A geometry lesson inspired by a silvering company – and a rant about computerized learning programs

Here is some information that teachers at quite a few different levels could use* for a really interesting geometry lesson involving reflections involving two or more mirrors, placed at various angles!

Certain specific angles have very special effects, including 90, 72, 60, 45 degrees … But WHY?

This could be done with actual mirrors and a protractor, or with geometry software like Geometer’s Sketchpad or Desmos. Students could also end up making their own kaleidoscopes – either with little bits of colored plastic at the end or else with some sort of a wide-angle lens. (You can find many easy directions online for doing just that; some kits are a lot more optically perfect than others, but I don’t think I’ve even seen a kaleidoscope that had its mirrors set at any angle other than 60 degrees!)

I am reproducing a couple of the images and text that Angel Gilding provides on their website (which they set up to sell silvering kits (about which I’ve posted before, and which I am going to attempt using pretty soon, on a large astronomical mirror I’ve been polishing for quite some time)).

At 72º you see 4 complete reflections.

When two mirrors are parallel to each other, the number of reflections is infinite. Placing one mirror at a slight angle causes the reflections to curve.

https://angelgilding.com/multiple-reflections/

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Rant, in the form of a long footnote:

* assuming that the teacher are still allowed to initiate and carry out interesting projects for their students to use, and aren’t forced to follow a scripted curriculum. It would be a lot better use of computers than forcing kids to painfully walk through (and cheat, and goof off a lot) when an entire class is forced to use one of those very expensive but basically worthless highly-centralized, district-purchased computer-managed-instruction apps. God, what a waste of time – from personal experience attempting to be a volunteer community math tutor at such a school, and also from my experience as a paid or volunteer tutor in helping many many students who have had to use such programs as homework. Also when I was required to use them in my own classes, over a decade ago, I and most of my colleagues found them a waste of time. (Not all – I got officially reprimanded for telling my department chair that ‘Renaissance Math’ was either a ‘pile of crap’ or a ‘pile of shit’ to my then-department head, in the hearing of one of the APs, on a teacher-only day.

Keep in mind: I’m no Luddite! I realized early on that in math, science, and art, computers would be very, very useful. I learned how to write programs in BASIC on one of the very first time-share networks, 45 years ago. For the first ten years that my school system there was almost no decent useful software for math teachers to use with their classes unless you had AppleII computers. We had Commodore-64’s which were totally incompatible and there were very few companies (Sunburst was one) putting out any decent software for the latter. So when I saw some great ideas that would be ideal for kids to use on computers to make thinking about numbers, graphs, and equations actually fun and mentally engaging, often I would have to write them my self during whatever free time I could catch, at nights and weekends. Of course, doing this while being a daddy to 2 kids, and still trying to teach JHS math to a full load of students (100 to 150 different kids a day at Francis Junior High School) and running a school math club and later coaching soccer. (I won’t say I was a perfect person or a perfect teacher. I believe I learned to give better math explanations than most, didn’t believe that you either have a ‘m,ath gene’ or you don’t, at times had some interesting projects, and at times was very patient and clear, but had a terrible temper and often not good at defusing things. Ask my kids or my former students!) Later on, I collaborated with some French math teachers and a computer programmer to try to make an app/program called Geometrix for American geometry classes that was supposed to help kids figure out how to make all sorts of geometric constructions and then develop a proof of some property of that situation. It was a failure. I was the one writing the American version, including constructions and tasks from the text I was currently using. There was no way I could anticipate what sorts of obstacles students would find when using this program, until I had actual guinea pig students to use them with. Turns out the final crunch of writing however many hundreds of exercises took place over the summer, and no students to try them on. Figuring out hints and clues would require watching a whole bunch of kids and seeing what they were getting right or wrong. In other words, a lot of people’s full time job for a long time, maybe paying the kids as well to try it out so as to get good feedback, and so on. Maybe it could work, but it would require a lot more investment of resources that the tiny French and American companies involved could afford. We would have really needed a team of people, not just me and a single checker.

