Saturday, November 8, 2014

Voting and the ID Requirement

All citizens have the right to vote.  You do not need an ID to be a citizen.
You need a license to drive because driving is not a right, not essential to being a citizen, and the citizenry have said that safety requires a license to drive ... but it doesn't have to be a photo ID. If I don't drive, then why would I pay for a license?
  • Does my choice to not drive mean that I am not a citizen and cannot vote?
You need an ID to purchase alcohol because the law said so, but you do not have to have an ID to drink it (you only have to be of legal age) and again, you do not have to be a drinker to be a citizen. If I am in my 50s, why should I need an ID to purchase? If I don't drink, why do I need an ID?
  • Does my choice to not drink mean that I cannot vote?
You do not need an ID to serve on a jury. If that were true, anyone could get out of jury duty by taking the bus and showing up without it. Why is jury duty a prerequisite for voting, anyway?
  •  If I never get called for jury duty or never get empaneled because I don't fit the lawyer's criteria, do I lose the right to vote?

If I am old and no longer need an ID, why should I be required to purchase one just because you have this fantasy that I am someone who might commit voter fraud? If I have no other reason to have an ID other than voting, then we are talking about a poll tax.
  • Is getting old a reason to lose the right to vote?
If I am too poor to own a car, or have a disease or a disability that prevents me from driving, why should I buy a driver's license?
  • Is being blind or poor a reason to lose the right to vote?
If I get married and change my name, or simply decide that my real father isn't part of my life and my adopted parents' name is the one I will use, do I need to schedule things far enough in advance so that legal paperwork can be filed and processed to change my name, social security and IRS information, which then can be taken to the appropriate DMV for a new license, which then can be taken to the appropriate town clerk to change my name on the rolls? Because if I don't and the new name doesn't exactly match the old one, I can't vote.
  • Is a legal name change a reason to lose the right to vote?
And think about the mechanics of voter fraud ... I show up to vote and give my name, and get checked off the list. I vote and then come back in a attempt to vote again under another name - how is that supposed to work out? Do I just pick one at random? Someone who I know is dead but somehow that information isn't known? This scenario makes it a very difficult crime to get away with and easy to get a significant fine.

If I show up and my name is already checked off, then I have to prove who I am and vote provisionally ... if there was voter fraud happening, this would be prevalent. It isn't.

Real voter fraud is more than 1 extra vote.
  • It's denying the vote to huge lists of people based on criteria that have nothing to do with a citizen's right to vote.
  • It's denying the vote for lack of ID which many people have no use for.
  • It's denying the vote to citizens in certain categories that you wish to disenfranchise.
  • It's denying the vote to classes of people who would vote for your opponent.

Why should I have to prove my identity, anyway? Are you saying that I am not a citizen if I do not have an ID?

What you should be demanding is that no one votes twice, like the "dip the finger in ink" trick. What you are actually demanding is that a large number of people not be allowed to vote at all.

That is wrong.

Testing Paradigm Needs to Change

Testing in the United States is a sick, diseased system. It is a malignant tumor that must be excised if we are to ever use testing results to improve students, teachers, schools,

Testing in the USA is NOT intended to help teachers or their students. It is only done to give a number that can be used or not, at the whim of the reader. Since most testing is for evaluative purposes, testing provides numbers to punish people with.

As a teacher, I get absolutely no useful information from standardized testing.


None.

On our "Local Common Assessment", I get to know a RIT range and a corresponding percentile, and breakdowns in "Algebraic Thinking, Real&Complex Number Systems, Geometry, Statistics and Probability."

Then, consider that we have our kids taking a test and one of the categories is Real & Complex Number systems - Really? These are 9th graders in algebra 1 ... is the score range of 233-245 based on their less-than-complete knowledge of real numbers combined with no questions on complex numbers or is that 75%-ile based on questions that they would have no reasonable knowledge of?

Okay ... I'm ready to adjust my teaching for Algebra 1 ... What changes should I make?

I see none of the questions, none of the individual responses. I have no idea what kinds of things the test-makers considered to be "Algebraic Thinking" nor do I have any sense of what my students might have replied or understood or didn't, except for the kids who told me they just clicked at random just to be finished more quickly.

Okay ... I'm ready to adjust my teaching for Algebra 1 ... What changes are appropriate? Does the kid who scored "LO" really not understand or is she just lazy?


Yeah, that's the breakdown measurement: LO, AV, HI. Useful? No.

And this is a Pre-Algebra class with some 9th and some 10th graders. I would hardly expect them to get anything other than LO. If they could, they wouldn't be in the class.

Okay ... I'm ready to adjust my teaching ... What changes to my pre-algebra curriculum are appropriate here?

But at least I got those few bits of data within a week, because it was a local assessment.

When it comes to SBAC and PARCC, the problems seem to be the same as for NECAP, and before that, the NSRE.  Too few questions, coupled with long wait times for the scores (test in October, scores in April) and very dodgy scoring of the results for the constructed response questions ...

and we're still not allowed to see the questions, see the scoring, see the individual results ... 
And there was no way you could trust those scores because of the manipulation of the raw score conversion tables for "continuity reasons."

Can't have a big improvement year to year because reasons. The first year of every test has to have similar results as the final year of the test we threw away, so yr1 NSRE was first 58% passing, but was re-scored so we only had 30% passing.

If we're getting rid of a test because it isn't working appropriately, why do we insist that the new test's scores match up with the old test's scores?

And about those scores ... I have never understood how the entire public school populations of five New England states can show results in the way they did:

Highly Proficient: 3%
Proficient: 30%
Below Proficient: 40%
No Evidence of Proficiency: 27%

Really? 33% "passed" a test and you're looking at the teachers, not the test? Of all the kids in all the classrooms with all of the teachers (in VT, NH, ME, RI, and somewhere else that's escaping me right now), how is it possible that only 33% of the students passed a test?


At least the SAT is open ... maybe we should use it instead of paying Pearson far more for less information.

If you can so blithely manipulate scores so as to get a result that your statisticians declare appropriate, maybe the problem isn't in your teachers or your students ... your system needs to change.

If you can so blithely assume that the teachers are the only ones who are responsible for scores but shouldn't be allowed to see any of the test papers or any of the questions ... your system needs to change.

If you can so blithely assume that the students are always "participating fully" and that the results on this worthless and pointless (to them) test, then your system definitely needs to change.

Tuesday, October 28, 2014

This is a test. This is only a test.

In teachers' professional development seminars and in-service meetings, We no longer use the word "test" very much, nor "quiz". It's always an "assessment". I suppose that the words "test" and "quiz" have become loaded with too much negative meaning, implying a bar that must be overcome to avoid "failure".

"Assessment" has no sense of "pass" or "fail" but merely a placement along a scale. It's funny because the kids live in a much more black and white world; they hate "assessment," perhaps because it's a complex word while "test" and "quiz" are short and pithy and to the point but also perhaps because it's non-judgemental to the point of insanity. They want to know, "Did I make it or not?"

Testing shouldn't always be one-shot ... and you're either a winner or a loser. There has to be growth opportunity, too.

When you learn to play soccer, you compete against your teammates to get better, failing over and over before you can ever learn and master the sport. Why should math be any different?

