A step-by-step solution to the classic alphametic.

These videos are still very much a work in progress but at least I'm seeing signs of that progress. Trying to do this in one shot and some parts are more confusing than they should be, but those mistakes can be learned from. I was more worried about getting the narration natural and conversational. and in that respect I feel things are definitely moving in the right direction.

I'll be experimenting with more puzzle videos in the future, though probably ones that require less than thirty slides to explain.

A blog of tips and recommendations for anyone interested in learning or teaching mathematics.

## Tuesday, February 23, 2016

## Monday, February 22, 2016

### "Slam the Exam" = "Game the System"?

**Some 2,300 Success Academy students attended a "Slam the Exam" rally before last year's state English tests. The network goes to great lengths to make sure students are ready for the exams. ( Photo by Success Academy )**

Data-driven strategies are a lot like market-based solutions. Properly applied under the right circumstances, they can be excellent, even optimal approaches, but if badly designed by people who don't understand the underlying principles (or who are looking to manipulate the process for their own ends), the results can be disastrous.

When designing a system of data-based decisions, perhaps the two most important considerations are:

Do your metrics have a strong relationship with what they are supposed measure? and;

Will that relationship continue to hold when the system has been in place for a while, particularly once the people affected figure out the rules?.

The Success Academy network is evidently gaming the achievement data in at least three ways:

Selection bias particularly in efforts to force out special needs kids;

Teaching to the test;

Changing the conditions of the test.

Let's focus on this last one for the moment. Check out the following excerpt from an article in Chalkbeat:

At Success Academy schools, high-octane test prep leaves nothing to chance

By Patrick Wall

Published: May 1, 2014

School leaders had provided teachers with color-coded agendas with precise instructions for every few minutes of test days, along with boxes of supplies that might come in handy — from pencils and tissues to extra clothes for students and deodorizing powder to sop up vomit.

Teachers had been taught the proper way to hand out tissues during the test (pass the student a new sheet first, then use a second sheet to grab the used tissue). They knew to set their classroom temperatures to between 66 and 70 degrees, and to call each student’s family every evening before a test to remind them of the next morning’s exam.

On test days, some teachers would take Success-funded cabs to pick up chronically late students (“Taxi Scholars,” as the agendas refer to them). Outside auditors, who had already observed the network’s practice tests, would monitor the real exams to safeguard against charges of test-rigging.

But students were perhaps the most prepared of all. They had spent weeks taking practice tests modeled off the actual state exams. They starred in test “dress rehearsals,” where exact testing conditions were simulated. Some had even practiced tearing perforated reference sheets out of mock test booklets.

If history is any guide, the preparation will pay off. Last year, Success students’ pass rates on the new and much harder state exams beat those of every other city charter school network and far surpassed the city and state averages. [Though these resullts have not carried over to other standardized tests -- MP]

Practices such as calling parents the day before the test very probably do improve test scores – – if, for no other reason, they make it less likely that kids will be allowed to stay up past their bedtime's that night – – but they can have no conceivable effect on the knowledge that is being tested.

It is notable and more than a little disheartening that this reporter, like most of his colleagues, seems to see all things that improve achievement scores as equally desirable, even those tactics that only serve to undermine the validity of the test.

## Friday, February 19, 2016

### What 1964 thought today would look like

Let Arthur C. Clarke handle your lesson plan for you. Show these videos, open the floor for discussion, assign an essay.

And don't say I never did anything for you.

And don't say I never did anything for you.

## Wednesday, February 10, 2016

### The cutting edge of transportation, 51 years ago

Changing Geometry of Flight -1965

"Mostly animated film made for the Boeing Company by Playhouse Pictures. Directed by Jim Pabian. It is preceded by a space-age commercial for RCA televisions, also from Playhouse Pictures."

"Mostly animated film made for the Boeing Company by Playhouse Pictures. Directed by Jim Pabian. It is preceded by a space-age commercial for RCA televisions, also from Playhouse Pictures."

## Saturday, February 6, 2016

### Feynman on the disease of increased precision

We want to be careful about arguing from authority, but it is also important to consider credibility.

Richard Feynman was, to put it mildly, a big deal in 20th century physics. His opinions on scientific and mathematical reasoning carry a tremendous amount of weight. On top of that, he spent a great deal of time and serious thought to digging into the state of elementary and secondary math textbooks. For all these reasons, when he argues forcefully against a certain trend or practice in mathematics education, we should certainly take his arguments seriously.

From NEW TEXTBOOKS FOR THE "NEW" MATHEMATICS

by Richard P. Feynman

ENG1NEERING AND SCIENCE

March 1965, Vol. XXVIII, No. 6

Feynman was, of course, writing in the Sixties, but we have a pretty good idea what he would say about this Common Core aligned handout for an eighth grade algebra class.

