The Difference between Teachers and Education Experts

Teachers want to change education back to what worked for them and for their students. "I need them to study fractions because fractions (and more importantly, the numerical sense that fractions develop) are so important in algebra and in life in general. They need to study algebra because the abstract mathematical ability that algebra develops and reinforces is critical to every single job I've ever had contact with, or my students have had contact with. Etc."

Education Experts want to reform the system to something different than what worked to teach them -- even if it was effective. Consider Conrad Wolfram, brother to Steven of Mathematica fame. He wants to eliminate every educational system that produced him and his brother and replace it all with computer software-based learning.

Corollary: If the Expert didn't like algebra, it was because he was bored and the teacher should have given out cookies and made the course more ! F ! U ! N ! , forgetting that it was normal teenaged angst that colored his appreciation or lack thereof.

Second Corollary: Education Experts have not been in a classroom for at least twenty years or not at all, and seem to feel that their dim memories of angst-filled 10th grade are sufficient experience.

One of the problems we face in education

I picked this up from Emergent Learner:

"I was recently emailed by a pre-K educator, Angela Yeaman, who will hopefully be using iPods in her pre-K classroom this coming school year. Below is Angela’s email to me and my response.
I recently submitted a proposal to my school division to purchase some IPods for use in my classroom. Although my proposal as been approved in principle I am now be questioned as to how developmentally appropriate IPods are in a 3-5 yr old classroom. My superintendent is wondering how a digital device like an IPod can be used to support play, exploration, learning, language, social interaction, etc.
Do you have any suggestions for information I can pass along to support the appropriateness of integrating these devices into my classroom. I guess I am facing bigger implementation obstacles than I anticipated."

The difference between education and the "Real World" ?

The real world requires that a problem exist before it feels the need to go buy technology to solve it.  The RW needs to know what to do with the new tech and be convinced that the new tech is an improvement, that it will provide better, cheaper, faster, more efficient output. Testing is done by the tech seller in order to create the glossy brochures and advertising. All this happens BEFORE purchase.  Tech is an answer to a problem in the Real World.

After purchase, and throughout the implementation phase, notes are kept as to the changes, difficulties and challenges. In-house data is recorded as to best use and procedures are setup for everyone so that the ideas of the best are understood and the best procedures are developed so that the least capable workers can effectively use the new toy.

Education, on the other hand, operates differently. Here, Shiny and New is purchased because it's Shiny and New and then teachers go try to justify the purchase and attempt to find a problem that this Shiny and New solution will hopefully solve.

Someone gets a "Great Idea" from a blog or an online PLC and implements it without considering the whats, whys, and wherefores. "Someone I know has a SmartBoard, so I need SmartBoard in my classroom." "That guy has iPods for each kid, so I need iPods for all my kids."  I don't exactly know how it'll all be used, I don't really know what problem I'm solving by implementing or whether this really will solve the problem, and I'm not sure if we'll get better, stronger, faster, cheaper, more effective output.

Money is spent and the teacher attempts to make use of the Great Idea, muddling through the implementation and adapting, reworking, to ultimately finish the year with something but no one is quite sure what. Was it worth it? Was the Shiny New Toy better or worse than the Trusty Old One? Did the students learn more, better, easier, faster, more efficiently or effectively? Will the next person (because teachers all eventually leave and the early-adopters most quickly) use the Shiny New Toy or will it be relegated to the corner to collect dust while the next teacher tries to institute the Next Big Idea using lots of money to buy the Next Shiny New Thing?

To paraphrase Reagan: Are those 4 year-olds going to be better off than last year's 4 year-olds?

Nobody knows. She may be screwing up those kids mightily or she may be on to something, but she has no idea. She's not even that invested in the iPods idea because she's getting a SmartBoard and she'll spend some time thinking about how to use that over the summer.  Isn't that cute?

Nobody has done any kind of testing; this classroom could be a source of data, but no one will record it. Nobody will set up controls to see if this works; a single class without them is unheard of because that's discrimination, don't you know?

That's American education for you.  Buy shit without knowing what, if anything, it will do.  Throw out what's working to focus on the Shiny New Toy and completely forget about the real purpose of education: education.  This is the only chance at an education this group of kids will ever get and we have no compunctions about testing new theories on them ... and we don't even give a damn about the results.

Food for thought - Hiring Practices

Mrs. C. reminded me the other day about the hiring practice at one local elementary school. The job would be posted on School Spring as per state law and all of the respondents would be vetted for license requirements and the usual administrative checkboxes. Those who passed this first round would be asked to come to school and take the final exams for eighth-grade math and English. Those who passed both would be considered for the job and interviewed.

You'd figure that this would be relatively easy to accomplish, wouldn't you?


The job listing for third grade teacher brought in the usual flood of SchoolSpring applicants since the button is so damned easy to push.  The list included the usual "I'm still in school and I have 2 years to go" and the "I have experience running a drill press, can I teach 3rd grade" as well as teachers from around the country and around the state.  The initial credential search narrowed down the list to 15 who were certified to teach in any state (we have reciprocity) or who could get certified by the start of school.

