Physics Education Continued

In a prior post, I discussed the problem of college students having poor physical intuition both before and after taking university physics. In another post I will discuss David Hestenes' proposed solution to this problem, but first I wanted to provide some examples of what kinds of errors these students are making.

Hestenes et. al. developed a test called the Force Concept Inventory, but they've embargoed online versions of it (it's available to you if you can prove you are a physics teacher or professor.) The following questions are similar to questions on the FCI, but I've respected their embargo, and adapted them from similar questions. Their own questions are taken from other papers as well, as the literature is filled with examples of how physics students don't understand basic mechanics.

Here are two test questions, the first adapted from Students' preconceptions in introductory mechanics, J. Clement, Am. J. Phys. 50(1), Jan. 1982, and the second adapated from Rule-governed approaches to physics--Newton's third Law, D. P. Maloney, Phys. Educ., Vol 19, 1984. Note that my adaptations haven't been tested on thousands, so they may not be as crystal clear as I hope...

1. A ball is tossed from point A straight up into the air and caught at point E. It reaches its maximum height at point C, and points B and D are at the same height above the ground. IGNORE AIR RESISTANCE.
Try to imagine that "up" on the page is the z direction, and that the horizontal direction is x. No motion is occurring in x.




a. Draw with one or more arrows showing the direction of each force acting on the ball when it is at point B.
b. Is the speed of the ball at point B greater, lesser, or the same as at point A?
c. Is the speed of the ball at point D greater, lesser, or the same as at point B?


2. Consider the following diagrams of two blocks on a frictionless surface and answer the following questions. Ignore air resistance.
a. Assuming both blocks are at rest:


How does the force that A exerts on B compare to the force B exerts on A, if A and B are equal in mass?
How does the force that A exerts on B compare to the force B exerts on A, if A and B have different masses?

b. Assuming both blocks are moving to the right with velocity v:


How does the force that A exerts on B compare to the force B exerts on A, if A and B are equal in mass?
How does the force that A exerts on B compare to the force B exerts on A, if A and B have different masses?

c. Assuming both blocks are moving to the left with constant acceleration a:


How does the force that A exerts on B compare to the force B exerts on A, if A and B are equal in mass?
How does the force that A exerts on B compare to the force B exerts on A, if A and B have different masses?
---
While the actual test employed some randomization and various other elements (set values for the masses, e.g.) the results for this last question were that less than 10% of experienced students (those who had taken college physics) got the right answer using the right reasoning, and 0% of the novice students (those who had not yet taken college physics) got the right answer.

UPDATE: See, I told you I hadn't vetted the questions. Updates are above in BOLD. College Physics above means college students taking a standard first term mechanics course. In the test they did with question c, the students were junior or senior year chemistry students who were required to take a 1 year physics course as a prereq for their major. The author was at Creighton University, so presumably these students were at Creighton University as well. The author points out that at least half a dozen of these students who got these wrong had also taken the MCAT, and possibly had studied physics AGAIN as well.

SECOND UPDATE:

how about some answers?

Problem 1: a. There's one force on the ball. it's Gravity, pointed down. b. The speed of the ball at B is less than the speed at A. The speed drops continuously until we reach C, in fact. c. The speed of the ball at B is the same as at D. In fact, the speed of the ball at any height X above the initial A is the same whether going up or going down. The ball speed depends only on height above our origin.

Problem 2: the answer to all problems is the same: the force exerted by A on B is the same as the forced exerted by B on A.


Physics Education and Failures in Conceptual Understanding
Fixing Physics Education: Modeling Instruction
Physics Education Continued
More Modeling Instruction: Techniques

Fixing Physics Education: Modeling Instruction

In prior posts, I referred to work done by David Hestenes and his colleagues at Arizona State University addressing the dismal results of traditional university level physics instruction. Hestenes and others developed the Force Concept Inventory, FCI, to demonstrate that even after a year of traditional instruction, college students had failed to create proper models in their own minds for how mechanics actually works. Specifically,

"Before physics instruction, students hold naive beliefs about mechanics which are incompatible with Newtonian concepts in most respects.
• Such beliefs are a major determinant of student performance in introductory physics.
• Traditional (lecture-demonstration) physics instruction induces only a small change in the beliefs. This result is largely independent of the instructor’s knowledge, experience and teaching style. "

Hestenes has gone forward from there, and developed a new curriculum design for high school and college physics instruction, and has pushed this curriculum design out to high school and college physics teachers on his own, and more recently, through NSF backing. He calls this new type of instruction modeling instruction.

What is meant by modeling instruction? He means that you learn physics by constructing appropriate models for the interactions in your system, and then you apply inference to your model to solve whatever problem you have. The emphasis is on getting the student to recognize the model at hand by getting them familiar with constructing models in the first place. What's a model? A model is a representation of your system and its properties. A model tells you everything you need to know. So a model tells you your system, the boundaries of your system, the state variables inside your system, the initial conditions of your system, the transition function for the state variables in that system, and whatever interactions you need to know. This sounds vague, but the point of the model is that you can explicitly say whether or not you've got everything you need to infer what happens if you write it all down.

In modeling instruction, the idea is that "the modeling method approaches the problem of restructuring students’ intuitions by engaging them in explicit construction and manipulation of externally structured representations. In the case of mechanics (6), we have found it advisable to engage students in explicit comparisons of the three major misconceptions in Box 1 with their Newtonian alternatives. When these three are adequately treated, many other misconceptions about mechanics fall away with them. "

To facilitate the teaching of mechanics by modeling instruction, the modeling group at ASU created course materials and curricula for a high school level mechanics class. Their modeling method for mechanics explicitly teaches 10 models, five of them models of motion (kinematical models): constant velocity, constant acceleration, the simple harmonic oscillator, uniform circular motion, and a collision model; and five models of force (causal models): the free particle, the constant force, the central force, the linear binding force, and the impulsive force. The idea is that by explicitly organizing the ideas of motion and force in this way, the student will see the common physics in each. This is as opposed to organizing ideas around "problems".

Here's an example. "oh, that's a projectile problem", " oh that's a block-siding problem" "oh, that's a orbit problem" is a typical way a student might think about the physics problem in front of them, but it doesn't help elucidate what were the relevant features of the problem at hand, whereas recognizing "oh, that's a constant velocity problem", "oh that's a free particle problem," "oh, that's a central force problem" leads you immediately to know or be able to infer the geometric structure, the interaction structure, the force structure, the changes over time, etc.

Enough talk! Let's jump in. Here are the course notes for unit on the free-particle model. The instruction goals are to use the free particle model to develop intuition for Newton's First Law (commonly stated as "an object in motion tends to stay in motion; an object at rest tends to stay at rest"), for Newton's Third Law , and to correctly be able to represent forces as vectors.


1. Newton’s 1st law (Galileo’s thought experiment)


Develop notion that a force is required to change velocity, not to produce motion
Constant velocity does not require an explanation.

