Thursday, May 30, 2013

Math problems of the week: 6th grade Connected Math vs. Singapore Math

A continuation of last week's problems-- the next pages in the chapters on circles sections of 6th grade Connected Math and Singapore Math.

I. From the 6th grade Connected Math "Going Around in Circles" section [click to enlarge]:




II. From the 6th grade Singapore Math Primary Mathematics 6 Workbook "Circles" chapter [click to enlarge]:



Tuesday, May 28, 2013

Letter from Huck: Rules of Engagement and a Fond Farewell

Out in Left Field proudly presents the sixteenth and final letter in a series of letters by an aspiring math teacher formerly known as "John Dewey." All personal and place names have been changed to protect privacy.

I’ve been told that bribery is not a good way to motivate your kids or your students. I’m afraid I break that rule quite a bit. I broke that rule long before I started teaching, when my daughter was in middle school. Her pre-algebra class was learning two step equations and she was doing fairly well. I felt with some more practice she would become fluent. So I brought out my old algebra book and turned to a page with a bunch of the same type of problems and offered her the following deal: “There are ten problems here just like what you’ve been doing. If you do these ten problems I’ll give you a quarter for each one you get right. So you can earn up to $2.50!”

At that time, her allowance was based on completion of certain chores. She did some quick reasoning and rejected my offer, explaining she could make that same amount by cleaning the toilets. Despite the warnings against bribing your kids, I saw the opportunity for a teaching moment and I told her “You’re right. But I’ll let you in on a secret. Solving these equations is a whole lot easier.” She looked at me. “Think about it,” I said. “Tell me what you decide.”

The next day, she came up to me and asked “Is the deal with the equations still on?” I was thus started on a career of carefully controlled bribe-based motivations.

Along with other motivational and engagement techniques, I use bribery carefully—I don’t overdo it. I will sometimes offer a quarter or fifty cents to the first student who can do a certain problem; it depends how much change I have in my pocket. Usually one student will respond, and I award the prize. In more advanced classes, like algebra 2, the prize is generally $1.00 and I require the student to explain their answer.

I find the most motivating prize (at least in the lower math classes) is dismissal two minutes early. As often happens, students begin to put their books away five minutes before class ends, and sometimes line up at the door. Rather than tell the students to get back in their seats, I will put a problem on the board pertinent to the day’s work and tell them: “OK, here’s the deal! Who wants to leave two minutes early?” The noise level of the classroom suddenly drops to that of a concert hall when the conductor raises his baton. “If anyone can do this problem, you all get to leave two minutes early.”

Suddenly there is a flurry of activity. The smartest students are drafted into service by the others and attempt to solve the problem. I try to make it challenging enough that it takes some effort. If the first attempts are wrong, more students get into action—you would think I was offering $100. At last someone gets it and I dismiss them, telling them to please be quiet in the hallways or I will be fired or executed or face some other grisly end.

There has to be a critical mass for these techniques to work, however. I had a class a few weeks ago that the teacher told me to be firm with because “they tend to get squirrely” which roughly translated means “They will cause you to seriously question your decision to go into teaching.”

To check what I was dealing with, I looked at the grade roster for the students in this class. About a quarter of the class had F’s and another quarter had D’s. This was the two-year algebra 1, and most of the students were ninth graders. Ninth graders are hard enough to deal with, but this was late April, so that those with F’s had pretty much given up.

I tried to help one boy, Miguel, but he was far behind. He did one problem with a lot of guidance from me so much so that I realized he clearly was lacking some basic knowledge. With the second problem, he put his head down on the desk and said, "I just can't do it."

In the last few minutes of class, students started lining up at the door. I knew no motivation was going to work with this class so I yelled “Sit back down!” Miguel took that opportunity to bolt out the door. I lost it at that point. “OK, everyone in your seats; you will stay one minute after the bell!” My voice was loud and my hands were shaking. I only made it to 30 seconds after the bell before I told them to leave.

It’s difficult to know what is going on with a student without knowing the background. Some might think that Miguel was of “low cognitive ability”. But I recall two girls in my student teaching days who, after my supervising teacher, Tina, held a conference with their parents, began getting high scores on tests and participating in class—until family life deteriorated again. Another student from those days, Antonio, was very smart but decided to goof off and was in danger of failing. Tina held a conference with Antonio and his father who told him “If you fail this class, you will work with me in the fields this summer.” Given such a choice Antonio probably realized what my daughter had learned: solving equations is a lot easier. He passed.