Every single candidate failed the 8th grade final exams. The school had to re-advertise.

Yeah, that was my reaction, too. Now clean up your keyboard.

Math Reform: Games, Practice and Psuedocontext

More interesting to students.
Probably not good at being a teacher.

Dan Meyer found Mathematics v. MTV by H. Wells Wulsin in this month's Stanford Sound Off. H. Wells, a former physics and chemistry teacher at a Washington DC private school, is making the case that math software (and by extension, teachers) must change because of competition with MTV for the eyeballs of our students. Which is kinda amusing, since none of my students watches MTV for more than a tiny percent of their information-absorbing time. Facebook, iPod, games, texting, Facebook, YouTube, cellphone, texting. The TV might be tuned to MTV in the background, but more likely it's on Spongebob.

Anyway, he does have a point when he says, "Mathematics educators now vie with a multitude of digital entertainment options to capture adolescents’ interest." "To compete more aggressively for students’ attention, mathematics software should adopt the very strategies that have made these other media so successful."

An issue I have is when he says, in the next breath, "Research shows that mathematics software can boost student learning, but these programs remain unpopular."  That's because software isn't always the answer. Teachers are primarily involved with new learning. New learning is rarely successful in a computer-learning environment because it usually needs an human explanation. If students could do this alone, you'd see a lot more kids taking summer classes online and getting credits. Repeat learning can be successful online (or by computer training) because the kids already know what the goal is, already have been taught the concept but just need repetition and practice.

The upshot of all of this?  You probably have done as much of this guy's ideas as is workable.

Back to our expert ... Wulsin offers recommendations that sound good in theory:

Presenting examples in high-resolution video. "Video lets students watch the sweat beading on the athlete’s temples, see the whoosh of wind in the skydiver’s hair, hear the rev of the daredevil’s motorcycle. A photograph or cartoon cannot beat video in its fidelity and power to captivate."

Connecting to students' interests. "Monitoring a breeding bunny population would show the process of exponential growth. Baseball batting averages could introduce percentages."

Showing appealing faces. "These videos could occasionally feature famous sports or entertainment figures. What if Michael Phelps calculated the volume of an Olympic swimming pool or Beyoncé computed the time delay needed for speakers at an outdoor concert? Why not let Danica Patrick figure the monthly payment on an auto loan?"

Holding students' attention. "Make students laugh through physical comedy or corny one-liners. Introduce them to interesting people with magnetic personalities."

Sounds good. Misses the point.

To engage learning, what you need is a good question that arises out of context, asked in a way that makes sense, posed by someone who actually needs to know the answer.  While I hate to push the button marked “Praise Dan” too often, I do think that he has given us a shorthand for much of this … pseudocontext … and the suggestions fail because of it.

Show appealing Faces

“What if Michael Phelps calculated the volume of an Olympic swimming pool”

Really? When would Michael ever care? On the other hand, he might be interested in split times and speeds and the differential changes made by a new type of suit with a 5% slicker surface. Build your question from that and you'll have the class hooked. Bring in data from your pool at home and calculate the chlorine percentage. How many tabs go into this pool? In my case, it was the number of bottles of medicine I needed to add to a fishpond.

“or Beyoncé computed the time delay needed for speakers at an outdoor concert?”

Don’t make me laugh. Beyoncé’s job is to sing. When the hall was built, someone cared. Once. Then the problem was solved and everyone moved on. The audio engineer needed to know when she placed the venue's sound system. The designer needed to know where to put the reflecting panels. But not Beyonce.

And the silliest one of all: “Why not let Danica Patrick figure the monthly payment on an auto loan?”

Because she cares even less than your students do and they know it.

In a sport like NASCAR, which is run using computers, analyzed to death with computers, which has something like 200 different sensors on the cars taking measurements every 1/300th of a second generating GBs of data which is endlessly broken down before, during and after the race … and all we get is a suggestion that Danica figure the monthly payment of an auto loan? Lame. (BTW, amortization schedules? Even bankers and loan officers run freely available spreadsheet tools.)

How about spring displacement, fore and aft g-loading, pressure, O2 vs Temperature, wing downforce? Suspension settings, pitch attitude, adjusting control parameters, understeer, optimize torque during power down? Why not do this? Probably because it's more information than your kids can handle, that's why.

Going too far into the real-world is not only confusing, it's counter-productive. You spend way too much time explaining something that winds up being taken on faith rather than being understood and the math you wanted them to get is lost in the descriptions of the curve of the wheel-wells. The jargon of the job overwhelms them. I love the concert hall question but you'd have to remove a lot before it became an algebra I question.

The other suggestions are interesting but not very particularly useful. Rabbit populations are not exponential (more sinusoidal) and not very relevant to the kids unless you have a fur farm nearby, in which case you'll start up the PETA alarmists instead of the graph-makers. Fibonacci was just doing a thought experiment anyway - in practice, the numbers are fairly complicated unless none of the rabbits ever dies and they all have 2 kits per litter.

