Physicist uncomfortable with irrational bears
Great post at a science blog called “Uncertain Principles” (that’s -le not -al but also a great prompt for some writing about today’s NYC Department of Education – but that’s off-topic) – great post about Goldilocks and problems with that damned porridge.
Why is the papa bear’s porridge too hot, and mama bear’s porridge too cold, but baby bear’s porridge just right?
Shouldn’t the baby’s be the coldest?
Read the blogger’s analysis, and read the variety of explanations in the comments:
Mama had a big, flat dish (more surface area, cooled quickly). Mama’s was actually the smallest portion (with extended discussion of the patriarchy). Mama ‘juices’ hers with a cold, alcoholic liquid (more discussion of getting through the day, and patriarchy). Mama dished her own earlier, did chores, then dished the boys’ (again with patriarchy). Baby’s was ladled a bit from each of the parents’ bowls.
Go, read. Add your own theory.
How the hell did Fellows get commitments for positions that had not been posted?
You don’t need to read this blog long to know that the two groups of teachers I am most concerned about, the two groups that face the worst abuse, are senior teachers, especially when they’ve ended up not in a position, and beginning teachers (and Fellows).
I am worried about how easily Bloomberg’s Chancellor, his stooges, and the MSM play our two most vulnerable groups against each other. We need to stick together to protect everyone’s rights.
That being said, definite priority on hiring is to get positions for senior teachers without positions, first, then do everything possible to help and train and protect new teachers.
The 2005 Contract established “open market transfers.” Big mistake. But at least there is some contractual language, and some side agreement… Unfortunately, it seems that we cannot even rely on that.
I already noted that positions were being advertised outside the system, and before the transfer system opened. I note, on Gotham Schools, there is discussion of Fellows or TfAers or similar new teachers who already have commitment letters from principals. And a Fellow told me recently that she was already going on interviews…
Every position must be posted (Article 18). I believe that the postings must be open for at least two weeks. But when did the open market actually open? Two weeks aren’t up. So how are commitment letters to anyone (let alone pre-service teachers) already written? The positions I caught being advertised on the web? Never made it to the open market. And the fellow who mentioned interviews? One, at a school near me, has no vacancies posted in the open market system.
So how are we going to stop this? Teachers get left with no position, because their school closed, and then they get ignored as vacancies get pitched to people who have not yet taught. The current freeze helps – but it just reflects a DoE spending priority, not a fix. What are we going to do?
Sorry
…for the blog break. This return from vacation has turned into the longest 2½ weeks of my teaching career in a full decade. I’m back, but the mix of posts may be weird for a while.
Math Teachers at Play #6
over here.
The host, Mr. D of I Want to Teach Forever, is a high school math teacher in Boston, and has a nice little blog. Go for the carnival, but stick around and check it out.
On-line HS math contest hosted by Math Notations
Here are the details:
The 2nd Contest is scheduled for the week of May 18th-22nd. You can administer the test on any one day during that week for up to 45 minutes. A couple of other changes…
- A school can field up to TWO teams
- This contest is designed only for upper level students (Algebra II, geometry, some trigonometry) but no calculus
To register, click the link at the bottom of this post, and complete the registration form and email it back to Dave Marain by Wed May 13th. He will send the questions between May 13th and May 15th. He’ll also enclose the rules/info sheet.
I hope you will be able to participate despite such short notice. If you could forward this to your colleagues in other high schools, Dave would appreciate it.
Here is the link to the online information about the contest: http://mathnotations.blogspot.com/2009/04/mathnotations-second-math-contest-free.html
UFT Memo: Swine Flu
[I received the following memo Sunday night, April 26. I will post it in my school tomorrow, Monday. While it is addressed to Chapter Leaders, District Reps and Special Reps, no part appears to be confidential. I am sharing it in the interest of sharing accurate, non-hyped information.]
Memorandum
April 26, 2009
TO: UFT CHAPTER LEADERS
UFT DISTRICT REPRESENTATIVES
UFT SPECIAL REPRESENTATIVES
FROM: RANDI WEINGARTEN, UFT PRESIDENT
MICHAEL MULGREW, UFT CHIEF OPERATING OFFICER
ELLIE ENGER, UFT DIRECTOR OF STAFF
STERLING ROBERSON, UFT DIRECTOR OF SAFETY AND HEALTH
CHRIS PROCTOR, UFT COORDINATOR OF SAFETY AND HEALTH
In response to the report of swine flu cases in New York City, we have been working all weekend to put this memo together so that you could have it tonight. We consulted with the Commissioner of Office of Emergency Management as well as a number of representatives from the New York City Department of Health and Mental Hygiene (NYCDOHMH). We have also been in contact with the NYC Department of Education (NYCDOE).
Swine Flu in New York City
The United States declared a public health emergency on Sunday, April 26, 2009. The New York City Department of Health and Mental Hygiene (NYCDOHMH) has been investigating a cluster of respiratory illness in students at St. Francis Preparatory (a non-public school) in Queens. On Sunday, April 26, 2009 the Centers for Disease Control and Prevention (CDC) confirmed cases of swine flu influenza among these students. The school is suspending classes on Monday, April 27th because there may be students who are incubating the disease. The affected students have only experienced mild symptoms and many are already improving.
