The Abelian Grape

Spelling activities, so called

2010-09-27T23:47:00.003-05:00

You've. Got. To. Be. Kidding.

Note 1: These activities are listed as options for students who missed their weekly spelling words. They have to choose two of these activities for the week.

Note 2: The students who received this list of options for their spelling assignments are eighth graders. In some societies, these students would be on the verge of adulthood. Here, we’re giving them the option of writing their spelling words in their choice of instant pudding or glitter.

Note 3: The teacher that published this list for her students is a writing teacher. That’s right: a writing teacher. Bear that in mind as you read Note 4 and the list of activities.

Note 4: The only changes in punctuation were to make the headings consistent. All the comma splices and other abuses of the comma, as well as other awkward wordings, are from the original.

Note 5: I’m well aware of the value of repetition in learning material. Any of these activities that encourage repetition will therefore have some value, but let’s not fool ourselves into thinking that the other bizarre aspects of these activities are going to be what magically locks a tricky spelling into a student’s brain.

Note 6: The sad (or funny; I haven’t figured out yet which it is) thing is that this is from a school district that has an undeserved reputation for “excellence in education.” You know - the school district where all the doctors, lawyers, bankers, and other various and sundry rich people live so their offspring can have a “quality” public education. Guess the laugh’s on them, unless they’re all a bunch of Auntie Mame types who mistakenly think that the latest also means the greatest.

Note 7: My comments below are italicized.

Glitter Words: Write your words out in glue and then sprinkle with glitter, sand, or jello mix to make the words visible.

How about cat litter? Wouldn’t that provide a more “tactile” experience for your “kinesthetic” learners? P.S. Don’t take me seriously; it’s called “sarcasm.”

Foldable Words: Fold a piece of paper in half (hamburger fold). Open it up and fold both outside edges to the center crease. Now fold into thirds. Open it up and cut from the inside to the outside seam. You should be creating six windows. Write one word on the outside flap and inside practice writing it 5x.

I’m trying to come up with a smart-aleck remark for this one, but so far words fail me. I’m stupefied.

Record a Word: Tape record yourself practicing the words. Spell each word 5x.

Now how many kids these days know what a tape recorder is, do you suppose? And I’ll bet your school is just gung-ho on using “technology,” too. Tape recorders are sooooo 20th century.

Spelling Magic: Use a white crayon and write your words on paper 5x’s. Now using watercolor paints, paint over the writing and watch your words appear.

Arts and crafts in English, eh? Don’t tell me that a well-to-do district such as yours had budgets cuts that eliminated your art classes.

Flashcards: Make a flashcard for each spelling word using index cards. On the front, print each word on a card. Write the words on the backside in cursive 5x each.

Now this is actually a sound idea. I would have thought it too mundane. Knock me over with a feather.

Spelling Puzzles: Type up your spelling words in large 18 inch font without spacing in between words. Print out the paper. Cut out each letter out and reform each word. Glue them down on a new piece of paper.

18-inch font? That produces letters that are a foot and a half high. Are you sure that’s what you really intend to say? I think perhaps you mean “18-point.” And just what are we supposed to do if we have incorrigible words that refuse to be reformed? Oh, wait – that’s not what you meant, is it?

Block Puzzles: Using small lettered blocks, spell and glue together your spelling words.

If students put the blocks on a string and use them as a bracelet, would it be cheating to wear it on spelling test day? What else are they supposed to do with these little blocks?

Spelling Dice: For each spelling word you have, roll a die and rewrite the word the number that appears.

I think I understand what you meant to say, but the thing is you didn’t say what you meant to say. You did say you were the writing teacher, correct? Did you even read what you wrote before you handed it out to your students?

Chalkboard/Whiteboard/Transparency Fun: Rewrite your words on an erasable surface. Practice 3x each.

This is another old school activity. How’d it make the cut?

Using magnetic letters, spell out each spelling word and take a picture of your work: You can send completed pictures to [email address redacted].

Icebox spelling homework. What next?

Unusual Flashcards: Be creative. Select a substance such as fabric, or wood and make your own flashcards.

Finally! An activity that allows students to “be creative”!! What a refreshing change of pace from the heretofore run-of-the-mill spelling activities!

Alpha-bit Spelling: You’ll need a box of alphabits cereal for this. Arrange and glue your spelling words together.

Isn’t this assignment in danger of suffering the old “dog ate my homework” excuse?

Salt Box or Sand Box Spelling: In a large bowl or dish, pour in salt or sand or sugar. Then practice spelling your words. Take pictures of your words and email them to me.

