Dividing We Stand

So there I was mulling over how to approach long division with one of my seventh-grade students. There are several difficulties involved in his learning of the process, and I’ve only identified a few of them. One thing I do know for sure is that he has a low frustration threshold, and that mathematics is neither an easy nor an interesting subject for him. (Last week he had a meltdown after just a few problems and wouldn’t do any work for the rest of the hour.)

I thought back to yesterday’s class. A large part of the problem is that he doesn’t have his multiplication facts memorized. This could be from problems with rote memorization, and it could be also from problems with retrieval of information he already knows. Either or both gives the same result behaviorally. I have to be able to sift through what I observe and what he says, to determine what’s happening. After watching him remember most of what we went over the previous day, and watching him have to stop and calculate 22 minus 18, I suspected that it’s probably more of a rote memorization issue than a recall problem.

He also needed a more efficient method of calculating. I showed him that instead of going through the whole rote process of subtracting 8 from 12 by borrowing the 1 from the tens column, he could count from 18 to 22, and (looking at his fingers) see that there’s a difference of four. That sped up his working pace and reduced the cognitive load. It also helped him see that subtracting is finding the distance between two amounts, rather than just cranking through stacks of numerals.

He can calculate his multiplication facts (every single time he needs one) because he understands them as adding by multiples, and he figures the product by adding, “4 …. 8 …. 12 … 16” with each group of four on one finger, then look at his fingers and know that 4 times 4 is 16. Doing all this arithmetic with every step (such as figuring out how many 6’s are close to 37 for the first value of the quotient) places heavy demands upon working memory, and thus reduces his ability to learn and recall the larger process. All that work makes it hard to keep the data in short-term memory, and without that, it never makes it to long-term memory.

So a couple of days ago I brought out a multiplication table, but he didn’t understand it. Time to backtrack and get a better grip on multiplication! I got some manipulative cubes, and we built up a partial table, setting up 2 sets of 3. He counted each cube, “That makes six,” and then 3 sets of 2, “That also makes six,” and he wrote 6’s in both squares. We went over 3×4 and 4×3, and he wrote 12’s in both squares. Ah-ha! The order you multiply doesn’t matter. “That’s called the Commutative Law,” I explained. “It doesn’t matter if you multiply 4×5 or 5×4, whatever order you multiply them, you still get 20. That means you only have to learn HALF of the multiplication table!” Then we went over 3×3 and 4×4 and 5×5 and learned why a number multiplied times itself is called a square – the blocks stacked up into squares. Finally he understood how the multiplication table is built and what he can do with it, so we decided to use it in his long division problems.

Sequencing is definitely a difficulty; he’s having problems remembering when he’s dividing and when he’s subtracting. He’s also getting confused on whether to put a number down as part of the quotient or as a product. That could also be a spatial processing issue. Some of our students have problems with their columns of numbers wandering about, which plays extra havoc when they get to decimals (I liken it to “getting decimated”), so I have them turn lined paper sideways and write their numbers in the columns between the lines.

One thing I had noticed yesterday was that he could describe the process to me verbally more easily than he could write the problem. He might very well be an auditory learner. This might also be a fine motor coördination issue (he writes his numeral 4 with three separate strokes) so we’ve been doing the problems with a whiteboard and marker. This makes it easier to write the problems down and also erase errors, in contrast to doing them with pencil and paper. The marker glides more easily, and the numerals are naturally larger. It’s also easier for me to see what he’s doing without breathing down his neck, which is more comfortable for both of us.

Today I started him out by asking him what his favorite sport is. Yes, that’s an odd way to start math class, and there was a few seconds of delay before he answered, “Baseball.” Tying the subject to his special interest makes it more interesting and relevant, and thus be more likely to “stick”. Starting with something that he likes also helps reduce his aversion to the subject. In this case, we needed to learn the names of the different parts of the division equation. Previously he’d been telling me to, “Put the 2 over the 3,” but knowing how to do one problem by rote process doesn’t always help when you get to a different kind of problem. He also needs to be able to understand that all the problems are built of the same types of pieces. So I explained that just as baseball teams all had the same kinds of positions (catchers, pitchers, basemen, outfielders and so on), so did division problems (divisor, dividend, quotient, product and remainder). Just as each team has different people playing those positions, different problems had different numbers playing different positions. Well, that made sense.