The DOH also investigated a cluster of children with illness in a Bronx Daycare facility but so far has not identified any confirmed or probable swine flu cases.
In response to confirmed cases of swine flu in Mexico, California, Kansas, Ohio and Texas, the DOH is working closely with the Centers for Disease Control and Prevention (CDC) to assess the possibility of the spread of swine flu.
What is swine flu?
Swine influenza (swine flu) is a respiratory infection caused by type A influenza viruses that regularly cause outbreaks of influenza in pigs. People do not normally get swine flu but human infections can occur.
Symptoms
The symptoms of swine flu are similar to the symptoms of regular human flu and include fever, cough, sore throat, body aches, headache, chills and fatigue. Swine flu can vary in severity from mild to severe.
Transmission
The CDC has determined that this virus is contagious and can spread from human to human. However, at this time, it not known how easily the virus spreads between people.
Human-to-human spread of swine flu has been documented and is thought to occur in the same way as seasonal flu. Influenza is thought to spread mainly person-to-person through proximity (within six feet) to infected persons who are coughing or sneezing. People may also become infected by touching something with flu viruses on it and then touching their mouth or nose.
Swine flu cannot be transmitted from eating pork or pork products.
How long can an infected person spread swine flu to others?
A person is infectious as long as there are symptoms and for up to 7 days following onset of these symptoms. Children, especially young children, may be potentially contagious for even longer.
Medicines to treat swine flu
The CDC says two flu drugs, Tamiflu and Relenza, seem effective against the new strain. These antiviral drugs fight against the flu by keeping flu viruses from reproducing in your body.
Is there a vaccine for swine flu?
There is no vaccine available right now to protect against swine flu.
Preventive measures
CDC has the usual recommendations for people, which are:
• Cover your mouth when you cough or sneeze.
• Wash your hands often with soap and water, especially after you cough or sneeze. Alcohol-based hand cleaners are effective.
• Avoid close contact with sick people.
• If you get sick with influenza, CDC recommends that you stay home from work or school and limit contact with others to keep from infecting them. Avoid touching your eyes, nose or mouth. Germs spread this way.
When to seek health care and treatment
Patients experiencing severe symptoms, such as difficulty breathing, should seek health care and treatment. Otherwise the NYCDOH recommends at-home care.
The UFT has been working with the NYCDOHMH and the NYCDOE to make sure the following measures are in place in schools:
1. Ventilation is important. Given the mild weather keep classroom windows wide open as much as possible, weather permitting.
2. Mechanical ventilation systems should be run with maximum outside air. Make sure all exhaust systems are operable.
3. Provide for stepped-up cleaning of all classrooms, cafeterias and lunchrooms, bathrooms, gymnasiums and other common areas.
4. Staff and students should be notified to wash hands frequently.
5. There must be running water and adequate amounts of soap and paper towels in bathrooms.
6. Staff with flu like symptoms should be seen by their personal physician and obtain medical documentation. Keep a copy of the documentation.
7. Children with unidentified respiratory illness should be sent to the medical room for assessment. According to the NYCDOHMH, if the nurse determines that the student has flu symptoms the nurse should keep the student in the medical room or nearby until they are picked up by their parents or legal guardians. Children with respiratory symptoms from known causes, such as asthma, should be managed as usual.
8. Staff and students with flu-like symptoms should stay home.
We will update you as more information becomes available.
Further information about swine flu can be found at the links below:
From New York City Health Department
Facts about flu
From Centers for Disease Control and Prevention
General information about swine flu
Teaching set theory in NY – more than the minimum
We didn’t used to teach sets in New York State; now we have to – to Algebra students (usually 9th graders).
It is not clear exactly what to teach.
There are only three indicators related to sets.
And the glossaries, indicators, and actual tests (3 of them) define a fairly limited set (ha ha) of items that need be taught:
- what a set is, how to write it (including both roster and set builder notation), what union and intersection mean, and what “complement” means. Also, the symbols for all of these. (for complement they offer prime and superscript C, but neither has occurred on a test)
It would be a shame to teach this topic to this test.
My suggestion is to link the set theory to as much of the rest of the course as possible. Here are some places to do it outside of the unit:
- Solution Sets. As we run into them, {-3, 5}, identify them as sets. Make certain we know they are not ordered.
- Natural Numbers, Whole Numbers, Integers, Rational Numbers, Real Numbers. To the extent possible, identify these as sets. For an advanced class, introduce set-builder notation for the rationals as a “gee whiz” wow them sort of thing. It’s actually not so terrible, since the “fraction” and the restriction should look vaguely familiar. (Ironically, simpler examples may be harder to understand)
- Problem Solving (see Subset Puzzle)
When we reach the unit, the concept of subset gets short shrift in the standards. It can be treated more fully. And cardinality, easy and useful, is omitted. It can painlessly be included. And why no empty set? Throw it in.
Here are some ways to draw links to other parts of mathematics and this course in particular, within the unit (I’ve never hit all of them). Special emphasis on differences from and similarities with properties of arithmetic.
- Use the “not” symbols: ∉, ⊄ which kids quickly figure out, and like (since they are analagous to ≠).
- Draw the analogy between union ∪ and addition, but run some compare and contrast.
- Draw the analogy between intersection ∩ and multiplication, but run some compare and contrast.
- Draw the analogy between the complement of a set and the opposite of a number.