Now this one is not only silly, it’s just plain wasteful. Who wants to use sugar or salt after having been played with by some grubby fingers?

Pudding Practice: Use instant pudding as finger paint to practice your words 2x each. (GET PARENTS PERMISSION PLEASE).

Another wasteful activity. Why instant pudding? How about the cooked variety? For that matter, why not honey, ketchup, or mustard? Parental permission or no, any one of those is guaranteed to make a mess. By the way, what was the objective of this little lesson? Oh, yeah – it had something to do with spelling, didn’t it…

Pyramid Power: Write your words in order of difficulty. At the top the easiest and gradually get more challenging.

Another failure to communicate. That last “sentence” isn’t even a sentence: where’s the subject (understood or otherwise), and the verb?

Rainbow Words: Write your words 5x each in a different color.

Do the various colors make it more pedagogically sound than repeating the words using just one boring color?

Spell It with Beans or Pasta: Using any form of dry beans or pasta, spell your words and glue down on paper.

Extra credit for students who don’t stick said beans up their nose? You are assigning these activities to junior high kids, after all. 35 years later, I still remember the kid at lunch in sixth grade who inhaled a cooked noodle up his nose and had it come out his mouth.

Pipe Cleaners: Use a pipe cleaner to bend into the shape of your word. Try it in cursive, or use one pipe cleaner for each letter.

Tsk, tsk. This smacks of political incorrectness. Pipe cleaners – are you serious? Don’t you realize how hazardous tobacco is to your health? Sounds like you’re trying to subvert the healthy lifestyle agenda by directing these tender young minds to utilize something associated with evil tobacco. For shame.

Toothpicks: Use toothpicks to make your words. Glue them down on paper.

If a student uses matchsticks rather than toothpicks, will he get extra credit for “creativity,” or will he be marked down for failing to follow directions? Inquiring minds want to know.

Magazine Letters: Using old magazines, hunt down the letters that form your words. Cut them out, and glue them on paper to spell out each word.

Great practice for would-be ransom-note writers.

Twist Tie Spelling: Using twist ties, arrange the letters your need to make your spelling words.

Oh good grief.

Alphabet Stamps: Using letter stamps, stamp out your words.

More arts and crafts? Do you really think time is better spent stamping words letter by letter is than writing them five times longhand? I’ll bet most of your students could benefit from the handwriting practice anyhow, and here you’re giving them plenty of excuses to avoid actual writing.

Playdough: Using playdough form your words, either stamp out letters or write into the dough.

I don’t think you grasp the difference between “in” and “into.” One is a preposition of location (static), the other a preposition of direction (expresses motion or change of location). In any case, “on” (not “onto”) is a better choice. And you are supposed to be the writing teacher??

Make a Word Search: You can use graph paper and do this by hand, or complete online. Be sure you find all your words before submitting it.

Another one that’s actually not too bad – a bit weak on the repetition, though, and so of limited pedagogical value.

Do you have your own suggestion, not found here? Tell me about it.

Oh, I don’t know – how about something novel, like write the word five times and use in it correctly in a sentence? Or is that too reactionary?

Here are my suggestions. Which ones do you think would be taken seriously?

Rice Carvings: Using a microscope and dentist’s tools, carve your spelling words 5x on a grain of rice. Use one grain of rice per spelling word, please.

Human Alphabet: “Write” your spelling words by bending your body in the shape of the letters needed to spell your words. Be sure to take a picture of each letter as you form it. Copy the pictures in a Word document, making certain to arrange the pictures in the correct order to spell your word, and email to me.

Petri Dish Orthography: Obtain several Petri dishes (one per spelling word) and grow bacterial cultures on them. Once the cultures are established, spray some disinfectant on a cotton swab and use the swab to write your spelling words on the Petri dishes (5x per word). Take a picture of the Petri dishes after the disinfectant has killed the bacteria, thus forming your spelling words.

Alphabet Soup Speller: You’ll need some cans of alphabet soup to complete this activity. Have a can of alphabet soup for lunch, and hunt for the letters needed to form your spelling words. Once you’ve found them, write your spelling words using the alphabet noodles, taking pictures of each word. Email me the pictures.

Gee, You Don't Say?

2009-11-10T21:13:00.002-06:00

There's an interesting article at The Chronicle of Higher Education. I applaud them for daring to ask the question whose answer so many people take as self-evident. Despite the insistence on post-secondary education for all, college is not a one-size-fits-all Good Thing. Some people are simply not cut out for (what should be, what used to be) rigorous academic work. Sometimes it's a matter of ability (normal curves being what they are, you're always going to have about 16% of the population more than a standard deviation below average, translating to an IQ of 85 or less; I would further argue that at the very minimum, one should be of at least average intelligence to attend college/university). Sometimes, it's a matter of temperament. People who lack either ability or desire to attend college should not be pressured to do so (Hello, high school counselors: are you listening?), nor should they be looked down upon for not going.

