Mental Math, Traditional Math, and Best Methods

James Tanton is one of the most insightful teachers of teachers of math I’ve come across in a long time.

In this video and this essay, he explains how some parents feel mystified by some of the newer style of math problems that children are bringing to their parents for help. Clearly, some of the problems (like the 32-12 one which fills up an entire page in a child’s workbook) are being done in a tortured, time-wasting method. However, if you take a more difficult problem, such as 103 – 87, you can do this completely in your head by adding small increments (MENTALLY) to the 87 until you get to 103.

This is a reasonable thing to do, much like people count out (or used to count out) change into a customer’s hand.

In this case, from 87 to 90 (which is a much ‘nicer’ number than 87) we need to go up by 3.

Then from 90 to 100 (which is getting closer to our goal), we go up by 10. So we’ve gone up by 13 all together.

Then from 100 to 103 is three more, so we’ve gone up by 16, which means that 103 – 87 is 16.

I would be crazy to write all those steps out! – which is unfortunately what the poor child was asked to do.

But doing it quickly in your head makes a lot of sense.

As Tanton says, let’s get rid of laborious, tortured, time-wasting algorithms and examples, but let’s keep the thinking and understanding.

Click on the picture for a larger view; it’s a slightly-modified still from his video.

Published in: on October 25, 2015 at 11:31 am  Comments (1)
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Bob Shepherd on what teaching is really like

An excellent description of how insanely hard teachers have to work, and why I am so glad I was able to retire before having a nervous breakdown or dying from stress and overwork. For many, many workers, including teachers, the idea of a ‘mere’ 40-hour work week is a joke. There is no possible way to get all the required tasks done even with a 100-hour work week, which ought to be illegal.

The only remedy is much, much smaller class sizes – like what they have at the very best private schools.

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For many years, I held various jobs as a publishing executive (in later years at very high levels). I thought that I worked very, very hard.

Then I returned to teaching.

Everything I did before was a vacation by comparison.

Teaching is relentless in its demands on one’s time and energy. I came to school this year and found that I had 190 students, 3 minutes between classes, no prep period on half my days, car line duty in the morning, 20 minutes for lunch, two extracurricular activities to coach (including plays to produce), administrative meetings one day a week after school, 20 detailed lesson plans to prepare each week (specifying the class, period, standards covered, lesson objectives, assessments used, bellwork, vocabulary covered, and ESOL strategies and 504 and IEP accommodations employed), a requirement that I post 16 grades per quarter per student (for 190 students for 4 quarters, that’s 12,160 grades in the school year, or 67.56 grades per day), enormous amounts of paperwork (filing, photocopying, keeping a parent/teacher log, filling out reports of many kinds, preparing class handouts and tests, keeping attendance logs, posting grades), many, many special meetings (parent-teacher conferences being among the most frequent), and classes and tests to take to maintain my certification.

If I assigned a five-paragraph theme to each of my students, I would have 950 paragraphs to read–roughly the equivalent of a short novel.

Basically, there isn’t enough time for ANYONE–even the greatest of teachers–to do the job at all adequately. This is the great unspoken truth about teaching. This is the real elephant in the room. If you want to improve teaching and learning, you have to give teachers more time–MUCH, MUCH MORE TIME.

And somehow, with all those demands, you are supposed to give each student the individual attention that he or she deserves. Anything short of one-on-one tutorial is a compromise, of course. And that’s that the job boils down to. A great compromise.

And the attitude of administrators is typically, “Well, what’s the matter with you? Why don’t you just do x? Why didn’t you just do y? Any good teacher would be doing z every day.” As though teachers were people of leisure with all the time in the world. I have noticed that administrators label practically every email that they send out IMPORTANT and use exclamation marks ALL THE TIME: “Due today! Must be completed by Thursday! Mandatory attendance!” I have sometimes wondered whether they shouldn’t be issued, at the beginning of the year, a maximum number of quotation marks that they can use. Of course, they are just responding to the similar insane demands that are placed upon them by the central office and my regulatory requirements.

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Spot-on article and comments in Daily Kos on teacher burnout

Excellent article on why many teachers are retiring early or just quitting.

I recommend the comments as well. (I am so glad I was able to retire in 2009!)