2. Force concept

View force as an interaction between and agent and an object
Choose system to include objects, not agents
Express Newton’s 3rd law in terms of paired forces (agent-object notation)


3. Force diagrams

Correctly represent forces as vectors originating on object (point particle)
Use the superposition principle to show that the net force is the vector sum of the forces



4. Statics

•F = 0 produces same effect as no force acting on object decomposition of vectors into components

Continuing, the teacher's notes state "It is essential that you get students to see that the constant velocity condition does not require an explanation; that changes in velocity require an interaction between an agent and an object. We quantify this interaction by the concept of force. After the dry ice and normal force demos, one can use worksheet 1 as an opportunity to deploy the force concept in a qualitative way. It is important to carefully treat how to go about drawing force diagrams in which one represents the object as a point particle. Drawing the dotted lines around the object helps students distinguish between the object and the agent(s). "
And

"Newton’s Third Law ...Researchers have identified and categorized many such misconceptions, but two of them are particularly important, because they are persistent common sense alternatives to Newton’s Laws. Ignoring variations and nuances, these misconceptions can be formulated as intuitive principles.
I. The Impetus Principle: Force is an inherent or acquired property of objects that make them move.
II. The Dominance Principle: In an interaction between two objects, the larger or more active object exerts the greater force."

The notes then describe detailed demos and labs, with pre and post discussion points as well:

"It is an indirect goal of this activity to provide students an opportunity for arguing that a free particle, i.e. one subject to zero net force, will have a constant velocity. Also, students should conclude that any apparent change in velocity of an object indicates that a non-zero net force is acting upon it, provided that the observer is in an inertial frame of reference. ,,,
Make the point that when no force acts on the block in the horizontal direction, the block maintains constant velocity.
* Point out that an impulse applied perpendicular to the original trajectory does not result in the block making a right angle turn.
* Be sure to ask why they think the block continues to move once it leaves the hand. Some are likely to answer " due to the force of the hand."

The notes continue in this fashion, with specific notes on what demos/labs, how to guide them, what the appropriate leading questions are, when to ask for students' input, when to build to consensus.

This might seem like a fairly normal course, being taught with a normal lab. But the structure is different. More on that in the next post.


Physics Education and Failures in Conceptual Understanding
Fixing Physics Education: Modeling Instruction
Physics Education Continued
More Modeling Instruction: Techniques

The Foundation of Ingenuity

"To Make Ourselves Indifferent"

A colleague once asked Loyola how long he would need to recover if the pope was ever to disband the Jesuits.^* Loyola's response surely shocked his questioner, and it quickly found its way into Jesuit lore: "If I recollected myself in prayer for a quarter of an hour, I would be happy, and even happier than before."

Perhaps there was a smidgen of posturing in his answer. Loyola had built what was rapidly becoming the world's most influential and successful religious organization. Could he see it dismantled and then stroll away whistling after a mere fifteen minutes in prayer?

Posturing or not, Loyola was sending an unambiguous message grounded in the lessons of the Exercises. Jesuits achieved what we today would call ingenuity--a mix of adaptability, daring, speed, and good judgment--only by first cultivating the attitude he called "indifference."

Trainees approach indifference by imagining three different men who have each legitimately acquired the fabulous sum of ten thousand ducats, then considering their varying reactions to their newly obtained wealth All three feel more than niggling discomfort with their growing attachment to the fortune. There's more to life than money, . . . but it feels so nice to have it. Suddenly it seems impossible to imagine doing without it. The first two types do little or nothing to rid themselves of the wealth that is leading to such inordinate attachment. What does the third type do about the ten thousand ducats? Here is the punch line of the meditation, the person we are to emulate, so the answer seems obvious: he generously distributes the money to the poor and piously rejoices, right?

Wrong. The role model for Jesuit indifference rids himself of the attachment to the money, "but in such a way that there remains no inclination either to keep the acquired money or to dispose of it." In other words, the money is not the issue. The problem is slavish attachment to money or to anything else. Inordinate attachments fog one's vision. . . . Only by becoming indifferent--free of prejudices and attachments and therefore free to choose any course of action--do [Jesuit] recruits become strategically flexible. The indiferent Jesuit liberates himself to choose strategies driven by one motive only: achieving his long-term goal of serving God by helping souls.

The meditation isn't about the money; it's about the attachment.

[snip]

This is what Loyola was really after: the internal fears, drives, and attachments that can control decisions and actions.

[snip]

Indifference is the right stuff of ingenuity. And once early Jesuits attained it, Loyola usually set them loose to lead themselves. "In all, I much desire a complete indifference; then with this obedience and abnegation supposed on the part of the subjects [i.e. individual Jesuits], I am very glad to follow their inclinations."

Heroic Leadership: Best Practices from a 450-Yaer-Old Company That Changed the World by Chris Lowney

I believe this absolutely.

In fact, I have a fair amount of what I think is indifference myself. Not to be confessional here, but I probably couldn't do my job (writing) or my edu-politicking (more writing) if I were "inordinately attached" to either.

Until I read this passage, though, I hadn't been able to put it into words. With education politics, whenever I have tried to explain to a friend why I'm happy to spend years of my life tilting at edu-windmills, the best I've been able to come up with is, "I don't care if anything I do makes a difference." Same thing with writing a book, or a book proposal. I don't care if it's a success.

That's not right, of course. I do care, or I wouldn't be doing it.

"Indifference" doesn't exactly describe my state of mind, but indifference as freedom to choose any course of action ---- that's it.

I need to do the Exercises.

Actually, I needed to do the exercises starting when I was 20.


^* Ed says the Jesuits were kicked out of France altogether at one point.

what is synthetic phonics?

What is Synthetic Phonics?

• Starts before children are introduced to reading scheme books, before any sight word recognition is established

• Teaches letter sounds very rapidly, explicitly showing children how to sound and blend letters in all positions of words right from the start

• Words are not pronounced for children prior to them

• Sounding and blending is taught in the first few weeks of formal sounding and blending them
schooling


What is Analytic Phonics?

• Children start out by recognising whole words.

• The sounds for the letters of the alphabet are taught in the context of alliterative words, often one week for each letter, e.g. gate, green, girl, glove etc

• Letter sounds are then taught at the end of words

• When letter sounds are taught in the middle of words, CVC words are introduced

• Sounding and blending is introduced when CVC words are taught

• It gradually progresses to teaching blends and digraphs, e.g. clip, coat, fast

What are the benefits of synthetic phonics teaching? (pdf file)
Rhona Johnston and Joyce Watson
powerpoint presentation on their Clackmannanshire study:
A seven year study of the effects of synthetic phonics teaching on reading and spelling attainment
and see: the Jim Rose report (UK)
Q&A: synthetic phonics

Skills taught in isolation: a good thing.


preventing the tragedy of content isolation

Schonell spelling test

In the wake of last night's comeuppance (scroll down to 3rd comment), I decided to give C. the 100-word Schonell spelling test (pdf file) today (here it is without directions - pdf file).^*

C. turns 15 at the end of the summer; his "spelling age" today is 13.5 13.8 years.^**

words missed:
yoke
cushion
familiar
permanent
sufficient
cemetery
subterranean
apparatus
portmanteau (almost got that one - !)
amateur
miscellaneous
committee

Since I have nothing to compare this to (how would most American 14 year-olds fare on this test?) I'm declaring this a 'perfectly acceptable' performance.

'Perfectly acceptable' meaning: I'm thinking by the time C. graduates high school he will easily have reached Spelling Age 15, which is 100% correct.

The good news: all of his misspellings were phonetically correct, if phonetically correct is the term I'm looking for, which I'm not sure it is. e.g.: He spelled "amateur" amature. That kind of thing.