You failed this quiz? Take it again. You can't do this homework? Let's discuss again how to do it. Now take the quiz again. I'm not throwing you off the team because you can't beat the starter.

Parent Threatens Disruption over Islam

So this guy threatens to disrupt classes if World History continues to contain mention of Islam.
Wood told Superintendent Morris that the school is violating his daughter’s “constitutional rights” and threatened to “bring down a shit-storm on them like they’ve never seen.”
Oh, brother. "Lighten up, Francis."

It's World History ... and WH has always taught the religions of the regions, from the Egyptian and Isis and the symbolism of the Ankh through the Greek and Roman religions (and mythology is actually an English course), Hinduism and Confucianism of the Far East, and of course, talks about Islam in the context of the development of Northern Africa and the Middle East, along with Judaism and Christianity.
After the meeting, Wood told reporters that his daughter, a junior at La Plata High, should not be forced to study a faith that she “does not believe in.”
Then take her out of school. Otherwise, World History teaches about History of the World and religion is part of that. But this statement from the teacher cracked me up:
“This is a world history class,” [O’Malley-Simpson] explained. “We are not teaching religion. Part of those world history studies involves the economics of a region and part of that is the religion which relates to the economy of that part of the world. In the Middle East, Islam is the only religion and it contributes greatly to the economics of the region.” (emphasis mine)
Oh, really? The only religion? I'm a math teacher and even I know that there are some other religions present in the Middle East.  Perhaps, you've heard of them?

Sunday, October 26, 2014

A Few Random Thoughts about the Time article.

Maybe you've read it.

A few things jump out at me. Here's a big one:
One research team relied on a "a controversial tool called value-added measures (VAM)" to measure teacher effectiveness, and they "found that replacing a poorly performing teacher with an excellent one could increase students' lifetime earnings by $250,000 per classroom."
That's a pretty big number alright, almost big enough to make you lose sight of the details ... if you're a low grade moron or someone with a axe to grind who doesn't mind being disingenuous.

Lifetime earnings of $250,000 per classroom works out to $10,000 lifetime earnings difference per kid.  Assuming the average person works for about 40 years, that works out to a difference of $250 extra dollars per year, a whopping extra 12.5 cents per hour ... and that's if you replace a poor teacher with an excellent one for all twelve years of schooling.

This is what is known in mathematical and statistical circles as an "insignificant" increase for which we have to use a tool that the Vermont Commissioner of Education (and pretty much everyone else) has said is a "broken measurement system" that "does not work". She went on to say that it would never be used in Vermont because of it's ineffectiveness. "It would be unfair to our students to automatically fire their educators based on technically inadequate tools."

And where, besides a hole in the ground, did that number get pulled from?

Let's not ignore the dubious premise that thousands of "excellent" teachers are just waiting to be hired ... ready and eager to take the place of the losers.


Funny thing is, we're doing pretty well despite the fact that we have been forced to label every single school in the state as "low performing": 
 In 2013, the federal Education Department released a study comparing the performance of US states to the 47 countries that participated in the most recent Trends in International Mathematics and Science Study, one of the two large international comparative assessments. Vermont ranked 7th in the world in eighth-grade mathematics and 4th in science. Only Massachusetts, which has a comparable child poverty rate, did better.
So Time magazine interviewed a couple of billionaires about their opinions of public education and teacher tenure. "Shocking!" they said. "You can't fire a bad teacher."

Really?  Have they ever tried? The usual reason that principals can't fire a "bad" teacher is because the principal has no way of knowing which teachers are "bad" teachers - the new evaluation procedures are long on typing every word but very short on actually listening to the teacher teaching the class. If you are focused on typing every word said, then you aren't paying attention and you aren't "taking notes" - the inability to multitask is something I warn my students of constantly. Incidentally, and ironically, so does the principal.

The other reason that most "bad" teachers can't be fired? They're not "bad" teachers. Most of the time a teacher who is labeled "bad" is someone who has spoken up at a faculty meeting, stood up for themselves or others, worked against the desires of the principal.

The truly bad teachers are the ones who don't get noticed because they never improve, who hand out the same worksheets year after year, who don't say anything controversial, who allow students to wallow and get mired in an academic mudpit ... but who somehow get As so their parents don't say anything, who have a degree from a prestigious university but who are universally reviled by their students as lousy teachers, who dutifully fill out the silly paperwork and follow every administrative whim with fervor, never considering the best interests of the students, doing just enough to placate but never enough to teach.

Here's how to get yourself fired in public schools WITHOUT tenure:
  • Be gay/lesbian, or any other LGBTQ. (Seen it.)
  • Be Experienced in a cost-cutting era. (Big pressure)
  • Be Muslim, or Black or Latino or other "minority" who is "uppity" or in some other way "doesn't behave" (actually has an opinion and isn't afraid to say something).
  • Get pregnant. (True story)
  • Speak up for the Rights of the students/ disagree with admin is any way.
  • Actually do something bad or criminal.
Except for the last one of course, that will never be the reason on the form letter. That would be discrimination. Rather, you'll find vague job performance metrics and "documented tardiness issues". You'll find overwhelming but never specified "evidence" of misconduct. You'll find everything but the actual discrimination.

Here are some ways you can get fired from a school WITH tenure:
  • Do something bad or criminal.
  • Be a bad teacher.

Monday, October 13, 2014

Stop Common Core (and replace it with what?)

Enough.

What utter dreck.

10. Your child is unique? Yeah, no two snowflakes are exactly alike, but they are all basically the same. After 30 years of teaching, I think I can lay this ego-driven, touchy-feely garbage to rest. Your child is special to you but he isn't different enough from the rest of the crowd to warrant special teaching.

9. Yup, CCSS was created by special interests. No, it's not perfect. No, I don't endorse all of it and I probably won't hold my breath and teach every part of it. I'm a math teacher. I have the intelligence to modify it when necessary. It is, however, better than that mess of garbage that it replaced.

8. I really don't want the legislature voting on math standards. They have zero experience in education. I don't want them to ask my opinion on the intricacies of healthcare for the same reason.

7. Does it matter that this is false? Does it matter that districts are spending that money on testing regardless?

6. The CCSS do not collect information.

5. The lack of attention for gifted learners is not the fault of the CCSS. And your child isn't gifted.

4. Again, not by CCSS. And again, this is false in many states. Mine for instance wrote definitively that test scores have not, are not and will not be used to rate teachers because it is inappropriate and wrong to do so.

3. Yup, this is the only thing you got right. We are not forcing them to read as much of the classics. Instead the English teachers are using SOME different works, such as essays and non-fiction. Unfortunately for your rather uninformed little screed, Shakespeare and Edith Hamilton Mythology are still very much in evidence.

2. No one changed who was in control. School Boards are still the only controlling bodies. Homeschoolers are not in any way, shape or form, under the control of any CCSS.

1. You have the power to stop common core but in #2 you didn't have any power? Come on, at least be consistent in your paranoid ramblings. The last people who should be exercising control over their kids schooling are people who can't even make a coherent argument.  Fortunately for me and my job, deluded paranoiacs like you are keeping me employed -- although usually I don't get your kid until after you've messed up his education and nearly ruined his chances at living a good and successful life.

But don't let me stop you. The Internet is free to use.