With this base of understanding, we began reviewing the process he’d mastered yesterday. Because of his low frustration tolerance, I wanted to be especially sure of emphasizing his achievement. Then we did four problems together, with me correcting errors and also doing the scribing. Having refreshed the process, for the second quartet of problems I had him tell me what do write, and he was nearly soloing. For the third quartet I had him tell me what he’s doing, and he did the writing as well. Then after all that achievement, we looked at the two different ways of writing the same problem, with the bracket or the dotted sign.

Of course, the big questions are whether or not today’s understanding made it into his long-term memory (if he can retrieve that process after a day or a weekend or a month), and if he understood what it is actually about.

Tomorrow we’ll go over again what a division problem means. 295 divided by 36 describes, “How many sets of 36 can we make from 295? Do we have any left over, or does it come out even?” I’ll also have him describe to me the overall process of long division, which I will type up for him to keep. Having the student explain something in their own words requires a higher taxonomic level of learning than just shuffling around a bunch of numbers. Using verbal description also ties the learning to another part of the memory.

The problem with learning rote processes without conceptual understanding is that the students will then stumble in pre-algebra. They will need to use abstract reasoning to evaluate which method to use when. Part of that abstract reasoning simply comes from the maturation of the brain, and part of it comes from creating that deeper understanding of different methods.

I can sympathize with our students’ mathematical difficulties. It took me four years to learn my multiplication tables, and even in statistics and calculus I still have pauses in recall. (Calculus concepts are a breeze, but I can’t memorize a formula to save my life.) I had also flunked a number of math tests when attending this very same school building, and now here I was teaching it to students. (The irony!) But I take that understanding of the frustration with me every day, and express it as patience. I apply everything I have learned (and continue to learn) about cognition and learning, and everything I have learned about observing people, and put them together in my work as a paraprofessional and as a college tutor.

All told, this student successfully completed 13 long division problems today. The whole process is making much more sense, and he persevered with the work through most of the class period. I told him that since he’d stuck with it so well (even when he got a bit frustrated) he could take a break for the last ten minutes of class. He commented that it was kind of fun. “Yup,” I agreed, “Math is like games or puzzles once you understand the process!” This is a good sign. It may not last – one good day after unknown months of difficulties isn’t enough to turn around a student, but it is part of a good start with a new teaching relationship.

Techniques & Tips from a "Professional Student"

It’s too easy for blogging to end up as nothing more than a series of rants, so here’s something positive.

It’s that time of year when millions of people (leastwise, those in the northern hemisphere) are starting new school years. As someone who tutors (other) students with ADD and learning disabilities, I thought I’d share a bevy of helpful ideas I’ve scraped together over the years.

GETTING READY TO READ

Put the material into the Big Picture. Before starting a chapter/ module/ unit, review your syllabus to see how the content of this one fits within the logical flow of the previous unit, and how it might be important to the next unit. This helps the material make more sense and seem less like a giant pile of loose facts.

Read the textbook backwards.
Start with the Summary in the back of the chapter; this is the “TV Guide” version to what the chapter is about, so you know what you’re heading into before you dive into all the excruciating details. Read over the new terms in the Glossary, so when you encounter them in the text you won’t have those unintelligible speed-bumps that interrupt your understanding of the reading.

This is helpful if this subject is entirely new to you and you have little or no background in the concepts and terminology of this particular field of study.

From the first day of class, create a personal glossary of new terms and their definitions. This is imperative if you are starting a new field of study because you will soon find yourself in possession of a swarm of new words for which you are responsible. Trying to look up a word for its definition by flipping through masses of notes, handouts and textbooks only slows you down and makes you frustrated. Staring into space, pacing, rocking or banging your head do not aid in remembering new terms, so having that personal glossary will give you a ready list to access. Don’t forget to add helpful tips to your definitions, such as cautions about similar-sounding words that you might confuse, or terms with complementary or opposite meanings.

This is especially helpful if you are slow at recalling words, or have difficulties with spelling.