Then there are some who simply have given up. The reasons are often unclear--whether you’re a teacher or a sub. I do believe that given the right math teaching from first grade on, if students put in the effort, they can get through algebra. Many think I’m a fool for thinking this way. Call me what you will.

School ends soon and I just had an interview for a math teaching position that looks promising. That’s happened before so I’m not going to make any predictions. In any case, I don’t think I have that much more to say, so this will be my last letter to Miss Katharine. I thank her for allowing me to tell what I think needed to be told and thank the rest of you for reading them.

Your Pal,

Huck

Sunday, May 26, 2013

Home schooling update: May, 2013

Our "classical education" continues--with an emphasis on systematic content, core knowledge, sentence construction, summarizing/outlining, straight-up algebra, French, and music.

Some things she's just recently begun: D'Aulare's Book of Greek Myths, The Story of the World Book 4, outlining chapters rather than summarizing them, and factoring polynomials.

Some things are still in progress: the Diary of Ann Frank, the Adventures of Dr. Doolittle, Sentencecraft, mom's syntactic paraphrase exercises, McDougal Littell's Earth Science (the best earth science book I've been able to get) and, for French, French in Action; ALM French Level II, and the Lu Lu Series. She also had a week of French immersion during a visit from some friends from France.

Some things are coming to an end. She's reading the last two tales in our collection of Arabian Nights--"Abou Hassan" and "Cadadad and His Brothers"--and the last few fables of Aesop. She's finished Pinocchio and the Story of Dr. Doolittle. And she's finished reading and copying maps (with the major cities and rivers) from the Scholastic Atlas of the World.

While she'll be able to continue horseback riding, violin, piano, and duo and trio practice on into the summer and beyond, and add theater camp to the mix for the summer, other extracurriculars may be coming to an end. She does cartooning, creative writing, and pottery at our local arts center, which currently only serves children up through age 12. She could theoretically do extracurriculars at the local public school that I pulled her out of 2 years ago, but it offers very little--particularly in art. Finding cartooning classes for middle school kids is going to be as difficult as it is desirable.

Especially in terms of non-academics, the middle school years are tricky. They're tricky if you go to regular school, and, I'm learning, they're also tricky if you don't.

Friday, May 24, 2013

Math problems of the week: 6th grade Connected Math vs. Singapore Math

A continuation of last week's problems-- the next pages in the chapters on circles sections of 6th grade Connected Math and Singapore Math:

I. First set: from Connected Math "Going Around in Circles" section:

II. Second set: from Singapore Math Primary Mathematics 6 Workbook "Circles" chapter

[click to enlarge]:












Wednesday, May 22, 2013

"Students will Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object"

There's something deeply boring about the way the Common Core Standards are written--so much so that nearly every time I read them I start to space out. For skills-intensive fields like math and language arts, perhaps this is inevitable: it's hard to make generalized skills sound interesting. But the same vague tedium pervades the newly unveiled science standards. Here, excerpted from a recent Edweek, are some examples:

Energy: (Kindergarten)
• Make observations to determine the effect of sunlight on Earth’s surface.
• Use tools and materials to design and build a structure that will reduce the warming effect of sunlight on an area.
Biological Evolution: Unity and Diversity: (Grade 3)
• Analyze and interpret data from fossils to provide evidence of the organisms and environments in which they lived long ago.
• Construct an argument with evidence that in a particular habitat some organisms can survive well, some survive less well, and some cannot survive at all.
Motion and Stability: Forces and Interactions (Middle School)
• Apply Newton’s Third Law to design a solution to a problem involving the motion of two colliding objects.
• Plan an investigation to provide evidence that the change in an object’s motion depends on the sum of the forces on the object and the mass of the object.
Engineering Design (Middle School)
• Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.
• Develop a model to generate data for iterative testing and modifications of a proposed object, tool, or process such that an optimal design can be achieved.
Earth and Human Activity (High School)
• Evaluate competing design solutions for developing, managing, and utilizing energy and mineral resources based on cost-benefit ratios.
• Use a computational model to make an evidence-based forecast of the current rate of global or regional climate change and associated impacts on other Earth systems.
Science is one of those fields that should be inherently interesting to nearly everyone. But what is it that makes someone want to study, say, biology or earth science? Is it so they can learn how to construct arguments about habitats, or is it so they can learn about the organisms that make up a habitat?  Is so they can learn how to evaluate competing design solutions for developing mineral resources, or is it so they can learn about minerals and how people use them?