If you want to model things, you need to pick the model carefully or the idea will disappear in the myriad details. If the relationship is supposed to be linear, stay away from the exponential data, and vice-versa. If you pick a real-world problem, you need to make sure that it will work out as you expect.

Appeal to Kids' Interests

Mindlessly connecting to kid's interests is a bad idea for a couple reasons.

One, the kids aren't interested in things that are mathematical right now. They are social beings and putting them in a social situation but wanting them to be mathematical is a frustrating and pointless exercise akin to moving Mt. Fuji with a spoon.

Two, which kid's interests? Baseball and softball overlap, but the goth kid is in his anti-jock mode and deliberately tunes you out for trying and nobody can understand the Valley Girl accent you're attempting.

Baseball batting averages are great for introducing percentages. Once. After that, only baseball freaks care and only if it's "their guy." The other 96% of the class is totally bored. If the entire software package is developed around baseball, I'd scream, too.

Third, How do you Know? If a kid is interested in something that you know little about, you risk looking foolish and stupid -- which doesn't achieve the goal you are trying for. Your "real-world" question is obviously contrived and tedious. This is why the "psuedocontext" questions in the book are so discordant. They aren't written by real people.

This may be hard to believe, but kids are okay with just learning something mathematical. Raw, pure math. Give them this just before they really are going to use it for a question THAT INTERESTS YOU and you'll have succeeded.  Forget their interests. "What use do YOU make of it" would be a better idea.

Finally, kids change. MTV is so last week. If you base your software on what was current just ten years ago, 95% of their world wouldn't exist. Are they interested in Spongebob or iCarly or Jimmy Neutron? Kid fads go out of style way too fast to try and keep up and there is nothing so dated as a teacher (or a computer tutor) trying to achieve "relevance."

Use Hi-Res Video

Hi-res video is valuable except when it’s not. The video has to show a problem. If it shows the sweat, blood and tears without a problem, then there is no point. Better to use a still picture that does than a video that doesn’t.

Make Students laugh

Making students laugh with corny one-liners that come out of nowhere only leads you nowhere. The jokes can be bad and yet still effective if they have context … like the joke that always comes up during discussion of integral of 1/x:

What’s the integral of $ \int \frac{dCABIN}{CABIN}$ ?
ln(cabin), of course. ("natural log cabin")
and when you add “C”, you get houseboat. (Better when you say it aloud.)

In the end

In the end, for me, it comes down to:
Get Real: real math, real problems.

Testing, Scoring and Trusting the Data

A fascinating case study is the NY Regents, scoring, and the unintended (or purposeful) consequences of a line in the instructions to the scorers.

First, here's the graph of the number of kids getting each score (from WSJ).  The issue can be seen quite clearly. The graph overall is a typical left-skewed distribution, as you'd expect from this type of test. The trouble comes when you explore that jump in the middle at the passing mark.

Of course, the nattering class is all up in arms over this, claiming fraud and misconduct.  You can almost hear jeers of "Union Bastards trying to save their jobs by lying on the tests."  Unfortunately for those people, the reason comes down to one sentence:

"[State officials] note that the state actually requires teachers to regrade certain Regents tests where the student barely fails in order to check for grading errors."

When you are singling out tests for special consideration, and the stated focus is to look for "scoring errors" on "barely failing tests", the only way for the scores to change is up.  Since it's easiest to give one or two points to a 64 or 63, it's logical that those would be the most effected.


Looking at the graphs, you can see that some teachers (probably a school at a time) set their cut off at 50 while the majority set the cutoff at 55.

Why the negative slope in that region? When looking for ambiguous answers which could be scored higher, you have to "rescore" each problem until you get an appropriate number of points. It's easier to find one such than 10 such.

Similarly, since there was no reason to check more answers than just enough to get the kid to pass, the uptick was only to 65, though it seems that many teachers weren't keeping close track of the extra points and brought the kid up to a 66 or 67.

Conversely, if the teachers had been instructed to rescore all students within ten points of the cutoff instead of just those who were below it, then you would have seen some students adjusted downward, balancing out much of the upward movement.  If there were a similar uptick at the 65 mark in this hypothetical, then and only then can you claim that teachers are deliberately mis-scoring to jigger their VA measures. (and even then, I'd put the reason as teachers wanting to help students rather than being so coldly self-interested.)

The place where I found the link to this article had this comment: "Teachers don't want to flunk kids that just barely miss the passing score. Until all responsibility for creating and scoring state exams is given to an independent body with no interest in the results of the tests, the results reported should be viewed skeptically."

Ummm, no. Scoring tests is really complicated.  Pearson, the biggest company, uses part-time, barely out of college, minimum wage people to do the scoring. Getting the "right" score is more a matter of whether or not the scorer speaks English and actually knows the material.

