help desk - even and odd functions

5. Determine whether each function is even, odd, or neither.
a. f(x) = x^4 = 3x^2 + 5
b. g(x) = 2x^2 + 6x + 4

Algebra and Trigonometry Structure and Method
Dolciani

First draft of New York teacher evaluation regs available for comment by the public

The first draft of the New York teacher and principal  evaluation regulations has been posted online for comments from the public.  It looks like it might be a slog to go through the 40-page document, but the six-page summary is here.  The deadline to submit comments is Friday, April 29.

In my first look at the proposal, it hit me that I probably oppose any evaluations based on New York state tests.  "Something fishy" about New York State Regents scoring
 

DRAFT REGULATIONS FOR TEACHER AND PRINCIPAL EVALUATION POSTED FOR COMMENT

Last year, legislation was enacted requiring an annual performance evaluation of all teachers and principals. These evaluations will play a significant role in a wide array of employment decisions, including promotion, retention, tenure determinations, termination, and supplemental compensation, and will be a significant factor in teacher and principal professional development. The Regents Advisory Task Force on Teacher and Principal Effectiveness -- composed of teachers, principals, superintendents of schools, school board representatives, school district and BOCES officials, and other interested parties -- has been meeting regularly since September 2010. And the Board of Regents has discussed various topics related to the evaluation system at its meetings in January, February and March 2011.

Earlier this month, at the Regents April meeting, the Task Force submitted a comprehensive report containing recommendations for implementing the evaluation system in New York. . . . . The draft regulations will be on the Regents agenda at their meeting in May.

Cross-posted at Education Quick Takes

sage on the stage bests guide on the side

new study

from the press release:

[P]rominent organizations such as the National Research Council and the National Council of Teachers of Mathematics, for at least the last three decades, have “called for teachers to engage students in constructing their own new knowledge through more hands-on learning and group work.”

Harvard Study Shows that Lecture-Style Presentations Lead to Higher Student Achievement

Thirty years.

merit aid at the University of South Carolina

anonymous writes:

The University of South Carolina has an extensive Honors College, which offers upper-division classes in a wide variety of fields, in addition to the more usual freshman-sophomore ones. All Honors College courses are taught by professors (no TAs) and the classes are small - my son and his wife had classes as small as 4 students (2 grad, 2 undergrad) and few above 20-25. An Honors College degree requires a senior thesis. The last I heard, the Honors College required at least a 1400 SAT, but most Honors College students receive merit scholarships - for out-of-state students, such scholarships qualify them for reduced tuition (essentially the in-state rate). The campus is right in Columbia, and the housing on the historic Horseshoe is reserved for Honors College students. It's not a big brand name, but the opportunity for a great education is right there and the Honors College faculty want to help their students with special programs, internships etc.

up the down staircase

Sara (not sure who Sara is!) sends a link to this Everyday Math problem posted on the Well-Trained Mind forum.

Up is negative; down is positive.

That strikes me as a bad mnemonic to teach kids who are going to be encountering coordinate planes just a few years from now.

She got the answer wrong, too.


Up the Down Staircase

Debbie Stier on online learning

Here’s What’s Wrong With Online Learning: Kaplan, A Case Study

Test Professors

looks interesting

not a teenager I know

Chaeran Chung reviews John Chung




Dr. John Chung's SAT Math

getting ahead of ourselves

from purplemath:

• Given that f(x) = 3 x 2 + 2x, find [f(x + h) – f(x)] / h.

This is actually something you will see again in calculus. I guess they're trying to "prep" you for upcoming courses when they give you exercises like this, but it's not like anybody remembers these by the time they get to calculus, so it's really a lot of work for no real purpose. However, this type of problem is quite popular, so you should expect to need to know how to do it.

I'm a big fan of purplemath.

Branching Out

In a completely throwaway gag line, football writer (and high school math teacher) Mike Tanier makes a mocking reference to Everyday Math in his offseason column.

I could never be a documentary cameraman. At one point in Sunday's episode of Human Planet (a BBC/Discovery Channel production in the Planet Earth vein) a father takes his two children on a five-day hike along the frozen Zanskar River in Northern India so they can attend a boarding school. The river slowly melts during their journey. At one point, the 11-year-old daughter must crawl along a tiny, cracking ice ledge over the rushing, freezing waters.

...With the poor girl's luck, the school she risked her life to attend just adopted the Everyday Math curriculum, making the whole trip worthless.

