I was not called back to that school.

One of the articles I've been looking at is How Students Learn: Mathematics in the Classroom from the National Academies Press. I was delighted to read this quote from another source, which corroborates my thinking:

A recent report of the National Research Council, Adding It Up, reviews a broad research base on the teaching and learning of elementary school mathematics. The report argues for an instructional goal of “mathematical proficiency,” a much broader outcome than mastery of procedures. The report argues that five intertwining strands constitute mathematical proficiency:

Conceptual understanding—comprehension of mathematical concepts, operations, and relations

Procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately

Strategic competence—ability to formulate, represent, and solve mathematical problems

Adaptive reasoning—capacity for logical thought, reflection, explanation, and justification

Productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

Note that only one of these mentions "procedures," while the others are about concepts, strategies, adaptive reasoning, and love of math. Not a word about "drill!"

The thing is, a lot of people think that this kind of mathematical thinking is only appropriate for the "gifted" students. The slow ones need drill and kill, evidently, which obviously does kill. These are the students who try and try and try again and don't succeed. Shouldn't we teach them what it's all about, since they don't "get it" through drill alone?

Studies (sorry, I'm not going to look for sources) have proved that students who have been taught to think do better on even multiple choice standardized tests, than students who have memorized all the steps of a procedure. Another quote from the book - observed by John Holt - tells the whole story:

One boy, quite a good student, was working on the problem, “If you have 6 jugs, and you want to put 2/3 of a pint of lemonade into each jug, how much lemonade will you need?” His answer was 18 pints. I said, “How much in each jug?” “Two-thirds of a pint.” I said, “Is that more or less that a pint?” “Less.” I said, “How many jugs are there?” “Six.” I said, “But that [the answer of 18 pints] doesn’t make any sense.” He shrugged his shoulders and said, “Well, that’s the way the system worked out.” Holt argues: “He has long since quit expecting school to make sense. They tell you these facts and rules, and your job is to put them down on paper the way they tell you. Never mind whether they mean anything or not.”

I've been reading that around 50% of gifted students drop out of high school - some figure out other ways to get to college and achieve their potential, others sell hamburgers, or get doped out. We are boring the gifted students with drill and kill, and we aren't helping the weak ones either. Isn't it time for a change?

An article (in Reaching New Horizons: Gifted and Talented Education for Culturally and Linguistically Diverse Students) I am reading for my very last Education class before I get my Preliminary Credential starts with a wonderful quote attributed to the German poet Goethe. I majored in German many years ago, and don't recall it (maybe its being in English, not German, makes it unfamiliar,) but it tells a lot about how I want to teach:

If I accept you as you are, I will make you worse; however, if I treat you as though you are what you are capable of becoming, I help you become that.

Wenn wir, sagtest du, die Menschen nur nehmen, wie sie sind,
so machen wir sie schlechter.
Wenn wir sie behandeln, als wÃ¤ren sie, was sie sein sollten,
so bringen wir sie dahin, wohin sie zu bringen sind.

There's a lot of talk in schools about giving students equal opportunity, which no one really knows what entails.
Does it mean equal teacher time, exactly the same books, problems, lectures, papers to write? Does it mean equal opportunity to succeed (or fail?)
On the other hand, what does Goethe mean by accepting "you as you are?" Can we teachers really know who our students are? Maybe he means "as you appear to me," instead.
My final class is about teaching students who are either gifted or have learning difficulties (which could be the same person.) Yesterday we talked out how students who are bilingual often have been tested to be more creative (and more "gifted?") than their mono-lingual peers. There can be many reasons for this, of course. A creative person may have left his country for another to be able to be creative, for example, so bilingualism is a result of his or her creativity. There have also been brain scans that show that bilinguals use their brain differently than others as well, which is one reason some middle class parents are enrolling their children in bilingual classes with students who are learning English as their second language, which appears to be advantageous for all of them.
An article we read yesterday compared the characteristics of creative people with those of bilinguals, which included:

Risk taking

Willingness to confront antagonism, ability to freely reject external limits and rules, and propensity for self-organization.