Frankly, given the mess that the testing industry is in when it comes to scoring, I have a feeling that the teachers are doing a more conscientious job. If you want a nasty introduction to the follies of testing company scoring sessions, check out Todd Farley's "Making the Grades." It's well-written but damn depressing if counting on accurate test scores because you're stuck in the hell of value-added and merit pay.

New is the Old New ... whatever.

Some years ago, Dan said

"The suspicion just creeps over me every coupla months or so that the constant introduction of new tools has left your average, well-meant educator a permanent amateur, able to save some time for herself using these tools, unable to do anything better. And since we're all in that same state, there exists very little peer pressure towards excellence, excepting occasional posts from certain School 2.0 curmudgeons."

 Add to that the constant introduction of "New and Improved" (read: different interface entirely) versions of the software we all depend on. In my career, I've gotten used to 13 different versions of Word which were mostly compatible with each other but only in one direction. Add to that, a couple of WordPerfects which were far superior to Word but the schools always used Word, so I had to change or suffer the incompatibility.

It's the same with a host of other software. I frankly don't see how most people keep up with it AND with the constant drumbeat of "better" ways to teach math. Throw in operating systems, schools behind the tech curve and the cost of software - and "Don't you dare install FOSS on your school computer.  That stuff is loaded with viruses."

Web 2.0 is little different. I've gone through three different blogging platforms so far -- fortunately they are roughly similar but they are constantly being bought, sold and changed.  The paradigm is changing monthly ... do you use blogs, forums, moodles, chat, text, email, IM, Skype?  Do you have any idea what your passwords are if you don't have them stored in your browser?  How do you circumvent the school filter to show YouTube video? (Me? I download the video and play it with VideoLAN.  Don't tell IT.)

Apparently, the only way to be a teacher nowadays is to be a tech expert.

Weight of the Argument

from Scott Macleod (Dangerously Irrelevant) comes this angst-filled twitter post:

and he asks: "Hmmm… What’s in there that’s not available in at least a dozen places on the Web for free?"

Well, organization, for one thing -- it's one book instead of "a dozen places on the Web" for each topic. Location, for another. Accuracy, for a third. Fourth, cost. Lastly, bias.

I'm all for free textbooks for the school, but those who write them occasionally want to get paid for their work. If the school buys a textbook, they have similar editions for all the students in the class and assurance that someone has vetted them for accuracy, minimal bias, and clarity for the level of student. It's also free to the student. The cost to the school is spread over several years. Online resources are currently too expensive or scattered and useless.

Bias is similarly easier with a book - Howard Zinn was a socialist. Knowing that meant you could easily work around it or extol it but you'd always be dealing with a known quantity. Websites change too often for you to trust them without verifying.

Hoo boy, trust. What if that website you linked to in August is kaput and serving ads in December when the parent tries to follow it -- or worse, gets squatted on by Stormfront -- and that parent hits martinlutherking.org (NSFW) instead of the main page for the King Center (the real one). A textbook gets vetted once.

Accurate? Accuracy matters: Read here:
Technology might be the Answer but not ... for the story of the definition of Radian.

I think the iPad (or similar) will be the textbook of the future, as soon as Apple drops the ridiculous iTunes Store file limitations and opens up the platform to flash. It would be wonderful. It's the right size, has color, can run video, touch screen and type, has everything except openness. We're close but until Steve Jobs realizes the goldmine he could be sitting on, we'll still have books. He'll charge for the convenience, but it would beat paper.

Free online doesn't necessarily mean free to the student. I've noticed that free materials invariably are better and easier to use when printed - that's a cost for the student, especially if we're talking about inkjets. It always amuses me when conference people make a big noise about "saving money, paper and the environment by not printing out notes and handouts" and then you look around at all the attendees who printed everything out themselves at their expense on less efficient inkjets. 

Then, there's readability. Those textbooks that are free on the web -- I'm thinking the California initiative -- are not easily read. I'm reminded of the study comparing ease of reading of Kindle, iPad, paper and computer screen (including laptop). "iPad, Kindle, and the printed book all scored fairly high at 5.8, 5.7, and 5.6, respectively. The PC, however, scored an abysmal 3.6." Imagine if they had been working with a math book? Again, I have hopes for the iPad or a similar, but it's not quite worth it yet.

Let's pretend that we're not printing out material, just accessing it.  How trustworthy is it?  Is it "Wikipedia good?" Has it been edited recently by someone who knows the truth or is the urban legend version of history taking hold here?  Just because everyone knows that "tea partiers" are the only true patriots doesn't mean that it's a true fact. I have confidence in that printed book.

Why is the online textbook free? Is it free because it's the pdf version of the second edition, copyright 1990?

Organization is another big issue for me. The material for a typical history or even math course would be so widespread over the internet, it would be a tremendous pain to find and collate. Why should I spend that time and effort finding and verifying what the book publisher is willing to do for me? Nothing will be free but I think that iPad (click above to enlarge) holds the most promise.