He starts an intensive 3-year French sequence in the fall, so that should help.


Lousia Moats on the English writing system

In addition, the English writing system reveals the history of the English language. For example, ch pronounced as /ch/, as in chair or chief, appears in Anglo-Saxon or Old English words; the same letter combination ch pronounced as /sh/, as in chef and chauffeur, appears in French words of Latin origin; and ch pronounced as /k/, as in ache and orchid, appears in words borrowed from Greek. Approximately 20 percent to 25 percent of English words are of Anglo-Saxon origin and about 60 percent are of Latin origin (of which 50 percent are directly from Latin and another 10 percent are from Latin through French, as in chef and chauffeur). The
remaining 15 to 20 percent of English words are primarily of Greek origin.

How Words Cast Their Spell by Louisa Moats
American Educator - Winter 2008-2009, pp. 6-16 & 42-43

^* posted at the Reading Reform Foundation

^** simple arithmetic eludes me (thank you, Michael Weiss) - and, yes, the formula is weird - not sure quite what's to the right of the decimal point

summer reading assignments

SusanS:

My son's list for incoming freshman (honors and regular) was a choice of three little books. He picked one and we ordered it. When it arrived, he read it in one day, then went back to the other more interesting books he was readiing.

Pathetic.

SusanS

anonymous:

Our high school insists on using the same reading list for honors and regular and there are only 2 tracks. The Honors class simply assigns 1 or 2 more from the same weak list.

They must not teach different material in the Honors classes so they require science fair participation or a research paper (not corrected for grammar) to justify the Honors points.

How unsurprising that the school's stated purpose is to close the achievement gap.

The saddest part is that this focus simply reenforces that what kids can be is coming from the home, not the school. The well educated, attentive parents can buy better math and science textbooks, pick out better books for summer reading, and hire tutors to teach grammar.

In the school's emphasis to obtain "equity" by just assigning work within the grasp of most kids, they perpetuate inequities and take away education as the avenue to move beyond the circumstances you were born into.

Susan S:

Seriously, even the regular English track can handle more than one naval-gazing coming of age mini-book.

The natives are restless.

WTM Forum on spelling programs

They like Megawords (Nick's Mama recommends!), Sequential Spelling,^* All About Spelling (Orton Gillingham approach) and Apples and Pears.


department of oldies but goodies (you may need to hit refresh a couple of times)

On being your child's frontal lobes 5-3-2005
Great Moments in World History 5.14.2005
How to Spell 6-14-2005
How to Spell, part 2: Spelling Inquiry 6-14-2005
Megawords saves a reader? 6-14-2005


Speaking of Megawords, C. is finishing Book 6 this summer.

When he started Book 1, C's spelling was psychotic. That was the word that used to pop into my head whenever I caught sight of his spelling: 'psychotic.'

Today he can spell.

He can also pronounce unfamiliar words phonetically. A couple of days ago a copy of the Barron's guide to colleges arrived, and C. started reading the Most Competitive list out loud. He was getting towards the end of the B's when he said, "bou - doin."

Bowdoin.

Pronouncing Bowdoin "bou-din" when you've never seen the word before probably doesn't sound like much, but the fact is: in 5th grade C. could not pronounce a two- or three-syllable nonsense word phonetically. A single-syllable nonsense word: yes. Two syllables: no.

He was two years above grade level in reading, and suddenly, at the beginning of 5th grade, he stopped reading. We didn't know why and neither did he. He just seemed to lose interest.

Not long after he started the Megawords program, he began reading again and hasn't stopped since. I have to think that wasn't a coincidence.


Phonics Page
Don Potter's Education Page


^* Ken's post on spelling, with comments about various programs including Sequential Spelling

Paul on military training

Paul: Having gone though a lot of military training myself I would note that it was excellent and every bit of it was DI [direct instruction]. Of course I didn't think much of it at the time but still it's amazing what it accomplishes in very short order.

Another point to ponder is the impact of military culture on the whole training system. From day one you're stripped of your individualism and made part of a group. It doesn't take long before your motivations are all about not letting your group down. You might even say that the last bit of remaining 'identity' that you have is your specialties and rank.

Powerful motivation, no fluff, intense focus, and high expectations, when brewed, create a potent drink. If all that doesn't work, there's the bad ass drill instructor/Master Chief/Master Sargent to provide 'direction'.

All of you.

Drop whatever you're doing right now.

Go read Work Hard. Be Nice.

it's official: afterschooling is a word

The first person I heard use the term afterschooling was Brenda, talking to Susan S, on September 15, 2005.

Thanks Brenda,

Even though I'm not a homeschooler (I guess I'm a supplementer) I'm a huge Story of the World fan and have them all, plus activity books. (We're in the middle of the third one.) I can't recommend them enough.

I still go back and re-read sections of The Well-Trained Mind every few months, especially now that my kids are moving into the aptly named "Pert" stage.

-- SusanS - 14 Sep 2005

SusanS^?,

You're what we call an "afterschooler", and there are a fair number of them at WTM. I think afterschooling is actually more difficult than homeschooling, in many ways. Hats off to you and the others trying to make it work.

--Brenda

-- KtmGuest - 15 Sep 2005

Now afterschooling has made it to listmania. So it's official (She's got a web site, too!)

How long has afterschooling been used on the Well-Trained Mind forum? Does anyone know?


Hi. I started afterschooling 30 minutes ago.

10-all

we're watching Wimbledon on DVR

unbelievable

announcer: "It's awesome to watch two guys play at this level for this long."

why parents pay for Catholic school

C's summer assignments from Hogwarts:

• read the first 15 chapters of the AP Euro textbook
• read & outline the first 6 chapters of the AP bio textbook
• watch Franco Zefferilli's Jesus of Nazareth
  
• read 3 books for English
• read 1 book on dealing with stress (guidance assignment)
  

Here's what Lefty's going-into-7th-grade son will be doing:

A Mathematical Scavenger Hunt at the Library

Go the the city library--either the main library or a branch library. Do the following activities and record all of this information in an attractive booklet or on a poster. Plan ahead since you may need more than one visit to do everything on the list

1. Draw a sketch of the front of the library on 8.5 X 11 paper. Show the windows and doors. Estimate the width and height of the building and show these dimensions on your sketch. Explain the strategy you used to make your estimate.

2. Go to a room in the library. Make a sketch of the floor plan of the room. Estimate the length and width of the room. What is your estimate of the area of the room? Explain the strategy you used to make your estimate

3. Find a section of the books that you like. Write down the types of books you chose. Place your forearm along the shelf and count how many books there are from the tip o your elbow to the tip of your fingers.

4. Estimate the number of books in this room. Explain what strategy you used to come up with your estimate.

5. Find a chart showing the Dewey decimal numbers for the categories of books in the library. Copy the information to the chart.

6. If you do not already have one, sign up for a library card.

7. Check out a non-fiction book that you would like to read. List its title, author, and Dewey decimal number.

Bring the project to school on the first day. Your teacher will use the data you have collected for class.

Left offers a suggested summer assignment for her school's teachers.

dreaming

from Paul B --

I have an acquaintance who was taught Chinese in the Air Force. The training was even more intense than the article describes. He was immersed in Chinese language 24 hours per day, having to wear earphones, while sleeping, that continued the immersion.