Missing the Point.

http://grantwiggins.wordpress.com/2014/10/10/a-veteran-teacher-turned-coach-shadows-2-students-for-2-days-a-sobering-lesson-learned/

Shadowing a student is a valuable idea, but she misses the point in the end.
I have made a terrible mistake.
I waited fourteen years to do something that I should have done my first year of teaching: shadow a student for a day. 
Which is a fine idea ... for an experienced teacher. The newbie? Not so much. That first-year teacher is just out of college and has no sense of what is appropriate for 15yo students, and probably would miss or misunderstand the important details in all of the other data and facts.

So, this teacher-turned-Learning Coach shadowed 2 kids ... for a day.
My class schedules for the day

The schedule that day for the 10th grade student:
7:45 – 9:15: Geometry
9:30 – 10:55: Spanish II
10:55 – 11:40: Lunch
11:45 – 1:10: World History
1:25 – 2:45: Integrated Science
The schedule that day for the 12th grade student:
7:45 – 9:15: Math
9:30 – 10:55: Chemistry
10:55 – 11:40: Lunch
11:45 – 1:10: English
1:25 – 2:45: Business
Here we begin to get the glimmer of the real problem. The block schedule was sold to faculty in schools as an improvement on some or all of the following grounds:
  • The students could focus on fewer things throughout the day, making for more deliberateness. The phrase "Mile wide and inch deep" is usually tossed in here, as well.
  • They'd have fewer passing times and those minutes could be filled with instruction or projects or meaningful discussion or labs.
  • 80 minutes was a better chunk of time.
  • Teachers would have fewer preps.
In some buildings, including ours, the change was implemented over vacation and the teachers returned to a different schedule. "Surprise!"
  • It's better. We decided. The schedule has changed.
Not a single thought was spared to ask whether 9th graders should be in 80 minute classes or whether Special Education students would benefit from the extended periods. Nobody considered whether having 8 periods for which students could have one or two "free" periods was better than requiring the students to have four academic courses per day and no down time. And nobody dared to question whether 80 minutes was too much math for one day.

Anyway, back to our Coach.
Key Takeaway #1
Students sit all day, and sitting is exhausting.
Thinking is exhausting. Focus is exhausting. Learning is exhausting.  If you're doing it right, education is hard, learning new things is difficult.  I'm not saying that students shouldn't move more, but that's not the issue.

Block scheduling is predicated on the idea that students will be allowed to focus on fewer things for longer periods, that mere "rote memorizing" of content would be subordinated to the intense, "deeper" thinking, critical thinking and problem solving.

If our coach could change the past, she would have implemented "a mandatory stretch halfway through the class", installed "a Nerf basketball hoop on the back of my door and encourage kids to play in the first and final minutes of class" and have built in "a hands-on, move-around activity into every single class day." 

In other words, 80 minutes is too long and teachers need to pretend it's really two 40 minute periods ... or 75 minutes, with a break in the middle and some games at the end.

The most telling comment? "Yes, we would sacrifice some content to do this – that’s fine."

Really? The block schedule selling point "Better use of time" goes out the window.  Her point in her article, and presumably to the teachers in her building, "I was so tired by the end of the day, I wasn’t absorbing most of the content, so I am not sure my previous method of making kids sit through hour-long, sit-down discussions of the texts was all that effective."

Instead of questioning whether or not students should get more of a break between classes, or have a free period to unwind, she is willing to advocate for giving that free time in the middle of the only time her students have to be with her. 
Key Takeaway #2
High School students are sitting passively and listening during approximately 90% of their classes.
So change that, if you feel that it's more appropriate to your discipline. The idea that you need to start
every class with discussion, blitzkreig-like mini-lessons is entirely dependent on what you're doing rather than an appropriate plan for every day.

Likewise, worrying overmuch about the length of time you speak (and setting a timer) is not terribly good practice. If you're talking *at* the students rather than talking *with* them, you have a problem. A good lecture, on the other hand, can keep everyone in the room engaged for hours. A constant droning lecture, like pre-recorded videos in a "flipped classroom" or a Rocketship academy or Khan Academy, won't work for much more than as a substitute in your absence.

The bigger issue is the admin's constant refrain that the teacher needs to fill the 80 minutes with something. My admin, for instance, mention that we should "teach bell to bell." I am certain that everyone reading this can also hear the drumbeat of "testing", "accountability", and the political pressure to "excel" and "fire the bad teachers". Remember, too, that one promise of block scheduling was that MORE would be learned, MORE would be retained, and MORE would be understood.
Key takeaway #3You feel a little bit like a nuisance all day long.
I lost count of how many times we were told be quiet and pay attention ... you start to feel sorry for the students who are told over and over again to pay attention ... that need to just disconnect, break free, go for a run,  ... That is how students often feel in our classes, ... because they have been sitting and listening most of the day already. They have had enough.
And what is part of that cause? In my mind, it's that we seem to have this idea that 80 minutes of math with no time between periods to unwind is a good idea. I am impressed that the schedule quoted above has 45 minutes for lunch - we have 22 - and that there is 15 minutes between classes - we have 3.

I'm going to ignore her comments about sarcasm, because they don't really matter to this discussion beyond the fact that kids not paying attention is a problem for us and that the whole multi-tasking thing is messing the students up something fierce.

We do need to pay attention to that but also remember that kids are kids, they're not allowed to vote, drink, smoke, drive a car, rent, sign a contract, go to war, or make decisions that matter ... and they're learning something entirely new.  Why should we be surprised that Johnny is not focused on the math for 80 straight minutes?

We need to remember that not every kid will be as enthusiastic about math, or learn at the same pace, or be 100% proficient by the year 2014, or care about all subjects equally, or have a home life that's stable, ... and so on.

But let's explore the aspects of Block Scheduling that our Coach didn't touch on, mostly because she seems to feel that it's "obviously" the correct schedule.

To a man, block schedule proponents claim that "more will be done" and that "students will understand the topic better because they'll have more time to work on it and discuss it" and be able to avoid that dreaded "mile-wide and inch deep curriculum."

As someone who has had roughly identical groups -- in the same year -- in 40 minutes classes yearlong and in semester-long block classes, I can tell you that the block classes do less, achieve less, learn less. Other teachers in my district report the same thing.

The differences are subtle but one thing sticks out to me: students in blocks run out of steam. You can't do twice as much all the time. You can't do lesson 6.1 for 30 minutes, stop and stretch, do a little practice, and then do lesson 6.2 immediately and expect that the two sets of homework are possible. Simply doubling the expected work isn't feasible. Sometimes, it works, but not always.


What you often get is Teach, practice, try a little more, and then let them get started on homework. The long period is just too long. If you restructure your course and completely change the way you teach, you can improve things a little but I would maintain that you should be doing that anyway ... and in 50 minute periods.

Other issues? The school's habit of constant interruption for assemblies, sports dismissals, announcements, calling students to the office, and so on. Snow days get in the way, too, as do Fun-time Fridays, and all of the days previous to holidays and days off.

And what of the Special Ed kids, the ADD/OCD/Ed/ODD and the kids who just aren't really thrilled to be there? Why 80 minutes? They have enough trouble settling down for 20; 40 is a stretch but 80 is unfair.

Look at those schedules above. 1.5 hours each of Geometry, Spanish, World History and Science. We don't even do that to college students. It's no wonder they're tired.