Perseverance, total absorbtion, focus, discipline, commitment

Curiosity, inquisitiveness

Openness to new experiences, deep emotions and drowth

High intrinsic motivation

However, often we fail to recognize creativity in language learners, because it "doesn't come through" in their second language, which we are using to communicate with them. We are treating them as they are, in Goethe's sense, instead of as they are capable of becoming. (You might be interested in the blog I wrote for another class on language learners a couple of years ago, Negotiated Identity.)
The same can be said for up to half of the gifted students in our classes (which is evidently statistically set at the 5% highest results on some test or other in a school.) Some of the most gifted live in another world, evidently, which does not include paying attention in class - because most of it they have already figured out with their own personal research and experiments. We don't see them as gifted, but rather, difficult.
On the other hand, there is a group of high achievers, who know well what they want to become, and let us know that, so we treat them as if they were actually gifted.
Personal experience, and a comment by a speaker yesterday, indicate that up to 50% of gifted students may drop out of high school and not achieve the potential they would have had if someone had treated them for what they were "capable of becoming."
In our class we are learning strategies that won't take too much of the stressed teacher's time, but can enable the creative and the gifted students not to have to waste time on what they already know, by "compacting the lessons," while challenge them with projects of their own choosing, so they learn the skills that "high achievers" learn - good study habits, the joys of learning, the satisfaction of working hard to do something.
As a high school student, I got easy A's, even in "honors" classes - we didn't have AP back then, but when I got to college I discovered that I didn't have a clue how to really study, so I saw those A's turn into B's and C's, my confidence turned into feelings of inferiority, I avoided some challenges because I was afraid of those C's, and stopped being a risk-taker, which has taken me years to recover.
I want all of my students to succeed, even the creative and gifted ones!

Our school year ended early, which has given me time for all those things I didn't have time for before: an on-line statistics class, my last class at CGU - and our first trip back to Denmark in 7 years, which had to be squeezed in between 2 CGU Saturday sessions.

Even though I probably could have continued with a part-time position where I was, I decided that the commute was impossible. After all I'm teaching now instead of retiring. I want to enjoy teaching, not wasting all my time sitting in my car!

Because of the last position, I will be able to qualify in Math and Science. In fact I'm really looking for jobs in continuation high schools, or other alternative schools, where there is a better chance of working closely with the students. I have always felt my greatest triumphs as a teacher when a student has regained his/her curiosity about school. Some of those kids are in fact quite gifted, but got left out somewhere, and gave up.

One of my special tutoring students told me he did great in math until 8th grade, when he began running with the wrong crowd. Then he discovered he'd missed out on so much that he couldn't find his way. He was very disappointed that I wouldn't be returning, since he said that I was the only teacher who had figured out how to help him learn.

My science classes were the really exciting part of this past semester, since I had not taken the official science pedagogy courses at CGU - just summer extension courses at UC Riverside. It was fun figuring out how to present the standards material to the students so they enjoyed it and wanted to learn. I had a lot of help from fellow NSTA email list participants, who suggested books, experiments, provided PowerPoints, etc.

Right now I of course don't know what I'll be teaching in the Fall. It's hard to prepare for the unknown. But I continue to read and take courses, above and beyond CGU. I hope it will be a position with both math and science - and students who really need me to guide their learning!

At my school we are experimenting with a "third trimester" after fairly early state testing in the beginning of April. Since many of our students need to catch up on papers and other work, the plan is to use this time for them to finish papers and do other catch up work.
For example, I have 2 seniors who really needed the chemistry class that got converted to "Integrated Science I" about when I started, so I meet with them about 4 hours a week going through the text book and exercises they should be working on independently. And then they join about 10 others who have "Science Enrichment" to do some real chem labs (except that we barely have any equipment. I just bought 10 inexpensive lab goggles to replace the cheap swim goggles they were using.)

But the 10 students felt duped that they had to have more chemistry, since they didn't have much say in the matter. So when they arrived in the first lab class last week they were mad.

Although they did enjoy getting into the disposable lab coats we save from lab to lab, they refused to read the 2 pages of lab prior to doing it, and wouldn't create the data table they needed.

But I tricked them. The lab was on purifying "foul water" (coffee grinds, garlic, veggie oil and salt.) So I took the jar of water, taking the top off so they could smell it, and everyone turned around, read the first lab section, created the table and got to work.