There are other problems with these content-poor standards. Make goals vague enough, as I've argued earlier, and nearly any strategy can justified as serving them. Which strategies then prevail isn't determined by the goals themselves, but by who's in power. In the highly problematic world of education, this dynamic makes the Common Core part of the problem rather than the solution.

The other downside of vague standards is that it's hard to know how to implement them. Ideally they give schools and teachers flexibility, but in an arena so pervaded by one particular ideology, educators must constantly second-guess what is the "right" way to, say, teach kids how to "construct an argument with evidence that in a particular habitat some organisms can survive well, some survive less well, and some cannot survive at all."

Americans tend to be highly critical of the centralized curricula of countries like France, in which all schools go through the same textbooks on more or less the same schedules. But there's something to be said for specific, content-based guidelines. I'm guessing that many teachers would prefer being told exactly what content to cover, and being given the flexibility about how to go about teaching it, to being handed some vague, uninspiring goals and an ideological environment in which only certain strategies are acceptable--strategies that must be justified every day with Common Core-flavored subgoals submitted with every lesson plan and posted on every whiteboard--and that, furthermore, provide no guarantee that students will actually learn and retain anything of actual substance.

Monday, May 20, 2013

A piano students' lament

In his A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form, Paul Lockhart opens with an allegory about a musician, who awakens from a nightmare in which the “curious black dots and lines” that “must constitute the ‘language of music’” become the center piece of what has become a universally mandated music curriculum. He proceeds to describe just how tedious this curriculum is for all concerned:

It is imperative that students become fluent in this language if they are to attain any degree of musical competence; indeed, it would be ludicrous to expect a child to sing a song or play an instrument without having a thorough grounding in music notation and theory.
And then, of course, he famously proceeds to connect this musical nightmare to the way K12 mathematics is supposedly actually taught: all meaningless, mindless drill.

As Alfred North Whitehead writes back in 1911, however, mindlessness is often a virtue:
It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.
Furthermore, while no sane piano teacher would ever make "curious black dots and lines" the centerpiece of music instruction, some of the best ones give top priority to mind-and-soul-numbingly tedious muscle exercises. I was reminded of this reading an accomplished pianist's recent New Yorker memoir about his "Life in Piano Lessons." Here's an excerpt (the student/narrator is Jeremy Denk, and the teacher is William Leland):
Learning to play the piano is learning to reason with your muscles. One of the recurring story lines of my first years with Leland was learning how to cross my thumb smoothly under the rest of my hand in scales and arpeggios. He devised a symmetrical, synchronous, soul-destroying exercise for this, in which the right and left thumbs reached under the other fingers, crab-like, for ever more distant notes. Exercises like this are crucial and yet seem intended to quell any natural enthusiasm for music, or possibly even for life. As you deal with thumb-crossings, or fingerings for the F-shart-minor scale, or chromatic scales in double thirds, it is hard to accept that these will eventually allow you to probe eternity in the final movement of Beethoven's last sonata. Imagine that you are scrubbing the group in your bathroom and are told that removing every last particular of mildew will somehow enable you to deliver the Gettysburg Address.
Of course, a certain amount of grit and gruel also underlies good writing. The Gettysburg Address doesn't just happen, either.

Saturday, May 18, 2013

A left-brained approach to getting along politically

It's become a truism that we live in a world increasingly segregated by viewpoint, rarely talking civilly and substantively about politics with those with whom we strongly disagree.

