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Two comments:

1) There are good teachers and there are bad teachers. Please don't tar all teachers with the same brush. (I know you said "tend" not "all" but every other part of this post implied a broad brush.)

2) Sometimes we really do need to teach process. If I wait until the programs are complicated and the algorithms can't be held in your head to teach test cases and documentation and encapsulation for the first time, then they're hard. If I step my students through the design process on something simple like is_equal_to or even get_x, then they can start to build good habits so they're ready when they need them. "But I can just write this method and know it's correct just by looking at it." "Well, I should hope so. Fortunately, that's not the point here."

If you're teaching the process, teach the process. Don't set up a project with a clear objective, force students to rigidly follow exactly the steps you yourself took to get to that objective, and assume the process transfers to the students through osmosis.

This is a sore point with me; I'm in a minor conflict with one of my 7th grader's over an assignment he aced in which he's being dinged for (bogus) process faults.

What's worse is, my 7th grader has generally excellent teachers. I don't buy that this is a "good teacher / bad teacher" issue. I think it's a methodological flaw common to all standard secondary schooling programs.

> If you're teaching the process, teach the process.

I do, thanks.

> Don't set up a project with a clear objective, force students to rigidly follow exactly the steps

I really do not understand what you're saying here. You want me to teach the process but then not evaluate whether students can do the process?

> you yourself took to get to that objective, and assume the process transfers to the students through osmosis.

With your "you yourself" comment you sound like you're objecting to the very idea of teaching process; and why are you assuming that I'm attempting some sort of osmotic transfer?

Here's a project: write a research paper. This paper accounts for 2/3rds this semester's English grade; in other words, it's the major learning objective of the class this semester.

What we're going to do is, here's a project rubric. It breaks the research paper into a series of steps. You make little cards for sources. You organize the cards to "brainstorm". Your turn your brainstorm into an outline. And so on. You're going to follow all these steps, and most of our class time will be spent with you working on these steps and then me, the teacher, evaluating your progress on the steps.

In the end, your grade will be 50% based on the outcome of the paper, and 50% based on your timely adherence to the rubric.

What's wrong with this teaching method?

It prioritizes the "research process" in the assessment, but does not actually explain what the research process is or why it works that way. It presumes that standing up in class spending 5-10 minutes saying "here's why we make little cards, so we can brainstorm" provides adequate context so that combined going through and following the steps, students are learning a research process. That it allows for no other alternatives to the process of organizing a paper is of secondary concern; the primary concern is, it doesn't sell the process, it simply mandates and then grades on it.

An alternative method to teach the research process: have the students pick a research topic and then write a paper on it without following a formal process. Evaluate the papers; they're poorly organized, they don't make coherent points, they lack sourcing, their sources are inadequate, &c. Now do another paper, focusing on how the research process is a corrective for the flaws in the first paper.

This seems strictly better than "You didn't turn in a printed outline in the correct format before handing in a fully cited first and then final draft of the research paper. 50 points on the paper. 10 points on the process. C- for you."

This example extends to every other process-focused assignment I've seen my kid deal with in school: "here's an ambitious outcome, here's a rigidly specified process, and here's a grading system that assesses each individually". This is a great scheme for teaching smart kids why not to take "process" seriously.

I am 1000% sure you do things better than this. This is a message board. Everyone is always the exception to the rule.

I had to go through this exact same process in High School. I almost shot my self. I ended up getting a D- on the paper.

The process is so deeply flawed here is one example. I have my sources, my note cards, and my outline. Each note card had on the front of it a single sentence and on the back of it the source written perfectly according to some standard (I lost many of my points because I would forget a period or comma). Each note card then had to be perfectly ordered (and wrapped with a rubber band and with each paragraph having a paper clip on it) and have the corresponding number written on the back and then circled.

If I wanted to change the 2nd sentence in my paper, I would have to completely renumber all the note cards.

If I wanted to change a word in my paper I had to cross out the word on the note card with ONE line through it and then rewrite it on the notecard and then change it on the computer.

If I wanted to change the structure of my paper, I had to go back and rewrite the outline. I've always considered the outline the "black dot" of a painting. It's hard to start painting on a blank canvas, but as soon as you put a black dot on it you have something to fix, build off of, whatever. The outline puts the first 2 -3 paragraphs on the paper and the rest of the time you ignore it.