And yet, with no significant change to standardized testing or SATs or ACTs or even the state-wide final exams, you get vastly "improved" grades. Interesting, no?



Sunday, September 14, 2014

Data Point #934 Showing Why Teacher Education is Problematic

I was perusing the blog feed and I come across my favorite source for "interesting" teacher education issues. Okay, most of what he writes seems flawed, but at least he's advocating to "Burn The Textbooks, Shred The Worksheets, Teach Math", but I digress.

Click to enlarge that image.

It's measures of central tendency from a stack of pennies. How far down the list of values can you get before you reach an inconsistency in the numbers?

How is this a sample of what you, as a real math teacher, would want to show the world as exemplar of your students' work? Why would this page be the one that you put out to the world ... unless you were deliberately showing how you gave feedback, a la @mpersham's mathmistakes.org.

The project itself is a fine one ... I did the same thing when learning to use Fathom, and I plan on using it with my class this year.  But, really, if showing teachers "cool" or useful projects, wouldn't you want to display ones that are at least mostly (>50%) correct?

While this page would be great to show the relationship between sample statistics and population statistics, it's not at all clear to me whether our blogger noticed any of the problems.

Here is the population, if anyone is interested:


Tuesday, September 9, 2014

Reason #438 why kids have trouble.

During the passing time, Student is telling a story of how she had $20 in her backpack and then couldn't find it.

Thinks maybe her father took it when he drove her to her friend's house.

Another kid chimes in, "Yeah, my father always takes money out of my purse to go buy beer."

Kind of a shame when they trust their math teacher more than their parent.

Tuesday, August 19, 2014

Regular Class work is so Helpful.

I find that a regular activity is a good thing. The students look at it as a useful digression and happily go about working on it ... then they realize it fits right in with what you've been doing.
@fawnpnguyen: "I was brainstorming with a couple of 6th grade math teachers at another district, and we were listing out a possible warm-up/math talk schedule, something like Monday: number talk; Tuesday: visual pattern; Wednesday: estimation 180; Thursday: fun fact, or WYR, or Keeping Skills Sharp, or SBAC/review question; Friday: personal reflection.
Here are a couple of those ideas and one or two others:

Estimation180 - building number sense by estimating values from images or video. This is valuable because so often we say "Does that answer make sense?" If the students have little to no experience with the subject of the question, and no practice making estimates, then answering our "Sense?" question is an exercise in random answer generation.

One Hundred and One Questions - An image or video is presented and students ask any question that comes to mind. While I personally wish the prompt was "What math question comes to mind here?", it is a good place to help them develop the ability to ask questions of the world round them and to see that math isn't just a classroom activity. Browse beforehand and record the links of the ones that fit your current material or your mood.

Math Arguments 180 - The goal is to have students question their assumptions and bring those assumptions to the front of their minds for conscious consideration instead of letting them hold on to common misconceptions that mess up their thinking.  Still in the development stages. The Math Concepts Challenge is also for teachers, though your students might be charged up for it.

Visual Patterns - Practicing the art of understanding the pattern and setting an equation to it in order to predict the value at step 43. I've been thinking it needs more patterns that aren't straightforward linear functions, but if that's the age you're working with then here is a bunch.

Math Talks - Prompts for discussion with your students.

Would You Rather? - students are presented with a choice. They choose and then have to justify their choice. "Would you rather have a bag of nickels that weighs as much as you do or a stack of quarters as high as you are?"

Graphing Stories - a video is shown and the students need to create a graph of some data from it. The video contains a graph blank that shows the independent and dependent variables. Usually, these are time-series graphs of height or altitude, but if you only show the "action" portion, you can have them graph whatever quantities that come to mind.

The UVM Math Contest - Problems from the University of Vermont High School Math Contest. These are given in the spring of Pre-Calculus and are meant for mature students who have had a good algebra II background. These questions are to be solved without a calculator or technology of any kind; figuring out the method is the whole point. Attempting a whole test in the allotted two hours would challenge even the best math teachers. Scores of 15 out of 41 are considered excellent.

Drilling basic facts pays off.

"Practice makes perfect."

Okay, we do have to differentiate between mindless drill & kill and what really makes kids better at math - focused practice, error correction, and repetition of correct processes.  Just as hacking around on a soccer field doesn't help the team nearly as well as a directed practice, endless pages of addition problems aren't useful in developing math skills.

Do ten at a time until you get them right. Examine the work, identify errors and don't repeat them .... which sounds like what Common Core asks math teachers to do and what math teachers have been doing for a long time.

This all sounds like what you've been doing, unless you have Curriculum coordinators like mine who denigrate practice as "drill and Kill. We should have the kids do critical thinking", as if critical thinking and error analysis were two different things.
"Healthy children start making that switch between counting to what’s called fact retrieval when they’re 8 to 9 years old, when they’re still working on fundamental addition and subtraction. How well kids make that shift to memory-based problem-solving is known to predict their ultimate math achievement. Those who fall behind “are impairing or slowing down their math learning later on,” Mann Koepke said. 
So, those teachers who insist that the kids should have a calculator and an internet connection so they can look it all up are really doing a job on their kids.
It turns out that adults don’t use their memory-crunching hippocampus in the same way. Instead of using a lot of effort, retrieving six plus four equals 10 from long-term storage was almost automatic, Menon said. In other words, over time the brain became increasingly efficient at retrieving facts. Think of it like a bumpy, grassy field, NIH’s Mann Koepke explained. Walk over the same spot enough and a smooth, grass-free path forms, making it easier to get from start to end. If your brain doesn’t have to work as hard on simple math, it has more working memory free to process the teacher’s brand-new lesson on more complex math. source.
So the next time someone says that elementary students should have a calculator, that "you can look that up" and "all we need is to teach them information retrieval skills", remind them that the brain needs to have some basic facts to work with before it can handle more complex tasks.


Currently, the argument point brought up here is the Japanese education system, which has been moving away from drill and practice and turning to the higher-order thinking that reformers here in the States are always going on about.

Remember, however, that a typical Japanese high school teacher does NOT have to do as much of this preparatory drill and skills practice ... because of the ubiquitous "jukus" - after-school academies that nearly every Japanese student attends to make sure that he/she has a shot at higher education.What do the "jukus" do? Drill. Basic skills. Practice, practice, practice. Because it works.

Here's a description of one of these "cram schools":
"This school broadcasts lectures to its 800 satellite schools all over Japan and supports students via telephone, fax and the Internet. Students can take math training menu and other drills on the Internet through a service called Toshin Home Lesson. They can choose from one series of lectures to a whole package."

Tuesday, July 15, 2014

50-cent solution to Car Seat Deaths


The Weather Channel has been making noise about kids left in carseats and dying from the heat ... an admirable cause, to be sure.  They had a short segment in which they talked to some people, ran a clip about some parent who forgot, and then tossed off an industry statement that "Monitoring the back seat for infants would be 'too costly'."

That is utter trash.

$0.50 and a bit of programming would knock down the rates by at least a half.

You know that beep that you get if your keys are in the ignition when you turn off the car and open the door?  It goes for maybe ten seconds and then the dome light and the beep shuts off.