Then there's linkrot. I took an online thing this summer and 1 of the links had expired and was serving ads - less than a month after the link was created. You would have to recheck everything every year to be sure that the page hadn't changed nor had any others on the same site.

Finally, there's cost. You can't carry a desktop computer. Laptops and netbooks have a serious distraction issue, they're delicate and they're tough to read because of that vertical screen. iPad shows the most promise but, starting at $499, isn't affordable by every student. With an initiative, we could supply them to every student -- cheaper than a laptop -- and escape the problems with laptops in the classroom, damage, viruses, etc.

In sum, we're close. I can taste it already. We just need a little push.

Curriculum Makeover and Problem 11

It's summer and I now have time to sit and think about things. This time it's math curriculum makeover. We start with Dan Meyer's Rethink of a textbook problem. (seen at right).

"A water tank is in the form of a regular octagonal prism. The base octagon has side length 11.9 cm.  Then lateral edge is 36 cm.
a) What is the surface area of the base? 
b) What is the volume of the water tank?
c) If you pour water into the tank at a rate of 1.8 oz/sec, how long will it take you to fill the tank?"

Dan's take: "claims real-world but its only clip-art or a line drawing. Specifies the exact method of solution, and only gives useful information." So he filmed himself with a garden hose filling the tank with a timer available. Show the film and let the students ask "How long will it take to fill?" Here's a textbook editor's discussion of this problem.

WCYDWT: Water Tank from Dan Meyer on Vimeo.


There's a couple of things about Dan's treatment of the question that bugged me but I hadn't really thought about it till now.

First, of course, is that subtly, he changed the question to be ONLY about part c. There was no calculation of area or volume, just an approximate measure of time. If I am doing proportions, then it would be okay but, to me, the real point was ignored. Let me be clear on this: that video is cool. It worked for my students in the same way in worked for Dan's. It's a good way to start a section on proportions or rates.

BUT. I find the immediate solution method his students (and mine!) choose as being too simplistic and hands-on. Elementary and Middle school students need tangible, hands-on material and filling a tank with a hose is a fine way to bring them up to higher levels of thinking but it's not the point of algebra; high school students should be beyond that kind of simplicity.

Algebra is more abstract, more at an arm's length from the immediate numbers of a problem. The idea of algebra (to me) is to model something without having to count squares, count seconds slowly or tick off every single mark. I don't like it when the only solution that students come up with is "guess-and-check" or "counting squares" if there's a better analytical solution.

The video only works because the tank in the problem is small but even then the video was too long. (I'm not sitting through 8.5 minutes watching a tank fill up.) What if this were a town water system or a swimming pool? What if this "real world problem" is too expensive for guess and check, which is what a real world problem SHOULD be? (If it weren't too expensive or time consuming, you WOULD guess and check or count squares.)

I agree with Dan's comments elsewhere when he says that problems should be solved in an appropriate fashion and that often textbooks will invent something just for the rather lame use of the topic du jour. I get that argument. I don't think problem #11 is such a problem.

It could have been stated with more pizzaz and could have been given more "connection" for the students, but AZZA math teacher, I should provide that myself. "I need to know the volume in liters because I have to add salts to my salt-water tank in exactly the right proportions -- the fish are delicate and EXPENSIVE. I can't guess and check with $100 fish."

Second, the givens should be real-world, too, and I think Problem #11 does that. Physically, you can measure the outside edge, the height. Had the problem given the apothem or the radius of the circle enclosing the base - how would anyone measure that accurately? Diagonal through the center - yes! Now you're thinking.

Showing all those measurements would be a good thing but ultimately you have to decide where this problem is in the scaffolding and plan accordingly. A few extra numbers go a long way in allowing the students to explore without having the tank in front of them but they also confuse the hell out of those who are just getting the idea.

Bottom line: Keep the video but don't use it for just a volume calculation. Use it for proportions or rates.

Go read something.

Go read Robert Talbert's comments on Calculus books, calculus reform and the best classes for freshman.

Teacher Magnet School is Bad

h/t to Darren,

Students at the Teacher Training Magnet School don't understand math, or English for that matter?

Crenshaw Senior High 5010 11th Ave., Los Angeles, 90043
» Schoolwide Performance California Standards Test (STAR)
Students scoring proficient or above: English 18.9% Math 2.3%
# Students in advanced math: 15%

No Child Left Behind (AYP)
Fail: Missed 16 of 23 federal targets for 2009
Fail: Missed 25 of 25 federal targets for 2008
Fail: Missed 16 of 22 federal targets for 2007

SAT Reasoning Test Composite Average 1098
Math: 363 Verbal: 367 Writing: 368
Source: state data reported for 238 participants

How is this possible? An average of 363 means that some were higher and some were lower. The standard deviation for the SAT is about 100 points. Think about that. Then consider that these folks are in the teacher training program.

This is Crenshaw Teacher Training Magnet School.