I had them come up table by table to ask for the materials they would need (mostly with apparatus I created myself) and sent them back to read if they didn't ask for the right things.

So they ended up reading, writing data in the table, discussing chemistry, and being amazed when they dropped activated charcoal capsules into their mixture for the last step, and discovering that the room no longer smelled like garlic. Most were very good answering the questions, being very realistic about the lack of proper chemical equipment.

I find it distressing that kids have lost the curiosity to want to learn. Some prefer sitting around doing nothing, or chatting with friends about nothing in particular, or doodling (we've had quite an outbreak of male organs this spring) than using their brains a bit to figure things out.

Students tell me I'm not teaching them anything if I ask them to read, or discuss something in groups. When I try to draw on prior knowledge or extend what they've learned to something they know, they say "but you haven't taught us that!"

They apparently think that "teaching" is presenting a PowerPoint, which they are expected to copy into their notes - and then forget!

I hope the students at our school, most of whom couldn't manage at the regular public high school, are the exception. Otherwise I fear for our future when these kids who have lost their imagination - and their ability to follow directions, or read or write their own thoughts - become the adults who are to lead this country on!

My charter school has decided to do alternative teaching the last 4 weeks of school after the California State testing.
We are doing blocks of 1 1/2 hours, instead of 1 hour, some twice a week, some every day. There is a lot of remedial work for kids who need it, as well as classes to prepare students for what comes ahead.
My biology class is working on group projects to fill out this PREZI:

I took the Reproductive System because I figured their parents wouldn't want them working on that.
I have 2 seniors working to get credit for chemistry with lab, and the rest of the class just 2 hours Wednesdays for labs, where we will be working on writing good lab reports.
And then I have an Algebra I remedial group who will all be retaking it next year. I'm working with using patterns and other representations for functions. They meet every day, so it has to be entertaining.
And a group of 9th graders are learning geometry using patty paper (the paper you put between hamburger patties) which is translucent, so they can see lines drawn on it. We should be able to get through most of the important concepts superficially but hands-on in this time, and end with a little origami, so they will be ready for the "real thing" in the fall.
And this week we're celebrating Earth Day Friday afternoon. I will have 4 groups about 45 minutes each doing alternative energy. I've ordered models of a windmill, solar panels, and a fuel cell, which I hope we'll be able to use then. As well as making pin-wheels out of the comics and ads from today's paper, using pencils as the sticks.
I'm enjoying the planning. The kids were skeptical last week that learning could be fun, but I think they're getting the idea. It's frustrating when they put on their "try me" attitude when I'm trying to do something interesting. In one class (the last period,) I asked each student if they wanted to learn, and placed them up front. The one student who didn't sat in the back, and after a while asked for a piece of patty paper anyway.

Have you heard about the next planned "Survivor" show?

Three businessmen and three businesswomen will be dropped in elementary school classrooms for one school year.

Setting

Each business person will be provided with a copy of his/her school district's curriculum and a class of 20-25 students.

Each class will have a minimum of five learning-disabled children, three with A.D.H.D., one gifted child, and two who speak limited English. Three students will be labeled with severe behavior problems.

Challenges

Each business person must complete lesson plans at least three days in advance, with annotations for curriculum objectives and modify, organize, or create their materials accordingly.

They will be required to teach students, handle misconduct, implement technology, document attendance, write referrals, correct homework, make bulletin boards, compute grades, complete report cards, document benchmarks, communicate with parents, and arrange parent conferences.

They must stand in their doorway between class changes to monitor the hallways.

In addition, each month they will complete fire drills, tornado drills, and [Code Red] drills for shooting attacks.

They must attend workshops, faculty meetings, PTA meetings, and curriculum development meetings.

They must also tutor students who are behind and strive to get their two non-English speaking children proficient enough to take the SOLS tests.

If they are sick or having a bad day, they must not let it show.

Each day they must incorporate reading, writing, math, science, and social studies into the program.

They must maintain discipline and provide an educationally stimulating environment to motivate students at all times.

If all students do not wish to cooperate, work, or learn, the teacher will be held responsible.