Here's the Keep Your Child Alive Solution: (edited after first comment)
If the LATCH system has a seat installed, when you turn off the ignition or open the driver's door, a beeper located behind the driver (in the dome light or even further back) goes off for a few seconds. It has to be a distinctive beep and it has to come from *behind* the driver. If the LATCH system cannot have a sensor in it, then place a switch there that turns on the system when the seat is installed. Sure, someone could turn it off, but that would take a direct act.

That's all it would take. Most of these deaths are caused by harried drivers, in a rush, forgetting that their child is in the back because he immediately fell asleep and hasn't made a peep for the last thirty miles. A simple chirping noise from behind or a flashing light on the dash is all that the vast majority of these cases would need.

No child in the back carseat? So what? You still think to check.

You're getting out at the gas station? So what? You hear a chirping noise from the back and you remember he's back there. It will become instinctive for parents to hear the beep, turn and check.

All this BS with reminder cards and BESAFE lists? Useless.  It's not that parents don't care. They are forgetting that their kid is in the back - why would a checklist help?

Putting a stuffed animal in the front seat to remind you? Marginally better, until you have more than one thing in the front seat, or you forget to throw that toy in the front, or your son screams for that EXACT toy and you hand it to him ...

Hanging an air freshener from the mirror? In addition to it being illegal in most states and a bad idea to obscure your vision, this "reminder" is constantly in your field of vision and will quickly be ignored.

The car companies can put in 12 airbags that are linked to the seatbelts and pressure sensitive seat sensors, coupled with instantaneous triggering mechanisms, they have hundreds of computer chips that monitor everything about the engine, they are all furiously installing driver-distraction devices like phone and GPS screens and computer-driven window and climate controls that can't be operated safely while the car is in motion ... I think they can figure this one out, too.


Come on, car people. THINK.

Thursday, June 19, 2014

The Highly Ineffective Principal: Clerical Error

A certain principal writes a letter for the school yearbook.  In his message, Roosevelt Principal Dr. Steven Strachan tells the graduates how proud he is of them and that they are a class of “great leaders, articulate orators, brilliant scientists, breathtaking athletes and extraordinary artists.”


He plagiarized the message.

Word for word. All of it.

From a principal in CA, uncredited.

But, but, but, but ... he "asked permission to quote"!

Here's the best part:
"I sincerely apologize to the Roosevelt community and to the class of 2014 for the inadvertent clerical error causing mistakes to be printed in the 2014 yearbook. An unedited draft of my remarks was accidentally published rather than the final version, and I take full responsibility for the oversight."
 Clerical error? A clerical error is misspelling the name of the guy you're quoting, or writing that the year is 2041. A clerical error is the yearbook editor rearranging the paragraphs inadvertently. A clerical error does not include you plagiarizing the entire message from another principal and then congratulating the WRONG SENIOR CLASS at the WRONG SCHOOL.
The Roosevelt principal even concluded his message like Barone did, writing, “Congratulations to the Albany High School Class of 2013.”

Blaming your plagiarism on the yearbook editor's "clerical error" is low-class, especially when you phrase it "clerical error causing mistakes to be printed." Passive voice apology fuck-you?

My favorite part of this is that he takes "full responsibility for the oversight." If one of his students did that, suspension would be in order. Nothing is happening to him ... he doesn't even have to pay the piddling amount of money for the reprint: the last line of the piece mentions that the pages are being reprinted with $800 from the "Principal's Discretionary Fund."

In case you're not familiar with public school budgetary BS, that's a slush fund that the principal may use at his discretion. Usually, it's used for things like buying a poor senior her cap and gown, or funding some low-income students tickets to a show that other kids are going to. Maybe supplying the SpecialEd department with some bit of tech that they can't get under normal budgets. Feel-good stuff or charitable-type things.

Educator of the Year.

Sunday, June 15, 2014

The Daily Schedule, or Why do we do this?

When Amnesty International works to ban a practice in prisons, you might want to rethink doing it in schools.

My school has 1.5 hour blocks separated by 3 minute passing times.  Long ago, I began to tell students that I didn't want to know when or if they were going to the bathroom, just go one at a time and don't dawdle.

"It's none of my business. The pass is right there. Carry it to get yourself past the AP.  I don't need to know why ... TMI, people."

You know what? They go if they need to. But the vast majority doesn't abuse that and class runs just fine.

"I know that sometimes you don't really need to go, but that you need to walk down the stairs, across the building and up the other stairs and then back.  Just realize that when you get back, we will be focused on something and you'll have to pick up the thread quickly. Be ready."

Yes, I admit. That kid in the third row goes every day. He's a wanderer and the AP gets on his case and wants me to restrict his movement, but I refuse. Having him sit and fidget and whine will only distract everyone -- far more than if I just let him go -- and letting him get it out of his system means that he can focus when he returns.

If the situation calls for it, I will ask him directly, "Do you NEED to go? These instructions are important and you'll need to be ready to start this when you get back. Can it wait?"

I don't like it much but it's necessary. 

Admin bitches about tardiness, yet we give them 3 minutes to move two floors and across to a different building. We are told to stand at our doors so we can greet the students but also to monitor the hallway and ensure the kids are moving in an efficient way.

Admin stresses about teaching "bell to bell" -- for 90 goddam minutes -- as if the stresses we put on students don't count. "Teach to the bell" means that kids have to write, think, or be doing something right to the last second, then collect all their stuff, make it down the hall or further, get into the next room and be seated before the tardy bell.

In three minutes?

Why do we torture kids in this fashion?

They have a cup of coffee in the morning to help wake themselves up ... and caffeine is a diuretic. who in their right mind thinks that students will be able to take care of business AND walk to the other building in just three minutes?  Apparently, we do.

At lunch, many will down a 3/4L bottle of Gatorade.

We're all instructed to let the kids drink as much water as they want. We're reminded that 8 cups of water is necessary, so water is the only thing we're all supposed to allow in class -- and many students have a water bottle and the school just installed those nifty water fountain extensions with the reusable bottle filler spout thing.

But you can't go to the bathroom? Does anyone understand how the human body works?

Apparently not.

What brought this up?  Taught by Finland, "For every 45 minutes of classroom instruction in Finland, students are entitled to a 15-minute break. This is guaranteed by law!"

I love this guy. He's an American teacher who moved to Finland and is a teacher there. Well worth reading regularly. What set him off? This Chicago Administrator's note:
In addition to scheduled restroom breaks, students will be given restroom passes to use if they need to use the restroom outside of the scheduled time. Students will be given two restroom passes to use between now and the end of the quarter. They can choose to hold on to them and trade them in for a reward at the end of the quarter. Following these guidelines:

Have students fill in their names as soon as they receive them. Passes are invalid if names are crossed out for another name.

 For the upper grades, students can use one teacher's pass in another classroom, but they still only get the same number of passes per quarter.

 Use a class roster to have student initial next to their name to indicate that they received the passes.

 Have students fill in the "time out" and "time in" and then turn the pass in to the teacher when finished. This will help them practice the [Common Core Standards] of telling time with both digital and analog clocks.

 Promote the benefit of not using the passes by reminding students that rewards will be given for left over passes at the end of the quarter.

Sunday, June 8, 2014

Teacher Preparation in the US

from Pasi Sahlberg
In the United States, for example, there are more than 1,500 different teacher-preparation programs. The range in quality is wide. In Singapore and Finland only one academically rigorous teacher education program is available for those who desire to become teachers. Likewise, neither Canada nor South Korea has fast-track options into teaching, such as Teach for America or Teach First in Europe. Teacher quality in high-performing countries is a result of careful quality control at entry into teaching rather than measuring teacher effectiveness in service.