Twenty years later, when he dreams, it's in Chinese.

I remember, years ago, a conversation with a woman whose sister was in the foreign service. She told me that the foreign service has precise ratings of people's level of fluency in foreign languages. (I think Concerned Parent knows all of this & may be rated or ranked herself. Hope she's around.)

As I recall, I think there is a very small group of non-native speakers who reach the level of native fluency.

(Is that right?)

Here are Foreign Service Institute courses in the public domain

And here's the book on second language learning Lefty recommended to me: Handbook of Research in Second Language Teaching and Learning by Eli Hinkel.

while you were sleeping

ERIN McAULIFFE had a vision for this summer. A 20-year-old junior at Bowdoin College, she had lined up an internship at a New York publishing house and imagined stimulating days leafing through manuscripts, and evenings of sparkling conversation with friends at downtown cafes.

She ended up starring in a real-life version of the movie “Adventureland” instead. In that recent comedy, a recent college graduate is forced by economic hardship to work at a suburban amusement park.

Life is imitating art for Ms. McAuliffe. With her parents unable to help bankroll three months of unpaid work in Manhattan, she gave up the internship offer and moved home to Andover, Mass., where she took the one job she could find: working 12-hour days at an amusement park. For $7.80 an hour, she tends bumper cars and the big swing, and endures the many carny jokes of her friends.

[snip]

In the short term, the lost summer of 2009 might actually be a blessing, some psychologists said, especially because members of this generation have lived their lives like track stars trying to run a marathon at the pace of a 100-meter dash — their parents typically waiting at every turn with a stopwatch.

“Parents have really put a lot of pressure on the kids — everything has been organized, they’re all taking A.P. courses, then summer hits and they’re going to learning camps,” said Peter A. Spevak, a psychologist in Rockville, Md.

Say Hello to Underachieving
By ALEX WILLIAMS
New York Times July 5, 2009

Learning camps?

summer 2009

In theory, C. is working through these books:

Megawords 6

Analyze, Organize, Write by Arthur Whimbey & Elizabeth Lynn Jenkins (text reconstruction)

Sentence Composing for High School: A Worktext on Sentence Variety and Maturity by Don Killgallon
Grammar for High School: A Sentence-Composing Approach---A Student Worktext by Don Killgallon & Jenny Killgallon
Sentence Combining Workbook by Pam Altman, et. al.

French by Association by Michael Gruenberg
Behind the Wheel French for the car^*
ALEKS Geometry

I have no idea whether the Killgallon books 'work,' whether Killgallon's exercises, in and of themselves, improve a person's writing. I don't care. I love them so much I'm insisting C. do them. I'm going to do the college book myself. Here's the Killgallons' web site.

As for the Whimbey/Jenkins book, I take Myra Linden's word for it:

"In a study of ‘before‘ and ‘after‘ papers of students who used text reconstruction, I concluded that text reconstruction was effective in helping students learn to organize their ideas into coherent paragraphs. The most marked improvement in their second samples was in content. Students were able to furnish specific details to support general statements. In addition, students showed consistent improvement in organization and style.

"I believe that this approach works because the constant practice in arrangement of content from the general to the specific provided by the text … fosters the most basic writing skills of presenting specific content and organizing it logically into a cohesive pattern. Students replace their faulty composing patterns with effective ones that become automatic skills. In addition, students who do significant amounts of text reconstruction learn indispensable techniques for effective study skills. It helps note-taking. It aids in learning outlining and summarizing skills, and it teaches the general-specific arrangement of ideas.

Why Johnny Can't Write by Myra J. Linden

^* Behind the Wheel Spanish & Spanish by Association for me -- also Fluenz

pop quiz

Are You Qualified to Teach Elementary School Math? (pdf file)

teach your babies to read, part 2

The persistent reading struggles and failure of nearly 40 percent of all American children, little improved over time, has led to aggressive government-funded efforts in school districts to train veteran teachers in the science of reading. The accumulated scientific findings of nearly 60 years of research gained the nation’s attention with the release of a number of significant reviews and compendia of the research beginning in 1990, but most notably the National Reading Panel report in 2000. The findings call for explicit, systematic teaching of phonemic awareness and phonics, guided oral reading to improve fluency, direct and indirect vocabulary building, and exposure to a variety of reading comprehension strategies. All this attention on veteran teachers begs the question: How are future teachers being prepared to teach reading? In this study, the National Council on Teacher Quality makes a unique effort to learn what aspiring teachers are taught about reading instruction. From a randomly selected, representative sample of 72 education schools, NCTQ reviewed 223 required reading courses, including evaluations of syllabi as well as 227 required reading texts. Schools were scored on how well their courses presented the core components of the science of reading. The findings are alarming. Only 15 percent of the education schools provide future teachers with minimal exposure to the science. Moreover, course syllabi reveal a tendency to dismiss the scientific research in reading, continuing to espouse approaches to reading that will not serve up to 40 percent of all children. Course texts were equally disappointing. Only four of the 227 texts were rated as “acceptable” for use as a general, comprehensive textbook. This distressing trend in teacher training demands attention from federal and state governments, professional organizations dedicated to improving and supporting education schools, textbook publishers, and educations schools themselves. The report closes with recommendations to ameliorate this serious failure in adequately preparing teachers in the best practices of reading instruction.

What Education Schools Aren't Teaching About Reading (pdf file)
May 2006
National Council on Teacher Quality


special ed teachers not trained to remediate dyslexia
what ed schools aren't teaching about reading

dyslexia & special ed

Liz Ditz left the link for this story:

Most college special education masters programs do not include comprehensive instruction in reading for dyslexics.

Yet, dyslexics or children with reading disorders make up 70-80% of the special education students. Is there any wonder why special education reading scores are so low?

At best, most potential teachers will get just an overview in reading. Few colleges, if any, teach one of the few methodologies proven by the International Dyslexia Association. These methodologies are taught by private companies or certified individuals, not colleges.

The owners of the methodologies are not big text book publishers like Harcourt, SRA, etc that can afford lobbyists to push state politicians and administrators to approve their curriculum's. Publishers make money by selling hundreds of thousands of text books.

True research based proven methodologies for dyslexics are multi-sensory based. The original is Orton Gillingham. The rest are based on the theories of Orton Gillingham are Wilson, Slingerland and Spaulding.

The exception to the rule is Lindamood Bell LiPS (Lindamood Phonemic Sequencing) which is a proven multi-sensory methodology.

In order to use these methodologies properly, teachers must have intensive instruction, consistent mentoring and follow up. Teachers cannot go to a two day or one week workshop and then come back and teach the rest of the staff. Unfortunately, this is the current model in SFUSD. Last year's professional development calendar did not include a single workshop in reading instruction for dyslexics.

For the last 90 years nationwide, college teacher training programs and public schools have ignored the fact that Orton Gillingham (O-G) methodology works for dyslexic children, to the detriments of millions of children and society as a whole. Famous dyslexic Special Education attorney Pete Wright had a very hard time in school and was taught to read using Orton Gillingham methodology.

Ironically, Pete would advocate for a dyslexic girl named Shannon Carter in front of the supreme court. He would win a unanimous decision in 1993. The court ruled that the public school did not provide Shannon Carter with a free appropriate public education (FAPE). The court ruled to reimburse the parents who found an adequate private school which taught Shannon via the Orton Gillingham method.