The comments in the article referenced above make worthwhile reading, too. Comment #11 is QFT:

College-level work = (at a minimum) the ability to read and comprehend on at least a 12th grade (standardized) level and to be able to express one's thoughts in writing coherently in complete sentences with minimal errors in syntax, grammar, spelling, and punctuation. Oh, and add to that the maturity to realize that one should spend more time on their studies outside class, rather than assuming that having their body sitting in class when it suits them is adequate.

Hear, hear.

Just for Grins

2009-08-14T22:07:00.004-05:00

(The following is from my grandmother's grade book, over a hundred years ago. She went to school in Kristiania (Oslo). The first entry is from when she was in the 4th class, in 1903. I've provided translations of the school rules.)

Til skolebørnene.

To the schoolchildren.

1. Vær høflig og lydig mod lærerne og lærerinderne ved skolen.

Be polite and obedient to the teachers at school.

2. Bliv aldrig borte fra skolen, hvis du ikke er syg eller har faat lov af klasseforstanderen. Er du syg, saa maa skolen faa bud om det.

Never be absent from school if you are not sick, or have gotten permission from the homeroom teacher. If you are sick, the school must be notified.

3. Vask dig og kjæm haaret, før du gaar til skolen.

Wash up and comb your hair before you go to school.

4. Hold alle bøgerne dine rene og ordentlige.

Keep all your books clean and proper.

5. Glem ikke noget af det, som du skal have med dig.

Do not forget anything that you are supposed to have with you.

6. Kom saa tidlig, at du kan stille op med de andre, naar det ringer ind.

Come early enough so that you are able to line up with the others when the bell rings.

7. Vær stille, opmerksom og flittig i timerne.

Be quiet, attentive, and diligent in class.

8. Vær ikke voldsom eller uvenlig mod kamerater. Yp ikke strid. Gjør ikke nar av nogen, og skjeld ingen ud. Tal aldrig usant. Det er feigt og stygt, om du lader en anden lide for din skyld.

Do not be unruly or unfriendly towards your classmates. Do not stir up strife. Do not make fun of anyone, nor scold anyone. Never speak untruthfully. It is cowardly and unseemly to let another suffer on your account.

9. Finder du noget paa skolen, saa bring det straks til vagtmesteren.

If you find something at school, bring it immediately to the custodian.

10. Spyt ikke paa gulv eller trap.

Do not spit on the floor or the stairs.

11. Rabl ikke nogensteds; gjør ikke skade paa nogen ting. Slæng ikke papir eller andet udover. Kast aldrig sten.

Do not scribble anywhere; do not damage anything. Do not throw paper or other items here and there. Never throw stones.

12. Vær ikke med paa nogetslags spektakel paa gaden.

Do not follow any sort of goings-on in the street.

13. Hils venlig paa alle, som du kjender. Vær høflig og hjælpsom mod alle. Vis ældre folk ærbødighed.

Give a friendly greeting to all whom you know. Be polite and helpful towards all. Show elderly people respect.

Logical Fallacies

2009-07-18T19:08:00.002-05:00

In teaching a math-literacy-type class, I cover a unit on basic logic. What follows are the dismal results of a quiz on logical fallacies. 23 students total took the quiz.

"Classes go more smoothly when the students and the professor are getting along well. Therefore, grading this class on a curve would be the fairest thing to do." - correctly identified as red herring by 4 students (17%).
"Every swan I have seen is white, so it must be true that all swans are white." - correctly identified as hasty generalization by 11 students (48%).
"I should receive an A in this class. After all, if I don't get an A I won't get the scholarship that I want." - correctly identified as appeal to emotion by 3 students (13%).
"More cows die in India in the summer months. More ice cream is consumed in summer months. Therefore, the consumption of ice cream in the summer months is killing Indian cows." - correctly identified as false cause by 10 students (43%).
"Most people approve of gun control laws. If most people approve of them, then they must be good." - correctly identified as appeal to majority by 16 students (70%).
"Paul must be telling the truth, because I have heard him say the same thing many times before." - correctly identified as begging the question by 5 students (22%).
"Senator Jones says that we should not fund the attack submarine program. I disagree entirely. I can't understand why he wants to leave us defenseless like that." - correctly identified as straw man by 9 students (39%).
"Since you cannot prove that ghosts do not exist, they must exist." - correctly identified as appeal to ignorance by 11 students (48%).
"Tobacco company representatives should not be believed when they say smoking doesn't seriously affect your health, because they're just defending their own multi-million-dollar financial interests." - correctly identified as ad hominem by 5 students (22%).
"You're either part of the solution or part of the problem." - correctly identified as false dichotomy by 6 students (26%).