Thursday, May 1, 2014

Questions for your 1:1 Initiative.

Although I suspect that a great deal of planning has gone into this initiative already, here are 10 important questions that parents should ask—and that school administrators should be able to answer.
  • What are the initiative's teaching and learning goals, and how will those goals be measured? Too many technology initiatives start with the technology, not the instructional goals. Clearly defined objectives should drive the choice of device being used. For example, if schools want students to read e-books, the screens and applications should support this use. In the planning stages of the project, the district should also determine how it will measure progress toward its stated goals, so that it will be able to answer the question, "What have we received for our money, time, and effort?"
 We went for the keyboard, low cost, natural integration with the Google suite ... Chromebook. After an initial bad phase of damaged hardware, it's evened out. Curriculum, teaching goals, measurement -- eh, not so much.
  • What training is in place for the teaching staff? Professional development is key to the success of any 1:1 initiative. The major shortcomings of most 1:1 professional development efforts are that they offer too little, too late—and focus too much on the device instead of on the pedagogy required for its effective use.
Damn little in our district. It's been hit or miss and mostly miss. Fortunately, there are a few people willing to train each other but that is an uneasy way to do this.
  • Is there a digital citizenship curriculum in place? Of utmost importance to many parents is their children's online safety. Schools can address this need by having a good plan in place to help students learn to use technology appropriately. Supplement the plan with a parent education program that includes guidelines—written in clear, understandable, and positive language—for when devices can be used in school, what applications and websites are appropriate, and how users must care for the equipment. (Our district's guidelines can be found on our 1:1 parent site. Like many districts, we have borrowed extensively from Common Sense Media.)
No. The AP will try to discipline students who cross an ill-defined line, but there is nothing in place that sets out any rules or guidelines to limit the students nor is there anything to guide them in using it more fully than for music videos.
  • What happens if a student breaks or loses the device? Clear procedures related to loss, damage, and theft of school-owned devices need to be in place. My own district, like many, offers parents a low-cost insurance plan that covers accidental damage. We also place mandatory, heavy-duty cases on student devices, dramatically improving their survivability.
We've got this covered. Admin tried to "go easy" at first and that was a total failure. Now that they have simplified things (replacement screen is $50; tough, you broke it, you pay) students are much more self-assured and they've come to understand what kinds of treatment will end up costing money.
  • How will these devices be managed and maintained? Unreliable technology is frustrating for both staff and students—and apt to go unused. The 1:1 plan should address the staffing and management systems necessary to troubleshoot hardware, update software, and install applications on student devices.
Yeah, covered. Important point.
  • What e-resources will accompany the hardware? Individualized instruction requires such resources as e-books and content databases, a course management system like Moodle or Blackboard, and software that enables students to access and process information. Cloud-based productivity and collaboration tools like GoogleApps or Office365 can support workflows and communication between teacher and students.
Google Applications Suite, Apps, Moodle (that I personally maintain, installed, support).  Yeah, this part is working really well for the faculty who've jumped in feet-first. For the others, it's been a struggle ... some people still want paper for everything.  The students are good for this. "Can I just share my paper?"
  • Is the network infrastructure in place to support the use of the devices, both internally and in the cloud? Although many schools have spent a good deal of time and effort in extending the reach of their wireless networks to all instructional areas of a school (coverage), they may not have the bandwidth needed to support dozens of devices trying to use the network at the same time (capacity).
Barely. Still takes time in the morning to navigate the wifi discovery, network login, etc. Once that's done, it pretty good. "Take out your Chromebooks." 30 seconds and we're using Desmos.
  • How will you ensure that all teachers use the devices to improve teaching and learning? Few of us like top-down mandates, so it's important that the teachers who are expected to implement this program have input during the planning process on goals, training, resources, and policies. Assessment of effective teaching using technology should be embedded in teacher evaluation practices.
First year ... a few teachers, most of the students. It's going pretty well and it's a definite positive slope.
  • What will happen in a few years when all these devices are obsolete? The plan should be specific about the project's long-term viability. Using one-time referendum dollars that will be repaid over 20 or 30 years to buy equipment that will need to be replaced in five years is like taking out a mortgage to purchase a car. A transparent budget for the project must clearly state both annual costs and long-term maintenance and replacement needs.
 It's handled.
  • Are other areas of the school's budget being cut to pay for this project? If the 1:1 initiative is being funded by general operating dollars, school leaders should be up-front about its potential impact on other programs. Given the zero-sum nature of most school budgets, somebody's priority program or resource may get reduced—and that somebody may not like it. If dollars are coming from places that will require less funding because of the initiative—such as textbooks, printing, or school supplies—the district needs to demonstrate these savings.
Nothing is being cut ... yet.  The textbooks are being replaced in part with FOS .... there are lots of math books out there. Some paper books that have  deteriorated over the years are being replaced - but pdf or active versions, rather than paper. We saved money by not buying the expensive version.

I think our feeling is that we'll save a little here and a little there while providing the students with tools they wouldn't otherwise have been able to get. It might not be a monetary zero-sum, but the benefits are worth the cost even though we haven't come close to fully utilizing the resource.

Sunday, April 20, 2014

Things We Need You to Stop Saying, part 1

There are a couple of things we really need you to stop saying. The first:
"The right answer isn't important. It's knowing what you're doing."
No matter how you parse this, it's ridiculous. The right answer is the whole point of doing the problem ... has always been, is now, and will always be. The "knowing what you are doing part" leads to the right answer. If it doesn't, then you don't know what you are doing.

Variations on this include: "It's the concept that matters" and "We're putting the emphasis on the method." It shows up as sarcastic responses from Institute Professionals and college professors, too:
What we should be saying is "The right answer is vitally important ... so important that we also want students to explain the method and how we all know the answer is correct; they must be able to detect an error if it occurs and describe how to fix it so that the solution IS correct."

If you go to the trouble of having the students communicate, verbally or in writing, how they solved a problem, then you are focused on the right answer ... there would be no need to explain anything, or fix errors, if you didn't care about it. You'd take any randomly achieved answer as long as it was correct, and move on.

Just cancel the 6s.

Does anyone ... ANYONE ... seriously think that the right answer doesn't matter here? I don't consider this a "right answer" even though it looks like it.

I'm going with "No."
You'd take a wrong answer that looked like a right answer if you weren't paying attention.

Just cancel the x² from numerator and denominator.
One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from.
That is a far cry from " The right answer isn't important."
For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge.
You can't detect errors unless you know the right answer, or at least have a sense of what that right answer should be.

Even the infamous "Letter to Jack" assumed that the kid could get the right answer, then could find the error made by the other kid ... the assignment took this two steps beyond the right answer: explain the error to the other kid and help him fix it.

JD2718 banned FOIL, Dan Meyer used immediate feedback, countless teachers rearrange PEMDAS (as BEDMSA) to avo
id this:


We need them to explain what and why.

I often "let them in on a secret" and share the mnemonics after they get the understanding ... especially if the mnemonics speed up computation so we can get on with what we are actually doing, but every teacher worth his salt knows that you have to periodically make sure that random, blind luck isn't at play.