There have been cases all over the country where the few parents who do fight back win when it comes to poor reading instruction. Even the dimmest hearing officer recognizes a child that can't read! With so much evidence available, one would think public schools would get the message, but they don't. Right now the deck is very much stacked against parents with the Office of Administrative Hearings in California. School districts win about 90% of the time. But even in that poisonous climate, a San Francisco Unified School District's "legal expert consultant" took a reading case to Court and lost. This student won 200 hours of Lindamood Bell tutoring. Read decision here

Is this how we spend money from the "rainy day" education fund? How much did this trial cost? Wouldn't it be a better idea to teach children how to read?

While politicians, educators, and administrators argue over reading, few listen to the sound, well researched International Dyslexia Association. With the advent of MRI's, whole new waves of understanding and research about how well these methodologies work have been published. There have been articles in Newsweek, great documentaries of powerful evidence of neuroscience but the public school officials and college special education departments still don't pay attention.

No Child Left Behind (NCLB) demanded evidence based reading programs with research behind them. Great idea. Except all kinds of educational publishers eager to get their piece of the money pie, came up with watered down textbooks and programs claiming to have O-G traits pushed their wares on gullible public school administrators who do not have the knowledge to be educated consumers. Publishers were just interested in just making money. School district administrators do not understand the difference between the "at risk" population vs Specific Learning Disabled population.

Neuroscience has proven beyond a doubt over and over that these are the methodologies that work.

It's a local and national shame.

The Best Kept Secret in Special Education
by Robin Hansen
March 29, 2009
SF Special Education Examiner

Under the heading it's always worse than you think, see: What Education Schools Aren't Teaching about Reading and What Elementary Teachers Aren't Learning

Fourth of July

how to chart it

This is synchronicity.

While I was upstairs finishing a post about how to chart stuff, C. was downstairs discovering GraphJam.

Teacher in America

Chapter 10: Tongues and Areas

Is a Frenchman a man?
Yes.
Well, den! Dad blame it, why doan’ he talk like a man? You answer me dat!
JIM AND HUCKLEBERRY FINN

Shortly before setting foot in the United States, I tried to learn something about the country from an old guidebook which had been around the house for years. With my imperfect command of the language, one sentence near the beginning, I remember, filled me with apprehension:

The European tongues are taught in the high schools all over the country, but the instruction is purely theoretical, and the number who can talk French, German, or Italian is very small. Tourists who wish to travel among the remoter districts of New England should be well acquainted with the language, which is the English of Elizabeth with a few local idioms. [1]

Having no idea whether I should be called upon to travel in the “remoter districts of New England,” much less what was meant by the “English of Elizabeth,” I pinned all my faith on this “theoretical instruction” of American youth in European tongues. I now know what it means It means that boys and girls “take” French or Spanish or German (never Italian: the guidebook is wrong) for three, four, or five years before entering college, only to discover there that they cannot read, speak, or understand it. The word for this type of instruction is not “theoretical” but “hypothetical.” Its principle is “If it were possible to learn a foreign language in the way I have been taught it, I should now know that language.”

Various things follow. One is that Berlitz Schools do a thriving business with people who are suddenly confronted with the need to travel abroad. Another is that there is a lifelong Sehnsucht about foreign tongues, which quack advertisements seek to satisfy: “Astonish your friends by speaking to the waiter in French.” A third is that advanced college teaching and graduate study are hampered at every turn by the students’ inability to pick up and read important foreign works. Every year in my senior and graduate classes, I ask those present to write after their names on the class list the languages that they know. Most of them put down French or German or both. But when they come to choose research topics and I suggest a foreign item for their bibliography, they retract their “knowledge” with an embarrassed smile. Some of these students are at the very time “taking” the language in college and some have passed the so-called proficiency test.

There are exceptions to this generality, but most often the exceptional student turns out to have lived abroad or had relatives who speak the tongue in question. When the Army, the Navy, and the civilian war services needed native-born linguists who were also college graduates in the prime of life, they discovered that they had to set up their own language schools and cram German, Russian, Japanese, Spanish, Italian, and French into people whose previous immunity to language seemed absolute. They could “take” it forever; it wouldn’t “take.”

Everybody knows the outcome: they’re all linguists now. My students send me Christmas cards in Japanese, or inform me that when they return they plan to study under my sponsorship the relations of the Third French Republic and the Tsarist regime. I see very clearly that I am going to have to learn Russian.

Characteristically, college administrators have jumped to the conclusion that the Army must have some secret “method”—held back until M-day—which the colleges ought to find out and apply. Campuses buzz with the spirit of reform, the language departments themselves being divided between the Old Guard, which defends its former “methods,” and the New, whose proposals combine elements of the army training with Area studies. I shall explain what these are in a moment.

Meanwhile, the Army and Navy’s victorious inoculation of the antilinguistic American boy is not hard to account for. It was not a secret; it was mainly Concentration. The men were segregated, put in charge of foreign instructors, drilled morning, noon, and night under conditions of prisonlike rigidity. Standards were high and failures from laziness or incapacity were weeded out as fast as they shoed up. A competitive game was set going, which keyed up the good minds to outdo themselves. Outside the class hours, the men would quiz each other, talk, joke, and write in the language they were learning. Two powerful motives were at work: the negative fear of not keeping up and therefore being returned to the ranks, and the positive wish for a commission and the pay that goes with it.

Clearly if these or similar motives could be brought into play in high school or college, language teaching—or for that matter the teaching of any subject—would yield astonishing results. If I did not mention as an incentive the very real desire to discharge a patriotic duty, it is because that motive already finds a parallel in the civilian’s academic career. The man with the moral fervor of patriotism is likely to be the man with the moral fervor of scholarship; in both cases, the student sees himself as owing a duty to something greater than himself. This kind of ambition no system can demand; it can only use it when found.

1 New England: A Handbook for Travellers (Boston: James R. Osgood, 1873).

Teacher in America by Jacques Barzun
Indianapolis: Liberty Fund 1981
first published: 1944
pp. 185-188

you are here

from Paul B:

Kids can't do 6 times 7 because they are 'taught' multiple ways to multiply. Then they discover the one they like best (usually involves fingers) and stick to it until somewhere along the way they are given a calculator to expedite things.

They are assessed subjectively. They are promoted without regard to those assessments. And finally, they're never given targeted remediation or practice that is up to the task of keeping them on track.

Other than that there's not much wrong.

I have already confessed my own problems with 6 times 7.

help desk: how to chart progress

Years ago the director of the charter school for autistic kids Jimmy & Andrew were attending told me that the only way to turn 'data' into positive reinforcement was to chart it.

That was a revelation. I already knew about the importance of "taking data," as behavior analysts call it. Taking data seems to be a pivotal behavior in behavioral treatment; just keeping track of what you're doing -- or what your goofy kids are doing -- helps. Knowing what you're doing changes what you're doing.

This is true even for children with severe autism, by the way. I've seen it. The minute you start counting & recording a child's behaviors to get a baseline, the behavior changes. It's uncanny.

In any event, the director's friend was working on his dissertation and had been recording his word count every day. But he'd stalled out & was stuck. Blocked.

