kitchen table math, the sequel: 7/5/09 - 7/12/09

Saturday, July 11, 2009

maths dunces

Jenny left a link to this story:
When the Bamberger family opened a haberdashery 65 years ago, they insisted their staff use mental arithmetic to price up customers' purchases.

Despite the arrival of calculators, that attitude has remained unchanged over the intervening years.

But now the family finds itself facing an unexpected maths problem - most youngsters it would like to employ are incapable of working out sums in their heads.

Colin Bamberger, 82, whose parents founded the Remnant Shop in 1944, said that less than one in ten applicants are now able to solve basic maths problems without turning to a calculator or till.

In the past, around eight in ten made the grade.

Mr Bamberger, who stills runs one of the family's two stores, yesterday blamed the decline on falling education standards and over-reliance on the pocket calculator.

He said: 'Most of the youngsters who come to us for jobs are unemployable because they are not numerate.

'It is a sorry situation and a poor reflection on the academic qualities of young people these days. I think it shows modern teaching methods are sadly lacking.

'It is all very well using calculators but if you have not got some idea what the answer is, how do you know if you have pushed the right button? It's so easy to make a mistake.

'It was much easier finding staff a few years ago when everyone coped with working out simple maths in their heads.

Around eight out of ten people who came to us for work were capable of doing it in the 1950s and 1960s - but now it is less than one in ten.

'You ask them how much they would charge for nine metres of material at £9.90 a metre and they fiddle about for ages.'

He said that mental arithmetic was essential in his shops because, if customers queried the final bill, staff could scribble their calculations on a piece of paper to show them how they arrived at the sum.


Robert said that even if applicants were 'massive at marketing, super at sales or even Alan Sugar's next apprentice - if they can't add up quickly in their head we won't have them'.

'My grandfather could add up a column of 50 figures in old pounds, shillings and pennies - including ha'pennies and farthings - in a matter of seconds,' he added. 'He used to insist that any staff we took on could do the same and we have carried on that practice.'

Maths dunces who don't make the cut: Haberdashers have to reject nine out of ten applicants because they can't add up

letter to the editor

Resident applauds district's revised mathematics curriculum

accountable, part 2



My view of education (by Mr. Rydberg, retired math teacher; adopted by Mr. Pearson.)
Since only about 3% of a child’s first 18 years of life is spent in school, I believe a child’s education is the primary responsibility of the parent(s); my role is to support and assist in that endeavor. Although I am committed to work hard, your student cannot do well without your help. You are crucial and indispensable. With these commitments in place, the success of your child will be a delight to us all. But, you are the key, without you, (checking homework and helping prepare for tests; providing a quiet place and time to study; being accountable for results; making time to discuss school work; and helping with organization), their success will be limited.

Steve H:
That pretty much covers it, and we parents are supposed to do it when tests and homework are hidden away in portfolios. We just get quarterly rubric grades that are meaningless.

And they wonder why there's an academic gap. How difficult is it to ask parents of the best students for exact details? They don't want to know the answer. They want to continue the dream that it's just about "checking" homework and providing a nice place to study. Therefore, if your child is not doing well, it's because you are not doing these simple things.

Are we are reaching a point of maximum absurdity, do you think?

math class in the 1970s (scroll down for CA Math Frameworks statement on parent responsibility)

Friday, July 10, 2009



My view of education (by Mr. Rydberg, retired math teacher; adopted by Mr. Pearson.)
Since only about 3% of a child’s first 18 years of life is spent in school, I believe a child’s education is the primary responsibility of the parent(s); my role is to support and assist in that endeavor. Although I am committed to work hard, your student cannot do well without your help. You are crucial and indispensable. With these commitments in place, the success of your child will be a delight to us all. But, you are the key, without you, (checking homework and helping prepare for tests; providing a quiet place and time to study; being accountable for results; making time to discuss school work; and helping with organization), their success will be limited.

I left a comment about parents (re)teaching math on Curriculum Matters.

The math tutor I know told me: "I get the call in 5th grade."