The last reason that we need to stop saying "The right answer isn't as important as knowing what you're doing" is that too often we teachers are speaking to people who don't know that it is merely step 1, namely school boards, administrators and parents.

I watched a young teacher from another school give a presentation to her school board. Among other weird things, she came out with this statement ... immediately, board members latched onto it.

"What do you mean? Of course the right answer matters."
"I've been in business for forty years; every time, the right answer matters."

She doubled down ... "No, they need to know HOW they are solving the problem." No one was buying it, nor should they have. Whether she didn't understand their concerns herself or honestly didn't believe that the right answer was so vital, she certainly couldn't communicate her stance to the Board.

A blind acceptance and repetition of poorly-understood Twitter broadsides and mindless slogans is the rhetorical equivalent of canceling the sixes.

That makes us all look bad and we're gonna need you to stop saying it.

Wednesday, April 16, 2014

Doing Things the Hard and Expensive Way

So this school had an election. Desperate to justify their purchase of enough TI-Inspire Navigator calculators for the whole school, they used them for voting for StC, because apparently:
  • the cellphone that every kid carries around were ... IDK ... banned, 
  • the free Socrative.com website was shut down undergoing maintenance at that exact moment, as were all of the similar, related websites, also free. .. like SurveyMonkey.
  • Google Forms was suspiciously locked and inaccessible ... 
  • the supplies budget didn't allow for 100ct note card pack at $0.39 per ...

but did allow for the Inspires:



For this misuse of funding, we hereby award them the US Armed Forces Monetary Memorial Medal, emblazoned with the image of Our Rich Uncle Pennybags.


Sunday, April 13, 2014

Snap Judgements

I love the kinds of conclusions people make on Twitter.


"Which looks more like a 21st century classroom?"

Neither. They're booths at a conference. I understand that the snap judgement goes against the top booth because the 21st century classroom isn't supposed to be about one person "lecturing" and 30 students quietly absorbing new information without "collaboration"; it's also missing a lot of misunderstood 21st Century Learning New-Age Idealistic Pedagogical Folderol.tm

But I digress.

In the Upper portion of the composite photo, we see a booth set up to present a lot of information. The people are encouraged by the layout to be seated, which means that they can all see because they out of each others way; no one is standing in front of the screen.

Think about this for a second. TI has a mission: sell calculators, at $150 each, with crappy screens and SLOOOOOOOW processors. They need to get you in a seat and show you the WOW factor. They need to get you past the basics fast and sell you on the tech because that $4500 classroom start-up fee is huge.  "Those regression functions don't come cheap, and aren't in any other package."

This is crying out for exactly what they've got here: a booth with a presenter who knows the machine inside and out, delivering information to as many people as they can, as efficiently as they can, in as little time as possible.

You put them in a seat where they can set down their stuff, see the big screen, write something down if they want to, hold the Inspire, swap out the faceplate, photograph it with their phones, set it down and tweet about it ... tables and chairs arranged in an efficient pattern, making best use of the space. Additionally, once seated, it's tough to leave politely before the end of the spiel and it's easy to control the technology and prevent theft.

Over on the side, some tall tables (which don't force you to lean over) for people who are browsing and don't want the whole presentation, or who want to stand and watch from the side.

BOOTH SCORE: 8 out of 10. Great for information transfer and for sales promotion. This booth is designed to have you linger and explore, try out and figure out, and to convince to you agitate for a major purchase back at your school.
CLASSROOM SCORE:  7 out of 10. "Boring" if you are looking for new-age learning styles, but effective as an organized setting for 30.


In the lower one, there is a guy on the left, holding a laptop in an awkward stance. One of the people he's talking to can see the screen. The other one can see the keyboard and be part of the conversation but unless he leans in and gets in the way of the other listener, he can't see much.

In the lower right, three people are crowded around a computer that desperately needs to be on a higher platform because all the people who want to look at it are standing -- it should be at eye height or, if not eye height, at least not "lean over and peer through the top part of your bifocals and then crane your neck back so you can see through the lower half of your bifocals" height - as the guy in white shorts is being forced to do.

In summary, a badly designed booth for this function, unless that function was "quick information shot and move on." This booth is designed to NOT allow you to linger and deeply explore the product.

There is no marketing director here trying to maximize anything, because there doesn't need to be. They only need to let you convince yourself that Desmos is cool - it is its own selling point. The website is free and doesn't have a large initial classroom purchase required, as TI does.

As a classroom, this booth is crap, too. There's nowhere for people to get comfortable. There's a giant graphic with some expression art. The displays / workstations are placed too low without any chairs so students have to type at weird angles. If the intent was for people standing, there should be some podiums so they can set down their devices and use both hands. If the intent was for people to sit, then the tables are at the right height, but there are no chairs.

This would be a horrible "classroom" for teacher/guide or for students.

BOOTH SCORE: 3 out of 10. (or 8 out of 10, depending on intent)
CLASSROOM SCORE:  1 out of 10.

But I guess I don't see things in the same way as other people do.

Tuesday, April 8, 2014

Volumes

Thanks to a sale at Jo-Anne Fabrics, I got this heavy-weight craft paper, 100 sheets of 12"x12" for about 5 bucks. Unfortunately, they were out of heavy weight linen for fighting tunics and cotton duck for banners. Satisfy one addiction, develop patience for the other.

Print the base functions.



Shells.



Same function photographed with foil crane. Looks creepy, doesn't it? Like Giant Spider in a Colosseum model.


Cross-Sections




Sunday, March 30, 2014

Retests.


I agree, mostly, which is why I have retests. 

However, many students need incentive to study now; instead of "I'll wait til after the first try at test. Then, I'll know what's on it." That's test-prep that won't last, not understanding.

Additionally, I do have other things to work on. Take algebra. Section 3 is writing and graphing linear equations. Section 4 is systems of linear equations.  Johnny can't do 4 if he truly doesn't understand 3.

I get the idea that students take different amounts of time to master material, but at some point, it is better to tell him that retaking the course would be a better option than retaking every test.  I don't mind if he completes algebra I in two years.

That image is being very disingenuous, though. Those exams don't lead to more learning ... they're the end-of-course exit exam, the final exam, the high-stakes test that so many reformers hate.

Common Core math thing, round two ... a mathematician.

I was floating around the Internet and came across The Mindful Mathematician's A Letter to Frustrated Parents
I was never taught to make sense of numbers, I was taught one way to solve every problem, every problem had ONE way, memorize these steps and you will be able to solve this problem.  Sorry if you can't remember the steps.  This is how we do it.  I was robbed.  I was not taught to persevere and try to make sense of the problem... who cares what it means, here's how you do it, just do this.  
I would feel sorry for you, but I cannot accept that this is truly what happened to you in school. As much as I get irritated by some of what I hear about elementary school teachers, I cannot believe that anyone took this approach.