- Draw the analogy between “is a subset of” and “is less than”. Enjoy the superficial resemblance: ⊂ and < . (It helps if they know what cardinality means)
- Show that union and intersection are commutative and associative
- Compare the distributive property of multiplication over addition with how distribution seems to work for union over intersection and intersection over union.
- Examine the complement of a union. Compare with the opposite of a sum.
- The union of a set and the empty set is the first set. (compare at addition of 0)
- The intersection of a set and the empty set is the empty set. (compare at multiplication by 0)
Some notes about the Chapter Leader who lost it
The story was all over the news yesterday, and it’ll be gone in a day. A teacher in the Bronx, a middle school teacher, chapter leader and Army Reservist, lost it. He barricaded himself in a classroom for a few hours, (no hostages involved). The building (3 schools) was evacuated, and then he surrendered. The MSM covered it all day, and the blogs picked up from there. In particular, it turned out that he appears to have maintained a website with some strange educational philosophy, and at least one (soft core?) porn novella. I don’t know what will happen next. Between yesterday’s crisis, the original charge, and the website, the DoE will likely build a big case against the guy.
But there are a few thoughts that the media and the blogs may likely miss. These are for teachers and our union:
- The Rubber Room is a horrible place. This guy was sent to the rubber room before (twice?) and cleared both times (?) This incident was (probably?) sparked by him getting sent there again. His reaction to being sent again was certainly nothing we would condone. But there is something really really bad about the rubber room, and the agreement from last spring does not seem to have made things better.
- The Principals In Need of Improvement program has an effect. The school New Millenium Business Academy (MS328) in District 9, is on the UFT’s PINI list. I don’t know the details in this school, but that likely means that grievances were being filed and negative publicity was being shared, perhaps with the community.
- Principals retaliate. It will (likely?) emerge that the initial charge against the teacher stemmed from breaking up a fight. (Normally?) the teacher would sit in an office for a couple of days while the principal investigated the charges, cleared the teacher, and returned him to the classroom. But this is a PINI principal. The Chapter Leader was probably actively involved in going after this guy, and he probably retaliated by rubber rooming him, all out of proportion.
- Chapter Leaders need protection. In the contract? I don’t know. But adding language would send a message. But maybe not in the contract. Bottom line: principals need to know that messing with a CL will result in immediate, uncomfortable consequences. That idea, we once had it. It’s been lost. It needs to be put back out there, yes in words, but more importantly, in deeds.
- Fights in the classroom put teachers in a bind. Let them tear each other apart? How can we? Yet try to break it up, and we might find charges leveled against us. Officially I have to say that you should not touch the kids. But as a person I have to say, don’t let them kill each other. Call for help. Try to “teacher voice” them apart. We are stuck in these situations.
- Evacuation plans still are not universal. I don’t know how the media missed this, but it will emerge that either the school had no evacuation plan, or it was completely ignored. We’re post- Columbine, post-9/11, but no one knew what to do, and the principal could not account for the kids.
- The DR – CL relationship is a special one. It didn’t get enough play in the news, but it was the Chapter Leader’s District Rep, Carol Harrison, who played a key role in ending the crisis.
- Nothing on the web is anonymous. Act as if everything you write, every image you upload, is public.
When was vacation?
I didn’t want to come back after last week’s vacation. By Wednesday and Thursday I was starting to relax, and by Friday I was uneasy about returning. Sunday night was awful. And then came the week.
I was exhausted, grouchy, on edge. I snapped a few times, grumbled at people instead of greeting them.
I barked instead of asking. Made myself generally unpleasant. But survived the week.
Now we need to catch up on some blogging. Set theory lessons for integrated algebra. Soon.
But a point here: I don’t think it’s just me. This has been an exhausting year. I’ve been doing this job for a while, but it’s not felt like this before.
And also, I’m at a good place. Nice school, nice kids, colleagues. Administrative is intelligent and collaborative (this week they instituted some changes, hallway stuff, that came out of real consultation with the chapter). So I’m not getting burned by working in a bad place, or by being mistreated. Just exhausted this spring. And can’t wait for June 26…
49, 50, um, um, um, 51
After a brief break, the Carnival of Mathematics returns!
A couple of notes:
the intro is short, funny (for us math-types, and maybe a few others), punchy.
there are math blogs that I check regularly, but there are others I don’t follow, but go to when the carnival sends me… which means I read a better mix the week after a carnival comes out. Especially this time, with the overall recreational tilt, I think this will be true.
there is a core of people, not huge, but larger than I suspected, who seem to care about the CoM’s continued existence.
serious discussion about having semi-regular hosts. I think I’d jump on that train.
(credit this carnival to Murray of SquareCirclez)
Third anniversary post
Today is this blog’s third anniversary.
Looking back, I started with an idea and a couple of directions: teacher union stuff in NYC, teaching math, math puzzles, NYC in general.
And while there have been tangents, and there is not as much NYC stuff as I’d intended, things have proceeded more or less as initially conceived.
NY Step streets are largely missing, as is NYC photography in general. It should be possible to remedy those. And including teacher salaries was an interesting idea. They need expansion and updating. And the specific focus on NY State mathematics seems boring, but necessary. And why did I write about vacations? I don’t know, but I do.