Richard Feynman was, to put it mildly, a big deal in 20th century physics. His opinions on scientific and mathematical reasoning carry a tremendous amount of weight. On top of that, he spent a great deal of time and serious thought to digging into the state of elementary and secondary math textbooks. For all these reasons, when he argues forcefully against a certain trend or practice in mathematics education, we should certainly take his arguments seriously.

From NEW TEXTBOOKS FOR THE "NEW" MATHEMATICS

by Richard P. Feynman

ENG1NEERING AND SCIENCE

March 1965, Vol. XXVIII, No. 6

Words and definitions

When we come to consider the words and definitions which children ought to learn, we should be careful not to teach "just" words. It is possible to give an illusion of knowledge by teaching the technical words which someone uses in a field (which sound unusual to ordinary ears ) without at the same time teaching any ideas or facts using these words. Many of the math books that are suggested now are full of such nonsense - of carefully and precisely defined special words that are used by pure mathematicians in their most subtle and difficult analyses, and are used by nobody else.

Secondly, the words which are used should be as close as possible to those in our everyday language; or, as a minimum requirement, they should be the very same words used, at least, by the users of mathematics in the sciences, and in engineering.

...

Pure mathematics is just such an abstraction from the real world, and pure mathematics does have a special precise language for dealing with its own special and technical subjects. But this precise language is not precise in any sense if you deal with the real objects of the world, and it is overly pedantic and quite confusing to use it unless there are some special subtleties which have to be carefully distinguished

A fine distinction

For example, one of the books pedantically insists on pointing out that a picture of a ball and a ball are not the same thing. I doubt that any child would make an error in this particular direction. It is there- fore unnecessary to be precise in the language and to say in each case, "Color the picture of the ball red," whereas the ordinary book would say, "Color the ball red."

As a matter of fact, it is impossible to be precise; the increase in precision to "color the picture of the ball" begins to produce doubts, whereas, before that, there was no difficulty. The picture of a ball includes a circle and includes a background. Should we color the entire square area in which the ball image appears or just the part inside the circle of the ball? Coloring the ball red is clear. Coloring the picture of the ball red has become somewhat more confused.

Although this sounds like a trivial example, this disease of increased precision rises in many of the textbooks to such a pitch that there are almost incomprehensibly complex sentences to say the very simplest thing. In a first-grade book (a primer, in fact) I find a sentence of the type: "Find out if the set of the lollypops is equal in number to the set of girls" - whereas what is meant is: "Find out if there are just enough lollypops for the girls."

The parent will be frightened by this language. It says no more, and it says what it says in no more precise fashion than does the question: "Find out if there are just enough lollypops for the girls" - a perfectly understandable phrase to every child and every parent. There is no need for this nonsense of extra-special language, simply because that type of language is used by pure mathematicians. One does not learn a subject by using the words that people who know the subject use in discussing it. One must learn how to handle the ideas and then, when the subtleties arise which require special language, that special language can be used and developed easily. In the meantime, clarity is the desire.

I believe that all of the exercises in all of the books, from the first to the eighth year, ought to be understandable to any ordinary adult - that is, the question of what one is trying to find out should be clear to every person. It may be that every adult is not able to solve all of the problems; perhaps they have forgotten their arithmetic, and they cannot readily obtain 2/3 of 1/4 of 1-1/3, but they at least should understand that that product is what one is trying to obtain.

By putting the special language into the books, one appears to be learning a different subject and the parent (including highly trained engineers) is unable to help the child or to understand what the thing is all about. Yet such a lack of understanding is completely unnecessary and no gain whatsoever can be claimed for using unusual words when usual words are available, generally understood, and equally clear (usually, in fact, far clearer).

Feynman was, of course, writing in the Sixties, but we have a pretty good idea what he would say about this Common Core aligned handout for an eighth grade algebra class.

Dilation: A transformation of the plane with center O and scale factor r(r > 0). IfThis is not an isolated case. Both the standards themselves and the materials associated with them are filled with obtuse, overly precise language often used in an alarmingly imprecise way.

D(O) = O and if P ≠ O, then the point D(P), to be denoted by Q, is the point on the ray OP so that |OQ| = r|OP|. If the scale factor r ≠ 1, then a dilation in the coordinate plane is a transformation that shrinks or magnifies a figure by multiplying each coordinate of the figure by the scale factor.

Congruence: A finite composition of basic rigid motions—reflections, rotations,

translations—of the plane. Two figures in a plane are congruent if there is a congruence that maps one figure onto the other figure.

Similar: Two figures in the plane are similar if a similarity transformation exists, taking one figure to the other.

Similarity Transformation: A similarity transformation, or similarity, is a composition of a finite number of basic rigid motions or dilations. The scale factor of a similarity transformation is the product of the scale factors of the dilations in the composition; if there are no dilations in the composition, the scale factor is defined to be 1.

Similarity: A similarity is an example of a transformation.

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