A quote or two:

Last fall, Kris Nielsen, who had moved to North Carolina specifically for a teaching job after years teaching in New Mexico and Oregon, wrote, “I am quitting without remorse and without second thoughts” because:

I refuse to be led by a top-down hierarchy that is completely detached from the classrooms for which it is supposed to be responsible.

I will not spend another day under the expectations that I prepare every student for the increasing numbers of meaningless tests.

I refuse to be an unpaid administrator of field tests that take advantage of children for the sake of profit. […]

I’m tired of watching my students produce amazing things, which show their true understanding of 21st century skills, only to see their looks of disappointment when they don’t meet the arbitrary expectations of low-level state and district tests that do not assess their skills.

In spring 2012, the “worst eighth-grade math teacher in New York City” decided to leave teaching. Not much of a loss if she was the worst, right? Yeah, well, Carolyn Abbott was teaching at a gifted-and-talented school, where:

The material covered on the state eighth-grade math exam is taught in the fifth or sixth grade at Anderson. “I don’t teach the curriculum they’re being tested on,” Abbott explained. “It feels like I’m being graded on somebody else’s work.”

The math that she teaches is more advanced, culminating in high-school level algebra and a different and more challenging test, New York State’s Regents exam in Integrated Algebra. To receive a high school diploma in the state of New York, students must demonstrate mastery of the New York State learning standards in mathematics by receiving a score of 65 or higher on the Regents exam. In 2010-11, nearly 300,000 students across the state of New York took the Integrated Algebra Regents exam; most of the 73 percent who passed the exam with a score of 65 or higher were tenth-graders. […]

How do her students perform on the content that she actually does teach? This year, the 64 eighth-graders at Anderson she teaches are divided into two groups, an honors section and a regular section. All but one of the students in the honors section took the Regents Integrated Algebra exam in January; the other student and most of the regular-section students will take the exam in June. All of the January test-takers passed with flying colors, and more than one-third achieved a perfect score of 100 on the exam.

Published in: on February 24, 2013 at 8:11 pm  Comments (1)
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An Article By A NYC Charter School Teacher for “PolicyMic”

I thought this was worth reprinting:

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Hi all,

I submitted this article about my experiences re: standardized testing and test-based evaluations in NYC schools to PolicyMic this afternoon.  I hope that it resonates with many of you!  Please feel free to read, comment, and forward as you wish.

And, in honor of Mr. Wellstone (July 21, 1944 – October 25, 2002), who reminded us that laborers and teachers are one in the same, “Stand up. Keep fighting.”

Thanks!
Allison LaFave

http://www.policymic.com/articles/17490/romney-loves-teachers-what-teacher-evaluations-and-tests-mean-for-american-teachers

Romney Loves Teachers: What Teacher Evaluations and Tests Really Mean for American Teachers

During Monday’s final presidential debate, Bob Schieffer spurred a collective American chuckle when he cut off Romney’s long-winded brown-nosing with the knee-slapper, “I think we all love teachers…”

I’d love to believe Mr. Schieffer, but as someone who hails from a family of public school teachers and spent last year teaching third grade in a New York City charter school, I have to say, “Bob. You’re adorable. But America’s teachers haven’t felt loved in quite some time.”

Last spring, my principal corralled our school’s third grade teaching team around a kidney-bean shaped table and apologetically explained that we needed to sign forms acknowledging the weight of our students’ test scores on our end-of-year evaluations. Ultimately, our students’ math and ELA scores would comprise as much as 40% of our annual rating.

Now, I don’t know a single educator who outright opposes the idea of fair evaluations and/or some level of teacher accountability. But as I sat quietly in that little red plastic chair, a voice in me cried:

“You want to evaluate me? Great. No problem.

“But let’s also evaluate the misaligned (or nonexistent) curriculum I was given to plan for my classes.”

“Let’s evaluate the number of chairs huddled around single desks, because there are more students in the room than there were last year, and the copy machine, the one that never works.

“Let’s evaluate the number of students with IEPs that aren’t being adequately serviced, and the number of English Language Learner students sitting voiceless in the back of the room, because they have yet to be admitted into nonexistent ELL classes.

“Let’s evaluate the employers who are smugly underpaying/underemploying my students’ parents or guardians, forcing them to work multiple jobs, likely without ever securing benefits for themselves or for their families. Or the number of students who have lost parents or loved ones due to gang violence, substance abuse, or the labyrinth that is our failing criminal justice system. Or the number of my students who didn’t eat dinner last night.