Retyping this and thinking about it has made me literally feel physically sick.

Thank you for spelling this out in detail.

I took a user interface design course a few years ago in college (good college, good lecturer, good students), and was frustrated by exactly the same problem.

The focus of the course was learning process rather than making things, but we only were able to touch each particular process step (paper prototyping, user testing, formal usability study, &c.) one time, for a week or two of an assignment about it, and so there was no great way to judge improved understanding after having done the exercise, or experiment with different methods to see what their faults were.

Because most of the actual effort in the course went into writing about what we had done, instead of doing it, I feel like we learned quite a bit more about (a) describing our group’s working habits and parroting back the theoretical benefits of particular processes than we did about either (b) performing those processes or (c) the actual project we were trying to build.

The only way to really make these meta-analyses of process and structure valuable is, as you say, to take them on after having tried doing the thing a few times. You can’t make a map in your head of ideas you’ve never experienced by just copying other maps. It’s like trying to design an API without knowing what the use cases are, or trying to pick a data structure before you have idea what the data looks like.

* * *

This type of instruction is far too common; pedagogical exercises are decontextualized and the means become the ends. Instead of learning languages by reading and speaking, with explanations of grammar and bilingual dictionaries as reinforcement and an ultimate goal of conversation/writing fluency, language classes help students to perfect their ability to learn and perform grammar drills. Instead of trying to write and discuss stories, using writing as a tool for clarifying thought and sharing ideas, English classes spend all their effort and attention on teaching narrow rather uninspiring process and rigid form. Instead of finding math and physics problems in the context of figuring out how something works, we put the problems in their own little boxes and pretend they’re discrete entities, and students are expected to just grok the patterns without having done the kinds of doodling and exploration that ever actually reveal their structure.

Unfortunately, without much smaller student:teacher ratios, it’s really hard for teachers to act as guides and mentors rather than lecturers.

> ... given a maze and a cheese, any route to the cheese more efficient than the one the teacher suggests is morally suspect.

Somewhat off-topic: The peer-instruction (PI) movement just launched an online community [1]. This semester I've started using a variation on PI in the law-school course I teach (advanced contract drafting and -review). It seems to be working well, and the students really like it.

"The PI technique relies on the power of the 'flipped classroom.' Information transfer (i.e., a teacher transferring knowledge to students) takes place in advance, typically through online lectures. In short, students study before rather than after class. ¶ As a result, the classroom becomes a place for active learning, questions, and discussion. Instructors spend their time addressing students' difficulties rather than lecturing. ¶ While originally developed for Mazur's introductory physics courses, PI is now used across multiple disciplines, from the sciences to the humanities."

Of course, this all presupposes that the students will actually do the reading in advance, which is not always a given with 3Ls ....

[1] http://www.seas.harvard.edu/news-events/press-releases/peer-...

You have what appears to me a bias against teachers. I find this curious given one of your products.

I personally think that bingo is a worthless activity but I don't thrust this opinion on other teachers. Personalities come into play with teaching. I could never make a bingo activity work in my class because it is antithetical to my personality. But some people do make it work. And with 30 people in a class is it reasonable to believe that all 30 will enjoy the activity or find merit in it?

I sometimes hide knowledge from my students because I want them to see it for themselves. Do you know how hard it is to get someone to understand that -4^2 is -16 and not 16? I can say this fact ad nauseam and it just doesn't click until a person sees it. They have to be guided into understanding this. Me telling them it is so and explaining it doesn't work.

At any rate it seems you have a bias against teachers. Have you taught much? When was the last time you were in a classroom?

Wait - I thought -4^2 was 16 not -16. But then the 2^3^4 discussion here lost me as well.

-4^2 is -16. (-4)^2 is 16.

Order of operations. -4^2 is equivalent to -(4^2).

heehee, programmer's error. -4 is assumed to be the value, and not seen as -1 * 4, which i believe is the interpretation.

order of operations is a useless source of confusion -- we should just use parens always and avoid ambiguity. #toomuchcprogramminglately

I tend to agree, and always did explicit parens for that sort of thing. Then again I use parens in ruby code, too, so maybe I just like them a little too much.