Privileges

The business people will only have access to the public golf course on the weekends, but with their new salary, they will not be able to afford it.

There will be no access to vendors who want to take them to lunch, and lunch in the school cafeteria will be limited to thirty minutes, which is not counted as part of their work day.

The business people will be permitted to use a student restroom, as long as another survival candidate can supervise their class.

If the copier is operable, they may make copies of necessary materials before, or after, school. However, they cannot surpass their monthly limit of copies.

The business people must continually advance their education, at their expense, and on their own time.

Reward for the winner

The winner of this Season of Survivor will be allowed to return to his/her job.

(I didn't write this! It's from an email to a teacher list I participate in.)

The past five weeks have been very hard, but I think I have had some small successes, and I can see light at the end of the tunnel!

I have had to figure out what to teach in these last few weeks before the State tests so that the students would do as well as possible under the difficult circumstances.

Evolution was one of the topics I had to cover, so I got a lot of help from a science list-serve I joined and jumped right in. They took tests for the unit on Friday, and I was pleased to see far more passing grades than "incompletes" (D or F) which has not been the case for earlier tests on subjects where I had to assume that they had learned at least something in the 6 months before I came. But now there are only 3 weeks to go, with spring break in between. For Biology we have Ecology, which I would have love to spend lots of time on, and we're going to end up pretty much going through the book. The last topic on the human nervous and endocrine system we may have to leave out entirely, or else give it just 3 days. Sorry, students. Next year will go better!

The students in Integrated Science yesterday were so hyper about it's being Friday that we didn't have time for the lab on the thermodynamics of changing state (ice melting.) I've moved it to tomorrow, when my adviser is coming for the next-to-last time. However they're getting better at converting between Fand C temperatures, and have a vague understanding of Kelvin, so there has been some progress. If only we had more time! I don't think we'll be able to get to the endo- and exothermic reactions I had planned, because we have so much to review in the next 3 weeks.

The other challenge has been getting students back to wanting to learn science after so many months of inadequate teaching. The grade-book shows A+ after A+ for all students, as they got grades for completing simple tasks rather than for learning. It has been a shock for them that (some of) their grades are so bad. So far only one student has asked what she can do to get grades up. Certainly not with extra credit. I told her to restudy everything, and then she'd be allowed to retake the tests.

When I started at the school I was surprise about the "redirects" and "detentions" given out. We can send students to the "annex" when they disturb the class too much. There they are kept busy by an excellently supportive aide. Some students just can't sit still or keep their mouths closed while I'm talking. Not that they want to be disruptive (for most, anyway) but I can't teach and the others can't learn, so I learning to take more advantage of the aide's help. I was used to having to solve all classroom management problems in my own classroom before. But then the students at this school, for a large part, are those who could not thrive in regular public school, so the conditions are different. I am really pleased about how supportive the staff is for the students with many problems. There are many options to help them succeed.

My colleagues are very understanding of the situation I have been placed in, and even given me a slightly lighter load, since I don't have any electives until after the State tests. They tell me again and again that they aren't expecting fantastic scores from my students because of the previous teaching.

I feel very comfortable about my new job. My colleagues are very supportive, and happy to have a teacher who can teach biology, chemistry and math. (The French didn't really materialize, thank goodness!)

I love having very small classes so I can work with each student individually when they need it. The 2 remedial math classes have about 6 students each, which is what the students need to be succesful. I am letting 3 students work ahead on their own in Algebra I, so they may be able to catch up with the rest of the class. Others are just filling in the holes in their math knowledge from too many years thinking they couldn't do math. I love the challenge of helping them understand what math is all about. We've been working on the substitution method for solving 2 equations. Today the light went on for one of the students and his face just shone! It has been a very difficult concept for them!

I'm constantly amazed at how much I know about the science subjects. I've not only studied for tests, but lived a whole long life being interested in science and soaking up so much about it that I can use to entice and motivate the students. But they are still new subjects for me, so I have to study the topics thoroughly to present them well. I finally got the electronic gradebook up-to-date with both attendance and quizzes. There's so much to do in the beginning! And I know the names of more than half my students (since there aren't that many) but that is a bit problem for me. Some of the students need so much help and attention, others act bored. Others escape from a difficult home-life. And still others just couldn't make it in big high school classrooms.