She told him he needed to chart his data. It isn't good enough just to write down numbers day in and day out, you have to see a line going up-up-up (or, in the case of weight loss, down-down-down) if your daily numbers are going to serve as a force for good.

Practically the instant the words were out of her mouth, I knew she was right, and I've been trying to chart stuff ever since. Problem is, I've never been able to figure out how to chart the things I need to chart. Weight loss is easy; it's weight against date. Page counts are easy. Pages against date & keep a running total.

But I've never worked out how to chart the other phases of writing (or anything else): planning, organizing, reading, interviewing, etc.

Just this week, I'm trying to figure out how to chart C's studies for the summer. He has a bunch of reading to do for Hogwarts, which is easy. Last summer I made a simple chart for both of us that worked like a charm. It's a good thing, too, because he had to read 2500 pages in 8 weeks. He may have been one of the few kids in the school who actually did it, and we have the schedule and the chart to thank for it.

This summer I want him to do a bunch of other things, too. On the advice of friends, I've decided to pay him to do some but not all of them, and I have no idea how to record these activities in a manner that will be a) clear and b) motivating.

Here's the scheme:



I don't know what to do with this, chart-wise.

Plus I'm befuddled on the question of positive reinforcement and intrinsic motivation, but that's another story.

Are there books to read on this subject?

And: has anyone used Chartdog?

Explanation of standard celeration chart
50 Google chart tricks for your next classroom presentation
free behavior modification charts

Physics Education and Failures in Conceptual Understanding

For decades, physics professors in universities and colleges in the US have known there is something wrong with physics studies in their schools. Their own physics majors have a poor understanding of basic concepts in mechanics, electricity and magnetism, and quantum mechanics.

Journals like The American Journal of Physics (devoted to teaching and pedagogy at the university level) and Physics Teacher (the same for high school and lower) bring up these issues, with a variety of proposed changes and solutions both at the individual classroom level and at the higher theory-of-ed level. D. Hestenes at ASU and his colleagues have done work in this area, both in questioning the failures of pedagogy and developing some solutions. First, the problems.

D. Hestenes wrote in "What Do Graduate Oral Exams Tell Us?" (Am J. Phys. 63:1069 (1995)) of finding a quote from physicist W. F. G. Swann, in "The Teaching of Physics", (Am. J. Phys. 19, 182-187 (1950)):

"Much can be said about oral examinations for doctor’s degrees, and in my judgment not much can be said that is good. I have sat in innumerable examinations for Ph.D. at very many different universities, sometimes as a member of the permanent faculty and sometimes as a visitor. In almost every case the knowledge exhibited was such that if it represented the true state of mind of the student, he never should have passed. However, after the examination is concluded there is usually a discussion to the effect that: "Well, So-and-so got tied up pretty badly, but I happen to know that he is a very good man," etc., etc., and so finally he is passed."

Hestenes goes on to quote Swann as saying [A student] "passes his tests frequently [including graduate comprehensive exams], alas, with very little comprehension of what he has been doing."

Hestenes diagnoses the problem as this:

It seems not to have occurred to the faculty that dismal oral exams may be symptoms of a severe deficiency in the entire physics curriculum. I submit that there is good reason to believe that they are symptomatic of a general failure to develop student skills in qualitative modeling and analysis.

These general failures mean that even students who have the grades to appear to have excellent mastery of the material do not understand basic elements of the material they have "learned".

It also suggests that college students who fail to understand the material may end up there because their confusion prevents them from attaining the mastery the "good" students have.

Of course, the errors didn't just start in college. Generally speaking, proper physical intuition is lacking in students who took high school physics, even in those who did well. Hestenes writes in "Force Concept Inventory", (Physics Teacher, Vol. 30, March 1992, 141-158)

"it has been established that1 (1) commonsense beliefs about motion and force are incompatible with Newtonian concepts in most respects, (2) conventional physics instruction produces little change in these beliefs, and (3) this result is independent of the instructor and the mode of instruction. The implications could not be more serious. Since the students have evidently not learned the most basic Newtonian concepts, they must have failed to comprehend most of the material in the course. "

Hestenes et. al. wrote the Force Concept Inventory, a multiple choice test whose aim is to "to probe student beliefs on this matter and how these beliefs compare with the many dimensions of the Newtonian concept. " It poses questions that force a choice between the correct Newtonian answer for an explanation of a given system, and other commonsense explanations that are actually misconceptions. After the test, interviews are done to determine students' reasoning.

Here's an example of a misconception that the FCI aims to tease out of a student:

[The misconception of "impetus":]
The term "impetus" dates back to pre-Galilean times before the concept was discredited scientifically. Of course, students never use the word "impetus"; they might use any of a number of terms, but "force" is perhaps the most common. Impetus is conceived to be an inanimate "motive power" or "intrinsic force" that keeps things moving. This, of course, contradicts Newton’s First Law, which is why Impetus in Table II is assigned the same number as the First Law in Table I. Evidence that a student believes in some kind of impetus is therefore evidence that the First Law is not understood.

The FCI has been given to thousands of college and high school students. The above paper details the results on the FCI, given as a pre and post test to both high school and undergraduate physics courses, with tremendous detail on similarities and differences across classrooms in the country. More, it provides strong evidence that traditional college physics pedagogy isn't doing anything to teach physics to the students who take it:

"The pretest/post test Inventory scores of 52/63 for [The Regular Physics Mechanics course at Arizona State University] are nearly identical to the 51/64 scores obtained with the Diagnostic for the same course...we have post test averages of 60 and 63 for two other professors teaching the same course. Thus, we have the incredible result of nearly identical post test scores for seven different professors (with more than a thousand students). It is hard to imagine stronger statistical evidence for the original conclusion that Diagnostic posttest scores for conventional instruction are independent of the instructor. One might infer from this that the modest 11% gain for Arizona State Reg. in Table III is achieved by the students on their own. "

Which brings us back to the state of physics majors going to graduate school:

One of us (Hestenes) interviewed 16 first-year graduate students beginning graduate mechanics at Arizona State University. The interviews were in depth on the questions they had missed on the Inventory (more than half an hour for most students). Half the students were American and half were foreign nationals (mostly Chinese). Only two of the students (both Chinese) exhibited a perfect understanding of all physical concepts on the Inventory, though one of them missed several questions because of a severe English deficiency. These two also turned out to be far and away the best students in the mechanics class, with near perfect scores on every test and problem assignment. Every one of the other students exhibited a deficient understanding of buoyancy, as mentioned earlier. The most severe misconceptions were found in three Americans who clearly did not understand Newton’s Third Law (detected by missing question 13) and exhibited reading deficiencies to boot. Two of these still retained the Impetus concept, while the other had misconceptions about friction. Not surprisingly, the student with the most severe misconceptions failed graduate mechanics miserably, while the other two managed to squeak through the first year of graduate school on probation.

Is it just that the Chinese students who manage to get into US physics grad schools are such creme de la creme that they are perfect? Or is Chinese instruction vastly superior?

(And for those who wonder about American instruction in other subjects, read this and weep:)

One disturbing observation from the interviews was that five of the eight Americans, as well as five of the others, exhibited moderate to severe difficulty understanding English text. In most cases the difficulty could be traced to overlooking the critical role of "little words" such as prepositions in determining meaning. As a consequence, we discarded two interesting problems from our original version of the Inventory because they were misread more often than not.