Other than that, the biggest surprise has been how many people read this stuff. There are visitors dropping in for salary info. But many more are interested in some other aspect of the content. Site Meter says 424,000 people have viewed 652,000 pages. And that was not expected. Google Reader says there are 186 subscribers to my feed through them, and I’m assuming more through other services. Again, unexpected.
My teaching posts are not of the quality of Frizzle in her heyday, or many other math teacher bloggers (or math teaching bloggers) today. My intra-union political commentary is not as sharp (intentionally) as NYC Educator‘s, nor is it as consistent or funny. My big-picture teachers-in-the-US posts can’t match Fred or his brother. My big-picture education in NYC posts pale next to NYC Public School parents. My salary data is spotty, and, depending on district, up to two years out of date. And I can’t be institutional, like EdWize. Rather than focus on just one area, I’ve developed a mixture. Right? Wrong? It doesn’t matter. This mixture is this blog, for better or worse.
The direction I developed most in the last year was the focus on new teachers. I think the salary info is valuable. But there was the series of Teaching Fellow posts from last summer, the bits of starting school advice, and of course, the Do Not Apply list.
Helping new teachers become experienced teachers is worthwhile. It helps all of us to have experienced colleagues. It helps students to have experienced teachers. Experienced teachers add stability to schools and to students’ lives.
But Bloomberg and his Chancellor, Rhee and TfA, the Leadership Academy and much of the charter movement, all work to create temporary teachers. In NYC they set unqualified administrators loose and violate contractual rights, abuse teachers, drive them out of teaching. They restructure and rearrange and slice and dice our schools, and in the disorganization leave many of our teachers, especially our new teachers, unprotected.
Organizing new teachers into their chapters, organizing chapters where they don’t exist, helping new teachers learn to teach, all are important. As a union we should be measured by our record standing up for our weakest and most vulnerable members.
The math, and math puzzles, and math pedagogy will remain. But standing up for new teachers, developing the capacity to stand up for new teachers, and helping new teachers stand up, helping all teachers, experienced and new, come together to retake what is ours, those will continue to be topics of the highest importance on this blog.
Thank you for reading this far.
What Set Theory is covered in the Integrated Algebra Curriculum?
It’s really a sort of trick question. New York State’s Integrated Algebra isn’t so much a curriculum as a set of “standards” and “performance indicators.” And the Standards and PIs aren’t really more than guideposts to what will be on The Test. And it is The Test (NYS Integrated Algebra Regents) that mot districts will look at in determining what to teach.
But before we move on, we need to look at two additional documents:
Suggested List of Mathematical Language for Integrated Algebra (HTML version, or page with links to HTML, doc, and PDF versions)
(for teachers) Commencement Level Glossary of Mathematical Terms (available as a document, on the same page)
Hidden (hidden? not really) in the algebra section of the List of Mathematical Language are the following:
- complement of a subset
intersection of sets
interval notation
roster form
set
set-builder notation
solution set
subset
union of sets
universal set
Here is what appears in the Glossary:
- complement of a set (A) The elements of a universe not contained in a given set; the subset that must be added to any given subset to yield the original set. The complement of set A is indicated by
. [there is a colored Venn Diagram]
- intersection of sets (A) (G) The intersection of two or more sets is the set of all elements that are common to all of the given sets.
Example: If A = {1,2,3,6} and B = {0,2,5,6,7}, then the intersection of A and B, denoted by A ∩ B, is {2,6} - roster form (A) A notation for listing all the elements in a set using set brackets and a comma between each element.
Example: The set of prime numbers less than 10, expressed in roster form is {2, 3, 5, 7}. - set (A) (G) A well-defined collection of items.
- set-builder notation (A) A notation used to describe the elements of a set.
Example: The set of all positive real numbers in set builder notation is This is read as “the set of all values of x such that x is a real number and x is greater than 0.” - solution set (A) (A2T) Any and all value(s) of the variable(s) that satisfy an equation, inequality, system of equations, or system of inequalities.
- subset (A) (A2T) A set consisting of elements from a given set; it may be the empty set.
Example: if B = {1,2,3,4,5,6,7} and A = {1,2,5}, then A is a subset of B. - union of sets (A) (G) The union of two or more sets is the set of all elements contained in at least one of the sets.
Example: if Set A = {2,4,6,8,10} and Set B = {1,2,3,4,5,6}, then the union of sets A and B, written asis {1,2,3,4,5,6,8,10}.
- universe (A) The set of all possible specified elements from which subsets are formed. Also know as the universal set.
- Venn diagram (A) A drawing showing relationships among sets.
Example: The Venn diagram below shows 14 students. Five students play basketball, seven run track, two play basketball and run track, three play only basketball, five only run track. Four students do not play basketball or run track. [there is a Venn Diagram drawn. An unlabeled, outer rectangle is the universe. Numbers are written in the four regions]
So, add to this the PIs:
Patterns, Relations, and Functions
A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form
A.A.30 Find the complement of a subset of a given set, within a given universe
A.A.31 Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)
And the questions they’ve used:
- 06/08 #18 (multiple choice, 2 points) Consider the set of integers greater than -2 and less than 6. A subset of this set is the positive factors of 5. What is the complement of this subset?