You are flat-out misrepresenting what the "traditional" approach was in order to bolster support for the New way of doing things - to the exclusion of the algorithm. "I call Shenanigans."
Hold on, why am I crossing out this number and changing that one? 
Because you don't have enough to take away.  Just do it!  
But wait, I have 453 and I'm just trying to take away 17. I think there is more than enough to take away.  
No you can't take 7 away from 3... Just cross out the 5. Just do it!
But wouldn't 3 take away 7 be negative...
NO! You can't take a bigger number from a smaller number, sit down, JUST DO IT MY WAY!
Bullshit. Or, to put it more kindly, IF this is a true and accurate transcript of the conversation, this teacher is not very good and probably would teach everything in the same tyrannical fashion. Rather, it sounds like the kid with a poor understanding and this is the "excuse" for why.
"Hold on, why do I have to have common denominators? "Because you can't add apples and oranges! Just do it"
"I was wondering... why do I have to flip the fraction upside down if I'm dividing?" "It's not your place to reason why, just invert and multiply!  JUST DO IT!"
Elementary teachers have enough problems teaching math, without your strawman argument and fairly obvious projection.

Second, isn't it interesting that you claim this fictional teaching method is the reason that all of our students hate math, yet you are the first counterexample among many ... most math teachers included. If you are looking for a cause-effect relationship, you've disproved it.

The probable causes for the lowered "love of mathematics" are the lack of enjoyment of the subject by those teachers, the nervousness and trepidation with which they approach math, and the over-reliance on discovery methods of teaching and the "Guide on the Side, not a Sage on the Stage."
The "new" methods you're seeing are not being taught.  They are methods that students naturally invent.  Just the way that mathematicians invented them before our formal mathematics system existed.  
That is the crux of the problem. Too much of teaching now is centered around letting the kids "discover" a way of their own. Having the kids to "discover" their own way does not create "better understanding", it merely forces them to re-invent the wheel ... and then go through the trouble of learning. (I guess this is the next post.)

But I digress.

Students find comfort in tried and true methods that work without major thinking. They'll accept the  struggle with any method at first, because it is new. Once learned, there is a sense of pride of ownership, of knowing that they've got something to call their own, something that eliminates the need to count by ones on their fingers. They could subtract 37 from 63 by counting but it's slow, so we give them new methods. One in which you count up like a shopkeeper making change and the other, the "algorithm."

The algorithm, originally developed for simplicity, required the student subtracting 37 from 63 to "borrow 1 ten from the tens place to make 13, and 13-7 is 6. Then 5-3 is 2. Ah, 26." That requires understanding of place-value. That's very important.

The "new method" takes a different kind of thinking. "Add 3 to get to 40. Add 23 to get to 63. Ah, 26." This thinking is also very important.

These two methods are not mutually exclusive in a student.

For 63-37, method 2 works better. For 8569 - 6325, the first one is superior because there's no cancelling and because the numbers are larger.
When people say that "borrowing" is unnatural, I present the addition to the right. Go.

Did anyone add 3 to one of the 27s to get to 30, then add 24 to get to 54? Probably not. That's the method for subtraction, done in reverse.

Did you add the twenties and then add the sevens? 20+20 = 40 and 7+7=14. Ah, 54." Maybe. Depends on how old you are. For 27+27, it's the most efficient.

More likely, you added 7+7 = 14, carry the 1; 1+2+2 = 5; Ah, 54.

If we're okay with "carry the one" why are we so all-fired-up about "borrow a 1" when subtracting?
Should kids be able to do it all three ways? Yes. It's math, and math is fun.

I'll leave you with this final example, from our intrepid mathematician -- right at the top of the page -- that exemplifies the best time to use the old algorithm.

Students must be able to do both. (or all three, or four).
Which they choose is up to them.

Why do we have so much trouble with that?

Wednesday, March 26, 2014

The Subtraction MathWars

I'm sure everyone has seen this "letter" from a"frustrated parent" who claims that despite having a degree in "electronics engineering", can't figure out the child's homework.


I call "Shenanigans", both on the letter and on the responses.

First, we must accept that the "parent" can't read instructions, is pre-disposed to being an asshole over the ways in which our children are taught math, and is probably not all that capable of understanding basic principles.

In addition, when claiming that "simplification is valued over complication", he failed to note that , in business, "Completing the Assigned Task" is given far more weight than "Over-simplification and pedantry."

 ... but I digress.

In the "Bad Old Days", I recall many instances in which people browbeat math teachers with the anecdote, "I went to the store and bought $13.82 of stuff and the kid behind the counter couldn't make change for a $20. You teachers need to teach them the basics."

The standard algorithm vs. The New Way (which isn't so new; it's "Making Change") - look at that problem up there. Pretend you just bought something worth $111 dollars and you handed the clerk a $427 check. How much money do you get back? Follow the little jumps and imagine someone slapping bills into your hand. Makes a lot of sense now, doesn't it?

So here's what needs to happen: Kids need both.

Sorry, Reforministas, the standard algorithm is more useful and easier sometimes.
Sorry, Ostrich-Headed Blowhards, the "New Way" is more useful and easier sometimes.

Let's face facts.
  427
- 316
is much easier when done vertically. No borrowing, no hassle.

Even a problem that contains a "borrowing" is often easier done with the standard algorithm. It's more compact and it's cleaner. 492 - 327, for example. On the other hand, the "Counting Up or Down" is easier when you are close to certain values, such as the infamous 30001 - 29999 question.

A professor suggests that anything that can't be done with the New Way should be done with a calculator or WolframAlpha, but I disagree completely. He provides research that states teaching algorithms to young elementary students is harmful. I read the studies but I don't agree that we should NEVER teach the standard algorithm and borrowing; I just feel we should be more intelligent about it.
  1. Kids should eventually be comfortable with both ways. 
  2. Timing is critical. Maybe the New should be taught before the Standard Algorithm. 
  3. Also, be more willing to MAKE kids learn the SA, even if it's temporarily painful. If they understand place value and the counting up and down, they can learn the SA.
  4. Be less anal-retentive about the size of the problems and the difficulty of the subtractions (7 digit from 8-digit is extreme).  
  5. Stop insisting that the calculator is the Deus Ex Machina of mathematics. It is a tool and should be used to make already-understood work easier, but not if it replaces the understanding with No-Think Monkey Push-Button
Teach them both and then let them choose. Each method has advantages and each has disadvantages.

We can't be doing this:
DC: "Go ahead, use your standard algorithm to compute: 4,000,002 - 3,999,999"
Me: "This problem is better solved by counting up. 41036 - 28569 is easier solved by subtraction algorithm.
DC: "That is better solved with a calculator. #justsayin"

No. NO. Goddamn it, NO.

"There's no longer a reason to memorize a mindless math algorithm."
What if it's NOT meaningless?
Jumping to the calculator the instant the problem gets slightly weird can only lead to disaster for students. If I gave the student four hundred of these, I'd expect him to cut and paste into a spreadsheet or WolframAlpha, but one problem and he gives up and reaches for a calculator?

"There's no longer a reason to memorize a mindless math algorithm. There's plenty of reasons to understand thinking behind them." I agree with that. Proper teaching starts with understanding ... but then, once you understand the method, the algorithm is no longer meaningless; memorization occurs organically. The algorithm NEEDS understanding of place value.

When I reply that "Algebra, messes it up for many: 410x - 36y - 285x + 69y, as does calculator madness" (see the madness) and the response is, "Thankfully WolframAlpha", well that's when you know someone is not dealing from the top of the deck.

Yeah, Wolfram gives you the answer, coupled with


How in the bloody blue blazes of hell is that useful to someone who can't subtract?