You could argue from consistency that the standard convention is more aesthetically appealing, though. I tried writing this in a HN post but it boiled my brain so I sketched it on the back of an envelope instead.

http://images2.bingocardcreator.com/blog-images/hn/arithmeti...

Basically, assume high school algebra works the way you think it works. If we treat unary negation like it magically grabs the nearest integer prior to the exponent happening, things we assume are equal in high school algebra start to break catastrophically. You'd have to invent a new and perhaps uglier way to do algebra which would lose properties like "moving terms around the same side of an equation on paper for clarity is allowed because it doesn't change what they sum to."

Anyhow, if this ever comes up in my household, I'm going with "Yeah, that one's weird. Your dad didn't like it either, but convention is that -2^2 is -4. That's totally separate from math, it's just how we choose to represent math in squiggles, and this collection of squiggles is supposed to be read as -1 * (2^2) instead of (-1 * 2)^2 . Why did we pick that math-to-squiggles mapping? Long story and kind of boring, but it's sort of important that everyone read the squiggles the same way, for the same reason that we don't get into an argument over which side of a road should be called 'left' and then smash our cars into each other. Either way would have been a perfectly good 'left' because left is ultimately just squiggles, but now we're stuck with one of the squiggles."

At the risk of getting off in the weeds, I'd rather re-frame the problem here as to wether unary negation makes sense as an operation, at all!

In my ideal world, -EXPR would be a parse error, and it would only be valid to write -LITERAL * expr. (-1 * a.) So, you could have -4^2 is 16 because the - would not associate to the nearest constant, but rather be part of the 4-value.

The reason for this is that -a^2 is super confusing, and I believe it should be treated as invalid. I do not think that promoting the order of precedence of unary - is the best solution because it leads to the common confusion of thinking "well, a is already negative, so there is nothing to do". if instead this was explicitly -1 * a ^ 2, then you can always "plug and chug" with simpler rules.

Essentially, the confusion is because unary negation is the only operation that is confuse-able with the value definition.

Final qualm against unary negation: what does --4 evaluate to in ruby? 3? No. 4.

If I had my way, then --4 would clearly be invalid because the inner -4 could not receive the unary negation.

In more programming stuff, I think that mixed-type operations should be illegal (no implicit casts!) adding an int64 to an int32 and storing the result in an int32 should be a compiler error!

I've found that most people will correctly do

1 - 4^2

The answer is -15.

So what is

0 - 4^2

Most will say -16.

To be consistent we must agree that -4^2 is -16 since it is the same thing as 0 - 4^2.

It takes a while for students to understand this. I still get calculus students who mess it up.

I am occasionally critical of every profession I've ever been a member of, including software developers (get me started on how well we understand the typical user someday), salarymen (get me started on... anything), translator (get me started on professional ethics), research assistant (get me started on code quality in an academic setting), and while I don't have a specific complaint about "seasonal order entry operator" if you give me a minute I can probably come up with one. I'm not even a very negative person -- I actually like teaching quite a lot. If it isn't obvious, pick a different set of two comments from me to generalize from and you'd assume that I'm a rabid fanatic about it.

Do you really want to play the "you're only allowed to have opinions on pedagogy if you're a real teacher" game?

The bias I perceive in you is not based solely on two comments you've made. It's just two comments that I've responded to.

I'm not playing

"you're only allowed to have opinions on pedagogy if you're a real teacher" game

as you put it. Anyone is allowed to have opinions about anything. Some opinions have more merit than others. Some people have worthy opinions on topics that they don't have direct involved with.

I've met lots of people with strong opinions on teaching. I've found that what superficially seems obvious to non-teachers often times miserably fails when you've got a class of 30 students with varying abilities and interest in learning. Anecdotally I'd say a majority of opinions from non-teachers about what would be great in the classroom only holds true if the classroom contains people desiring to learn.

Well, I asked about your experience in the classroom because I wanted to know if the thoughts and ideas you've expressed about what is not useful in the classroom is based on your teaching experiences on your student experiences.

I used to have strong feelings about k-12 teaching. Two years ago I was in a project that paired a college teacher with an 8th grade teacher at a local school. It took one day in the 8th grade class to realize that I don't know squat about k-12 teaching.