Football Outsiders is largely a sabrmetrics site, so the readership is more numerate than average. Still, it warms my heart to see Everyday Math mocked so casually outside of the usual context. I had been planning a post linking Bill Walsh to practicing to mastery, so I guess this serves as a nice segue.

anonymous on the SAT math learning spike

anonymous writes:

I am like that with names. At the start of the school year, I need to learn 150 names. For the first week it is slow going and mostly by memory tricks. Then all of a sudden, I know almost every name automatically.

I wonder if your speed has increased because you have become better at instantly categorizing the math questions.

That's a good question!

I'm going to start keeping notes.

I continue to have the "implicit learning" experiences I've mentioned before, where I'll know that an answer is right without knowing why -- or, in some cases, I'll find myself on the path to solving a problem correctly while consciously thinking I'm doing it wrong.

I'll have to check my books on learning and memory to see if it's the case that implicit knowledge shows up before explicit knowledge. (Implicit knowledge is sometimes called the "cognitive unconscious," a term I'm keen on.)

If I had to guess, I'd say anonymous is right: I'm recognizing problems faster. I'm already as fast as I'm going to get at doing the actual calculations, and I don't think I've boosted my speed at setting up word problems (which I need to work on).

Also, my 'number sense,' for want of a better term, isn't especially good. That is, I don't read a problem and think 'the answer has to be in the neighborhood of thus and such because of thus and such.' My math knowledge continues to be fairly inflexible, so I don't take shortcuts doing the problems because the obvious shortcuts aren't obvious to me.

Not unless the problem is super-easy. Here is problem number 2 from yesterday's test:

A machine requires 4 gallons of fuel to operate for 1 day. At this rate, how many gallons of fuel would be required for 16 of these machines to operate for 1/2 day?

I started out setting up unit multipliers and quickly got stuck: I cannot for the life of me make unit multipliers work on an SAT math section. Why? Very frustrating.

So I was sitting there burning time on QUESTION NUMBER 2, the 2nd easiest question I was going to be doing, and finally I just bagged the dimensional analysis, looked at the problem again, and said to myself: "If it's 4 gallons for 1 machine for 1 day, then it's 2 gallons for 1 machine for 1/2 day, so if I've got 16 machines that's 16x2 and that's 32."

I was very happy to see 32 amongst the answer choices.


SAT genre

The other piece of evidence that anonymous is right -- our increase in speed is due to increased recognition (categorization) of what we're looking at -- is the fact that I can now tell a "genuine" SAT math problem apart from an ersatz SAT math problem. (I'm going to try to find out whether C. can tell the difference.)

Interestingly, I could tell the difference between a real SAT reading question and an imitation SAT reading question from the get-go, just about, and of course the reading section is what I'm good at.

the learning curve

re: C's and my apparent learning "spike," here are Frank E. Ritter and Lael J. Schooler on the learning curve:

Most tasks get faster with practice. This is not surprising because we have all seen this and perhaps know it in some intuitive sense. What is surprising is that the rate and shape of improvement is fairly common across tasks. Figure 1 shows this for a simple task plotted both on linear and log-log coordinates. The pattern is a rapid improvement followed by ever lesser improvements with further practice. Such negatively accelerated learning curves are typically described well by power functions, thus, learning is often said to follow the "power law of practice". Not shown on the graph, but occurring concurrently, is a decrease in variance in performance as the behavior reaches an apparent plateau on a linear plot. This plateau masks continuous small improvements with extensive practice that may only be visible on a log-log plot where months or years of practice can be seen. The longest measurements suggests that for some tasks improvement continues for over 100,000 trials.

[snip]

The power law of practice is ubiquitous. From short perceptual tasks to team-based longer term tasks of building ships, the breadth and length of human behavior, the rate that people improve with practice appears to follow a similar pattern. It has been seen in pressing buttons, reading inverted text, rolling cigars, generating geometry proofs and manufacturing machine tools (cited in Newell and Rosenbloom, 1981), performing mental arithmetic on both large and small tasks (Delaney, Reder, Staszewski, & Ritter, 1998), performing a scheduling task (Nerb, Ritter, & Krems, 1999), and writing books (Ohlsson, 1992).

[snip]

Averaging can mask important aspects of learning. If the tasks vary in difficulty, the resulting line will not appear as a smooth curve, but bounce around. Careful analysis can show that different amounts of transfer and learning are occurring on each task. For example, solving the problem 22x43 will be helped more by previously solving 22x44 than by solving 17x38 because there are more multiplications shared between them. Where sub-tasks are related but different, such as sending and receiving Morse code, the curves can be related but visibly different (Bryan & Harter, 1897).

[snip]

The learning curve has implications for learning in education and everyday life. It suggests that practice always helps improve performance, but that the most dramatic improvements happen first. Another implication is that with sufficient practice people can achieve comparable levels of performance. For example, extensive practice on mental arithmetic (Staszewski reported in Delaney et al., 1998) and on digit
memorization have turned average individuals into world class performers.