What is truly disturbing is that this is the generation that voted overwhelmingly for Obama. Given their ineptness in spotting bad arguments and logical fallacies, I suppose that goes a long way towards explaining why they fell for that Chicago pol hook, line, and sinker.

But it still doesn't inspire confidence in the judgment of the next generation.

Critical Thinking Non-Skills

2009-03-31T07:00:00.000-05:00

I tend to laugh maniacally (or at least snort derisively) whenever I hear the educrats boast about how their pet theories are teaching all students the 21st century skills they’ll need for success. Their prime example is “critical thinking,” and of course their implicit assumption is that hitherto schools have been doing a wretchedly poor job of this. We’ve all heard the canards: old school methods (like “drill and kill”) and “rote memorization” are antithetical to new ed school methods that teach “higher order skills” like “critical thinking.”

Why am I skeptical regarding these claims? Behold one of my typical classes on a typical day:

The class: Basic statistics for non-math majors.

The topic: Discrete random variables.

A student asks a question about one of the assigned homework problems. The problem involves the probability of an archer hitting various regions of the target with one shot. The target is a 6’ x 6’ square, with a bullseye of radius 1’ and one ring (inner radius 1’, outer radius 2’) around the bullseye. A hit in the bullseye scores 5 points; a hit in the ring scores only 1, and a hit on the target outside the ring scores 0. For simplicity, the assumptions are 1) the archer will always hit the target, and 2) every spot on the target has an equally likely chance of getting hit with an arrow. To solve the problem, the student has to find the probability distribution of the discrete random variable (the score received in one arrow shot) and then use this distribution to determine the likelihood of getting various overall scores.

Clearly (at least it should be clear to people with “higher order skills” such as “critical thinking”) the probability of getting a specific score on one shot is nothing more than the percentage of the area occupied by that score. Thus, since we have

area of bullseye
= (pi) square feet

area of ring
= [4(pi) – (pi)] square feet
= 3(pi) square feet

area of target outside of ring and bullseye
= area of square – area of ring and bullseye
= [36 – 4(pi)] square feet

we have the following probabilities for a single shot (rounded):

P(score of 0)
= [area of target outside of ring and bullseye] / [area of target]
= [36 – 4(pi)] / 36
= 0.6509

P(score of 1)
= [area of ring] / [area of target]
= 3(pi) / 36
= 0.2618

P(score of 5)
= [area of bullseye] / [area of target]
= (pi) / 36
= 0.0873

So, these students, who have been sucking at the constructivist teat for however many years, should have absolutely no problem solving this straightforward application of “critical thinking skills,” right?

Uh – huh.

“Has anyone done this problem?”

[crickets]

“Does anyone have an idea where to start with this problem?”

[crickets]

Some intervention is obviously needed to get this ball rolling.

“Okay, let’s draw a picture.”

Even with intelligent Socratic questioning, I can’t imagine how I’m ever going to get them to see (at least within the time constraints of the classroom) that the key is to consider the areas occupied by the different score zones. I prime the pump by giving them that little tidbit directly, and then ask:

“Now, how can we figure out the area occupied by the bullseye?”

[crickets]

Hello – junior high math, people. You do remember the formula for the area of a circle, no?

At this rate we’re going to be here all day, something which is definitely not in my lesson plans. If it were a review session, that’d be a different story, perhaps, but I do have other material that needs to be covered.

So, of course I must completely set up the problem for them. Spell it out in gory detail.

Critical thinking, my arse. Tell me another funny.

Test-Taking 101

2009-03-30T17:11:00.002-05:00

One of my students complained about a test. (Fancy that! I just know that the rest of you have model students who never do that type of thing. For some reason the whiners end up in my class, instead.)

Without going into detail, I will admit that there is room for improvement on my part, and in my quest for reasonableness I am willing to adjust and make amends where necessary. However, in listening to the student harangue me after class (which, btw, is what frosts my shorts just as much as anything else – listen, you don’t have to like me or agree with me, but whatever happened to respecting someone on account of their position? There is still respect due them because of the office that person holds, regardless of your personal opinion as to whether or not respect has been earned), she made a telling admission:

“There were so many questions on this test, I didn’t have time to look at them all.”

That statement right there clued me in that whatever percentage of blame lies with me due to my shortcomings, Little Miss Innocent shouldn’t get off scot-free, either. Why?