---

LA's 141 Magnet Schools, Ranked in Ascending Order.
(percentages are percent proficient in Math, English

Dorsey Police Academy Magnet 0.0% 16.3%
Washington Communication Arts Magnet 0.0% 29.8%
Crenshaw Teacher Training Magnet 1.1% 28.6%
Washington Music Academy Magnet 1.2% 45.5%
Washington Math/Science/Technology Magnet 2.1% 36.5%
Fremont Math/Science/Technology Magnet 3.7% 39.8%
Dorsey Math/Science/Technology Magnet 4.4% 38.3%
Jordan Math/Science/Technology Magnet 4.9% 45.1%
Wilson Police Academy Magnet 5.0% 25.0%
Dorsey Law/Public Service Magnet 5.6% 36.6%
Manual Arts College Prep Magnet 7.0% 30.9%
Wilson Administrative Law Magnet 7.5% 44.9%
...

Teacher Training Magnet is one of the worst. Couldn't see that coming.

Majoring in Math

EdWeek has an article on this. It's behind a login portal, but they made it available for a while.

Essentially, they argue that the value of a math major for middle teaching is small but noticeable. I'm not surprised that there isn't much benefit. People who enjoy math enough to major in it are not usually the ones who can deal with teaching kids how to add fractions. They are also VERY unable to deal with other teachers who insist on using calculators instead of teaching long division.

What we need, however, are elementary and middle school teachers who are capable of doing higher level math and who understand what's going on.

Gee, is American Thinker Conservative?

Read this American Thinker article on paying students to work and go to school.

Here's my response, lost amoung all of the ditto-heads who are condemning these kids as shameful losers:

This sounds fishy to me. The writer can't write clean, grammatically correct sentences - this is a teacher? I'd have to see corroboration before I believe it.

It reads like he is mentioning only the extreme cases that feed his own pretentious ego. "Look at all those losers. I, the great and mighty know-it-all white boy, would never do something so stupid."

Dude. The first time ANY kid gets $600, they're going to blow it on stupid things, and any group of kids will have some with alcohol and drug problems. If the deal is made - do this and we'll pay you - then the "teacher" should get off his high moral ground and let them make mistakes and learn from them. If he can't do that, he shouldn't be in that position.

Also, they were scheduled to clean for five hours and school for three. How about we find out whether they worked well for that time and earned the right to "waste" their money? You know, by buying a computer and wasting all their time reading American Thinker and making snarky comments.

Methodology

I am a collector of methods. I like finding new ways to do the simple operations and neat new ways to look at mathematics. I do not feel these methods should be shown to students.

Teach one method. I am in favor of the algorithms that I grew up with. Old fuddy-duddy? Maybe. Tough. The old ways work. The old ways are usually simpler and easier to use.

Think subtraction. 759-384. Do it your way. Now try to follow this.

Why are we bothering to re-invent this wheel?  Isn't one way sufficient for the students?  I feel we should wait until they have completely understood one method before we confuse them with "Other" possibilities.  If a student comes up with this on his own, great. 

Sheesh.  No wonder kids get confused if this is what they're taught.
h/t to parentalcation

Fun on the Stairs = >> Fun in the Classroom

In the Fun Theory, Joanne Jacobs points to this youtube video of people using a staircase piano instead of the escalator ...

We see some people using the stairs instead of the escalator because it's "more fun" and immediately, everyone thought of the connection between "making the classroom fun" and learning. The comments range from gushing enthusiasm for fun in the classroom to a resigned knowledge that the next Professional Development will be centered around "Games, Games, Games!"

Interestingly, (to me at least, but I think deconstructing studies is fun) the researchers claimed that "fun" was why the people took the stairs. I tend to think they did so because they just got off the subway and for twenty seconds or so, they are mindlessly entertained by stepping on the "keys of the piano." I'm sure that many people were interested the first time, mildly interested the second, annoyed the third time and royally pissed off thereafter. "Stop repeatedly pressing that key. You're not being clever!" How many people just wished the thing would go away after three days? How many just wished that there was a staircase they could run up to avoid the "newbies" who thought it was cool? No one knows because no one asked.

How much did people learn? Nothing. What the researchers were trying to do was see if people would take the stairs rather than the escalator - a fitness and exercise question. It took teachers to make the mental leap to education. Thus is educational research performed.

The reality is that learning something new takes concentration and work on the part of the learner. There is no "Royal Road to Mathematics". A Game might spark interest, or might take the student on a temporary hiatus from their concerns, but the hard work needs to be done eventually.

Hard work is not always hateful. Several hours of shoveling a hole for a gazebo foundation can make you feel exhausted but invigorated. For me, three hours of a math contest is fun. The fun comes not from the game, but from the overcoming of a challenge. For others, it's seven straight hours practicing a snowboard trick and finally "nailing it." The ADD kid in one of my classes will spend hours practicing his guitar, fully focused and on-task. For the kid next to him, that would be torture.