One of the few proposed "remedies" is the open-ended discussion session. Get groups of people with opposing viewpoints talking to one another about how they feel, and they will become more open and respectful towards those with widely differing opinions, moderating their own views along the way. It turns out, however, that such open-ended discussions have the opposite effect, with those on opposing sides digging in and becoming even more entrenched:

Rather than adopting a middle ground, continuing discussion and debate often result in more extreme positions. In such a condition, consensus building is difficult and temporary when it is achieved at all because individual group members tend to shift away from an average attitude rather than toward it.
A recent study finds that a more analytical "left-brained" approach to be more fruitful. The best way to get someone to question and moderate their views, as it turns out, is to ask them to explain in detail how it is that a policy that they either support or oppose actually works. In response to such questions:
They become more moderate in their political views — either in support of such policies or against them. In fact, not only do their attitudes change, but so does their behavior. In one of our experiments, for example, after attempting to explain how various policy ideas would actually work, people became less likely to donate to organizations that supported the positions they had initially favored.
Interestingly, asking people to justify their position — rather than asking them to explain the mechanisms by which a policy would work — doesn’t tend to soften their political views. When we asked participants to state the reasons they were for or against a policy position, their initial attitudes held firm. (Other researchers have found much the same thing: merely discussing an issue often makes people more extreme, not less.)
Why, then, does having to explain an opinion often end up changing it? The answer may have to do with a kind of revelatory trigger mechanism: asking people to “unpack” complex systems — getting them to articulate how something might work in real life — forces them to confront their lack of understanding.
Reviving our country’s civil discourse, in other words, means constantly asking one another for detailed explanations of "how.” Back in the pre-pc, pre-Constructivist Dark Ages, this was routine, particularly in school settings. In my experience, it was what distinguished the best teachers and classmates. With the decline in both the analytical essay and the multiple revisions-feedback loop, I wonder how often today's students--let alone today's adults--are ever asked to flesh out the practical ramifications of their opinions. Indeed, in an age in which even asking someone for a specific example of what they're talking about can totally derail a conversation, many people seem to find it downright rude when their personal opinions are met with anything other than reflexive, unconditional respect--however vacuous this often must be.

Thursday, May 16, 2013

Math problems of the week: 6th grade Connected Math vs. Singapore Math

A continuation of last week's problems-- the next pages in the chapters on circles sections of 6th grade Connected Math and Singapore Math:

I. From Connected Math "Going Around in Circles" section [click to enlarge]:



II. From Singapore Math Primary Mathematics 6 Workbook "Circles" chapter [click to enlarge]:




Tuesday, May 14, 2013

Letter from Huck: I Guess I’m Just a Cheater

Out in Left Field proudly presents the fifteenth in a series of letters by an aspiring math teacher formerly known as "John Dewey." All personal and place names have been changed to protect privacy.




With all the scandals about teachers and administrators cheating to raise their students’ scores on standardized tests, Miss Katharine was a bit concerned over my letter of a few weeks ago in which I described how I handled an assessment I had to administer. I told her she didn’t have to worry: no one was out looking for me, and the only knock at my front door was from a young man who was selling magazine subscriptions that would serve some worthy cause which had benefitted him somehow and which slips my mind at the moment.

Recently I was back at the same school where I had administered that Common Core flavored exam and ran into one of the students from the 8th grade algebra class. They were the ones who had demanded to know what “explain your reasoning” meant.

“Oh, you’re the guy who gave us that explanation for how to do the problem that no one could do,” she said. Interesting that the explanation I gave took less than a minute but apparently was enough to get the point across; so much so that I’ve become somewhat of a legendary sub. Which perhaps suggests that explicit and direct instruction might not be the “rote learning” approach feared by otherwise sane and pleasant people.

The “understanding” and “connection” mantras are prevalent in the groupthink that makes up much of the education establishment’s view of math education. It was at play big time with the algebra program I had to use when I was student teaching—a program called CPM algebra. I’ve mentioned it before and it seems appropriate to mention it again what with Common Core surfacing and being interpreted along the ideologies of reform math.

With CPM algebra, students were taught “slope” in a series of discovery lessons that spanned many weeks. They had to make “connections” between tables of values, and equations, how both described the patterns of growth, how the y interecept value helped to draw a graph, how to draw a graph given an equation, and how to determine the slope and y intercept when looking at a graph. All well and good, but the point-slope form of finding an equation was not presented initially; students were left in the dark for quite a while about how to determine the equation of a line given the coordinates of any two points on the line.

I kept to the script of the algebra text as best I could. This turned out to be disturbingly easy. You just went over the previous problems, gave a short intro for the topic of the day to get them going and then assigned the problems in the book for that day. They then worked on them in groups and Tina and I circulated to answer questions. I could see how if a teacher were lazy (which I hasten to say Tina, my supervising teacher, was not), they wouldn’t have to do very much, and lesson plans were pretty much automatic. Tina bought into the program; she believed in it and worked hard to make it work. But it also seemed she was seeing what she wanted to see. There were times when, circulating around the classroom, she would say to me “They’re getting it! They’re making connections!” Yet, there were students who seemed quite confused and some of them knew that if they pushed me hard enough during my circulatory tour of the classroom, my hints (given while Tina was working with other students and out of earshot) would often tell them what they were supposed to discover. Maybe the connections she was seeing the students make were because of that.