I find that none of these computer-dominated online learning programs (much less the one I worked on) can take the place of a good teacher. Being in class, listening to and communicating logically or emotionally with a number of other students and a knowledgeable adult or two, is in itself an extremely important skill  to learn. It’s also the best way to absorb new material in a way that will make sense and be added to one’s store of knowledge. That sort of group interaction is simply IMPOSSIBLE in a class where everybody is completely atomized and is on their own electronic device, engaged or not.

Without a human being trying to make sense out of the material, what I found quite consistently, in all the computerized settings, that most students absorbed nothing at all or else the wrong lessons altogether (such as, ‘if you randomly try all the multiple choice answers, you’ll eventually pick the right one and you can move on to some other stupid screen’; it doesn’t matter that all your prior choices were wrong; sometimes you get lucky and pick the right one first or second! Whee! It’s like a slot machine at a casino!).

By contrast, I found that with programs/apps/languages like Logo, Darts, Green Globs, or Geometer’s Sketchpad, with teacher guidance, students actually got engaged in the process, had fun, and learned something.

I find the canned computer “explanations” are almost always ignored by the students, and are sometimes flat-out wrong. Other times, although they may be mathematically correct, they assume either way too much or way too little, or else are just plain confusing. I have yet to detect much of any learning going on because of those programs.

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Why A New Generation of Teachers is Angry at Self-Styled Education ‘Reformers’

This is an excellent essay at Medium that I learned about from Peter Greene of Curmudgucation. I copy and paste it in its entirety in case you don’t like signing into Medium.

Why New Educators Resent “Reformers”

Let’s consider why so many young educators today are in open rebellion.

How did we lose patience with politicians and policymakers who dominated nearly every education reform debate for more than a generation?

Recall first that both political parties called us “a nation at risk,” fretted endlessly that we “leave no child behind,” and required us to compete in their “race to the top.”

They told us our problems could be solved if we “teach for America,” introduce “disruptive technology,” and ditch the textbook to become “real world,” 21st century, “college and career ready.”

They condemned community public schools for not letting parents “choose,” but promptly mandated a top-down “common core” curriculum. They flooded us with standardized tests guaranteeing “accountability.” They fetishized choice, chopped up high schools, and re-stigmatized racial integration.

They blamed students who lacked “grit,” teachers who sought tenure, and parents who knew too much. They declared school funding isn’t the problem, an elected school board is an obstacle, and philanthropists know best.

They told us the same public schools that once inspired great poetry, art, and music, put us on the moon, and initiated several civil rights movements needed to be split, gutted, or shuttered.

They invented new school names like “Green Renaissance College-Prep Academy for Character, the Arts, and Scientific Careers” and “Hope-Horizon Enterprise Charter Preparatory School for New STEM Futures.” They replaced the district superintendent with the “Chief Educational Officer.”

They published self-fulfilling prophecies connecting zip-coded school ratings, teacher performance scores, and real estate values. They viewed Brown v. Board as skin-deep and sentimental, instead of an essential mandate for democracy.

They implied “critical thinking” was possible without the Humanities, that STEM alone makes us vocationally relevant, and that “coding” should replace recess time. They cut teacher pay, lowered employment qualifications, and peddled the myth anyone can teach.

They celebrated school recycling programs that left consumption unquestioned, gave lip-service to “student-centered civic engagement” while stifling protest, and talked up “multiple intelligences” while defunding the arts.

They instructed critics to look past poverty, inequality, residential segregation, mass incarceration, homelessness, and college debt to focus on a few heartwarming (and yes, legitimate) stories of student resilience and pluck.

They expected us to believe that a lazy public-school teacher whose students fail to make “adequate yearly progress” was endemic but that an administrator bilking an online academy or for-profit charter school was “one bad apple.”

They designed education conferences on “data-driven instruction,” “rigorous assessment,” and “differentiated learning” but showed little patience for studies that correlate student performance with poverty, trauma, a school-to-prison pipeline, and the decimation of community schools.

They promised new classroom technology to bridge the “digital divide” between rich, poor, urban, and rural, while consolidating corporate headquarters in a few elite cities. They advertised now-debunked “value-added” standardized testing for stockholder gain as teacher salaries stagnated.