As Churchill was rumored to have said, "There is nothing more exhilarating in this world than to have your enemy shoot at you ... and miss." If the "enemy" is the complicated new material, and the "miss" is your succeeding at the task in spite of a perceived "trick question" or a difficult learning process or a "difficulty with math", then the students do in fact achieve learning with that sense of exhilaration that we so often attribute to "fun activities."

The thing to keep in mind, though, is that the "fun" and the exhilaration came AFTER the success and hard work. The success was not caused by the fun.

All that you do by stressing the fun game that happens to teach math facts is to cement your place in the world as someone who is hopelessly lost, clueless and unconnected to the students.

Most of the time, the fun activity doesn't achieve anything other than to be a fun activity and save the teacher and students from working. They aren't going to learn much beyond the first gee-whiz moment. Certainly not any details or deeper understanding.

It's as simple as one blink of an eye. Take a look at these two pictures. Which kids are learning?
See what I mean?

But then I read the comments.

I loved this video! I think there is a lot of potential for making learning fun. Why assign a worksheet on multiplication facts when kids can play a game that reinforces the same concepts?
When I was a psych major in college I had a stats professor who felt that students learn best when experiencing an emotion – he chose fear, which doesn’t seem like the best choice. But why not excitement – joy? Thanks for sharing!

You can hear the ProfDev now: "Math should be fun. The kids should learn effortlessly. Video games will teach them. Why shouldn't we make shoot-em-ups that require the kids to solve math problems?"

What's wrong with this picture? For one thing, this wants to teach without working at it. "Math should be exciting, joyous?" Why does she feel this way? Perhaps it's because, for her, math isn't fun and games are the only thing she can think of. The sheet of multiplication facts might not excite you, but completing one correctly can excite a student.

...With the test in front of me, I started sweating, and my brain began buzzing, but I forced myself to calm down and keep my fingers still. Most of the problems seemed easy now, although I realized all my "shortcuts" had left me weak in long division. There were no red marks this time — I had gotten 100 percent right!

The shortcuts she's referring to are the calculator, counting on fingers, not completing certain practice drills by herself. Drill and kill. It wasn't "fun" so she "cheated."

There are plenty of puzzle-type video games. I happen to know many of them. Why don't kids play them? "Because they are BORING." The puzzles and problems are artificially inserted into the "story" and the whole thing runs counter to the reason most kids play video games. For fun, to conquer, to compete and win, to create and display, to show-off. "To solve math problems" isn't usually one of those reasons.

What happens almost immediately to kids playing a game with puzzles? If it has some fun elements, the kids will play it. If they run into a puzzle they can instantly solve, they solve it and move on. If they can't instantly solve it, they use cheat codes or look up the answer online. Then they go back to shooting monsters.

Great if you're selling a video game. Not a good model for education.

Math in the Crosshairs again, this time Maryland

"... many graduates do not have a grasp of the basics."
"... schools have deemphasized drilling students."
"... taught too early to rely on calculators."

A calculator is a tool. It should be used as a tool. As soon as it replaces thought, it should itself be replaced.

I have decided to make a new slogan, signifying my reluctance to rely on the thrilling new technology of calculators because of the very real effects on the kids' development.

"Thrill and Kill."

"... ninety-eight percent had to pay for remedial classes." Okay, it's a community college and you expect that many of the attendees would be looking to improve their math skills. But 98% ??

"Across the nation, slightly more than one-third enroll in remedial classes." That's bad, people.

The report gets specific but, in my view, misses the mark. " ... particularly critical of the Algebra I standards, saying that they are watered down because educators must teach material for the High School Assessments, which includes data analysis. It is not what any mathematician would consider an algebra course."

No, I think the algebra I course is watered down because, (A) it is taught to eighth graders and they had to water it down so they could pass more easily and (B) mainstreaming and the refusal to place students in an appropriate class means that every room has kids who slow down the group. This insistence on placing kids in a course based on emotion, faulty pedagogy, self-delusion and parental desire instead of mathematical ability will ruin your classrooms every time.

Anyway, the article that started this train of thought appears below the fold.

A failing grade for Md. math
What is taught in high schools seen as insufficient for college
By Liz Bowie | Baltimore (MD) Sun
July 12, 2009

Maryland's public schools are teaching mathematics in such a way that many graduates cannot be placed in entry-level college math classes because they do not have a grasp of the basics, according to education experts and professors.

College math professors say there is a gap between what is taught in the state's high schools and what is needed in college. Many schools have de-emphasized drilling students in basic math, such as multiplication and division, they say.

"We have hordes of students who come in and have forgotten their basic arithmetic," said Donna McKusick, dean for developmental education at the Community College of Baltimore County. College professors say students are taught too early to rely on calculators. "You say, 'What is seven times seven?' and they don't know," McKusick said.

Ninety-eight percent of Baltimore students signing up for classes at Baltimore City Community College had to pay for remedial classes to learn the material that should have been covered in high school. Across Maryland, 49 percent of the state's high school graduates take remedial classes in college before they can take classes for credit.