- 06/08 #33 (free response, 2 points) Maureen tracks the range of outdoor temperatures over three days. She records the following information: [the exam has three number lines, for Day 1, Day 2, and Day 3 respectively. The ranges indicated are -20 ≤ t ≤ 40, 0 ≤ t ≤ 50, -23 ≤ t ≤ 45]. Express the intersection of the three sets as an inequality in terms of temperature, t.
- 08/08 #25 (multiple choice, 2 points, I don’t think this should count, either) Which ordered pair is in the solution set of the following system of inequalities
and
- 08/08 #33 (free response, 2 points) Twelve players make up a high school basketball team. The team jerseys are numbered 1 through 12. The players wearing the jerseys numbered 3, 6, 7, 8, and 11 are the only players who start a game. Using set notation, list the complement of this subset.
- 01/09 #17 (multiple choice, 2 points, I have included the first response) The set {1, 2, 3, 4} is equivalent to (1) {
, where x is a whole number}
And that’s all we have to go on.
So, what do we have?
A loose definition of set. A loose definition of subset. Curly braces all over the place (the idea of solution set permeates the curriculum, without any recognition that it is a kind of set). A mention of “empty set.” Symbols also include the vertical bar “such that.” Included are intersection and union, (strangely without binary descriptions), and their respective symbols. Venn Diagrams are included. “Complement” is included, with two possible symbologies.
Missing is the word “element” and the cute, associated symbol: ∊ Also missing is the concept of proper subset. Symbology for the empty set. Symbol for subset. Missing is the word “disjoint” and any hint about the concept. No reference is made to cardinality. And obviously, no associated symbols.
[edit: also missing are the symbols for not an element of, ∉ , and not a subset of, ⊄. Vlorbik reminded me.]
In addition, notice that the Regents questions have not used any of the associated symbology except curly braces and the vertical line. Empty set has not shown up. Subset has not shown up in a way that requires students to understand what the word means. The symbols for intersection and union have not shown up.
Sounds like we’ve defined a minimum: Teach what a set is, how to write it (including both roster and set builder notation), what union and intersection mean, and what “complement” means. And we’re done?
Unfortunately, in many places, the answer will be yes, we are done. But I will be recommending in upcoming posts that we teach more than this, that we create a small unit, and that we embed hooks to it in other parts of the course.
Math Teachers at Play #5
Click here to visit. MTP is back home at Let’s Play Math.
(think about it, great name for a blog, isn’t it? but a better thing to say to kids. Fairly closely related to me saying “puzzle” instead of “problem” – it’s good packaging)
Now in its third month, the new math teaching carnival continues to improve.
This one is big, has five sections: Basics, Arithmetic, Basic Algebra and Geometry, Advanced, Teaching Math.
I have a post in (after forgetting to submit, submitting late, or getting my submission mangled by the tool the last few times).
There are illustrations, poems, apt quotes. It is, in part, a visual carnival.
Part of what’s happening, Denise taps into several different circles. There are math teachers. There are homeschoolers who care about math. And the intersection creates something interesting.
I really liked, by the way, a little fraction puzzle she included.
Unicorns roaming the æther – NY State Mathematics in context
While I am focussing on set theory, that does not mean that bad questions get a free pass. So far, in just three Integrated Algebra Regents exams, the NY State Education Department has offered two free response questions relating to set theory. And both of them, don’t act surprised, stink.
Let’s look first at poor Maureen:
- 06/08 #33 (free response, 2 points) Maureen tracks the range of outdoor temperatures over three days. She records the following information: [the exam has three number lines, for Day 1, Day 2, and Day 3 respectively. The ranges indicated are -20 ≤ t ≤ 40, 0 ≤ t ≤ 50, -23 ≤ t ≤ 45]. Express the intersection of the three sets as an inequality in terms of temperature, t.
Dear readers, can you help me identify the poor community that is plagued by 50, 60 or even 70 degree swings in temperature over consecutive days?
In Washington DC this year, there was a 42 degree swing in a day. The Washington Post saw fit to write an article:
March Temperature Swings Gone Wild
Between Tuesday and Saturday last week, the high temperature at Reagan National Airport (DCA) soared from 29 to 71. I went back into the record books (since they’ve been kept at the airport in 1942) to see if there had been other instances when the high temperature had risen that much in 5 days or less. The answer: no. That 42 degree rise was the biggest such 5-day rise in March in at least 65 years.
Five days or less? Forty degree swing? Record? The Post writers should travel to Albany. Perhaps they should fly up on unicorns, and stop at Oz along the way.
Now lets look at some poorly coached players:
- 08/08 #33 (free response, 2 points) Twelve players make up a high school basketball team. The team jerseys are numbered 1 through 12. The players wearing the jerseys numbered 3, 6, 7, 8, and 11 are the only players who start a game. Using set notation, list the complement of this subset.
T them up! The digits 6, 7, 8 and 9 are never allowed in NCAA or high school basketball. That will be a technical foul. Or will it be one for each illegal jersey? Unless King Arthur and Spider Man and Harry Potter intercede, and suspend the normal rules.
The New York State Education Department brings in teachers and then blames them for okaying this crap, but it is SED’s process that produces nonesensical question after nonesensical question. It is time to clean up the question writing/vetting/approving process. This is not ok.
Set theory in the New York State Curriculum – 3 days in 13 years
There is something ironic about the New York State Core Curriculum in Mathematics.