Block off distracting printed material with a mask. Use a half sheet of thin cardboard, a 3/4 sheet cut into an “L” shape, or two blank index cards to mask off distracting graphics, or simply to block off everything but the single question, objective, or paragraph you need to focus upon.

This is helpful if you are someone who is easily distracted by fascinating pictures, or if you have reading difficulties.

TAME THE PAPER TIGER

Assign a particular color to each class. I like to have the binder match the textbook color, so when I’m getting things together for class I only have to grab “two red things”. After the test, keep the notes and handouts in the colored binder or manilla folder. Use that color of ink to mark due dates for assignments and test dates on your calendar. Use that color of manilla or pocket folder to keep all the stray bits of useful stuff you are collecting for a report/project – having that special “parking place” will help organize and reduce the “file by pile” mess on your desk, floor, table, window ledge and other random surfaces…

Buy a hole punch with a trap. The trap collects all the “dots” so they don’t litter the floor. A 3- or 4-hole punch (depending on whether you use 8.5″ x 11″ or A4 paper) is vastly easier than a single-hole punch, as it not only reduces the number of clenches you have to perform, but also because it makes hole spacing that is perfectly even for the binder. Hole-punch all of your handouts and put them into the binder with your notes, so the two can live in wedded bliss.

Buy several packages of index dividers so you can separate the different chapters/units in your binder and more quickly flip through them for studying.

Make liberal use of colored sticky-notes. These are the greatest invention since the microwave oven! They will save tremendous amounts of time from having to endlessly flip through textbook, lab manual, handout, and note pages to track down important information.

Use colored sticky-notes to mark where important graphs, lists, charts, and diagrams are located in the textbook – write a key word on the external, flagging end of the sticky.

Use different colors of sticky-note for different chapters/modules/units, to make studying easier when you have tests that come after you have begun the next chapter/module/unit.

Use sticky-notes to mark chapter sections for those classes that skip around a lot within a textbook. If you are only using section 3.2 of a chapter, then you may begin by reading the summary for just section 3.2 of that chapter, but it might also be helpful to briefly review what the rest of the chapter summary has to say, to understand how the ideas in this section are connected to other ideas.

NOTABLE TIPS FOR NOTE-TAKING & STUDYING

Always take notes in black ink. There is nothing more horrifying during Midterm or Final Exams than discovering that a semester’s worth of pencil-written lecture notes has turned into a smeary, unreadable mess. Oh, the horror… Also, some kinds of blue ink are close to “non-photo / non-repro” blue, a color that’s nearly invisible to many photocopiers; this is usually not a problem unless you need to photocopy those notes for any reason.

Always date and/or number your note pages. Of course, if you live a charmed life and never have sudden “gravity fluctuations” in your part of the planet that cause you to drop or spill note papers, or you never own binders that lose their “bite”, then don’t bother. Otherwise, dating the pages lets you keep track of what was lectured on at a particular time (handy if someone asks to borrow your notes from last Tuesday). If you take more than one page of notes per day (which is nearly always) then numbering the pages instead of or in addition to dating them makes it even easier to put spilled pages back to rights.

Title each page.
Even if it’s just by abbreviation, describe the page of notes by the lecture topic, the unit or chapter title. This not only makes it easier to find the right notes when studying for tests, but it also helps you remember what the overall pattern of ideas is during the course of the class across the semester.
Example:
MITOSIS WED 2 FEB p.1

Take notes in two columns: the left side for listing the main idea titles, important names, terms, dates or formulae, and the right side for all the regular details and sentences. If there is a page in your textbook, lab manual or whatever that has a particular graph, chart or listing, write down that page number on the left side as well, as well as a word or two to title why that page number is important. This speeds up your test studying because you can glance through pages of notes to find the one that has the specific information you’re looking for.

Use the Objectives listed in the chapter/unit/module as your study guide for the test, and write out a full answer to each one as though it were a question. Pay attention to key verbs such as Describe, Compare, List, Define or Identify – these can give you an idea of what kind of test question could be asked. Writing these out does two things: it not only helps you self-test your own understanding before you get to the class test, but it also changes your answers from something you have to invent during the test (which is time-consuming) into something you just have to recall during the test (which is much quicker and easier).