In that case, most of my teaching experience was at the K-12 level, in small groups and classes of 25 through 40. Some in a classroom, some outside. I also tutored college students for a bit. Many kids wanted to learn, some not so much.

Your turn. Do your opinions come from actual experience or do you have a bias against elementary schoolteachers?

You taught in k-12?

I have no experience in k-12 teaching other than the project I was on two years ago. The project I mentioned in my previous post. I definitely have a negative bias toward what is done in k-12 but my experience two years ago made it clear that my views on what should be done to fix k-12 education were not based on sound evidence.

I do have 17 years of teaching experience in higher education.

I once co-taught a class with a colleague. She taught the first 8 weeks. I taught the second 8 weeks. It was calculus II. Students getting Cs and Ds under her did quite well with me and vice versa for the A/B students. Personality plays such a great role in the whole issue that I've begun to think that there is no way to fix education. I think it is a hugely complicated issue and that positive results are local to a classroom and the personality of the students/teacher.

This is the second time in 2 weeks someone has chimed in on an HN thread to change a discussion from "something involving education" to "whether Patrick McKenzie has a bias against teachers".

If you disagree with a thought someone expresses on HN, address a comment to the thought. Redirecting the discussion towards the motives of the commenters isn't simply uncivil; it's boring. No. Worse. Hygroscopically boring. It sucks all the juice out of the whole thread.

I am partly irritated by this because I know Patrick does not have a vendetta against teachers. I am partly irritated because I know the "bias" Patrick is displaying here is a hacker trope: if you interviewed 100 hackers, 95 of them would say the same thing about secondary education. But I'm mostly irritated because it's a clear example of a superficial argument. "Hacker vs. teachers". Who could possibly care? He's not biased against teaching... but if he was, so what? In what sense would the thread possibly be different?

He makes a product geared toward teachers. He made a comment about busywork in the classroom and, what appeared to me, to be against this and against activities that hold brighter students back. I find it interesting because using bingo cards in the classroom can easily fall into this category. My comment addressed this apparent disparity. There was nothing uncivil about making an inquiry into this.

It's too bad you don't see something interesting in this. I do and hence made the comment I made. I strongly disagree with your view that my post was inappropriate or should not have been made. I'm not planning to change.

You don't appear to understand how Bingo Card Creator works. Go visit the website. I'll wait.

Back? Did you notice, on the website, the near total absence of advocacy for using bingo cards in lesson plans? Or even how classroom bingo works? Patrick sells BCC passively. His entire marketing system presumes a continuous feed of people who already wanted bingo cards.

The pain point he solves isn't "how to automate classrooms with bingo cards".

It's "how to automate the bingo cards for your classroom bingo day".

There's exactly one argument you can make about Patrick's business that would even be germane to your argument: that classroom bingo is so radioactively evil that simply enabling teachers to do it is harmful. I don't think you believe that. Instead: you didn't like something someone said on a message board, so you went looking for reasons to discredit them. In this case, you failed.

You should have more confidence in your own opinions. You have actual K-12 educational experience; it should be easy for you to use actual logic to refute things people say about it.

Wow. Your logic is quite bad.

1. Man criticizes worthless activities in the classroom. 2. Man creates product to help teachers with their bingo day. 3. Bingo day can be considered to be a worthless classroom activity (I'm such a person. I'd never use bingo in the classroom.) 4. I point out an apparent disparity.

It's ironic that a person who decries worthless classroom activities creates a product to make it easier for people to engage in a worthless activity. I made this clear in my previous post.

What I wrote is quite logical and reasonable. Your second to last paragraph contains assumptions not supported by the evidence.

Bingo obviously can be considered a worthless classroom activity, but so far that seems to be nothing more than your personal opinion, which is not binding on Patrick or other teachers.

I would say it is worthless only if you do not value the students' enjoyment. Teachers usually turn to bingo to help keep students engaged, which is the opposite of what Patrick seemed to be referring to as "busy-work." Accusing somebody of hypocrisy because he violates your standards is not remotely fair or reasonable.

Of course it's my opinion. I think it is a worthless activity. I would never use it. Others would be successful with it. That was my point to Patrick. He found some activities worthless and abstracted that to an opinion about worthlessness in the classroom. In a classroom with 30 people some are going to find virtually any activity worthless. You can't please everyone and so making a general statement about worthless classroom activities is not helpful.