All that takes time, of course, on top of nearly 2 hours daily travel time partly through the lovely Cajon Pass. (The time and direction I drive is with very acceptable traffic. I had a couple of foggy days in December, and gusty winds that blew over some tall, lightly loaded trucks. But the wind doesn't bother my little Insight and I keep as far from the trucks as possible.)

This shows the southern end of the Cajon Pass.
and no, I did not take the picture! I'm down on the ground!

This cartoon by Ed Wiley really struck a note with me.
I will be starting my new teaching job tomorrow, and I will post this on the wall to remind my students that they (not just I) have work to do so they are prepared to make their "Real Life Choices."

I will be teaching 2 small sections of Biology, 1 of Integrated Science, with about 4 students working independently in Chemistry, 1 with about 10 students who are falling behind in Algebra I, a math remediation class for seniors who haven't passed the math of the California HS Exit Exam ... and working with a new student who was completing French II in her old school (since I used to teach German, and used to know French!)

I expect my days will be varied and interesting, and hope I can motivate the students to make the right choices!

I seem to have a new title now. I am no longer "just" a math teacher. On Monday I will be teaching Biology, Integrated Math, with some few students trying to do Chemistry, Algebra I and CAHSEE prep for students who haven't passed the state graduation requirement in math.

My new school is a tiny charter school, so my classes have fewer than 20 kids per class, and some closer to 10. It is also in an unusual setting, the former kitchen of a defunct Italian restaurant up in the high desert in Hesperia (which people from Los Angeles got by on their way to Las Vegas.) The school has been around for more than 10 years, although the high school is relatively new.

That means that the room isn't really set up well for fancy chemical experiments, so we will be using things like lemon juice, vinegar and baking soda. I think most of the books are gifts from other schools who have gone on to a new textbook. I will have to pick and choose between lessons and materials.

We are also in a rush, because unfortunate circumstances mean that the time up to now has not been used as efficiently as I would have hoped. I will try to introduce the students to as much of the curriculum as possible, but I would rather go into depth than "cover" everything superficially. I hope they will learn those things well.

Many of our students have learning disabilities and have not done well in the large impersonal classes of public school. I know that many of them are actually quite smart, and maybe have been lazy because they have been bored. I just finished reading a book called "Teaching Gifted Kids in the Regular Classroom," which has inspired me with some great strategies. I will be trying several, and report back here how they go.

As if learning all this math wasn't enough, I've applied for a job where I would be teaching chemistry part-time, which seems like an ideal way to start out teaching! Since I am very interested in sustainability, and most everything "green" and I remembered reading about "green chemistry" when I was studying for the qualifying exam, I checked out my links again.

The EPA has a whole section on Green Chemistry, from which their are links to the American Chemical Society's website section of Green Chemistry, with the slogan "Chemistry for Life." There are lot lot of resources on Green Chemistry for various age groups, including high school. In fact they have been publishing Chemistry textbooks called Chemistry and the Community for high school and Chemistry in Context for college (which I had bought earlier, so I'm reading it now along with the math.) There is also an inexpensive magazine for high school students called ChemMatters, with extensive teacher's guides.

Learn something new every day. That's a great motto!

The title was attributed to Aristotle in today's Daily Ray of Hope from the Sierra Club, which included the photo shown here.I'm not quite sure what the duck is learning, but it's nice to have an illustration.

It's strange that so many math teachers think "doing" means doing drills, rather than doing something to make the math they are learning make sense, as in "doing math."

Reading these has led me on to other discoveries of my own, since they often use math that I haven't used very often, like polar coordinates, matrices or graph theory.

I'm enjoying my little break here learning about learning. But I hope I soon have students with whom I can practice what I've learned (learn teaching by teaching!)

Several well-meaning friends have asked me why I don't just give up. Why don't I find a job tutoring and stick with that? Or volunteer, or do something completely different?

First of all, I started all this because I wanted a meaningful way to be active, and I felt that I could help fill up a tiny gap in the need for math and science teachers. I love math, and thought that I could extend my love to inspire students to enjoy it as well.