Writing out answers to the objectives in full sentences is especially helpful if English is not your first language, and/or if you are slow at remembering words,and/or otherwise have difficulty expressing the knowledge that’s stuck in your head.

DECIMATED BY NUMBERS

Turn lined paper sideways to have ready-made columns for keeping your place-values straight in big arithmetic calculations. Another option is to use green “engineer’s paper” that has graph squares on one side and is blank on the other side, but the graph grid is still somewhat visible on the blank side, and the green tint is more restful on the eyes.

This is especially helpful if your handwriting tends to wander around or slope down a page, and will keep your numbers and decimals in order.

If you are doing mathematical equations or other things that are processes, write out your own set of numbered directions describing how to do the process. For instance, it may not be as obvious to you as it was to the author of the formula that you need to determine the value of “C” before you put the other values into the formula. So in your own directions, you should note “Find the value for “C” by ~ ~ ~” as one of the earlier steps.
Whenever you solve an equation or do a statistical analysis, write out in a complete sentence what the answer to the calculations MEANS in regards to the original problem/story/question given.

These are especially helpful if you are more of a “words” person than a “numbers” person.

If you have several different formulae , make yourself a flow-chart (meaning, a series of decisions) that helps you figure out which one you use for different kinds of circumstances. When you are studying a chapter or doing that day’s homework, it’s obvious which one you need to use – it’s the one you’re learning that day! But come test time, you will need to be able to understand which one you use for each kind of situation.

This is especially helpful if you are one of those people for whom “all the formulae look the same”.

Use name and address labels on everything, and add your phone number or email as well. Put them on your textbooks, lab manuals, various notebooks, calculator, data CD, flash/keychain drive, assorted binders, notepads, calendar-organizer, each piece of art & drafting equipment plus the carrying case, and all the other things that you need to survive as a student, to help guarantee that the person who finds them can help get them back home to you.

This is especially helpful if you are forgetful, distractible, prone to leaving things in various places, and/or are juggling a variety of classes and jobs. (You can imagine why I know this.)

Bibliomeme

Mum-is-thinking tagged me to answer a book survey. My answers are a motley collection, and I think that motley collections are always the most interesting. I’m guessing that people like to read these kinds of meme-tag surveys because they either want to hear how others have loved the same books they have, or else want to hear about books they had not yet (or possibly would not have) encountered, but would also enjoy.
One book that changed my life
I’ll have to take this is “one of many” rather than as “the one with the greatest impact” because surely different books have had done this at different stages in my life. There are a lot of contenders for books that were the first (if not always the best) to open up my knowledge-base to completely new fields of understanding, such as those on AD/HD or autism. Those are valuable in that regard, but more important are the books that give a different kind of insight, looking behind social paradigms to critically analyse the how and why of human interaction.
For the way that humans interact with their environments, Donald A. Norman’s The Design of Everyday Things looks at the problems that bad design causes people, and how people assume that their difficulties are considered to be their fault, rather than bad design. He touches but lightly on the issues of handicap accessibility, and I don’t think he mentions Universal Design at all, but the central message is still the same. My inner geek adores good, useful, imaginative and æsthetic design, and it drives me nutz when tools, machines or environments are badly designed.
For the way that humans interact with medical & emotional health care providers, Paula Kamen’s All In My Head: An Epic Quest to Cure an Unrelenting, Totally Unreasonable, And Only Slightly Enlightening Headache that describes some of the problems with the medical models of psychology, such as being a problem patient rather than a person with a problem, or the need to find “cures” for everything when instead one can be helped and be healed without being cured.
Strong messages from both of these books.
One book that you’ve read more than once
Who doesn’t have a comfily-tattered set of J.R.R. Tolkien’s four-volume Middle Earth trilogy? (Yes, trilogy means three books, but The Hobbit is part of the Lord of the Rings, and science fiction & fantasy is rife with trilogies composed of more than three volumes.) For my favorite re-read when stuck abed with a nasty virus, I really enjoy Anne McCaffrey & S.M. Stirling’s The City Who Fought. It’s a fun piece of adult science fiction with the well-drawn characters and nitty-gritty techy details and swashbuckling action that make for a engaging read.
One book you’d want on a desert island
Most people like to pack either something really long, or else an extensive practical reference book. But I don’t think that I’d want to be stuck with some interminably long piece of fiction, no matter how well-written, and I’ve probably read enough references over the years that I could eventually solve any manner of functional issues. What I want would be a huge book of blank pages, so I could keep a journal of thoughts about various things. It’s often difficult for me to work out mental explorations without a written medium. I’ll remember or figure out the right knots for lashing together poles, but being able to compose my thoughts is integral to my equalibrium.