Draft version of:
Ritter, F. E., & Schooler, L. J. (2002). The learning curve. In International encyclopedia of the social and behavioral sciences. 8602-8605. Amsterdam: Pergamon.

Don't know how this relates to the experience of having a sudden jump in learning....

the learning spike?

As I mentioned the other day, C. and I have suddenly jumped a good 50 points in our math scores on Blue Book tests.

On April 6, C. missed 7 and skipped 1 on a 20-item math section.

Four days later, on April 10, he finished all 8 questions in an 8-question multiple choice section and missed just 1. He got 7 of the 10 grid-ins right, missed 2, and skipped 1.

And: all three of the questions he missed were dumb mistakes. He knew how to do the problems, and did them quickly enough to finish the test.

I've had the same experience. Last summer I couldn't hope to finish a math section; yesterday I finished early enough to go back and check my bubbles.

At first I thought the higher scores were a fluke. But C. has now turned in the same performance on 5 math sections in a row, and for me that number is probably 6 or even 7.


the power spike of learning?

I'm surprised. I don't remember ever experiencing a sudden jump in learning like this, and my understanding of the "learning curve" is that it's a power curve (if that's the right term), not a right angle. You make more gains early on than you do later.

C. and I made practically no gains early on. While C and I weren't doing a lot of SAT practice fall semester, we have been working with some regularity since January, and in that time we've gotten nowhere. He's been stuck in the high 500s, and I've been stuck in the low 600s. (Very low.)

In fact, I've been stuck in the low 600s for a good two years now. Not that I was practicing SAT math per se -- I wasn't -- but I have been studying high school math off and on during that period, and I've seen no transfer to SAT math at all.

Yesterday, my score on all 3 sections of Test 2 in the College Board online course was 690. C.'s score was 640.

C. said, "It's like I jumped over a wall."

If you graphed our scores on an xy plane, it would be more like we leaped a tall building in a single bound. 

Now we have to leap another one.


arguing in French

The other night at dinner we were talking with our friends about whether they'd had this experience. One friend, an attorney, said tax law was her version of SAT math. She didn't get tax law at all until one day she did. 

Then Ed remembered learning French in France. He was doing what C. and I have been doing: grinding away, putting in the time, having nothing much to show for it. 

Then one day he was sitting around with some friends, and one of them made a provocative statement about something or other. Ed disagreed, an argument ensued, and at some point Ed realized he was arguing in French.

Arguing in a foreign language is the equivalent of an 800, I think.


10 tests

What does this mean, if anything?

Well, first of all, I have to see whether C. and I really are stable at this new level. I suspect we are, but we'll see.

Second: start early. I have no idea why it's taken us so long to experience this leap, but no one becomes an expert - or even a proficient novice (which is probably what we are now) - in a day.

Third: The Blue Book has 10 real SAT tests. C. and I have taken all of the math sections in all 10 tests, and I have taken all 3 math sections in Debbie Stier's January 2011 test.^* Our scores jumped somewhere in the neighborhood of 30 math sections taken over several months' time.

My current thinking on SAT prep is that students should do all 10 sample tests in the Blue Book at a minimum and should spread that work out over at least 4 months.

I'm also thinking it would be a good idea to do the 9 tests College Board offers online for $70.


reading and writing

I'm going to start paying attention to the reading and writing sections. We've done far fewer of those because C. is a very good reader and has been since he was little. He was one of those kids who taught himself to read. That's a funny story, which I know I've told before. C's Kindergarten teacher called us in for a parent-teacher meeting and told us C's handwriting indicated that he was at risk for a reading disability, which was true. Very bad handwriting is a flag.

Naturally, I figured: we've got two autistic kids so now we're going to have a dyslexic kid, too. Just our luck. 

Two weeks later, C. could read. All of a sudden. He went from not reading to reading.

(Another case of a power right angle?)

Back on topic: because C's SAT reading scores are routinely in the low 700s, there's not a lot to learn about SAT prep from observing him, I don't think. He misses or skips questions when he absolutely does not know a vocabulary word and can't figure it out from context. I told him yesterday he has to get back to memorizing his SAT vocabulary words, so the challenge will be remembering to nag him to do it.

("Have you studied your SAT words?" "No." "Do you know where your SAT flash cards are?" "I have an iPod app I use." "Fine, but do you know where the cards are?" "They're in the family room." etc.)

The writing multiple choice questions are more interesting; he misses more of them and presumably will benefit from more practice. (We've done very few writing sections.)

I'm going to start paying attention and will report back.