This gal apparently forgot all about Test-Taking 101: Look over the test completely before you plunge ahead and start answering questions. Before you make a single mark on your scantron or write a single jot in your blue book, you need to see what you’re up against so you can prioritize and pace yourself accordingly.

How many questions are on the test? You’ve got to figure out the average length of time you should spend on any given question. (Skip this step, and you'll regret it. I guarantee it.)
Are all questions weighted equally? If not, which ones are worth more?
Mentally sort the questions into three categories:

Really easy – ones that can be answered without too much thought.
Really hard – ones that you haven’t a clue about, or you know are going to be time-consuming.
Everything else.

Since you (presumably) want to maximize your points, you have to use these categories (and point values of the individual questions, if they’re not weighted equally) to help you prioritize. Why lose easy points by spending too much time on hard ones that you probably won’t get anyhow? This should be a no-brainer.

Yet I suspect that’s where Little Miss Innocent flubbed up. Since, by her own admission, she hadn’t bothered looking at all the questions on the test, she evidently didn’t prioritize, and spent too much time on the wrong types of problems. Well, yeah, if you do that, of course you’re going to complain that the test is “too long” and / or “unfair.”

If Little Miss Innocent had looked at the questions first, she would have seen that there were a number of concept questions that didn’t require long, tedious calculations. (Yes, I admit it – that’s the way some of this stuff is. Like it or not, tedium just goes with the territory sometimes.) If she had spent some time answering those concept questions, she could have improved her score significantly.

But, you know, it’s just a lot easier to blame everything on the teacher.

Test-Taking 101, folks. Ignore it at your own peril.

Evolution - Extracting the Square Root of a Number (Illustrated)

2008-11-22T14:44:00.003-06:00

I had previously given written instructions on how to extract the square root of a number. To get a better idea of the process involved, I've scanned in a picture illustrating how to find the square root of 2 to five decimal places. I used color-coded digits in an attempt to help you see which numbers arose from the calculation, and what role they played in the answer.

Art. 390 To Extract the Square Root of a Number,

Rule.---1. Separate the given number into periods of two figures, commencing at units; the left hand period may have 1 or 2 figures.

2. Take the square root of the nearest square below the left hand period: this will be the first figure of the root.

3. Subtract the square of this figure from the left hand period, bring down the next period; divide the result exclusive of the right hand figure, by twice the part of the root already found: the quotient will the be 2d figure of the root.

4. Set this figure of the root on the right of the divisor; multiply the divisor thus completed, by the 2d figure of the root; subtract the product from the last dividend, and bring down another period.

5. Double the root already found for a trial divisor, find another figure of the root, and proceed as before, until all the periods have been brought down.

Notes.---1. If any product is larger than the dividend from which it is to be taken, the last figure of the root is too large.

2. If any dividend, exclusive of its right-hand figure, is not large enough to contain its trial divisor, place a cipher in the root, and at the right of the divisor; bring down another period and continue as before.

3. When a remainder is greater than the previous divisor, it does not follow that the last figure of the root is too small, unless that remainder is large enough to contain twice the part of the root already found, and 1 more; for this would be the proper divisor to go into the remainder, if the root were increased by 1.

Sad Update

2008-11-07T22:16:00.003-06:00

Well, I'm a bit behind in some of the things that I've been planning on posting. Part of the reason is due to regular teaching type stuff - mainly mid-terms and grading. But in addition to that, this past week has been somewhat heavy. Last weekend, one of my students was killed in a car crash on his way home from work. So that class has been awkward for me, to say the least. We meet twice a week, and the first class of the week there were only a handful of students in attendance. The funeral was that day, so several students were out due to that. I broke the news to the students who were in class, and we talked about the accident, the student, and the brevity of life. Of course, no one was in the mood to do any math, so I ended letting them out early.

The second class (which was a couple of days later) was a bit better, but one student ended up leaving after ten or fifteen minutes because of grief. We did do some math, but for right now I'm not pushing to stick to my lecture schedule like I normally would. I'm trying to help them with the grieving process by sticking to a somewhat normal routine, yet keeping things flexible enough to give them any space they might need.

I think the rest of the semester might be a little awkward.

Evolution - Extracting the Square Root of a Number

2008-09-09T21:33:00.002-05:00

(The following is an excerpt from Ray's Higher Arithmetic.)

Art. 390 To Extract the Square Root of a Number,

Rule.---1. Separate the given number into periods of two figures, commencing at units; the left hand period may have 1 or 2 figures.