They preached “cooperative learning” while sending their own kids to private schools. They saw alma mater endowments balloon while donating little to the places most Americans earn degrees. They published op-eds to end affirmative action but still checked the legacy box on college applications.

They were legitimately surprised when thousands of teachers in the reddest, least unionized states walked out of class last year.

Meanwhile……

The No Child Left Behind generation continues to bear the fullest weight of this malpractice, paying a steep price for today’s parallel rise in ignorance and intolerance.

We are the children of the education reformer’s empty promises. We watched the few decide for the many how schools should operate. We saw celebrated new technologies outpace civic capacity and moral imagination. We have reason to doubt.

We are are the inheritors of “alternative facts” and “fake news.” We have watched democratic institutions crumble, conspiracies normalized, and authoritarianism mainstreamed. We have seen climate change denied at the highest levels of government.

We still see too many of our black brothers and sisters targeted by law enforcement. We watched as our neighbor’s promised DACA protections were rescinded and saw the deporters break down their doors. We see basic human rights for our LGBTQ peers refused in the name of “science.”

We have seen the “Southern strategy” deprive rural red state voters of educational opportunity before dividing, exploiting, and dog whistling. We hear climate science mocked and watch women’s freedom erode. We hear mental health discussed only after school shootings.

We’ve seen two endless wars and watched deployed family members and friends miss out on college. Even the battles we don’t see remind us that that bombs inevitably fall on schools. And we know war imposes a deadly opportunity tax on the youngest of civilians and female teachers.

Against this backdrop we recall how reformers caricatured our teachers as overpaid, summer-loving, and entitled. We resent how our hard-working mentors were demoralized and forced into resignation or early retirement.

Our collective experience is precisely why we aren’t ideologues. We know the issues are complex. And unlike the reformers, we don’t claim to have the answers. We simply believe that education can and must be more humane than this. We plan to make it so.

We learned most from the warrior educators who saw through the reform facade. Our heroes breathed life into institutions, energized our classrooms, reminded us what we are worth, and pointed us in new directions. We plan to become these educators too.

Hechinger Report on Finland’s Schools

Here are some of the recommendations made after a visit to Finland to visit their schools:

8) Shorten the school day. Deliver lessons through more efficient teaching and scheduling, as Finland does. Simplify curriculum standards to a framework that can fit into a single book, and leave detailed implementation to local districts.

9) Institute universal after-school programs. Include play clubs, homework help, decompression and relaxation time, as well as academic and non-academic enrichment activities. Make them free or low-cost. This will significantly boost parent and family well-being by allowing parents to harmonize their schedules with their children’s.

10) Improve, expand and destigmatize vocational and technical education.   Encourage more students to attend schools in which they can acquire valuable career/trade skills.

11) Launch preventive special-education interventions early and aggressively. Destigmatize and integrate special-education students as much as possible, as is done in Finnish schools.

12) Revamp teacher training toward a medical and military model. Shift to treating the teaching profession as a critical national security function requiring government-funded, graduate-level training in research and collaborative clinical practice, as Finland does.

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John Merrow’s Takedown of the Gates-Jobs Takedown of America’s Public Schools

I don’t know if you watched it (I didn’t), but apparently there was a major TV extravaganza last night about how America’s high schools are obsolete and need to be re-invented. John Merrow did watch it, and was rather disgusted. Here is a bit of his commentary:

Last night’s program was high energy and cute without being daring.  For example, it had a clever ‘red carpet’ segment but with teachers as the stars.  Lots of cheering, but that was it.  That’s sadly timid.  Imagine if Melissa Rivers, the host on the red carpet, had asked teachers the question she always asks the Hollywood stars: “You look marvelous. What are you wearing tonight?’

And picture a male teacher responding:  “These old things?  I bought these khakis 12 or 13 years ago. I was going to buy a new pair for tonight, but I just spent \$380 on basic supplies for my classroom.  Oh, and would it be rude of me to ask how much your outfit cost?”