^* We had also re-taken all 3 sections of the first test in the Blue Book as well as 1 section of the first test in John Chung's book.
 

Education Quick Takes on College Board reading list

books AP students read

merit aid for scores and grades?

A card from Miami University arrived in the mail yesterday promising X amount of merit aid for Y scores-and-GPA.

How do you find out what other colleges and universities are offering?

Have people out there received offers?

I'd like to put together an informal list or database of what's possible----

OCTOBER 11, 2006
Amid Rising Costs and Criticism, Some Colleges Cut Back Merit Aid
By ROBERT TOMSHO


JANUARY 13, 2009
States Weigh Cuts to Merit Scholarships
Budget Shortfalls Threaten Popular Programs That Aim To Keep Top Students Close to Home; 'I Kind of Feel Betrayed'


APRIL 20, 2006
Saying 'No' to the Ivy League
By ROBERT TOMSHO

found art

CRIB SHEET For a management final at Ohio University, one page of notes is allowed. Adrianna Berry, a junior, made the most of it.



source:
The Default Major Skating Through B-School
By DAVID GLENN
Published: April 14, 2011

I love this.

I want one for my wall.

waiting for the teacher, part 2

part 1 is here

Allison writes:

Oh, one other tidbit: the activities in Everyday Math ALWAYS involved manipulatives being arranged in some way. That meant you HAD to stay at your table and wait for the teacher--you couldn't carry it up to the teacher's desk and show your work and ask where you were stuck because it was impossible to transport.

more time in groups, less learning

Speaking of group work:

PAUL M. MASON does not give his business students the same exams he gave 10 or 15 years ago. “Not many of them would pass,” he says.

[snip]

Business majors spend less time preparing for class than do students in any other broad field, according to the most recent National Survey of Student Engagement: nearly half of seniors majoring in business say they spend fewer than 11 hours a week studying outside class. In their new book “Academically Adrift: Limited Learning on College Campuses,” the sociologists Richard Arum and Josipa Roksa report that business majors had the weakest gains during the first two years of college on a national test of writing and reasoning skills. And when business students take the GMAT, the entry examination for M.B.A. programs, they score lower than students in every other major.

This is not a small corner of academe. The family of majors under the business umbrella — including finance, accounting, marketing, management and “general business” — accounts for just over 20 percent, or more than 325,000, of all bachelor’s degrees awarded annually in the United States, making it the most popular field of study.

[snip]

IN “Academically Adrift,” Dr. Arum and Dr. Roksa looked at the performance of students at 24 colleges and universities. At the beginning of freshman year and end of sophomore year, students in the study took the Collegiate Learning Assessment, a national essay test that assesses students’ writing and reasoning skills. During those first two years of college, business students’ scores improved less than any other group’s. Communication, education and social-work majors had slightly better gains; humanities, social science, and science and engineering students saw much stronger improvement.

What accounts for those gaps? Dr. Arum and Dr. Roksa point to sheer time on task. Gains on the C.L.A. closely parallel the amount of time students reported spending on homework. Another explanation is the heavy prevalence of group assignments in business courses: the more time students spent studying in groups, the weaker their gains in the kinds of skills the C.L.A. measures.

The Default Major Skating Through B-School
By DAVID GLENN
Published: April 14, 2011

teacher evaluation

I talked to a high school teacher last weekend who told me teachers are being evaluated on:

• arrangement of furniture in the classroom (desks not in rows)
• presence of group work
• students sharing personal details of their lives with the teacher

I didn't get the sense that 'personal details' meant inappropriately personal. It seemed to mean students sharing biographical detail with the teacher during class time.

I think that is a dreadful criterion - and I would bet a modest sum that students sharing biographical detail with the teacher during class time would be associated with lower achievement, not higher.

I don't want to see students in, say, a U.S. history class talking about themselves.

I want to see students in a U.S. history class talking about U.S. history.

progress report, part 2

C. and I took another math section of the SAT today, and it looks like I am now definitively finishing math sections. In fact, I'm starting to finish with a minute or two to spare. C. is finishing, too, although he's still not able to do all the problems. He skipped 3 today and probably got everything else right. I skipped none and probably missed 2. (We can't check our answers 'til we enter them online.)

I'm still making dumb mistakes. Typically, I'll miss one of the very first questions on the test, which C. never does but enjoys watching me do. We're starting to have a ritual: I miss question 2 or 3, and C. says, "You always miss the easy one and get the hard ones right."

Today I misread the number 6 on a graph as the number 5. Arrrgh.

The good news: I seem to have stopped making bubbling errors. Thank God. Losing points to bubbling errors when you can't even finish the damn test is uniquely demoralizing.