“Let’s evaluate how many hours of sleep I got last night, because I was not afforded adequate prep time during my 10 or 11 hour day in the building, or how many times I’ve skipped out on doctor’s appointments and family events to be here for my students.

“And, finally, let’s evaluate my motivations for being here — because it sure as hell isn’t for the money.”

Last week, Deborah Kenny wrote an op-ed piece decrying the heavy influence of test scores on teacher evaluations. Kenny rightfully claimed that the practice “undermines principals and is demeaning to teachers” and leaves little room for innovative teaching and learning. She went on to say that test-based evaluations inhibit the “culture of trust” between principals and teachers and “discourage the smartest, most talented people from entering the profession.”

While I agree that test-based evaluations are inherently flawed (when was the last time our politicians, Democrats or Republicans, truly analyzed aPearson test?), I am baffled by Kenny’s ultimate argument. It seems that Kenny bashes test-based evaluations because … wait for it … they make it harder for her to fire teachers she doesn’t like – specifically a teacher whose students performed “exceptionally well” on the state exam.

Teachers aren’t statistics, but they also aren’t part of some school-wide homecoming court. Administrators shouldn’t cast votes for the teachers they like or dislike. They should work to support all teachers who act in the best interest of students.

Ms. Kenny also takes a not-so-subtle jab at teachers’ unions, attacking evil tenured teachers in America, who are clearly exploiting their glamorous roles as K-12 educators. However, unions don’t grant tenure; PRINCIPALS grant tenure. And, moreover, Ms. Kenny, like nearly all charter school administrators in America, likely prohibits her teachers from joining their local union.

As someone who has worked in a non-union school, I can tell Ms. Kenny what violates trust between teachers and administrators. Knowing that you can be fired for your personality.  Knowing that there is a fresh crop of well-intentioned, starry-eyed Teach for America kids who can take your place in the time it takes to make a phone call. Knowing that you will be scorned for using your allotted sick days and guilted into working through lunch, during prep time, and hours after the final school bell rings.

I encourage our presidential candidates (and all Americans) to listen to the voices of practicing teachers, who are so often talked about and around during national education debates.

Says Kelly G., a third grade teacher in Brooklyn:

“These teacher evaluations are complex. I honestly used to think that a teacher could indeed be evaluated and held accountable using test scores. And then I started teaching at school that didn’t allow me to do the kind of teaching I thought needed to be done in order to develop intelligent children. There’s nothing quite like having your teaching micromanaged and then being told it was your fault the kids didn’t achieve exemplary scores on the state exam.

“My kids are capable of so much already. Come in and look at their writing. Listen to their discussions. Watch them solve math problems. Their tests scores will not reflect their growth from the school year. A one shot assessment does not give a good picture of student achievement. Have you read those exams? Have you been in the room during testing? Test anxiety vomiting is a real thing in the third grade. Too bad they don’t evaluate me on sick child comforting and vomit clean up. I’m sure my scores on those evaluations would be proficient.”

In popular media, teachers are cast as heroes or villains. They are either lazy, money-grubbing, ne’er-do-wells or Jaime Escalante, the “teacher savior” of the acclaimed film Stand and Deliver.

The truth is, as in most professions, the majority of teachers lie somewhere in the middle of this spectrum. Such romanticized notions of teaching make great stories, but that’s just it; they are stories that too often exaggerate and obscure the truth. Jaime Escalante spent years preparing his students for the AP Calculus exam, not a few inspired semesters. Does that mean that he was an inadequate teacher during the years he spent honing his craft and teaching foundational math concepts to his students? How would Escalante have been rated under the New York City evaluation system?

In his research paper entitled “Effects of Inequality and Poverty vs. Teachers and Schooling on America’s Youth,” David C. Berliner (Regents’ Professor Emeritus in The Mary Lou Fulton Teachers College of Arizona State University) finds that “Outside-of-school factors are three times more powerful in affecting student achievement than are the inside-the-school factors.”

Consequently, he concludes, “The best way to improve America’s schools is through jobs that provide families living wages. Other programs…offer some help for students from poor families. But in the end, it is inequality in income and the poverty that accompanies such inequality that matters most for education.”

America’s education system is in crisis; of this, we can be sure. But let’s stop blaming the dentists for their patients’ cavities.