The reason why CPM eschews procedures like the point-slope method of finding an equation is that it supposedly gets in the way of true understanding. I heard this recently from a teacher, in fact: “Kids buy into the slope formula, plug in numbers, do the calculations and yet they still do not understand what they are doing. They are simply memorizing yet another formula for some unknown reason.”

I don’t know. I just don’t find slope all that terribly difficult to understand. Similar triangles and proportion seem to explain why the slope of a straight line is always going to be the same for any two points you pick. But people seem to think that if a kid is doing procedures without “complete and true understanding” he's doomed to a life of failure. It is as if the moment a student stops doing all the intermediate steps/algorithms and fails to make the appropriate connections each time, then he or she is using a trick or rote memorization to jump to the end result and not using understanding or strategies to solve something.

I recall one time when student teaching, talking to a fellow math teacher. This was during the time that Tina was gone for two weeks when her father passed away. The teacher was telling me about the math teaching philosophy. “Tina always says we can teach them how, but what’s really important is that they understand ‘why’". As she told me that, she looked to me as if she wanted me to say something. I sensed that underneath it all, she felt the same way I did—but was afraid of being disloyal.

I think of that hallway conversation often. I think of it when I see the posters for the Standards for Mathematical Practice on the walls of the various classrooms in which I substitute. They make me feel as if I’m back as a student teacher, trying to figure out the best way through a ridiculous program. And despite my strong beliefs about what I talk about here, I still feel like I’m cheating when I teach the way I see fit, as if maybe 1) there's something wrong with me, or 2) I’m being disloyal. I’ve only met a few teachers who have told me they don’t like the trends I’ve been describing in math education. They’ve usually been teaching for over 30 years and are about to retire.

Friday, May 10, 2013

Math problems of the week: 6th grade Connected Math vs. Singapore Math

A continuation of last week's problems-- the next pages in the chapters on circles sections of 6th grade Connected Math and Singapore Math:

I. From Connected Math "Going Around in Circles" section [click to enlarge]:


II. From Singapore Math Primary Mathematics 6 Workbook "Circles" chapter [click to enlarge]:




Wednesday, May 8, 2013

Autism Diaries XLVII: A Roundup of the Latest Mischief

J has had a very productive couple of days. He’s gotten way ahead in his homework, has thoroughly cleaned up and organized his bedroom, has assisted me in setting up mosquito larva lures around the yard, and has spent hours on Chess Master improving his game. In other words, he’s doing penance for his latest round of mischief.

You’d think April 1st would be J’s big day, but for some reason it wasn’t until several weeks later that the excitement began. Now 6 foot 4, he looks down on the rest of the family, and down on our household fixtures, even those up close to the ceiling. But when the light switch in our living room suddenly stopped turning on the chandelier, it didn’t occur to me that anyone would have taken the trouble to unscrew every single bulb.

Patience, indeed, is a great virtue, and if you stick it out, it can pay off big time. Eventually, for example, your homework tutor will forget to log out of her gmail account before leaving, allowing you to send a message, say, to everyone in her address book (“My house burned down”), or, once you realize that some of the people in the address book (say, your parents) might catch you red handed, then to just a select few addressees (say, to one of E’s other employers, 100 iterations of “my f***-ing keyboard doesn’t work, flanked by 1000 iterations of f***).

For J, so oblivious to so much around him, including (thankfully for now) the facts of life, is always attuned to signals of anger, and, just this weekend when Daddy took a wrong turn and said “s***”, observed that he first heard the word “s***” when he was three, but back then didn’t know what it meant. (He still didn’t know its literal meaning, but could tell me “it’s a bad word that you’re not supposed to use.”)

His greatest coup, just one day earlier, also involved Daddy driving. He was out at a chess tournament with E, his tutor, and suddenly decided that he’d prefer to be with Daddy instead (Daddy being his favorite person in the universe). So when E let him play a game on her cell phone during one of the breaks, he surreptitiously texted Daddy, capitalizing on the fact that E is periodically struck with debilitating headaches. Here’s the text exchange between Daddy and “E”:

”E”: I’m having a terrible headache right now.