And the problem has been getting worse. The need for remedial math classes among Maryland high school graduates who had taken a college preparatory curriculum and went on to one of the state's two- or four-year colleges rose from 23 percent in 1997 to 32 percent in 2007, according to an Abell Foundation report released this spring.

While the problem is worse at community colleges, 15 percent of the freshmen at the University of Maryland, College Park must take a remedial math class before being able to move into college-level classes, said Denny Gullick, a math professor there. Some of those students come from out of state.

For Gabrielle Martino, holder of a doctorate in math from the Johns Hopkins University and a co-author of the Abell Foundation report, the bottom line is that students are being harmed because they have to pay for the remedial classes. When they get to college, "they are uniformly shocked that they were put into remedial math," she said.

The report recommends that the Maryland State Department of Education revamp its math standards and curriculum. The standards and curriculum determine what is tested on the Maryland School Assessments and, therefore, the material teachers are told to cover in their classes. And each year, the number of students passing the math MSAs has gone up, even as graduates are increasingly in need of remedial classes.

State education officials do not believe that major changes to the standards are needed.

"Obviously, we want our students to be successful when they go to college, but we also know that a number of the students who go to university haven't taken the math preparation that would enable them to be prepared," said Dixie Stack, director of curriculum at the state education department.

The call for change comes at a crucial time. The state is reviewing its five-year-old standards, and the National Governors Association is expected to release its common core standards in a few months. Maryland is one of 46 states that have agreed to support the development of those standards, essentially setting a national curriculum and testing in the core subjects of reading and math.

The question of how math is taught and what should be emphasized has been the subject of a long-running debate across the nation. Some math teachers have advocated giving students a deeper understanding of how math works while de-emphasizing the drill of solving many problems and learning math facts. On the other side, teachers say students need to be well grounded in the basics in order to move on to higher-level math.

State school board member Kate Walsh does not believe the state is alone. "Maryland has as much of a problem on its hands as any other state," she said.

Across the country, slightly more than one-third of college students enroll in remedial courses.

"This is really a national problem. States are working hard to address it, but the fact is that too many students require remediation when they enter college. The problem is more severe in math," said Danette Howard, director of research at the Maryland Higher Education Commission.

The National Council of Teachers of Mathematics has argued that no matter how math is taught, students should be focusing on fewer concepts each year. The group said students have knowledge that is a mile wide and an inch deep, and that school districts should teach fewer concepts each year and in greater depth. Presumably, that would enable students to master each concept and move on so that yearly review would be unnecessary.

Maryland public schools seem to be doing a better job in teaching math to top students, Gullick said. More students have been given the opportunity to take higher-level classes during their elementary, middle and high school years, and they end up not only having completed calculus, but often having taken the rigorous Advanced Placement calculus and scored at the top level on the exam.

"A third of the freshman class has taken AP calculus and placed out of calculus" at College Park, Gullick said, adding that the percentage of these high-level students has been growing.

On the other hand, he said, "we have seen a marked decline" in the skills of the students at College Park who are not considered in the "top caliber."

"We have an enormous number of students who have no arithmetic skills. This is a big issue," he said.

The Abell report is particularly critical of the Algebra I standards, saying that they are watered down because educators must teach material for the High School Assessments, which includes data analysis.

"It is not what any mathematician would consider an algebra course," said Stephen Wilson, a math professor at Hopkins and a co-author of the Abell report. "It is Maryland's image of what math is without consulting a mathematician."

Stack said the Algebra I High School Assessment is not intended to ensure that students are ready for college but to make sure they have the minimum skills needed to get a diploma. The standards that the test is based on are "intended to establish a floor for freshmen in high school, and by itself it does not constitute an Algebra I course," she said.

The fact that the state has a minimum standard does not mean a school system cannot teach at a higher level, she said.

Stack said she does not believe the state should make changes until after the release of the national standards being developed by a grass-roots coalition of 46 states. To do so would be a waste of time and taxpayer dollars, she said, because Maryland probably will adopt those standards.

However, Walsh said Maryland should alter its standards to meet mathematicians' concerns. She said she does not believe in waiting, because the process could take years.

"Maryland is taking a go-slow approach," the state school board member said. "I am afraid the push for national standards, while a good sign, will delay the equally important examination we need to take. ... I would prefer to move aggressively."

Frederick Chapple, an assistant professor of mathematics at Baltimore City Community College, said the city schools require students to take an Algebra II class before they can graduate, a requirement that is more stringent than the state's. But the level of the course, Chapple said, isn't Algebra II.

"There should be more collaboration with colleges to be sure that the Algebra II that is being taught in high school is on the same level as the Algebra II that we are teaching in remedial classes," Chapple said. He said high schools should provide all students with a college preparatory curriculum, so that if they decide in their last year of high school that they want to attend college they will be prepared.

Gullick and other professors say they want to work with public school teachers and administrators to determine what must be done to remedy the problem.

Students are being hurt by the current system, Gullick said, and changes should be made at high school and college levels.