Then there is the resources aspect to not giving up. I've invested a lot of money, time, effort, interest and even passion - in my graduate school education, as well as numerous other courses, seminars and conventions. I've bought - and read - almost every book the National Council of Teachers of Mathematics offers on Reasoning and Sense-making and other topics I deemed useful for the subjects I've been teaching.

I read great blogs about teaching, not least Coach G's Teaching Tips on the Education Week Teacher website. There I just found another blog posting that inspired me: How Teachers Can Build Emotional Resilience by Elena Aguilar. She lists a number of ways that teachers become emotionally resilient:

Have personal values that guide their decision-making. They often feel they were "called" to this profession and a commitment to social justice keeps them in the classroom.

Place a high value on professional development and actively seek it out.

Mentor others.

Take charge and solve problems.

Stay focused on children and their learning.

Do whatever it takes to help children be successful.

Have friends and colleagues who support their work emotionally and intellectually.

Are not wedded to one best way of teaching and are interested in exploring new ideas.

Know when to get involved and when to let go.

I think I do all of these things (except maybe realizing when to let go!) I am particularly flexible about #8, ready and willing to try many different methods (except "drill and kill," which one adviser insisted was the only way to get kids to learn.) Furthermore, Ms. Aguilar says, principals can help their teachers become emotionally resilient.

Trust has been called "the connective tissue that holds improving schools together." Organizational consultant Margaret Wheatley has written beautifully on the impact that having meaningful conversations and listening to each other can have in changing environments. Principals can ensure that these conversations happen. We can’t support each other intellectually (or create Professional Learning Communities) if we don’t trust each other.

At my previous position, we math teachers had no preparation period, and no common time where we could get together to help each other (different lunch breaks.) And the principal was quick to fire rather than support teachers. (The teacher before me managed to find another job and quit before the principal dismissed her - he had already announced her position as open. He also let most of last year's math teachers go since school scores on the state math tests were ridiculously low - more likely because the school expected most learning to happen through projects, where math was ancillary to other projects, than because of the teachers' competence.)

My Christmas present from that school was an At Will Employmentdismissal. "You don't fit in here," they said.
I think what really happened was that the son of a benefactor was one of the students who did poorly on the tests I gave in the 3 weeks I had before semester grades went in.
My faculty adviser (the principal) only came in to observe one day - the day he had filled my classroom with an absent teacher's students, where the combination of 2 classes was like adding lemon juice to baking soda.
My grad school adviser thought things were going as well as could be expected under the very difficult circumstances, and that I fit in well at the school.
My colleagues were amazed, and the department head wrote me a recommendation.

So, what did I learn?

Be very careful about working in charter schools.

Insist on getting the book immediately, as well as information from the previous teacher about where they've gotten to, and what her plans were (I left that information for the next teacher at this school.)

Since I evidently teach differently than many other teachers - I believe that students have to create their own learning (sense-making,) rather than my presenting them with steps to solve a particular problem - I have to prepare the students for working together to figure things out, and not expect me to give them the answer immediately.

I'll have to work out some initial lesson plans that teach collaborative learning

Talk with colleagues about methods, ideas, resources (I discovered the last week that there were carts with computers. Unfortunately, we did not have a staff room, my lunch was different from the other math teachers, and we math teachers had no prep period.)

As a new teacher, don't take the job if there is no preparation time, mentoring, etc. You're only setting yourself up for failure.

And what am I doing now - besides looking for another job?

I am reading lots of books about how to teach geometry. I discovered that the students were very reluctant to work with proofs, and I didn't know well enough how to engage them in that. I've found fantastic online resources and books, particularly through the National Council of Teachers of Mathematics. I hope I get to teach geometry now! All new teachers discover that just because they can solve problems, do proofs, pass the qualifying exam, doesn't mean that the students will be as engaged in the subject as much as they are.

Inspired by Nelson Mandela's claim that the impossible is just waiting to be done, this blog chronicles my own journey to do the impossible. I am embarking on another new career as a high school math and science teacher . . . and I don't really think it's impossible - just really hard these days to land a job. I am finally a credentialed "single-subject" teacher of math, science, physics, chemistry and biology -- looking for the job to use my skills to help motivate students to enjoying my favorite subjects!