Imagine a female teacher responding, “What am I wearing?  Actually, I’d rather talk about tomorrow’s field trip….I’m taking my kids to the Getty Museum, where they will….. see provocative art and meet contemporary artists.  And the next day my students will be on Skype, talking with students in a high school in Paris about climate change. We’ve been measuring the air quality here and sharing the data with them for purposes of comparison and analysis.  But I have to charge the kids for the bus to the Museum and I had to ask some wealthy parents to pay for the scientific equipment because the school district has been cutting our instructional budget.”

And another teacher could have said, “To be honest, I’m happy for this attention, but I can’t help but thinking about the fact that you make 17 or 18 times more money per year than I do.”

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A Cartoon Strip I Like – TeachingTed.Com

I just found out about this cartoonist from Diane Ravitch. He’s a good artist and has something to say about education and the world that teachers inhabit. You might like his work, too. Here are a couple of his strips:

Why ‘School Choice’ is actually a Bad Choice

Read Steven Singer on this, inlight of what we already know out Betsy DeVill Devos.

An Immodest Proposal

If you look at the lingo used to justify all the horrendous crap being imposed by “Ed reform”, you’ll see that it’s all couched in lefty-liberal civil rights language. But its results are anything but. Very strange.

Q: Can you cite some examples?

GFB: Yes.:

“Everyone has a right to learn. But in our country today, the education you receive depends on where you live, what your parents earn, and the color of your skin.

“That’s a serious injustice. And in the national movement to right  our contribution is the leadership of remarkable people.

“Our people—diverse and passionate—start in low-income classrooms, where the stakes are highest. We help them become teachers who can dramatically expand students’ opportunities. But our teachers don’t just teach their students, they learn from them.

“They gain a better understanding of the problems and the opportunities in our education system and use those lessons to define their path forward. Many stay in the classroom. Others leave. Both paths matter because to set things right, we need leaders in all areas of education and social justice united in a vision that one day, all kids will have access to an excellent education.”

GFB: However, the way TFA works in practice is that the kids who need the most experienced, skillful teachers, instead get total newbies straight out of college with no teaching experience, no mentoring, and courses on how to teach whatever subject they are they are assigned to. Their five weeks of summer training are mostly rah-rah cheerleading and browbeating. Their only classroom experiences during that summer are a dozen or so hours teaching a handful of kids, **in a subject or grade level totally different from whatever they will be randomly assigned to**.

What underprivileged students do NOT need is an untrained newbie who won’t stick with them. If anything, this policy INCREASES the ‘achievement gap’.

Q: I’m sorry Guy, but none of this poses a solution. Paying the teachers more is not the answer. I know this because I would quit my engineering job in a heartbeat to teach. I honestly would. And I would do it for 1/4 the pay. But not under these  conditions. Not with “father education” telling me how to use fancy calculators to educate kids. Not when you take what I love about math and turn it into garbage. The paradigm sucks, independent of the lousy pay.

GFB: That’s yet another reason to oppose Michelle Rhee. She and her allies have figured out how to micromanage teaching down to the minute and to the very sentences teachers are required to read — from a script. Yes, she and Jason Kamras and Raj Chetty and the other billionaires friends have made it that teachers have no say whatsoever on content or methodology.

If they are not on the same page exactly, down to the minute, they can get marked down, harassed, suspended and fired.

Want to teach under those conditions for twice the pay? Me neither.

It’s not “Teach Like A Champion” as Doug Lemov puts it: it’s teach like a robot.

Q: Plus, their answer to teaching is to integrate technology. They think that if they use technology, everybody will be prepared for the “real world”. Unfortunately, the technology they use isn’t utilized in the real world. So…useless. Somebody needs to tell them this!

GFB:  That’s often true. However I think the teacher should be the one to judge how much technology to use and when. Occasionally we should show them really OLD technology like carving quill pens from turkey feathers, or making their own batteries from copper pennies and galvanized iron…

But you can’t do that with Value Added Measurements and rubrics testing whether you are on the Commin Core Crapiculum to the minute.