2. Take the square root of the nearest square below the left hand period: this will be the first figure of the root.

3. Subtract the square of this figure from the left hand period, bring down the next period; divide the result exclusive of the right hand figure, by twice the part of the root already found: the quotient will the be 2d figure of the root.

4. Set this figure of the root on the right of the divisor; multiply the divisor thus completed, by the 2d figure of the root; subtract the product from the last dividend, and bring down another period.

5. Double the root already found for a trial divisor, find another figure of the root, and proceed as before, until all the periods have been brought down.

Notes.---1. If any product is larger than the dividend from which it is to be taken, the last figure of the root is too large.

2. If any dividend, exclusive of its right-hand figure, is not large enough to contain its trial divisor, place a cipher in the root, and at the right of the divisor; bring down another period and continue as before.

3. When a remainder is greater than the previous divisor, it does not follow that the last figure of the root is too small, unless that remainder is large enough to contain twice the part of the root already found, and 1 more; for this would be the proper divisor to go into the remainder, if the root were increased by 1.

Here, cipher means the digit 0.

Sound confusing? It really isn't - just think of the expansion of the square of sums:

(a + b)^2 = a^2 + 2ab + b^2

The method of extraction as described above is essentially the process of finding a and reducing b by repeated applications of the method. The result is a number that converges on the desired square root - that is to say, a converges on the square root, and b converges on zero.

Blogger not being conducive to displaying arithmetic problems, I don't have a ready example. I'll do one up by hand and scan it in, to give you an idea of how this process works by looking at an example.

Common Sense, Where Art Thou?

2008-08-28T13:33:00.003-05:00

Quiz question:

Human hair can grow as fast as 0.0000000043 meters/second. About how long would it take for a strand of hair to grow to be 1 meter in length?

One student's answer (after various feeble attempts at calculation):

56 seconds.

Now, wouldn't you think that common sense would kick in somewhere here, especially given all the hype and hoopla in the public schools these days about "critical thinking" and "logical reasoning"? Evidently not.

The truly scary thing about this is that this quiz was for a math for elem. ed. class. Future teachers like this we don't need.

Small wonder that more and more people are choosing to homeschool.

Let the Games Begin!

2008-08-21T13:53:00.004-05:00

Ah, the fun has started already. Below is an email that I received after the second session of class. I have edited it to remove identifying details. Interspersed is the answer I wish I could have given, in a sense. Sometimes it takes restraint to avoid being snarky, and this is one of those times. But hey, that’s one of the purposes of this blog – a safety valve for these types of situations, where your reaction ranges from “Oh, come off it!” to “What planet are they from?”

Fortunately for civilization, professionalism retained the upper hand. No sense in stooping to the other guy’s (gal’s?) level.

-----Original Message-----
From: a student
Sent: [ ]
To: P
Subject: [your class]

Hello Professor P:

I am a student in [one of your classes] this semester. I wanted to tell you how stunned I was by your pop quiz in class today (well, not just me, judging by the agape mouths I saw in class).

I’m actually rather impressed by your vocabulary (“agape”), but “expect frequent quizzes throughout the semester” was clearly indicated on the syllabus. No need to be “stunned.”

The first week of class is a time where students are trying to coordinate buying books, finding their classes, and getting accustomed to those classes and it is such a stressful period made incredibly worse by professors that are unwilling to be understanding of this process (instead expecting us to memorize many logical fallacies in one day).

Although it’s been a few years since I was a student, I know what’s involved. Stress? Well, maybe, but I think that a student at a four-year-school, perhaps hundreds of miles from home, has a bit more “stress” than you do as a community college student.

The logical fallacies were the topic of the first class session. You were there, weren’t you? Or were you sleeping? I also assigned homework on that, so you should have had ample opportunity to play around with the concepts.

Besides, you had two days to work on it, since we don’t meet on consecutive days.

Furthermore, your testing over your own syllabus is truly unfair and sort of self-important.

Syllabi are not handed out to supply you with free wallpaper for your room. They contain important information that you, as a student, need to know. I even mentioned that in class as I passed them out. Why should I not quiz you over important information that you need to know as a student in my class? That’s neither “unfair” nor “self-important,” that’s “checking to see if you’re doing what’s required.”

If these are the unfair, out-of-left-field quizzes you intend to give this semester, students are not going to succeed in this kind of class environment, because it's not conducive to learning to always be afraid

You’re splitting your infinitives.