5th grade.

That's when the highly educated parents whose children he tutors max out their reteaching skills.

If parents are crucial and indispensable to their children's math education, the only children learning math are going to be the ones whose parents can afford to hire tutors.

parents are responsible for results
CA Math Frameworks: parents must be "involved" in math education at all grade levels
CA math framework: Responsibilities of Teachers, Students, Parents, Administrators
parents are the problem
outsourcing to parents

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?

anonymous on IB & math/science

I've heard quite a bit from other parents about the various magnet programs in the DC area and I'd agree that IB isn't the best fit for math/science types. Some of the local high schools have had very strong math/science AP programs for decades. I know that Wootton (Montgomery County, MD) regularly competed successfully against the top math/science magnets in the country in math and science competitions. I don't know if they still use the same structure, but all the AP sciences used to be second-level courses, preceded by the Honors course, and all were double-period. 80-85% of the kids typically had 4 or 5 on the AP tests. The IB programs had nothing comparable. The only calculus offered was BC.

le radical galoisien:

It really depends on the school.

ACSI in Singapore has implemented the IB program since 2004.

IB, despite being 'international', really assimilates to each host country's culture.

As I recall, the highest level math exams in IB cover linear algebra and ordered differential equations -- presumably that's what they would have to cover in Singapore in order to be eligible to replace the British A-levels.

comments needed, part 2

Sorry - I'm horribly late with this, but it's probably worth taking a few minutes to leave a comment here.

parents are responsible for results
CA Math Frameworks: parents must be "involved" in math education at all grade levels
CA math framework: Responsibilities of Teachers, Students, Parents, Administrators
parents are the problem
outsourcing to parents

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?

Thursday, July 9, 2009

More Modeling Instruction: Techniques

Continuing the discussion of modeling instruction for physics education, we look to specific techniques to facilitate the model instruction. The modeling instruction method emphasizes that students must construct models and then infer results from those models. The idea is that the teacher need not appear to the student as the authority on what is true; the physics is the authority, and by investigating the physics (with carefully calibrated help from the teacher) the student will build his own intuition about that physical authority. At the same time, as the teacher purposefully falls back so the student can investigate and come to understand the model, the teacher is guiding the inquiry so that in the end, a model is clearly delineated and evaluated. "The modeling view is that students learn best from activities that engage them in actively constructing and using structured representations to make sense of their own experience and communicate with others. To optimize learning, the activities must be carefully planned and managed by the teacher. This requires considerable knowledge and skill on the part of the teacher which our Workshops are designed to cultivate."

Given the lab reports and worksheets shown in the prior post, this may not seem much different from a standard lab class, where the teacher directed the student-inquiry with the lab, and then received a lab report. But it is in several ways. First, the teacher himself is expected to have internalized that the students are generally operating on false premises, and his role is to uncover and replace those misconceptions. Second, the organization of the material into models may well lead teachers who held those same misconceptions to adjust their own teaching. Finally, the main difference comes from the use of interaction during and after the lab, in how the results of the lab work are turned into a model:using the Socratic Method and whiteboarding.

Consider a lab where the students designed the experiments themselves after using whiteboarding to generate a list of what variables they could investigate. Then after completing the lab, whiteboarding and teacher inquiry lead them to define and explain the system schema, for example. The system schema is a graphical representation of what elements of their lab were "in the system" and which were out of it. It should show a simple line drawing the interactions between the things in the system.

For the two blocks on the table, here's a system schema:

System schema drawings are extremely powerful representations, as they can lead directly to understanding when and where forces act on an element in the system.
"How does a system schema minimize the difficulties students have in constructing accurate free-body diagrams?
• By counting the number of interaction lines that end on the body of interest, the student will know the correct number of forces that act on that body.
• By looking at the body at the opposite end of an interaction line, the student can identify the body exerting a given force.