Daddy: I’m in Fort Washington getting the car serviced; I’m kind of stuck. Could someone there get you aspirin? 
[We have only one car]
“E”: My headache is really terrible right now. 
Daddy tries calling E, but for some reason she doesn't pick up.

An aggravating hour-long drive later, poof!, Daddy appears at the chess tournament, slightly baffled; E goes home, slightly baffled (J having deleted all his text messages from her cell phone); and it’s only a couple of days later, when E returns and we examine Daddy’s text messages, that we all sort out what had happened.

Monday, May 6, 2013

Letter from Huck: The Diversity of My Experience

Out in Left Field proudly presents the fourteenth in a series of letters by an aspiring math teacher formerly known as "John Dewey." All personal and place names have been changed to protect privacy.



The other day I was at a middle school in a 7th grade math classroom. The class had taken the Common Core district assessment that I described and they now had to do their homework, which was difficult given that there are only 28 school days left to the school year, plus I’m only a sub, and the weather is nice.

In the midst of my telling multiple students to get in their seats and do their work, one boy confronted me and said, “You’re just picking on me because I’m Mexican.”

“No, I’m not,” I said.

He pointed to some students talking and said, “You didn’t tell them to be quiet.” True. I told some students on the other side of the room. I didn’t continue the argument but told him to sit down and do his work.

In my travels down the cultural divide, I have had to adjust from my student teaching days when all my classes were 100 percent Mexican students to my present situation in which my classes now are mixed and Mexicans are in the minority. Rules are in place in all schools against prejudicial and hate language--to the extent that middle-schoolers will sometimes try to blame someone for saying something that is racist in the hopes of getting that person in trouble. I have heard comments muttered about Mexicans, but nothing loud enough for me to “write anyone up”.

Since the incident with the Mexican boy, I’ve been thinking back to my student teaching days in the heart of strawberry country. My drive was a tiring one--an hour and fifteen minutes each way. The majority of the drive was along Highway 101, one of the major north-south highways of California. It took me past farms that grew lettuce, broccoli, tomatoes, apples, avocados, alfalfa, and strawberries. The strawberry fields became more plentiful the closer I got to my destination.

A long bridge that crossed over a dry riverbed and the county line marked my entry into the city where my school was. There used to be shrubbery in front of the school but it was removed because it became a place where students could hide weapons. I was told this on my first day. I was also told that there are two gangs in the area, and there are gang signs for each. Displaying a gang sign while at school is grounds for suspension. Drinking bottles and water bottles are banned because students were putting alcoholic beverages in them. This was discovered the year before I started, when a student passed out and had to be taken to a hospital. Students can be suspended for fighting, for using racial and sexual slurs, for continued violations of rules, and for talking back to a teacher.

During my 15 weeks there, I did not come into contact with these things any more than I come into contact with the ills of society in my everyday life. What I did see were the effects of one-parent families, students having to miss school so they could care for their baby brothers or sisters on days both parents were working in the fields, or, in the case of a boy named Isaiah, missing school because of ongoing doctor appointments due to severe allergies. He was asthmatic, could not go near grass, and frequently experienced nausea and hives in addition to asthma attacks.

My supervising teacher, Tina, thought Isaiah’s allergies were because of the pesticides sprayed on the fields. I sometimes smelled pesticides when the helicopters would spray the various fields. I never saw the helicopters, but Tina would see them sometimes. She told me one day about a helicopter she saw spraying a field and the clouds of gas that spilled into the neighborhoods where kids were walking to school. “It’s no wonder we have so many kids with respiratory problems,” she said.

Isaiah was a quiet boy who managed to get the highest scores on tests in the class if he didn’t get too far behind in his homework. He didn’t like to speak up in class and so I got into the habit of leaving him alone—I could see he knew the material. One day, shortly after Tina returned to class after her father passed away, I was teaching and hadn’t noticed that Isaiah had his head down on his desk. Tina did, however, and she suddenly came over to him and asked if he were OK.

“Come on, Isaiah, I’ll take you to the nurse’s office. He stumbled to his feet and she grabbed hold of him to keep him from falling. I managed to continue through the day’s lesson, assuring the students Isaiah would be fine. And he was. Fifteen minutes later, Tina and Isaiah came back to class; he just needed a dose from an inhaler.