Quizzes are a didactic tool. They are diagnostic for me, so I know what you’re getting and what is going over your head, and they are diagnostic for you as well, so you have an honest idea of your grasp of the concepts that you will eventually be tested on. Homework, by contrast, is for practice, and really not a good indication of how well you understand the material. Why? Because when you do homework, you have the textbook and your notes to look at, you have friends you can consult with, and you have virtually all the time in the world to spend on it – none of which is pertinent to actual test situations. Read any decent book on study skills, or how to improve your grades, and they’ll mention the same thing: quizzes (whether self-quiz, or in-class quizzes) are essential for learning.

of what kind of crazy quiz you'll come up with next.

Real crazy quizzes – exactly like the homework. Did you do any? I started off the class by specifically asking if anyone had any questions over the homework. Since no one responded, the only logical conclusion that I can draw (since it was an assignment, after all), was that all was wonderful, and no one had any problems.

Sorry – you’ll have to come up with a better example than that when you complain about “crazy quizzes.”

Memorization of your phone number is likely the last thing on a student's mind as they are trying to adjust to a new semester, and it's certainly not worth testing on, especially when a student can call [the switchboard] and be transferred to you, as well e-mail you.

I suspect you’ve been brainwashed by the constructivist anti-memorization crowd. You’ve probably been told that memorization is pointless in today’s society since you can just look up anything that you don’t know, or use a calculator instead of learning the times tables. Balderdash. What’s the point of running to the encyclopedia or internet every time you need to find some information?

Contrariwise, essential contact information is well-worth memorizing, which is why it’s worth testing on. I want to make sure you hang on to the syllabus, and know how to get a hold of me if you have any questions.

It's not like community college students trek to a professor's office so much that their office number requires memorization, *especially* by the second class period. Plus they're probably not going to come ask your help when you have displayed what they consider to be total unfairness already.

You know, you use the term “unfair” and its derivatives rather freely, but you haven’t really given any good examples of what constitutes “unfairness.” Let me help you out here: UNFAIR – anything that I don’t like, or I think is “mean.”

That’s your working definition, isn’t it?

How about this alternate definition of “unfair”? UNFAIR – whiny students who start off on the wrong foot by not doing the assignment, and then complaining about quizzes that they were told to expect.

I hope that you have a sense of fairness enough to drop those questions from the exam, especially given that you didn't even somewhat imply your personal information was to be memorized (and *never* do students memorize such information anyway when you give a syllabus for that exact reason).

I hope you will develop a sense of responsibility and quit your whining. Drop the attitude, and grow up.

At the risk of sounding like a broken record: Syllabi are given to impart essential information. Quizzes are given to spur you on to learn the material. I quizzed you to see if you absorbed that essential information.

I have never, in my college career, seen a professor not go over the syllabus in class, yet test on it. We should have been warned to STUDY your syllabus.

What, exactly, did you think the syllabus was for? Why was a tree killed to print off information that you were going to ignore? I can’t speak for your other teachers – they do what they want to do. It’s their discretion, as it is mine.

Listen: if it’s assigned, it’s fair game. No whining.

I'm also really disappointed because think it's [sic] important to foster a class environment that is personal and comfortable and I don't see that here, especially since you show little interest in even learning your students' first names.

And you’re doing your part to foster a healthy class environment by sending whiny, anonymous emails? What do you think will be going through my mind now every time I’m in that class? Yup, in the back of my mind I’m going to be looking at each one of you and wondering which of you is the whiny coward.

Real personal and comfortable – yup, you’re helping that along swimmingly.

First names? Oh, come off it. This isn’t grade school. Who’s the instructor, and who’s the student? Personally, I disagree with the overly familiar attitude that dictates first-name basis amongst strangers.

Perhaps you have better things to do than conduct class in a way that shows respect for your students; if this is case, they will likely not respect you, nor succeed in your class, and that is a shame.

I have not conducted myself in an unprofessional manner, so I am baffled as to how I’ve neglected to “show respect” for my students. You, on the other hand, have a lot to learn about respecting those in authority over you – and yes, for better or for worse, as your teacher I fall into that category. If anyone is not getting the respect they deserve, it would be me, as a recipient of a whiny, cowardly, emotional email. Take a good, long look in the mirror and see if you can figure out the incongruity of your attitude. That's the real shame - you're missing a golden opportunity to demonstrate that you are a mature adult.

See you next week.

I’ll be there. In the meanwhile, I hope you grow up.

============

My actual, measured response:

I am sorry that you felt stressed out with the first week of classes and everything. I was a student once, too, so I know everything that's involved. Nonetheless, homework is assigned (including reading the syllabus - I pass it out because it contains information that you need to know, which is why I included that on the quiz, BTW - nothing to do with "self-importance") and you are expected to complete the assignments.