I wasn’t really giving THE or even A solution. I was objecting to the solution we are having imposed on us right now. If you want proposed solutions, here goes:

1. Get people who don’t have actual, extensive teaching or research experience out of the command and control centers of education except as advisors.so, no Michelle Rhee, Andre Agassi, Arne Duncan, Billionaire Broad at the helm.
2. For our poorer kids, make sure they have free, high quality wraparound services of every kind from the moment their mother notices she’s pregnant.
3. So for example good well-qualified dentists, ophthalmologists, psychologists, general practitioners, and other doctors should come to each school and check eyes ears nose throat etc and give immunizations to every kid, no more than a single hour of class needs to be missed. If they get hurt on the playground or suddenly vomit in class, it’s really taken care of, right away.
4. There should be all sorts of remedial help available for kids AS SOON AS help appears to be needed: eyesight, hearing, balance, coordination, mental math, memory improvement, spelling, reading, writing, walking, emotional difficulties, etc. (Right now, the provisions of ADA and IDEA are not funded, so school districts have an incentive to NOT diagnose those with deficiences or learning disabilities, because then they would have to take care of them. Charter schools for the most part just pretend that there are no IEPs.)
5. Every kid gets a lot of ‘gross motor’ outdoor activities – not just team sports but also things like wilderness hikes, camping, horse care and riding, farming, boating. And music and drama and arts of all sorts – not just for the talented few, but everybody. Lots of after-school activities of these sorts.
6. Teachers (and parents) should select their principals from among the ranks of the teachers. The principal should also teach, part-time.
7. Teachers should have at least two years of education theory (and human psychology) and a full year and a half of student teaching, and at least a college major in their area, under experienced mentors. Teachers should be given help o0n how to defuse tense situations and child psychology, and should be chosen from the ranks of those showing
2. the ability to empathize and
3. the ability to explain patiently and clearly.
8. Classes should be much, much smaller. If 12:1 is good enough at Phillips Exeter Academy with their Harkness Tables, why not at Malcolm X ES in far Southeast Washington DC? And if it’s a hands on activity like a chemistry lab or using compasses & straightedges or making birdhouses, get an assistant or two so that it’s more like 3:1.
9. Let the teachers wrangle over curriculum. State level is fine. County level is fine. School level is fine. To hell with these state-wide standardized tests and curricula, be they bubble type or click and drag.
10. Actual hands-on vocational training that leads to actual jobs should be available to all who want it, and corporations must engage to hire those grads at decent rates of pay and with promises of additional training.
11. State-college or  state-university higher education needs to be much, much cheaper. Student debt, like all other debt, should be dischargeable upon bankruptcy, and should be payoff able by many kinds of national service. (Exact provisions TBD, but teaching should definitely be one of those forms of national service. Payments and interest in limbo for the first X years, paid off at Y percent per year, fully paid off after Z years. Exact values of X, Y, Z are TBD.)
12. Teachers should be paid well enough that they don’t need to get second jobs. Pay in DCPS is not the problem. Working conditions are the problem.
13. I think that 3-4 hours of personal contact time with kids per day is enough. Planning for each class and heading papers can easily take 2x the amount of class time. So each paper turned in by a student should be returned the next day, marked intelligently.
14. Since the bosses have their own organizations (NAM, Chamber of Commerce, ALEC, the Koch Brothers network, Council on Foreign Relations, the Cosmos Club, etc) so should the employees. Teachers’ unions should continue to exist but should be more democratic.
15. Students should, in fact, be held responsible for their success or failure. It’s not all on the teacher, as it is now. Social promotion for a number of years is OK, many countries do it without bad effects, but there should be some sort of a test, I think, of all sorts: practical (eg drawing something, playing a musical piece, climbing a wall, drilling a hole, writing an essay, doing a proof, viewing something under the microscope, etc) as well as a pencil-and-paper or mouse-and-screen test of some sort. Not just arcane reading and math.
16.  Those who don’t meet the mark should obviously be advised as to what their options are, and those options should be available and well-funded, whatever they might be.
17. We should strike a balance between having kids go to their walk-to neighborhood schools and having truly integrated schools where each school has a mix of kids of all ethnic groups and incomes. How to do that, exactly , under our current mega-segregated urban patterns, is beyond me. The superhighways and redlinings of the last 80 years are not going to be overcome overnight, but having kids ride for hours to charter schools where there is no neighborhood connection – that’s not the answer.
18. Anything I left out?
Published in: on November 21, 2016 at 2:19 pm  Comments (3)
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Super Scenario for Tonight’s Debate

Wonderful screenplay for an alternate-reality presidential debate, from Aaron Wiseman, who’s been a friend of my own kids for decades – they’be been to each others’ weddings, etc. I had no idea he could write like this. It’s fantastic, don’t you agree?