The ideas “set,” “subset,” and “universe” can be found throughout, as if there is an expectation that the reader knows the concepts. Students should be familiar, at several grade levels, with “data sets” or “subsets of ideas,” or “complements of events” or even “solution sets.”
But actually teach about sets? Just three indicators, all from the Integrated Algebra course. Nothing earlier. Nothing later. 3 days in 13 years for concepts that we assume are understood.
Patterns, Relations, and Functions
A.A.29 Use set-builder notation and/or interval notation to illustrate the elements of a set, given the elements in roster form
A.A.30 Find the complement of a subset of a given set, within a given universe
A.A.31 Find the intersection of sets (no more than three sets) and/or union of sets (no more than three sets)
How do these translate onto the Regents Examinations? We now have three exams to look at (June 2008, August 2008, January 2009). Lets examine the problems they have put on so far. (Examinations are available by clicking here) Excluding the “solution set” questions, we have 1 or 2 questions per exam, worth 2 or 4 points.
- 06/08 #18 (multiple choice, 2 points) Consider the set of integers greater than -2 and less than 6. A subset of this set is the positive factors of 5. What is the complement of this subset?
- 06/08 #33 (free response, 2 points) Maureen tracks the range of outdoor temperatures over three days. She records the following information: [the exam has three number lines, for Day 1, Day 2, and Day 3 respectively. The ranges indicated are -20 ≤ t ≤ 40, 0 ≤ t ≤ 50, -23 ≤ t ≤ 45]. Express the intersection of the three sets as an inequality in terms of temperature, t.
- 08/08 #12 (multiple choice, 2 points, I don’t think this one really should count) Which ordered pair is in the solution set of the system of equations
and
- 08/08 #25 (multiple choice, 2 points, I don’t think this should count, either) Which ordered pair is in the solution set of the following system of inequalities
- 08/08 #33 (free response, 2 points) Twelve players make up a high school basketball team. The team jerseys are numbered 1 through 12. The players wearing the jerseys numbered 3, 6, 7, 8, and 11 are the only players who start a game. Using set notation, list the complement of this subset.
- 01/09 #17 (multiple choice, 2 points, I have included the first response) The set {1, 2, 3, 4} is equivalent to (1)
- 01/09 #38 (free response, 4 points, I don’t think this should count) On the set of axes below, graph the following system of inequalities and state the coordinates of a point in the solution set:
,
Carnival of Math is still alive
The coordinator, Alon, has been swamped. And there were no volunteers. And the Carnival went dormant for a few weeks.
But it will reappear April 24, at one of Murray Bourne’s websites, probably Squarecirclez.
Folks, the carnival needs volunteer hosts. Some of us have hosted a few times, and it gets tiring… Maybe a less frequent CoM would conserve our energy? Every 4 weeks?
Also, Math Teachers at Play #5 is due tomorrow at Denise’s place. This really has been a positive addition (ha ha).
Puzzle: How Many Subsets?
I think I’ve blogged this before, but it’s a great problem.
I would not use it as part of a unit on sets. In fact, I used it every year when sets were not in the curriculum. Now that sets have returned, I’ve tried to use the subsets at a completely different time of year (very early). Off-topic problem solving doesn’t have to be completely off-topic, but it feels better when it is.
Now, just a note up front: students are allowed (encouraged) to ask questions to clarify. In this case they would certainly ask what a subset is, and some groups will ask if “order matters.” Occasionally a group has asked whether the whole set is a subset of itself. I don’t recall anyone ever asking upfront about a set with nothing in it… that’s just completely off the radar.
How many subsets does S = { ×, /, ∇, ☺, ☐} have?
Normally I would let a class play with this. I would offer some advice to groups completely stuck. And then we would review solutions and partial solutions – I like to get to it the same period. Generally we start, since everyone wants to speak, with idea that looked promising but didn’t pan out. And then we review approaches that worked. And then I take over, and link different approaches, and maybe offer one or two more.
Challenge for you, readers, how many fruitful approaches can you find? Recall, the kiddies will be high school freshmen with no background in sets (and probably none in counting). Do you have some approaches that work and are good for these kids? that work, but are not reasonable for these kids?
How to teach set theory to freshmen in New York State
For the rest of this vacation week, I will be posting a series of entries related to set theory, and how might teach it in New York State.
Quick background: Some basic set theory is in the Integrated Algebra curriculum. (new, last year). There had been no set theory in New York State high school math for at least a full generation previous.
Posts may include:
- some set theory basics
- what’s actually in the NY State standards? what’s shown up on the 3 Integrated Algebra Regents exams so far?
- Problems of vocabulary
- Teaching topics vs teaching a unit
- A suggested unit
- Not allowing set theory to be “stand alone” – creating links in other parts of the curriculum
- Some extra topics
- problem solving related to sets
- thoughts about professional development and set theory
Here are some previous posts related to teaching set theory:
And we end with this bligblug morsel:
More resolutions
On the heels of two (and then a third) highly successful New Years resolutions, I thought I would push my luck and try a few more.
Now, my success was due in large part to two things
- these were single event resolutions, not running resolutions; and
- I had already completed them, or started them to a degree that there was no looking back.