I didn't accuse Patrick of hypocrisy. I accused him of irony. Big difference.

Next, Mr. Taylor announces it's time for Multiplication Bingo. As Mr. Taylor reads off a problem ("20 divided by 5"), the kids scour their boards, chips in hand, looking for 4's. One girl is literally shaking with excitement. Another has her hands clasped in a prayer position. I find myself wanting to play. You know you're in a good classroom if you have to stop yourself from raising your hand.

http://www.theatlantic.com/magazine/archive/2010/01/what-mak...

For whatever the data point is worth to you, I don't think you have a strongly-held opinion about bingo in classrooms. I think you have strongly-held opinions about anyone who criticizes standard K-12 education orthodoxy.

  >> Have you taught much? When was the last time you were in a classroom?

I have spend at least 20 years in classrooms as a student. I think this qualifies me to have an opinion on what teaching methods I found effective, and observed to be effective with others.

I don't believe that having been a teacher is a requirement in order to have come to valid conclusions.

It qualifies you to have a worthy opinion about what works for you.

Are you sure that what works for you scales well? I don't remember much of day to day activities in elementary school. I did go to elementary school. But I don't think my opinions on elementary school teaching necessarily are accurate even when applied only to myself as a youngster.

One doesn't have to be a teacher to come to valid conclusions. I think though that most conclusions that don't include an acknowledgement of the importance of the teacher's personality coupled with students' personalities is most likely not valid.

  >> One doesn't have to be a teacher to come to valid conclusions.

I apologize if I misunderstood you, but your previous post gave the impression that that is precisely what you thought.

>> Have you taught much? When was the last time you were in a classroom?

I must say your chosen example is a bit poor since the precedence of unary negation vis a vis the binary exponent operator is arbitrary and varies according to the arbitrarily selected rule system selected for the task at hand.

Promoting one arbitrary choice over all others as if it is natural, obvious and correct is clearly the source of difficulties explaining to students. When I have taught this topic, I cover precedence rules as being arbitrary and show a chart of the rule system in play for western math textbooks. This clears up confusion, or rather prevents it from occurring in the first place.

"This clears up confusion, or rather prevents it from occurring in the first place."

Not in my experience and I venture to guess that you haven't taught developmental learners. Obviously one discusses the order of operations and the fact that the order is arbitrary. This does not prevent confusion from occurring in developmental learners.

I don't know about these "developmental learners". I've taught students in college, high school, and elementary school. Mostly bright kids in elementary, and a wide range of skill levels in high school and college. Your responses to others here consistently dismiss others' personal experiences and knowledge while touting yourself as the only reliable expert. Frankly your responses here to others are so argumentative and belligerent I'm having a hard time imagining you're really such an expert in the things you claim.

You are incorrectly interpreting what I've written if you think it has been belligerent. I'm not an expert and have not claimed to be an expert. I do have extensive experience with developmental learners of mathematics. Think adults who are innumerate.

I did preface my response to you with, "not in my experience". It is not a valid conclusion to say that my remarks have been belittling. Based on what you wrote above it looks like my guess that you haven't had much experience with developmental learners appears to be correct. I stated my experience was different than yours. What is there to be upset about?

Yup, same thing all around the world. Teachers have "off" days too where they do the same thing. Crossword puzzle is a common one they keep in the backdraw just in case they don't feel like teaching that day.

It's one reason I'm pro electronic teaching aids like Khan Academy - more suitable learning, at the kids level and less "human downtime".

I wrote about it in my app to startupworkaway but I was chastised for programming a solution to a 'math challenge' in the 9th grade. The challenge was to take the numbers 1 4 7 9 and the operators ( ) * / + - and using each number exactly once formulate expressions that equal 1 to 100. So 1+4+7+9=21, etc.

I wrote a bash script to do it for me and came to class with every possible answer printed out. I was disqualified for 'cheating'.

To be fair, on occasion the journey is the real reward - e.g. learning to do arithmetic versus using a calculator. This is a global maximum vs. local maximum problem.

Unfortunately, it's extremely rare for a teacher to use this argument for the right reason; much more often they're doing exactly what you describe.