“Best case scenario for tonight’s debates?

10-minutes in, we’re seeing the same bullshit.

Suddenly, all the house lights go down. The arena is awash in total darkness. Panic begins to set in when the lights flicker and momentarily reveal a cloaked figure in the rafters.

The lights flash again and the figure is gone. Suddenly, a crushing guitar riff fills the entire venue. A spotlight shines down on the arena floor. The figure from the rafters has magically moved with supernatural speed.

As the music builds, the cloak falls to the floor. IT’S JOE BIDEN! He’s wearing a crisp blue two button suit complete with arm tassels and full Warrior face paint.

As the music hits full crescendo, Joe takes off towards the stage at a full sprint! In one graceful move he slides onto the stage and hits Trump with a forearm to the dome.

The Great Pumpkin, takes the blow like it’s nothing. That doesn’t slow ole Joe and he hits the Cheeto Demon with a super kick to the face. B-Side Beelzebub just smiles.

Is he even human? How can he take so much punishment? Joe looks to the audience pleadingly.

As if to say, “I hit him with my best shot. How?” But then the carroty façade begins to falter and Trump’s knees buckle. His eyes roll into the back of his head and he begins to stagger around the stage.

Joe goes in for the finisher and hoists Trump into the air by his belt. As Trump begins to flail, Joe sends the would-be-dictator-tot crashing to the floor. A perfectly executed Gorilla Press.

Hillary walks up to Joe, her arms open in gratitude. But instead of matching her embracing, Joe grabs the mic from the former Secretary of State.
This wasn’t for you. Hill. A. Ry. Clin. Ton” Joe growls, “It was for America!”
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Or,

One of the many reasons I rejoice every day that I was able to retire!

Read what classroom observations have devolved to:

http://nyceducator.com/2016/10/you-will-differentiate-instruction-same.html

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What A Joke DC Education Chancellor Kaya Henderson Was – City Paper

Very detailed article in the Washington City Paper showing how our recently-resigned Chancellor, Kaya Henderson, failed to do much of anything to narrow DC’s extremely-high gap between high-achieving and low-achieving students, even though she had oodles of money, complete control over resources, and the ability to fire teachers and administrators almost at will.

As I have shown repeatedly (see , and here for starters. Or else here) DC has the widest gap of the entire USA between the scores of poor kids vs the non-poor, between white kids and black or hispanic kids, and between those in Special Ed and those who are not. This article shows how the Henderson and Rhee administrations failed to do pretty much anything to improve conditions at schools where there were large concentrations of ‘at risk’ kids, other than saying that by some miracle, they would improve scores by 40 percentage points at all of the schools where 40% of the kids were ‘at risk’.

(A quote from the article: ‘ “No school in the history of time has achieved such goals,” counters a D.C. Council staffer familiar with DCPS school reform. “On its face, the concept of this as a reachable goal was ridiculous.” ‘)

And of course, it never happened. No extra resources, and no miraculous gains.

But according to the article, Kaya has an excuse – just the sort of thing that she and Michelle Rhee used to berate actual, um, educators for saying:

‘ when Payne persisted with a question about Henderson’s “personal goal of closing achievement gaps,” the chancellor explained: “I am not exactly convinced that schools alone can close the achievement gap. I think about the fact that in Washington, D.C., we have the greatest income inequality in the country. That gap is only growing, and the fact that our achievement gap is growing in a similar way shouldn’t be baffling. But I think what we’ve learned is that equity is really more appropriate, giving different people different kinds of support…And for different groups and different kids that means different things.”

My friends and colleagues Elizabeth Davis and Mary Levy are quoted. It’s a long article, but well worth reading.