The new resolutions, all are running resolutions. They will be tougher. But, indeed, I have had them up and running for a week now, so at least there’s the start:
- Walk at least an hour each day, preferably in one big chunk. There’s really no reason not to. And if time is tight, I can always leave an hour early, and walk before the day starts.
- No chips. Can I make one “no ______” something resolution and keep it? We’ll see.
- Breakfast. For years and years breakfast has been coffee, strong, or green tea, brewed and concentrated beyond what most would tolerate. And nothing solid. Not such a good thing. And laziness may prevent me from doing something fancy, or with major preparation. But rinsing a few vegetables and tossing them on a plate, not so hard. Started off today with a carrot, 2 radishes, a celery thingie (stalk?), a little cucumber, and 3 smallish tomatoes. Doable.
Some Green Dot/NY Questions
Over on Edwize I asked a series of questions about hiring and contractual rights at the Green Dot NYC Charter School. That was three weeks ago. So far, no answer (questions reprinted below the fold).
But now I have some more questions – or, more like, comments/observations.
Yesterday I went to the Green Dot/NYC website, and looked through their student handbook. I visited the UFT page where they advertise new positions. And I thought and tried to calculate some things.
- The school year is very close to that of the NYC Public Schools, but not exactly. They start 3 days earlier. Some of our PD days are regular days for them, and vice versa. They teach through January Regents (as do some of our small schools, especially in their first years when there are no January Regents to be administered)
- The school day appears to be far longer than ours. They do not seem to have the “Professional Day” that we heard so much about. Rather, it seems that their day normally goes 8 – 4, and is extended to 5:30 once a week. I count 41 hours and 30 minutes. NYC public school teachers work 34 hour 10 minute weeks.
- Combining extra days and a longer week, it appears that Green Dot/NYC teachers work a 23% longer year than NYC public school teachers.
- Green Dot teachers earn 10% over UFT contract for NYC public schools. I do not know if that includes steps and differentials (see questions, below fold)
- Green Dot /NYC is in its first year of existence. It clearly did not hire all brand new teachers. I was a bit surprised by this.
- Green Dot /NYC’s student handbook is massively dominated by rules and regulations. About 3 of 24 pages are devoted to academics, and they are in the main, general remarks.
- Is Green Dot /NYC exempt from New York State education law? They claim they will graduate students with 2 years (4 NYC credits) of physical education. In fact, it looks like they intend to give PE to sophomores and juniors only. Might there be an issue with the current freshmen, who currently have zero credits?
- Green Dot /NYC punishes a student’s parents if the student does not show to detention. Apparently, they assign the parent the job of “shadowing” the student through the school day.
- Green Dot/NYC has an expulsion policy that will look unusual to those who work or study in the NYC public schools. I’ll reprint the list of expellable offenses below the fold, but, notably, the list includes truancy and also includes “Any infraction considered sufficiently serious to the principal.”
- Green Dot/NYC has a harassment policy that seems a bit strange. The Principal appears to be the lead investigator, and decisions are made in consultation with their Board of Trustees.
- The handbook discusses demands for sex in return for grades, but seems to ignore other forms of sexual harassment.
- Parents are required to perform 15 hours of mandatory volunteer labor each school year.
I suspect that they lifted this from one of their handbooks in California, and then modified it. Lots of places where I would expect reference to NY Education law, they are missing. The discussion of “school grounds” and “campus” seems a bit odd as well.
My previous questions and Green Dot/NYC expellable offenses, below the fold Read more…
No current UFT age discrimination suit
At last Monday’s Executive Board meeting a question and follow-up about the UFT’s age discrimination revealed:
- the suit was withdrawn, without prejudice, when the ATR side agreement was reached.
- to refile the suit, the UFT would need to collect fresh information.
- members individual suits were not withdrawn.
early spring school and math odds and
ends
The Association of Mathematics Teachers of New York State (AMTNYS) has a summer conference (Summer Math Institute) every year or every other year or something like that. This summer, August 2 – 6, no excuses, I’m going. The area, Wells College in Aurora, New York – it’s supposed to be gorgeous.
I lost track of Jackie (Continuities) for quite some time. Somehow I left her out of my reader (not smart!). Anyhow, she recently linked to a great on-line grapher, GraphSketch. Give it a try.
Many of you know Donors Choose? A (friendly??) competitor, ClassWish, wrote to me asking for a plug. I can’t tell the difference. Maybe you can?
Is Vlorbik right? Is the Carnival of Mathematics really dead? For the record, of fifty carnivals, I hosted four: IX (the best of them) 18 (the biggest) 1000 (cutesy) and 47 (Trekked out).
Now, Denise (Let’s Play Math) does have “Math Teachers at Play” up and running. The fifth is due next Friday. But any chance to revive the old C of M? Even once every four weeks? Anyone?
Also via Denise, More New Math. These are equations, with real life applications.
Onions = Weeping – Catharsis
Rat = (Mouse x 4) – cute
Uniqueness = Uniqueness
You get the picture. Hundreds of them. Go, bookmark, chuckle while wasting time. Like the rest of us…
Done scheduling
No, I don’t mean I’ve created the September schedule for my school. I mean I’m done with the job, or will be, some time in the medium term.