And yet, those who make it through physics graduate school to professordom mostly correct these errors, at least in mechanics. (Though not necessarily. In quantum mechanics, new professors are notorious for teaching elements of the material incorrectly. In special relativity, David Mermin, prof at Cornell, believes many professors teach the entire subject wrong. (He discusses this in a paper called something like "how to teach Special Relativity.") Hestenes suggests this is due to the realities of post quals grad school: the day in, day out teaching and researching refine one's intuition over and over again.

I think this implies something else as well. Error correction in intuition can only occur and stick if the mastery of the manipulation of the equations is so strong that you (correctly) believe what they tell you. If you can be forced to do the math on the board, and forced to read and think about what it says, then you can learn the truth counter to what your intuition tells you, but only if you are utterly sure you did the math on the board correctly.

If instead, you doubt yourself, doubt your manipulation of equations, doubt your application of the laws as you understand them, then you will get confused, doubt your answer, default to your intuition, and scrap learning the correct way to think.

That means you need a tremendous amount of mastery. How in the world to achieve that?

Hestenes' answer --changing how physics is taught in high school and in college--will be explored in a week or so.


Physics Education and Failures in Conceptual Understanding
Fixing Physics Education: Modeling Instruction
Physics Education Continued
More Modeling Instruction: Techniques

Richard on proof by obfuscation

re: TERC on Establishing Truth in Geometry

Oh really .... I don't know where to begin!!!!

"establishing the validity of ideas is critical to mathematics"

I know straight away that my blood pressure will need to be checked by the time I get to the end of this!!!

But wait, there's more!!!

"Most mathematics instruction and textbooks, however, lead us to believe that mathematicians make use only of formal proof -- logical, deductive reasoning based on axioms."

Of course, that should read "Most mathematics instruction and textbooks AND ALL MATHEMATICIANS ..."

"evidence for its validity in the form of a proof"

By this stage, it's pretty obvious to me that the author isn't a mathematician. "Validity in the form of a proof" ..... what other type of validity is there??

Of course, the trained mathematician should have their 'proof by obfuscation' alarm bells ringing by now.

"For a mathematician, often this internal testing can take the form of proof as one attempts to perform the socially accepted criticism of one's argument."

Is this even English? [ed.: I've been asking myself the same question. When I finally learn how to diagram sentences, I'll be able to answer it.]

"However, does proof convince students? Do they see it as a way to establish the validity of their ideas or, as Hanna (1989) suggests, as a set of formal rules unconnected to their personal mathematical activity?"

They'd better see it as (ahem) "a way to establish the validity of their ideas" or their teacher hasn't really communicated the difference between Science and Mathematics too clearly.

Worthy of mention is the desire to "convince students" .... you may accuse me of semantic nitpicking here, but it's important!!

"Ironically, the most effective path to engendering meaningful use of proof in secondary school geometry is to avoid formal proof for much of students' work."

Which roughly translates as "In order to save the village we had to destroy it!"

---------------------------------

I think Melanie Philips (British author) summed it up best in her book 'All Must Have Prizes':

"A fundamental shift in emphasis from knowledge transmitted by the teacher to skills and process 'discovered' by the child has undermined the fundamental premises of mathematics itself. The absolutes of exactness and proof on which the subject is based have been replaced by approximation, guesswork and context."

Melanie Phillips, All Must Have Prizes

Mastery and Conceptual Understanding in Physics

For decades, physics professors in universities and colleges in the US have known there is something wrong with physics studies in their schools. Their own physics majors have a poor understanding of basic concepts in mechanics, electricity and magnetism, and quantum mechanics.

Journals like The American Journal of Physics (devoted to teaching and pedagogy at the university level) and Physics Teacher (the same for high school and lower) bring up these issues, with a variety of proposed changes and solutions both at the individual classroom level and at the higher theory-of-ed level. D. Hestenes at ASU and his colleagues have done work in this area, both in questioning the failures of pedagogy and developing some solutions. First, the problems.

D. Hestenes wrote in "What Do Graduate Oral Exams Tell Us?" (Am J. Phys. 63:1069 (1995)) of finding a quote from physicist W. F. G. Swann, in "The Teaching of Physics", (Am. J. Phys. 19, 182-187 (1950)):

"Much can be said about oral examinations for doctor’s degrees, and in my judgment not much can be said that is good. I have sat in innumerable examinations for Ph.D. at very many different universities, sometimes as a member of the permanent faculty and sometimes as a visitor. In almost every case the knowledge exhibited was such that if it represented the true state of mind of the student, he never should have passed. However, after the examination is concluded there is usually a discussion to the effect that: "Well, So-and-so got tied up pretty badly, but I happen to know that he is a very good man," etc., etc., and so finally he is passed."

Hestenes goes on to quote Swann as saying [A student] "passes his tests frequently [including graduate comprehensive exams], alas, with very little comprehension of what he has been doing."

Hestenes diagnoses the problem as this:

It seems not to have occurred to the faculty that dismal oral exams may be symptoms of a severe deficiency in the entire physics curriculum. I submit that there is good reason to believe that they are symptomatic of a general failure to develop student skills in qualitative modeling and analysis.

Of course, the errors didn't just start in college. Generally speaking, proper physical intuition is lacking in students who took high school physics, even in those who did well. Hestenes writes in "Force Concept Inventory", (Physics Teacher, Vol. 30, March 1992, 141-158)

"it has been established that1 (1) commonsense beliefs about motion and force are incompatible with Newtonian concepts in most respects, (2) conventional physics instruction produces little change in these beliefs, and (3) this result is independent of the instructor and the mode of instruction. The implications could not be more serious. Since the students have evidently not learned the most basic Newtonian concepts, they must have failed to comprehend most of the material in the course. "

Hestenes et. al. wrote the Force Concept Inventory, a multiple choice test whose aim is to "to probe student beliefs on this matter and how these beliefs compare with the many dimensions of the Newtonian concept. " It poses questions that force a choice between the correct Newtonian answer for an explanation of a given system, and other commonsense explanations that are actually misconceptions. After the test, interviews are done to determine students' reasoning.

Here's an example of a misconception that the FCI aims to tease out of a student:

[The misconception of "impetus":]
The term "impetus" dates back to pre-Galilean times before the concept was discredited scientifically. Of course, students never use the word "impetus"; they might use any of a number of terms, but "force" is perhaps the most common. Impetus is conceived to be an inanimate "motive power" or "intrinsic force" that keeps things moving. This, of course, contradicts Newton’s First Law, which is why Impetus in Table II is assigned the same number as the First Law in Table I. Evidence that a student believes in some kind of impetus is therefore evidence that the First Law is not understood.