One book that made you laugh
Terry Pratchett’s Mort was the first Discworld novel I ever read, and Death is still my favorite character, possibly because he’s so practical and the human world doesn’t always make sense to him. Plus, he talks in ALL CAPS. Soul Music is damn funny, too. I love the puns and unexpected turns in Pratchett’s books.
One book that made you cry
Ebbing & Gammon’s General Chemistry (sixth edition). The authors of this uninspired, heavy tome had an interminable number of equations to solve. I made it through four semesters of chemistry and sweated through this volume for half of them.
One book you wish you had written
Actually, I’m still compiling thoughts for my next book. I don’t tend to dwell on wish-I-had’s.
One book you’re currently reading
I never read just one book at a time, which explains why it takes me so long to finish anything! I just finished Joseph P. Shapiro’s No Pity. I’m furthest into Majia Nadesan’s most interesting Constructing Autism, which I will finish as soon as I remember where the hell I left the book laying about.
Currently my bedside pile contains: Thomas Skrtic’s Behind Special Education, Alfie Kohn’s What Does It Mean to Be Educated?, Kegan & Lahey’s How the Way We Talk Can Change the Way We Work, Marshall B. Rosenberg’s Nonviolent Communications, Fisher & Shapiro’s beyond reason, and Walter Kauffmann’s translation of Basic Writings of Nietzsche (maybe after finishing the book I’ll be able to spell N’s name without looking it up every time). I had just started on Richard Dawkin’s The Selfish Gene and then my daughter took it back with her to college; bad girl. By default I’m also reading Hardman, Drew & Egan’s Human Exceptionality: School, Community and Family because it’s my current textbook.
One book you’ve been meaning to read
The future pile-by-my-bed: Daniel C. Dennett’s freedom evolves, John H. Holland’s Hidden Order: How Adaptation Builds Complexity, Douglas R. Hofstadter’s Gödel, Escher, Bach: An Eternal Golden Braid (I think that one may take a study-buddy to gain the most benefit), the Routledge Critical Thinker’s series editions about Gilles Deleuze, Jaques Derrida, and Michel Foucault, Eli Maor’s e: the Story of a Number, and David Darling’s Universal Book of Mathematics. Doubtless there’s more, but that’s what’s on that section of my bookcase.
Tag five other book lovers
Anna, Catana, David, Liam, and Whomever wishes they’d been tagged but felt like they needed some kind of “official” sanction to simply write and post a list!