These days I have enough time to check each page for bubbling errors, but I don't find any when I check. More and more, I think speed is the answer -- whatever speed means, exactly, which is more than simply finishing early.

I'm probably talking about fluency.

As I become more fluent in SAT math, I'm becoming more fluent in bubbling, too.

Next challenge: no more dumb mistakes.

how many times should a junior take the SAT?

Any thoughts?

waiting for the teacher

Allison writes:

In the last few months, I visited over a dozen elementary schools. Mostly I visited kindergartens, but whenever possible, I visited the 1st, 2nd, 3rd and 4th grades as well.

Over and over I saw schools where "math class" was the same template: children doing activities from Everyday Math on their own in chaotic, loud classrooms where students didn't have individual desks but had to sit at group tables (sometimes putting up their books and folders to act as little cubicle walls) while they waited for a teacher or an aide to interact with them. Uniformly, I saw half a dozen kids doing nothing at all in those times; another half a dozen chatting or playing but obviously not doing anything, and a precious few trying to block out the stimulus. Some read cheap fiction books.

No one could have learned anything in such a room even before you find out that the task at hand is some bizarre manipulative task in Everyday Math that had no goal or explained purpose anyway.

The teacher didn't spend more time with those having trouble it seemed, either, because those having trouble weren't even bothering to do the activity.

bring back recitation

I was just reading a short article in Education Week about Bill Gates' "Gold Star teacher" plan when I came across a letter criticizing the concept.

First, here's Gates:

Bill Gates closed the National Governors Association's 2011 winter meeting last week by urging the governors to consider increasing the class sizes of the best teachers.

Under the Microsoft founder's model, a school's most effective teachers would be given an additional four or five students. Less effective teachers could then work with smaller classes and receive professional development.

A 2008 study supported by the Bill and Melinda Gates Foundation determined that 83 percent of teachers would support increasing their class sizes for additional compensation. (The foundation provides grant support to Editorial Projects in Education, which publishes Education Week.) In 2009, a Goldwater Institute report argued for tying teacher effectiveness to a higher pupil-teacher ratio and a higher salary.

The endorsement by Mr. Gates now could push the proposal further into the mainstream, given the level of support shown at the NGA meeting.


Gates to NGA: Tie Class Sizes to Teachers' Skills
Education Week
Published Online: March 8, 2011
Published in Print: March 9, 2011, as Gates to NGA: Tie Class Sizes to Teachers' Skill

And here's the reaction from a letter writer:

What makes a teacher of young learners effective is his or her ability to work with individuals in ways that are appropriate to their needs. During whole-group lessons, such teachers move around their classrooms, spotting those who are having difficulty and taking the time to give a little help and encouragement. Later, when planning future lessons, they include modifications for the range of abilities in their classrooms and figure out ways to have most students working on their own or with a partner, so they can meet with small groups.

It is only the least-competent teachers who stand in front of their classrooms and give the same instruction to all, blind to the boredom of those who already know the material, the confusion of those who aren’t ready for it, and the tuned-out state of the few who don’t care.

Although the notion of getting extra pay for taking on more students might have seemed attractive to most of the teachers responding to a survey funded by the Bill and Melinda Gates Foundation in 2008, the situation at that time was only hypothetical.

Today thousands of teachers all over the country have classes of 30 and up. I wager that neither Bill Gates nor the governors who agree with him could keep order in such classrooms, much less teach anybody anything.

Linking Pay and Class Size Hurts Teaching Quality

And here is Doug Lemov:

[Many] to most of the top-performing urban charter schools of which I'm aware buck the otherwise orthodox belief in heterogeneous classroom grouping and solve this problem by homogeneously grouping classes.

Teach Like a Champion
p. 256

With homogeneous grouping, the teacher is always teaching to the level of the entire class because the entire class is on the same level.

Also: whole-group instruction does not mean whole-group lecture. Whole-group instruction means  "Call and Response," "Pepper," "Cold Call," "Wait Time," "Everybody Writes," etc. In the well-taught homogeneously grouped classes Lemov describes, the situation is pretty close to 100% of students learning from the teacher 100% of the time because 100% of students are directly engaged with the teacher for 100% of the class. That's the goal.

How much time are students directly engaged with the teacher in a heterogeneous class?

Not much.

Say class time is 50 minutes and you've got 20 kids.

• 12 minutes for the mini lesson

• 2 or 3 minutes for transition-time (sit on the floor to observe mini-lesson; re-group for partner-work; sit on floor again for mini-lesson; etc.)

• 35 minutes for individual time with teacher

That's maybe 3 minutes of direct instructional time with the teacher per each two-child pair and another 12 minutes of time directly engaged with the teacher during the mini-lesson if the mini-lesson happens to be pitched to the child's level.