• Given a force on a body of interest, the student can identify its reaction force at the opposite end of its interaction line.
• Internal forces are associated with interaction lines that do not cross the system boundary.
• External forces are associated with interaction lines that cross the system boundary.
• Perhaps most important of all, a system schema provides the student with an easily understood process for creating accurate free-body diagrams.

There are additional benefits to having students constructing system schemas. The schema reinforces the idea that forces on one body are always caused by some other body. The schema also gives a visual reminder that any object also exerts a gravitational force on the entire Earth. With a system schema, the process of constructing a free-body diagram becomes an exercise in analysis instead of memory and/or educated guesswork. When mistakes do occur, good dialogues can occur between teacher and student because together they can examine the process for the source of the error. System schemas ultimately empower the students to select an appropriate system on their own.

The schema are the beginning of the modeling method, but not the end. The schema are expected to be arrived at using the techniques of Whiteboarding and the Socratic Method. The Socratic method of teacher inquiry is meant to direct them toward the correct answer while forcing them to justify their reasoning. Asking "why" they believe that, why they know that, may yield very different answers than expected, especially if the system graph seems right.

The Whiteboarding comes in when the students are asked to construct the model, and the components of it, such as the system schema, a motion map, an interaction map, the geometric or temporal structure, etc. Each of these details is supposed to be constructed by the group based on their data collection and work with each other. Basically, they are being asked to identify the properties of interest they discovered in their lab, and specify the variables that represent them. Students are expected to explain their solutions, and to justify these solutions. The whiteboards allow the teacher to see the students' reasoning in nearly-real-time, and allow the students to participate actively by questioning each other.

Is the model building all left up to student inquiry to drive it in the correct direction? No, absolutely not. Well, not at least in the best teacher's classrooms. Here's an excerpt from a paper on Whiteboarding listed in the Resource section of the Modeling website (italic emphasis his, bold emphasis mine):

The impression we instructors gave, unfortunately, was that the whiteboarding should be mainly student driven. This is unfortunate, because in attempting to make the WB sessions student centered, you lose much of its power and bring in irrelevant issues such as grading the white boards...The power of whiteboarding lies in its ability to allow the instructor to follow the learning process as it is happening, and to control that learning process in a way that optimizes learning. Whiteboarding should not become a report about the learning process to be scrutinized and evaluated by a group of peers. It is a process designed to let the professional guide and evaluate the learning process as it takes place...
This means that instead of standing in front of the group, a round table presentation showing everyone's work together is preferred. It means that mistakes should be correctable during the process; no one should have to parade their mistakes to the group after they realize that they are mistakes.

Of course, now we're getting to the real meat. Can everyone make this model work? Here's another teacher (same paper as above) discussing the whiteboarding model:

I find that I am often dissatisfied with the "Wells" model of whiteboarding. The main problems are: 1. Ideally, the dialogue should be between students, with me (the teacher) offering occasional guidance. Instead, I ask most of (if not all of) the questions. As a result, students sometimes feel that they are being publicly grilled rather than engaged in a genuine public conversation. When I try keeping my mouth shut for long periods of time, the conversation quickly loses its focus. 2. I have difficulty keeping 20+ students engaged in a single conversation. As soon as someone says something really interesting, it stimulates a half-dozen small group conversations, rather than a single large-group conversation. I grow weary of constantly regrouping the class, particularly when the small-group discussions result from genuine curiosity. I would like to see a video of Wells or some other expert in this technique. I suspect that I am missing something. In the last two years, I have been experimenting with the following reforms in whiteboarding methods:

1. Using the "board meeting" ideas presented in this listserv, I have rearranged my classroom so that students can sit in a large circle while presenting. This helps somewhat with issue #2, but does not address issue #1.

2. I have been experimenting with a "whiteboard gallery." I ask the students to present conclusions, solutions, etc. on their whiteboards, along with three check-boxes across the top. One box is labeled "yes," one box is labeled "no," and one box is labeled, "maybe." The students prop their boards around the classroom. Then each student (or group of students) examines the other boards and places a tally mark in the "yes" box, the "no" box, or the "maybe" box of each whiteboard. Afterward, I go from board to board, asking for comment. This seems to improve the student-to-student dialogue, and also greatly
reduces the feeling of a public grilling.