Walking the Mine Field: Misadventures in Mathematics

Doing a complex calculation is not the simple matter than many people perceive it to be. “It’s simple,” I’ve heard repeatedly, “Just memorize the equation. Then it’s just ‘plug-and-chug’.”
In truth, performing calculations requires a great many steps, any one of which can be mistaken (or miss-taken), leading to disaster. It doesn’t matter if we’re doing calculus or statistics; either way, there’s a formula to choose and data to crunch through.
Identify the data from the problem. Not as straight-forward as you’d think; often there is extraneous data running around in there that’s not needed. We also run into charming instances of professors and books using different terms to mean the same thing, or handwriting that makes the same term look like a completely different character. “Is that a sigma or a delta?” Pro mea lingua Graeca est. For added entertainment value, let’s have a hand-written test.
Be able to correctly transform the data into the necessary forms, pre-flight. Are the numbers in the correct units? Do we first need to find means and standard deviations of the 30 values listed in the table? Do we need to flip through 15 pages of lecture notes and a chapter of textbook pages to find or verify the transformational technique? Yes, I have a page of formulae that I’m building. As we slog through the class, this is how I know what to put on the page. Let us hope that I don’t have a transcription error on my formula page!
Be able to correctly transcribe the data, without transpositions, morphing of numerals, or loss of data. This is often where I get into trouble – there’s a sense of spatial meandering as the numbers seem to wander around like ants. Pages with several problems on them make this worse, cluttering the search image. Sometimes I cover over parts of the page with index cards to reduce the visual clutter, but then I have to turn the pages… Double-check the numbers you’ve entered into the calculator before punching Enter. Oops, dropped a digit; re-enter all the numbers again.
Identify which procedure is being called for. Often indirectly stated, especially on tests. Once you know what you need to do, then you need to select which of that mass of massive, messy equations does that trick. It sure would be nice if the professors would spend less time explaining how someone derived the formula – for all I care, it could have arrived fully-formed, like Athena from the forehead of Zeus. Copying down all the steps someone used to transform one formula into another nifty new formula is not helpful to me – it just gives me pages of notes of half-cooked formulae that I need to puzzle through while trying to track down the one I really need. I’d rather they spent more time taking us through a flow-chart of how we determine which formula we need.
Transcribe the formula onto the homework page, without error. Then be able to correctly transcribe the data into the formula format, without transpositions, morphing of numerals, or loss of data. Stop and compare the numbers here with those in the problem. All systems “GO”? Clearance from the control tower?
Be able to remember where in the sequence of functions you are in the procedure. What was a bit awkward in “borrowing” during subtraction, became confusing in long division, and is downright maddening in regression analyses where each problem is a series of computational subsets. (I sure hope this problem doesn’t take more than one side of the page.) Sometimes I put labels alongside the subsets so I know what the pieces are, but sometimes writing ∑xy or s2 on the page only adds more ants. The page is already messy looking from several erasures. Flick rubber crumbs off the table.
Double-check the numbers you’ve entered into the calculator before punching Enter. Got “decimated” – transposed a zero and the decimal point. Re-enter all the numbers again.
Be able to correctly transcribe the correct data, in its proper transformation, without transpositions, morphing of numerals, or loss of data. Yes, we’re stuck in a loop of trying to keep track of a swarm of answers, some of which are raw, some of which are cooked, and it’s not impossible for one to roll off the counter and end up forgotten on the floor.
Next step of the procedure: double-check the numbers you’ve entered into the calculator before punching Enter. So now what do we plug this answer into?
Be able to interpret the significance of the numeric result. So what does “17.2” mean? (Do I care?) Re-read the problem again. Did I use the right formula? Oh, yeah. Write out the answer verbally, because by tomorrow in class this home-work page will have reverted to an unintelligible ant-farm of digits. I really do NOT recall what I did on a math problem from one day to the next.
Congratulations. You have finished the first homework problem. Only fifteen more to go. Um, are we doing problem 56 or 65? Did I get the right answer, or am I practicing doing the problem incorrectly?
In the Final analysis. Of course, in a homework assignment, you know what formula(e) you’re supposed to be using; it’s the one related to that section of the book. Now let’s go to a test, where we’re doing several different kinds of problems.
The test questions written by the professor state the problems differently than the book did, and require using the formulae in different ways than in the homework, to asses our understanding of the concepts. Naturally, this means that the problems on the tests don’t look at all familiar, because they aren’t set up the same way that the problems were on the homework. Before tackling the brute calculations, we have to decipher just what is in front of us. (Where are we going, and what am I doing in this hand-basket full of eraser crumbs and ants?)
“It’s simple,” they tell me, “Just memorize the equation. Then it’s just ‘plug-and-chug’.”
::sigh::

Cognitive Bias, Patterns & Pseudoscience

(It’s been a long, long day. So here’s an only-slightly-used, gently-recycled essay, but with an Brand New! hyperlink for your enjoyment. Bon appétit!)