If the mini-lesson is not pitched to the child's level, then 3 minutes max.

One of these days I'll have to write up my notes from the 5th grade writing workshop I observed. I think it's fair to say that the two boys I was sitting closest to learned nothing at all for the entire class period. Learned nothing and practiced nothing.

I don't know whether the other kids were engaged in productive partner work.

the other Salman Khan

Found him while searching for 'my' Salman Khan at the Wall Street Journal -----

Salman Khan at WSJ

Salman Khan writing in the WSJ:

I soon discovered that people all over the world were watching my YouTube videos. More important, teachers were using them to change the basic rhythm of their classrooms. They asked their students to watch the videos at home and then used class time for actual problem-solving. Instead of 30 students listening passively to a one-size-fits-all lecture, they were learning at their own speed. Some could focus on filling in gaps in their arithmetic while others were able to jump ahead to trigonometry—and it all took place in the same classroom. It is often said that technology makes modern life less personal, but in this case, it has allowed teachers to take a big step toward humanizing their instruction.

[snip]

Last fall, we began a pilot program with the public schools in Los Altos, Calif., in the heart of Silicon Valley. The initial results are very promising. In order to help teachers customize their instruction, we created a dashboard of robust data for them to follow, linked to their students' online exercises. Students don't move on to more advanced concepts until they have mastered basic ones. Those who get "stuck" promptly receive help, often from peers who are already proficient in a subject. The overall effect has been to create a more collaborative classroom culture.

Turning the Classroom Upside Down
APRIL 9, 2011
By SALMAN KHAN

I'm skeptical.

I'm a fan of the videos, but when the content is slightly over my head, hitting pause doesn't help. Also, in spite of the fact that I have now read a bazillion articles on the disruptive possibilities of online learning, I still prefer books to videos. I don't know why. (Debbie Stier is having the same problem.)

e.g.: I've plowed through nearly 100 pages of Introduction to Counting and Probability on my own - not easy - without having looked at a single Khan video. I keep telling myself I should watch the Khan videos. . . and then I don't watch the Khan videos. Watching a Khan video on counting and probability seems like a chore; studying counting and probability in a book seems like fun.

I'm also skeptical that having students watch videos at home and then work problem sets in class eliminates all the efficiencies of grouping.  But we'll see.

Very interested in the Dashboard, though.

And I do watch the SAT solutions. Those are great - fantastically helpful.

progress

I think I'm starting to finish SAT math sections pretty reliably.

I think C. is starting to finish SAT math sections pretty reliably, too.

We'll see.

anonymous on college enrollment

anonymous writes:

All of the stats about success, completion, etc. are based on "first-time freshmen who enroll in the fall."

Students outside of that specific description are not included in statistics.

We find that our athletic department encourages spring enrollment for many of their most notable recruits.

Cambridge pre-U

What do you think?

All the syllabi.

teachers in the hall, lockers in the homeroom

from The Fragile Success of School Reform in the Bronx
By JONATHAN MAHLER
Published: April 6, 2011

Upon arrival at 223, students pass through a gantlet of smiling teachers. González requires that faculty members stand outside their doors at the start of the school day, part of his effort to set the school off from the grim streets surrounding it. “In our location, kids have to want to come to school,” he says. “This is a very sick district. Tuberculosis, AIDS, asthma rates, homeless shelters, mental-health needs — you name the physical or social ill, and we’re near the top for the city. Which means that when our kids come to school in the morning, when they come through that door, we have to welcome them.”

There’s another, no less compelling reason for this policy: posting teachers outside their classrooms helps maintain order in the hallways. It’s one of a number of things, like moving students’ lockers into their homerooms, that González has done to ensure that kids spend as little time as possible in the halls, where so much middle-school trouble invariably begins. (Chaotic hallways also tend to make for chaotic classrooms.)

I went to an NEA session on bullying in schools a couple of weeks ago. The presenter stressed that the adults in the school - including "ESPs" (education support personnel, I think) - are the ones who must deal with bullying.

You can't leave it up to the kids and their parents. Kids aren't grownups, and parents aren't on site.

deferred admissions

Interesting article in the Times today:

Admission to College, With Catch: Year’s Wait

By LISA W. FODERARO
Published: April 10, 2011

How difficult is it to transfer into a selective school?

in the mail

My copy of Arthur F. Bentley's The Process of Government just arrived.

What was I thinking?

Pascal

All man's troubles come from not knowing how to sit still in one room.