Mercifully, Tina did not mention that I should have been more aware of what was going on, and should have seen that Isaiah was ill. She didn’t need to. Since that time, I have made it a point to be more vigilant and have excused students who looked ill to go see the nurse.

My subbing assignments are no longer in the heart of strawberry country, though there are fields near some of the schools in which I sub. Also, as I said, my classes are now more “diverse,” to use a term I’ve never liked because it's phony. For one thing, there are some who would say that my totally homogeneous Mexican classes were diverse because they were non-white. Also, the term reminds me of the Weekly Reader exercises from long ago that asked students to find four “friends” in a picture of a parade or something similar. The “friends” of course would be the distinctly foreign people. The “friend” who thought I was picking on him was using diversity and school policy against racist actions to his advantage. He wasn’t very good at victimization and definitely needed improvement in math. I’m pulling for improvement in the latter.

Saturday, May 4, 2013

Another false choice in remediation: "addition and subtraction over and over again" or Marxism and Shakespeare

A recent New York Times Education Supplement article entitled "Rigorous Schools Put College Dreams Into Practice" showcases Bard College's new "early college high school" for disadvantaged students in Newark.

For the uninitiated (like yours truly until I read this), an early college high school is one that merges high school courses with "some college." As the article explains:

Students can earn both a high school diploma and an associate degree, and some are set on the path to a four-year degree.
The early college high school is also a growing movement:
There are now more than 400 early college high schools across the country — North Carolina has 76 of them — educating an estimated 100,000 students.
Across the country in communities like Newark, the early college high school model is being lauded as a way to provide low-income students with a road map to and through college.
What makes early college high schools different from, say, a college prep track of a regular high school? For one thing, they seem to be specifically geared at students who need "catching up," and they aim to offer an alternative to remediation:
The ethos of early college high schools: catch students up, not by relegating them to the kind of remedial classes required at community colleges but by bombarding them with challenging work. At the Bard school, that means works by Dante, Locke and W.E.B. Du Bois that have populated and enriched the lives of their more affluent peers.
Can Dante really replace traditional remediaton? At Bard's Newark branch:
Students say the transition has been tough. Al-Nisa Amin, now a sophomore, remembers slumping over a math problem that first year, crying out of sheer frustration. But she has stuck it out, partly because she is scared of being sent to a zoned high school.
In particular, the article cites students who were getting A's at their zoned high schools now getting D's and F's. And here's what their Shakespeare seminars are like:
Flipping through their Signet Classic paperbacks and scribbling notes, they reviewed the first act of “Twelfth Night,” intuitively understanding that Orsino, Duke of Illyria, had become obsessed with Olivia. When their professor, David Cutts, asked what was going on in Orsino’s heart, several called out matter-of-factly: “Love.” The class then discussed the vagaries of love at first sight, and voted on whether they believed in it. Most didn’t.

Some were confused by the shipwrecked noblewoman Viola and her motives in disguising herself as a servant. “He’s rich, so why is she trying to hide?” one student asked, befuddled. Another hypothesized: “I think she’s interested in him.”
Then there's the Marxism and Postmodernism seminar:
...which on this day involved mulling over a densely written essay by the Marxist political theorist Fredric Jameson on the meaning of self in a postmodern world. Reading aloud a 2006 article in The Economist titled “Post-Modernism Is the New Black,” one student stumbled over “facade,” “anachronistic” and “grandeur” — words that would seem fair game for late high school.

Another student wanted to know: “What’s a phenomenon?” One inquired about the meaning of “sinister.”
The article cited Auschwitz as an example of how the Enlightenment had “given birth” to totalitarianism. Not one of the 10 students knew what Auschwitz was. Debate ensued over whether it was a city in Switzerland, Russia or Poland. Their professor finally interjected: “It’s usually used as the big example of the Holocaust.”
It's important to note that this may not be representative of early college high school seminars in general:
In similar classes in Bard’s New York schools, students’ vocabulary, communication skills and historical knowledge appear noticeably more advanced.
But, as the article notes:
The disparity raises an uncomfortable question. Can students who are so behind be brought up to college level in a few efficient years, even with good teachers and good intentions?