Given the breadth of whiteboarding experience, what is the value of this presenting and discussion? It increases physical intuition in part by properly modeling how science is spoken and done. "Students learn to replace vague descriptive terms of ordinary language with precisely defined scientific terms like “system, interaction, velocity and force.” And to articulate reasons for doing so. They learn to coordinate these terms with increasing skill in generating coherent scientific descriptions, including the specification of system schema and escriptive variables. "

This means their mind is fertile ground for science in the future, since even if they know little, they know less that's just plain untrue. But what elements are the gains really due to?

It's clear from the writing that modeling instruction depends STRONGLY on the quality of teachers involved, and their ability to live up to the high standards that Hestenes et. al. are demanding. Is it possible? Under what circumstances? More on that later.

another nail in the coffin

Is Traditional Teaching Really All that Bad?

answer: no

College Board: 101 Great Books

Speaking of books, I found a copy of College Board's 101 Great Books Recommended for College-Bound Readers in last year's PlannerPad.

I think I've read 33 of them.

Am contemplating reading the other 67. Just by coincidence, I began reading All Quiet on the Western Front just yesterday.

I guess that gives me a running start.

Nicholas Kristof book list

I'm amazed by the number of these books I haven't read - or even heard of in a couple of cases (Freddy the Pig).*

On the other hand, I had all the Anne of Green Gables books when I was a kid & never managed to get through even one of them, as I recall.

I've ordered The Dog Who Wouldn't Be & it may be time to finally read Lad A Dog. My neighbor has been telling me about that book for years. And Little Lord Fauntleroy sounds great!

Also: C. and his friends love the Cherub series.

And don't forget Work Hard. Be Nice.

I am insisting that C. read Work Hard. Be Nice. "I'm not interested in EDUCATION!" doesn't cut it with me as a reason not to read a book your education-obsessed mother thinks you ought to.

* 1000 readers left Comments on his blog about their favorite books.

The Runner

This is an amazing story. (via Frontal Lobe)

Australian spelling test

Anonymous left a link to the Australian Spelling Test, which was normed across 10,000 children in Southern Australia in 2004. I've just given it to C., who turns 15 at the end of the summer:

70 words
59 correct

53 correct: above 15.5 yrs


Words missed:

more fun with Dick and Jane:

me: "Apparatus."

C.: "a - p - p - e - r - a - t - u - s"

me: "Wrong. It's a - p - p - a - r - a - t - u - s. With an e."

C.: So? It's a verb.

WTM on spelling programs
Schonell spelling test
Megawords posts

what is a plosive, Mommy?

Master Green, commenting on What is a consonant, Mommy?:

I can only speak from personal experience, but most of the high school students I teach in Latin had (before they came to me) no idea at all what the differences are between consonants and vowels, never mind the distinctions between the types of consonants. When I explain the shift of 'n' to 'm' before plosives, and then explain what plosives are and why we call them that, it invariably prompts immediate "ooh"s and "aah"s before triggering a digression into all the English words they know that now "make sense" to them. There's also usually at least one student in the class for whom this revelation explains how the English prefix "im-" is the same as "in-" but they never knew it.

I'd give this all up and go teach basic English to small kids if I didn't know that I'd be drummed out in a week. But we do what we can, with a smile and a quiet sigh.

Tell us, too!


what is a consonant, Mommy?

le radical galoisien writes:
I do sometimes wonder about introducing linguistics topics early. I remember when I first went into it I did wonder often, "so why didn't I learn this in elementary school?" Things like what exactly is a consonant, what exactly is a vowel, or a liquid, and what's the exact difference between [p] and [k] and [s].
I agree.

I think Diane McGuinness makes the same point in her book, though I can't find the passage now: why would you deliberately withhold this knowledge from children?

on French:
I do think an emphasis on sound is helpful when you're trying to teach young children *foreign* languages in the classroom. Take French for example -- if you think English spelling is hard, wait till you see the homophony of French and I know French adults who regularly misspell basic conjugations because they all sound the same.