-Blaise Pascal

Quoted in Introduction to Counting and Probability

a chapter title I wasn't hoping to see

Chapter 6: Some Harder Counting Problems

Introduction to Counting and Probability by David Patrick

Headsprout question

Does anyone know whether you can use the Headsprout software on a Mac?

Thanks!

keep it simple

A complex system that does not work is invariably found to have evolved from a simpler system that worked just fine.

from David Kirby's website

You probably all know this, but it's the first time I've seen it ----

Love it!

help desk - triangle

In triangle PQR, PQ = 4, QR = 3, PR = 6, and the measure of angle PQR is x°. Which of the folllowing must be true about x?

(A)  45 ≤ x < 60
(B)  x = 60
(C)  60 < x < 90
(D)  x = 90
(E)  x > 90

help desk - combinations

In the integer 3,589 the digits are all different and increase from left to right. How many integers between 4,000 and 5,000 have digits that are all different and that increase from left to right?

implicit learning, verbal reasoning, and personality

This looks interesting:

Implicit learning as an ability.
Kaufman SB, Deyoung CG, Gray JR, Jiménez L, Brown J, Mackintosh N.
Cognition. 2010 Sep;116(3):321-40. Epub 2010 Jun 22.

Looks like math is more heavily dependent upon explicit learning than language --- which makes sense, given that language is innate and math isn't (or not so much, at any rate).

Yet more evidence that the K-12, constructivist preference for tacit or implicit learning as opposed to direct, focused, conscious learning is a very bad idea when it comes to math.

implicit learning

I re-took another Blue Book math test I'd taken some time ago. I again had no conscious memory of any of the problems, but did them all (save one) fast, finished early, and got everything right.

The problem I couldn't do was the last one in the set and thus the most difficult. My conscious thought was that I had no idea how to do it, a conclusion I arrived at after having in fact done the problem and finding that my answer wasn't amongst the choices. I left it blank.

After the timer rang and I had checked my answers, I went back to the last question.

Turned out my solution was right. It was my arithmetic that was wrong.

Not only do I not recognize the problems, it appears that I don't recognize the solutions, either, even a solution I have just written myself.

I'm going to re-read Arthur Reber, I think. One of my favorite books.

testing buttons

fiddling around with Blogger...

Education in Singapore -- the role of good teachers

I found an adorable video on the Singapore Ministry of Education's page. Blog post and video discussing the role of teachers in education is on Throwing Curves: Education in Singapore - the role of good teachers.

David Steiner resigns

Terrible news.

help desk - how many vertical angles

Here's a problem from The Art of Problem Solving Counting Introduction to Counting and Probability by David Patrick:

How many pairs of vertical angles are formed by five distinct lines that have a common point of intersection?

p. 64

Peter Meyer on the Forum

I am not alone

Be sure to read his March 30th post, too.

Gymnastics and Ed Reform -- something in common

Just wanted to let you know about a new post on Throwing Curves.

Parents and Coaches -- An interesting interaction.

You do not need to be particularly interested or knowledgeable about gymnastics to appreciate the similarities.

August Wren

Jennifer Orkin Lewis is doing the paintings for Perfect Score Project.

I love Jennifer's work. I have boxes of her stationery.
 

Perfect Score Project

It's here!

I've been having beaucoup fun with SAT math (not so much with SAT reading, which is TAXING).

I've just started re-taking the Blue Book math tests.

I don't consciously remember the questions, but I'm a hell of a lot faster -- I finish with time to spare -- and I get almost all of them right.

Which I think is interesting.

sick!

Sorry to have gone missing -- I was thinking the virus that waylaid the household was going to pass me by, but noooooooo.

Public schools have experienced "negative productivity"

Read more about it here at Education Quick Takes.

Connecticut May Make Changes to MBR

One of the more bizarre aspects of funding schools in Connecticut is the "Minimum Budget Requirement" -- a law that requires towns to budget AT LEAST as much for the schools as they did the year before, no exceptions. The penalty? For every $1 drop in spending, the State takes away $2 in town grants.

This year, a very small change to the MBR is being considered at the State legislature. It isn't enough, but it is a start.

Throwing Curves has a new blog post up on the changes to Connecticut's Minimum Budget Requirement - Small Changes to Town Education Budgets May Be Possible.

"The Death and Life of the Great American School System"

Ravitch suspects, with good reason, that her favorite teacher, the intelligent, exacting, and highly literary Mrs. Ratliff, would languish under NCLB. But would Mrs. Ratliff even have become a teacher in today's world? Would someone who is "stifled by the jargon, the indifference to classical literature, and the hostility to her manner of teaching" last through even one week of ed school pabulum, projects, peer-group activities, and proselytizing about Balanced Literacy?

An excerpt of my review of Diane Ravitch's latest book at the Nonpartisan Education Review. You can access the entire review here.