The FCI has been given to thousands of college and high school students. The above paper details the results on the FCI, given as a pre and post test to both high school and undergraduate physics courses, with tremendous detail on similarities and differences across classrooms in the country. More, it provides strong evidence that traditional college physics pedagogy isn't doing anything to teach physics to the students who take it:

"The pretest/post test Inventory scores of 52/63 for [The Regular Physics Mechanics course at Arizona State University] are nearly identical to the 51/64 scores obtained with the Diagnostic for the same course...we have post test averages of 60 and 63 for two other professors teaching the same course. Thus, we have the incredible result of nearly identical post test scores for seven different professors (with more than a thousand students). It is hard to imagine stronger statistical evidence for the original conclusion that Diagnostic posttest scores for conventional instruction are independent of the instructor. One might infer from this that the modest 11% gain for Arizona State Reg. in Table III is achieved by the students on their own. "

Which brings us back to the state of physics majors going to graduate school:

One of us (Hestenes) interviewed 16 first-year graduate students beginning graduate mechanics at Arizona State University. The interviews were in depth on the questions they had missed on the Inventory (more than half an hour for most students). Half the students were American and half were foreign nationals (mostly Chinese). Only two of the students (both Chinese) exhibited a perfect understanding of all physical concepts on the Inventory, though one of them missed several questions because of a severe English deficiency. These two also turned out to be far and away the best students in the mechanics class, with near perfect scores on every test and problem assignment. Every one of the other students exhibited a deficient understanding of buoyancy, as mentioned earlier. The most severe misconceptions were found in three Americans who clearly did not understand Newton’s Third Law (detected by missing question 13) and exhibited reading deficiencies to boot. Two of these still retained the Impetus concept, while the other had misconceptions about friction. Not surprisingly, the student with the most severe misconceptions failed graduate mechanics miserably, while the other two managed to squeak through the first year of graduate school on probation.

Is it just that the Chinese students who manage to get into US physics grad schools are such creme de la creme that they are perfect? Or is Chinese instruction vastly superior?

(And for those who wonder about American instruction in other subjects, read this and weep:)

One disturbing observation from the interviews was that five of the eight Americans, as well as five of the others, exhibited moderate to severe difficulty understanding English text. In most cases the difficulty could be traced to overlooking the critical role of "little words" such as prepositions in determining meaning. As a consequence, we discarded two interesting problems from our original version of the Inventory because they were misread more often than not.

And yet, those who make it through physics graduate school to professordom mostly correct these errors, at least in mechanics. (Though not necessarily. In quantum mechanics, new professors are notorious for teaching elements of the material incorrectly. In special relativity, David Mermin, prof at Cornell, believes many professors teach the entire subject wrong. (He discusses this in a paper called something like "how to teach Special Relativity.") Hestenes suggests this is due to the realities of post quals grad school: the day in, day out teaching and researching refine one's intuition over and over again.

I think this implies something else he doesn't say. Error correction in intuition can only occur and stick if the mastery of the manipulation of the equations is so strong that you believe what they tell you. If you can be forced to do the math on the board, and forced to read and think about what it says, then you can learn the truth counter to what your intuition tells you, but only if you are utterly sure you did the math on the board correctly.

If instead, you doubt yourself, doubt your manipulation of equations, doubt your application of the laws as you understand them, then you will get confused, doubt your answer, default to your intuition, and scrap learning the correct way to think.

That means you need a tremendous amount of mastery. How in the world to achieve that?

Hestenes' answer --changing how physics is taught in high school and in college--will be explored in a week or so.


Physics Education and Failures in Conceptual Understanding
Fixing Physics Education: Modeling Instruction
Physics Education Continued
More Modeling Instruction: Techniques

test

what time does blogger think it is

who made the list

Curriculum Matters links to the list of people writing the Common Core Standards.

I don't see any parent reps.


CT Coalition for World Class Math
NJ Coalition for World Class Math
PA coalition for World Class Math
United States Coalition for World Class Math
Parents' Group Wants to Shape Math Standards
Common Core Standards: Who Made the List?

no one can teach

In reality, no one can teach mathematics. Effective teachers are those who can stimulate students to learn mathematics. Educational research offers compelling evidence that students learn mathematics well only when they construct their own mathematical understanding (MSEB and National Research Council 1989, 58).

Constructivist Learning and Teaching

Time to put the public back in public schools.


CT Coalition for World Class Math
NJ Coalition for World Class Math
PA coalition for World Class Math
United States Coalition for World Class Math
Parents' Group Wants to Shape Math Standards
Common Core Standards: Who Made the List?

What Is Constructivism?

Constructivist Learning and Teaching
Douglas H. Clements
State University of New York at Buffalo, Buffalo, NY 14260
Michael T. Battista
Kent State University, Kent, OH 44242



CT Coalition for World Class Math
NJ Coalition for World Class Math
PA coalition for World Class Math
United States Coalition for World Class Math
Parents' Group Wants to Shape Math Standards
Common Core Standards: Who Made the List?

TERC on Establishing Truth in Geometry

No one would deny that establishing the validity of ideas is critical to mathematics, both for professional mathematicians and for students. But how do people establish "truth"; how can they prove things? According to Martin and Harel (1989), in everyday life, people consider "proof" to be "what convinces me." Most mathematics instruction and textbooks, however, lead us to believe that mathematicians make use only of formal proof -- logical, deductive reasoning based on axioms.

But mathematicians most often "find" truth by methods that are intuitive or empirical in nature (Eves 1972). In fact, the process by which new mathematics is created is belied by the deductive format in which it is recorded (Lakatos 1976). In creating mathematics, problems are posed, examples analyzed, conjectures made, counterexamples offered, and conjectures revised; a theorem results when this refinement and validation of ideas answers a significant question. Hanna (1989) argues that because mathematical results are presented formally by mathematicians in the form of theorems and proofs, this rigorous practice is mistakenly seen by many as the core of mathematical practice. It is then assumed that "learning mathematics must involve training in the ability to create this form" (pp.22-23). The presentation obscures the mental activity that produced the results.

In fact, according to Bell (1976), personal conviction grows out of internal testing and forming a judgment about whether to accept or reject a conjecture. Later, one subjects this judgment to criticism by others, presenting not only the generalization formed but evidence for its validity in the form of a proof. For a mathematician, often this internal testing can take the form of proof as one attempts to perform the socially accepted criticism of one's argument.

In sum, formally presenting the results of mathematical thought in terms of proofs is meaningful to mathematicians as a method for establishing the validity of ideas. However, does proof convince students? Do they see it as a way to establish the validity of their ideas or, as Hanna (1989) suggests, as a set of formal rules unconnected to their personal mathematical activity?

Let me guess.

No?

No, students do not see proof as a way to establish the validity of their ideas?

Is that it?

Conclusion

Ironically, the most effective path to engendering meaningful use of proof in secondary school geometry is to avoid formal proof for much of students' work.

I had a feeling.

By focusing instead on justifying ideas while helping students build the visual and empirical foundations for higher levels of geometric thought, we can lead students to appreciate the need for formal proof. Only then will they be able to use it meaningfully as a mechanism for justifying ideas.
Geometry and Truth
by Michael T. Battista and Douglas Clements

Only then, after sophomore year has come to an end and so has geometry.

Here's a question.

How many sophomores in high school have mathematical ideas?

Dobbs Ferry adopts Singapore Math

District adds new program to Springhurst

Robyne Camp, who was elected to the board in May, has asked the district to pilot Primary Mathematics in 2 first grade classes next fall and to give parents the choice of enrolling their child in the pilot class or in a class using Trailblazers.

This passage is one to cite often:

Dobbs Ferry isn’t alone in rethinking its approach to teaching math. In recent years, there has been a shift away from more traditional methodology, including so-called “reform” math programs like Trailblazers which have drawn criticism from some teachers and parents.