So far, the school has lost 7 of the 36 students who entered in 2011 as first-year college students and 20 of the 87 who entered as high school freshmen.

Najee has repeated one class. Both Miles and Billy have repeated several. More than half the class had to repeat one of the required seminars in a monthlong intensive at the end of the last school year.
The article proceeds to elaborate on the pedagogical philosophy of these early college high schools:
Taken as a group, early college high schools place a premium on teaching rudimentary study skills — how to take notes, how to interact with professors, where the best spot is to sit in a classroom. But the greatest emphasis is on thinking. Students are encouraged to see themselves as participants in an academic world, and as interested in gaining knowledge as in getting good grades. Dr. Ween calls it “joining the debate.”
So far, so good. But, as the next paragraph makes clear, "thinking" and "joining the debate" mean something troubling specific and Constructivist:
The students at Duplin Early College High School in eastern North Carolina take an applied math class in which they learn about velocity and graphing by building roller coasters out of wire, piping and masking tape. Then they are asked to defend the project. At the Dayton Early College Academy in Ohio, students learn about constitutional law in mock trials. And at Bard, in an environmental science class, students read articles about the effect biofuel is having on corn prices and debate the merits of renewable energy.
These activities do not address the deficits that colleges most often need to remediate: those in essay writing and pre-calculus.
“You cannot pull off an early college high school successfully without fundamentally changing pedagogy,” said Joel Vargas, vice president of Jobs for the Future, a nonprofit organization based in Boston that develops early college high schools. He calls it the opposite of “chalk and talk.”
I agree with Vargas' first statement. But fundamentally changing pedadogy in a way that prepares disadvantaged kids for high school means less project-based learning and more direct instruction and pen and paper exercises ("chalk and talk"?).

As articles like this one make clear, the edworld is increasingly convinced that remediation can be bypassed:
Gone is the thinking that students must master all the basics before taking on more challenging work.

“Traditionally, what has happened is that kids who come in below standards are put in a remedial track and they do addition and subtraction over and over again,” said Cecilia Cunningham, executive director of the Middle College National Consortium, a network of more than 30 early college high schools. “They’re bored out of their minds and the message is: ‘You really can’t do this.’ ”
To maintain beliefs like these, the edworld depends on such false dichotomies. Remediation = doing addition and subtraction over and over again = boring kids out of their minds and telling them they're incapable. The only alternative is project-based learning and Postmodernism seminars. It simply doesn't occur to them that remediating a child's academic skills at their Zone of Proximal Development is less likely to bore them and make them feel incapable than forcing them through a seminar on the meaning of self in a postmodern world (even with the implicit threat of having to return to their local high schools if they don't play ball).

Do such tactics nonetheless work? In general:
Studies show that high school students who take classes in which they get both college and high school credit — often referred to as dual-credit courses — fare better academically.
A study last year of more than 30,000 Texas high school graduates found that those who took college-level classes in high school were more likely to have finished college after six years.
Studies like these, however,
aren’t able to determine if it is the type of students drawn to college-level coursework that makes the difference. And no long-term studies have been conducted about early college high school students and college graduation. [Italics mine]
A refreshing voice in the edworld wilderness comes from emeritus professor Sandra Stotsky
who notes that there is not any substantial evidence that the model being tried out in Newark will help at-risk students get through four years of college. Dr. Stotsky finds the idea that students should have to go to college to get a good high school education counterintuitive, and has called on educators to refocus their efforts on making high school coursework more challenging.
Otherwise, the opposite may happen--at the college level:
Critics also worry about rushing students through the material and pushing them prematurely onto college campuses, thus dumbing down classes for the other students.
It's interesting that, for all the permeation of the "learning differences" and "differentiated instruction" memes, what current trends in education have most amounted to in practice is a one-size-fits all curriculum in which the same hands-on, arts-based "multiple learning styles" assignments are inflicted on everyone and neither advancement nor remediation are allowed.

Thursday, May 2, 2013

Math problems of the week: 6th grade Connected Math vs. Singapore Math

A continuation of last week's problems-- the next pages in the chapters on circles sections of 6th grade Connected Math and Singapore Math:

I. From Connected Math "Going Around in Circles" section [click to enlarge]:



II. From Singapore Math Primary Mathematics 6 Workbook "Circles" chapter [click to enlarge]:



III. Extra Credit

Which problem set better prepares students for algebra and higher-level geometry?