In this book Ravitch brings up her next most recent book: The Language Police. Intrigued (and embarrassed that I hadn't yet read it) I devoured that one a few days ago. If you haven't read it yet, it's a great read.

number sense

from Number Sense with Whole Numbers: 

Some adults lack a sense of the "equal distance of 1" between the whole numbers (the numbers on a number line). Without this concept, addition makes no sense. All math including basic addition is learned by rote as a mechanical process.

I have a memory of Dehaene arguing that people have an "innate" number line inside their minds.

[pause]

yup

It was Dehaene:

I propose that the foundations of arithmetic lie in our ability to mentally represent and manipulate numerosities on a mental “ number line ”, an analogical representation of number ; and that this representation has a long evolutionary history and a specific cerebral substrate. “ Number appears as one of the fundamental dimensions according to which our nervous system parses the external world. Just as we cannot avoid seeing objects in color (an attribute entirely made up by circuits in our occipital cortex, including area V4) and at definite locations in space (a representation reconstructed by occipito-parietal neuronal projection pathways), in the same way numerical quantities are imposed on us effortlessly through the specialized circuits of our inferior parietal lobe. The structure of our brain defines the categories according to which we apprehend the world through mathematics. ” (TNS, p. 245).

Précis of “The number sense”
Stanislas Dehaene
INSERM U.334
Service Hospitalier Frédéric Joliot
CEA/DSV
4 Place du Général Leclerc
91401 cedex Orsay
France
Phone +33 1 69 86 78 73
Fax +33 1 69 86 78 16
dehaene@shfj.cea.fr

Makes people who don't seem to possess an internal number line interesting.

I've been relying on number lines to explain things to myself and to C. ever since coming across Dehaene's work.

how to remember

FedUpMom on remembering area vs circumference:

I had the following brainstorm at an embarrassingly advanced age:

For a long time, I knew there were two formulas that were somehow relevant to circles, namely 2πr and πr², but I could never remember which one was area and which one was circumference.

I finally realized that  πr² must be the formula for area, because area is described in square units. 

Tell your kids.

progress report

C. and I just took a timed math section in the College Board book.

I missed one question and skipped none.

The question I missed was number 4 out of 16, which means it was super-easy. It was so easy, that I'm not going to tell you what the question was. Too embarrassing.

I had brain freeze. Number 4 was one of those "which value can't be the answer?" items. I took a quick look at the 5 possibilities, spotted the one value that was glaringly different from all the other values, and then eliminated that answer because it was different from all the others.

aaarrghh!

Then I spent precious minutes trying to figure out how all the other answers, which obviously could be the answer, could conceivably not be the answer.

oh, man

I think I'll go spend some quality time with Dr. Chung.

Jo in Oklahoma on exercises vs problems

re: SAT problems, Jo in OKC said...

I asked my daughter today. She took the SAT this fall and got a score in the range you mention.

She said the questions are all routine exercises.

She would agree the AMC questions and AIME questions are problems.

One of her favorite areas of math is counting. :-) I remember covering permutations and combinations in high school math. However, what I learned was just a small fraction of what's covered in Art of Problem Solving's Intro to Counting and Probability course or book.

Carnegie Hall

from Dr. John Chung's SAT Math:

Achieving a perfect score on any math exam is quite simple. Though this may sound cliched, all it takes is practice. Practice by taking as many mock tests as you can, and take the time to go through and correct all of your incorrect answers. Keep your mistakes in mind as you take your next mock test.

Since 1992,1 have personally helped more than 50 students each year achieve perfect scores on the SAT Math, SAT II Math I & II, and AP Calculus AB & BC exams. As you might imagine, during my many years of teaching, I have gone through almost every single SAT Math test preparation book out there. I have come to realize that every book is loaded down with explanations and not enough tests! What a waste of money!

Therefore, it is my honor to introduce to you my first test preparation book, Dr. John Chung's SAT Math. There are no tricks or fast-track methods in this book. I have put together 20 mock exams, complete with answers and explanations, to help you PRACTICE your math test taking skills. These are the mock exams that I have used in my private tutoring sessions with my own students, most of whom have gone on to achieve perfect scores on the SAT Math exam.

Special thanks to my latest star students, Angela Lao, Priya Vohra, Devi Mehrotra, Donna Cheung, Jennifer Wong, Amos Han, and Shalini Pammal, who provided invaluable feedback on the format of this book and assisted in the final proofreading session. They all achieved a perfect score on the math section of the PSAT, SAT Math, and SAT II Math I and H.

I hope this book helps you as much as it has helped my students.

Dr. John Chung
President, NYEA