I am more than willing to help students do well in the class (which is one reason why I have office hours as well as take the time to go over questions in class), but it's not a one-man show. Students need to do their part as well. The typical, minimum recommendation is 2 hours of study for every hour in class, to give you an idea of the time commitment needed not only for this class, but other classes that you will take in your college career.

With 28 students it's a challenge to learn all the names, and it typically doesn't happen until after I start passing back quizzes. Furthermore, last names are necessary to help distinguish among students with identical first names. Personally, I am not comfortable being on a first-name basis with people I've only just met (not a sign of "disrespect" - you've evidently got a different definition of "respect"), so I tend to use last names and titles (the latter sometimes being problematic when first names are gender-ambiguous, so I have to wait until I actually meet the person).

I hope this helps you to understand where I'm coming from as a teacher. If you have any other questions or concerns, please feel free to stop by my office and discuss them with me. I'm not the ogre you've judged me to be, and if you'd talk to me you'd find that out.

Regards,

P
Adjunct Instructor, Math

Practice Makes Perfect

2008-07-18T00:09:00.002-05:00

If you want to have some practice on the abacus (soroban), click on the top red button for a pop-up. The default operation is addition - other operations may be selected via the blue at the top of the pop-up. It's easier if you use a mouse rather than a touch pad, if you happen to be working on a laptop. Using an abacus is wonderful for developing number sense.

Crazy Constructivists

2008-07-11T23:24:00.002-05:00

I’ve been teaching math at the local community college for several semesters now. My first course was a finite math course, with non-math, non-science majors being the primary target. One of the things that immediately struck me about the book was its apparent backwardness: in introducing a new concept, the book would invariably present some examples, then posit a definition of sorts, then enumerate any steps or processes involved. I was extremely puzzled by this order of presentation. Why on earth throw up some examples before defining or even describing whatever it is that you wish to illustrate? I simply didn’t get it.

Since then, I’ve had several other courses: business calc, probability & stats, “quantitative literacy,” math for elementary ed teachers (the latter being a whole ‘nother story in itself). All of these books followed the same order of presentation – bass-ackwards. I couldn’t fathom why, and I merely continued preparing my lectures in a more logical format: definition, example, steps, problem.

Concurrently, I’ve been reading more about the current state of the American educational system. A common theme seems to be how the progressive-constructivist philosophy has by and large supplanted the traditional, instructivist methods in the classroom. This philosophy, in turn, has resulted in less and less actual learning taking place in our schools, a phenomenon I’ve noticed as a community college instructor and as a private tutor.

I didn’t put two and two together, though, until the other day, then it dawned on me: the textbooks for the courses I’ve been teaching have all been written by authors who have imbibed from the constructivist well. They’ve bought into Piaget’s odd little notion that knowledge is not “true” knowledge unless you’ve “constructed” or discovered it yourself. Aha – so that’s why these crazy books obdurately insisted on placing examples before giving any definitions or enumerating any steps. That explains that.

I still don’t get it, though.

Ray's Higher Arithmetic

2008-07-10T14:56:00.000-05:00

For some years now, I’ve had in my possession a copy of Ray’s Higher Arithmetic. I’m not exactly sure how old my particular copy is. There is no copyright date on it, but the original owner evidently studied it nearly a hundred years ago; some portions of the books are penciled in with dates like “9 – 23 – 13,” most likely indicating the date that section was either assigned or due.

Anyways, it is a neat little book; although it is merely “higher arithmetic” as opposed to Ray’s “New Elementary Algebra” or “New Higher Algebra,” there are nonetheless quite a number of involved concepts covered that would be thoroughly unfamiliar even to current university students, whether at the graduate or undergraduate level – things like “evolution” (extraction of roots) and “casting out nine’s” (a method for checking the accuracy of lengthy sums). I plan on sharing some of the more interesting tidbits from the book on this blog.

A note: English has changed somewhat since Mr. Ray wrote his book, although it remains readable by modern students. One of the most striking examples of this is Ray’s periodic inclusion of sets of “promiscuous exercises” – which makes sense when you remind yourself that the essence of “promiscuous” is a variety or mixture of things; a miscellany. Unfortunately, “mixed review problems” is the last thing that contemporary students would associate with Ray’s terminology.

Introduction

2008-07-10T13:11:00.000-05:00

I've started this blog to focus on things related to math and education. Most of my thoughts and insights vis-a-vis education will be education as it pertains to the teaching of arithmetic, but that is not to say that I won't foray into other subject matters as well.

Now, you may be wondering about the name - The Abelian Grape. It's one of many nerdy math jokes I picked up in grad school:

Q. What is purple and commutes?

A. An abelian grape.

If you don't understand it, please go review some abstract algebra :)