Comment en est-on arrivé là? 4.25.2008
French spelling 11.16.2008
Le scandale de l'illettrisme 9.14.2007
Dyslexie, vraiment? 9.14.2007
French spelling 11.16.2008


I continued to do arithmetic with my father, passing proudly through fractions to decimals. I eventually arrived at the point where so many cows ate so much grass, and tanks filled with water in so many hours I found it quite enthralling.

--Agatha Christie (1890 - 1976)

Arithmetic for Parents by Ron Aharoni
What I Learned in Elementary School by Ron Aharoni (in American Educator)

from ktm-1 (you may have to hit refresh a number of times):
Aharoni article, part 1
Aharoni article, part 2: America's 'new math' goes to Israel
Aharoni on the fifth operation of arithmetic
Ron Aharoni on teaching fractions & forming units

Wednesday, July 8, 2009

Facts, Facts, Facts!

I've just written review of Dan Willingham's book "Why Children Don't Like School." Here it is:

Every once in a while, an empirical study comes along that provides solid evidence against one of those Constructivist practices that some of us whose thoughts on education come more from actual practice than from education theory have often been skeptical about. There is, for example, Jennifer Kaminski’s Ohio State study, which suggests that too much of a focus on “real-world” math obscures the underlying mathematics, such that students are unable to transfer concepts to new problems.

Dan Willingham's book Why Don't Students Like School presents a whole bunch of these experimental results. Together, they challenge the notions that:

1. Students need to learn inquiry, argumentation, and higher-level thinking rather than tons of facts.

2. Integrating art into other subjects enhances learning; so does integrating computer technology.

3. Children learn best through self-guided discovery.

4. Drill is kill. Multiple strategies in a given lesson are better than a single strategy practiced multiple times.

5. Students learn best when constructing their own knowledge.

6. The best way to prepare students to become scientists and mathematicians is to teach them to solve problems the way scientists and mathematicians do.

The empirical data that Willingham cites show that, in fact:

1. Factual knowledge, lots of it, is a prerequisite to higher-level thinking.

2. Students are most likely to remember those aspects of a lesson that they end up thinking about the most. Corollary: Incorporating art or computer technology into another subject may sometimes cause students to think about the art or the technology more than the lesson content, such that they don’t retain the latter.

3. Discovery learning should be reserved for environments where feedback about faulty strategies is immediate: "If students are left to explore ideas on their own,” Willingham writes, they may “remember incorrect 'discoveries' as much as they will remember the correct ones."

4. In Willingham’s words, "it is virtually impossible to become proficient at a mental task,” or transfer ones learning to new environments, “without extended practice."

5. Unlike experts in a field, "students are ready to comprehend but not create knowledge."

6. Novices don’t become experts by behaving like experts do. "Cognition early in training,” Willingham writes, “is fundamentally different from cognition late in training."

Of course, Willingham could be making all this up. But consider just one of his empirical claims:

"Data from the last thirty years lead to a conclusion that is not scientifically challengeable: thinking well requires knowing facts... The very processes that teachers care about the most--critical thinking processes such as reasoning and problem solving--are intimately intertwined with factual knowledge that is stored in long term memory..."

This is a strong statement that could easily be debunked by anyone who knows the empirical literature. There are plenty of highly articulate, outspoken people out there who don’t like what Willingham has to say, but I haven’t seen a single critical review that contradicts his empirical claims.

Of course, if all that matter in life are inquiry, argumentation, and “higher-level” thinking rather than lots and lots of facts, one can say whatever one wants to about Why Children Don’t Like School.

Tuesday, July 7, 2009

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.


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). "

"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.


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


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

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:
portmanteau (almost got that one - !)

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

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.




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.

Sunday, July 5, 2009

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."


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


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.


-- 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.


we're watching Wimbledon on DVR


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.


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.


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
New York Times July 5, 2009

Learning camps?