Strange story: an educator, the mom of a former student, asked me to write an essay for an anthology on teaching she was compiling. I agreed, and started to write about the different directions I felt pulled in — teaching kids who need a strong math teacher, teaching gifted kids, teaching struggling kids, teaching Bronx kids, teaching younger, older, helping other teachers teach, doing union work in my school, outside my school, doing scheduling, helping with my school, teaching college, getting involved in state math stuff, studying math…
And it hit me. Some choices needed to be made. I started with one.
I announced at chapter meetings in March, and then told the principal… me? scheduler? it’s been long enough. I’d like to end it now, but under no circumstance I am working per session past June of 2010… I immediately felt both regret – I am convinced I do a superior job that seriously benefits teachers, students, and school – and an absolutely amazing sense of relief. That proverbial weight? I really felt it lift off my back…
Over the last few years I wrote several posts about scheduling. You’ll sense the mixed emotions: Programmer, too! (mixed feelings about being Chapter Leader and Programmer) / Language and Schedule Conflict (scheduling a small vs large school) / Novaya Metla (grateful for an administrator who stayed out of my way and let me work) / Teaching vs Comp Time (verdict, teaching is more exhausting, but doing comp time with no time off is idiocy) / HSST, a little background (showing off some specialist knowledge. I’ll be losing that, I suppose).
(Oh, yeah, the essay? I got a start, but it forced all this thinking forward, and the writing lost all momentum. I thanked her for getting me thinking, and apologized for dropping the ball.)
early spring sunday odds and
ends
Saw Sin Nombre last night. Good, but still, wait for Netflix.
First real spring cleaning day. Laundry (ucch). Lots of it. How do I store away clothes, say, for next fall? or, say, that aren’t quite, ahem, fitting just now?
Lost friends week? I wrote Gm (friend from far away); even though we can chat on line, it’s not the same thing, so we don’t, and then we forget to write, too. On a lark, I searched for Ay, hadn’t seen him in years and years; I found a photo of a bald professor at an Australian University. Took me a day to decide it really is him… now I’ll see if he writes back… And today, Da, out of the blue, called. Hadn’t spoken in maybe 6 years? So, nice things to smile about while I folded (for what seemed like hours). Maybe I’ll try to reconnect with a few more?
A guy named Craig started backpacking a few years ago, and never plans to come back. All web-documented, with photos, at Travelvice.
Bathroom? Done. Kitchen? Next. (new appliances have arrived, making the living room feel a bit, cramped?) That makes 2 + 1 New Years resolutions kept (hair cut, car, bathroom). I rock (for today, at least).
It’s never to early to start planning summer vacation. Among my many open browser tabs right now: Kayak (last search was NY-Sofia), the Coastal Ferries page at Croatia Traveller (Jadrolinija), Novi Sad on WikiTravel (an unlikely stop), the Balkan Pass page on the Europrail site, and DB (German Rail)’s search site (reise auf kunft) – searchable rail schedules for all (most?) of Europe. Who knows? I’ll go somewhere, I’m sure.
Some New Links for Spring
It’s been months since I overhauled the blogroll. In the interim I’ve probably added and deleted without notice, which is not good.
Anyhow, here are some that I either just added, or added and think I forgot to mention. If I missed you, let me know:
- Tanya Khovanova. She knows math (for real) and has a great sense of what puzzles should do. She also reduces my degree of separation from Israel Gelfand by 1 (her advisor). The variety and playfulness of the puzzles, but from a serious perspective, those are the main selling point. Spend time in the archives, very rich.
- The Washington Teacher. Candi is a Building Rep (that would be Chapter Leader in NYC), a delegate, and a Trustee in the Washington Federation of Teachers. She’s active, she’s very critical of the WFT president, but Rhee is her main target. I don’t know enough details on the ground to have a sense of how much I agree, but I recognize and appreciate the activism and the tone.
- The Frustrated Teacher. Education, Politics, Humor. Generally progressive. From San Francisco.
- Nick Hershman at Divide by Zero. I usually don’t go in strong for web-too-oh guys, but Nick, against form, takes the math seriously as well. We should have more reflective math teachers blogging…
- Mr. D writes Mr. D’s Neighborhood. Sharply written, new(ish?) Bronx Teaching Fellow. History. New, as of a month or so ago. Lots of potential. Take a look.
- Vlorbik shut down, and moved to Community College Calculus. Let’s see where that leads…
Also, an individual post worth pointing out:
- Joel’s 20 Blogs I wish were around when I started teaching. He includes me! But there’s 19 more to look at. So you want to teach is a nice source of general advice, and then very specific band teacher stuff.
Lately I’ve been much liking (this list should look familiar!):
- Math Notations, Kate(t), and 360 for math teaching and math fun
- Jose and Fred for laying down a political/educational bassline/theme
- NYC Public School Parents for dredging up the muck in NYC Ed politics, with an agenda I feel comfortable with. (and yes, that’s a knock on any blog site that thinks it is possible not to have an agenda, and that considers passing slips of paper to be worth five stories if the slips are white, come from a union, and have questions on them but to be worth zero (0) stories if the slips are green with Ben Franklin on them, go from the mayor to a chancellor to a former chancellor and are then used to secretly purchase a celebrity endorsement.)
Finally, a story that you should read somewhere, doesn’t really matter where, Bloomberg is recruiting student interns for his next campaign in the schools. Just in case you hadn’t noticed that his power was going largely unchecked….
JD2718 