“It has been said that man is a rational animal. All my life I have been searching for evidence which could support this.”
~ Bertrand Russell

Here’s our new word for the day: pareidolia. It comes from the Greek, para = almost and eidos = form. The word itself originates in psychology, and refers to that cognitive process that results in people seeing images (often faces) that aren’t really there: the man or rabbit in the moon, canals or face on Mars, faces of holy people in tortillas or stains in plaster … It also sometimes refers to hearing things that aren’t really there in random background noise (Electronic Voice Phenomena: EVP). Pareidolia is what makes Rorschach inkblot tests possible (attribution errors are what make Rorschach tests fairly unreliable).
The human brain is “wired” to see patterns, especially those of faces. Creating and perceiving patterns is what allows all animals to operate more efficiently in their environments. You need to be able to quickly find your food sources, your mates, your offspring, and the predators in the busy matrices of sensory inputs. Camouflage relies upon being able to become part of a pattern, and therefore less recognizable. Aposematic warning coloration, such as black and yellow wasps, does the reverse, by creating a specific kind of pattern that stands out.
Sometimes people subconsciously assign patterns and meanings to things, even though they don’t intend to do so. This is why we have double-blind studies, so the people who are collecting the data don’t unconsciously assign results to the treatment replications by increasing or suppressing or noticing effects in some trial subjects. Prometheus has a lovely blogpost about this: The Seven Most Common Thinking Errors of Highly Amusing Quacks and Pseudoscientists (Part 3). (This series of his just gets better and better!)
Seeing patterns can lead to weird cognitive biases and fallacies, like the clustering illusion, where meanings are falsely assigned to chunks of information. The fact is that clusters or strings or short repeats of things will naturally happen in random spatial or temporal collections of objects or events. A lot of people think that “random” means these won’t happen (which makes assigning correct answers for multiple choice tests an interesting process; students get suspicious if they notice too much of a pattern and then start out-guessing their correct answers to either fit or break the perceived pattern).
Sometimes the reverse can happen, where instead of seeing patterns in data, people put some of the data into patterns. This is known as the Texas Sharpshooter Fallacy: a cowboy randomly riddles the side of a barn with bullets, and then draws a target where there is a cluster of bullet holes. People will perceive a pattern of events, and then assume that there is a common causal factor to those, because of the perceived pattern. This is why statistics was invented – to suss out if there is a pattern, and how likely it is. Mathematics takes the cognitive kinks out of the data so the analysis is objective, rather than subjective.
Statistics also gives research rules about how best to proceed in experiments, to avoid various errors. One of those is deciding what kinds of analyses will be used for the type of data set that is produced by the experimental design. Note that this is decided beforehand! The reason for that is because people want to see patterns, and (even unconsciously) researchers want to see results. The purpose of testing for a null hypothesis is to try to disprove the given hypothesis, to avoid these kinds of issues.
It doesn’t matter how noble your intentions are – wrong results are still wrong results, no matter how they are achieved, or to what purpose.
To look at the data and then start picking through it for patterns, (“massaging the data” or “datamining”) is inappropriate for these very reasons. The greatest problem with doing analyses retroactively is that one can end up fitting the data to their pet theory, rather than testing the theory with the data. Mark Chu-Carroll’s post on the Geiers’ crappy and self-serving data “analysis” is an elegant dissection of how this kind of gross error is done. (Note that is MCC’s old blog address; his current blog is here at ScienceBlogs.)
Doing this intentionally is not only bad statistics, it’s bad science as well. The results come from anecdotes or data sets that are incomplete or obtained inaccurately. Correlations that may or may not exist are seen as having a common causality that also may or may not exist. It’s pick-and-choose and drawing erroneous, unsupported conclusions. People want to see patterns, and do. Even worse, they create patterns and results.
The seriously bad thing is that con artists and purveyors of various kinds of pseudoscience do this a lot. The intent is to deceive or mislead in order to sell something (ideas or objects or methods).
The people who then buy into these things then think they are seeing treatment results because they want to see them. Take this secret herbal cold medication, and your cold will be cured in just seven days! (Amazingly, one will get over a cold in a week anyway.) Give your child this treatment and they will be able to learn and develop normally! (Amazingly, children will learn and develop as they get older, for all not everyone follows the same timelines – developmental charts are population averages.)
Meanwhile, the well-intended but scientifically ignorant people who buy into these things are being duped by charlatans, sometimes with loss of life as well as with great monetary expense.
Economists will tell you that the cost of something is also what you did/could not buy, and when time and money is spent on false promises, it deprives everyone involved of the opportunity to pursue truly beneficial treatments.
Then the problem is propagated because those well-intended but scientifically ignorant people become meme agents, earnestly spreading the false gospel …