Monday, July 21, 2014

How do you accommodate a complex information processing disorder?

How do you accommodate a complex information processing disorder? Here are some of neurologist Nancy Minshew’s findings about individuals on the autistic spectrum, including those with normal to above-normal IQ‪‬s:

  • In autistic individuals, there is “a problem with the brain’s fundamental mechanisms for processing complex information.”
  • There are “deficits across multiple domains that selectively involved higher-order abilities that involve the processing of complex information”
  • Particularly impaired: “higher-order language comprehension” and “mental inferencing.”
Here, meanwhile, are some of the Common Core Standards that all children are expected to meet, with “appropriate accommodations”:

For 5th grade:
  • CCSS.ELA-LITERACY.RL.5.5 Explain how a series of chapters, scenes, or stanzas fits together to provide the overall structure of a particular story, drama, or poem.
For 8th grade:
  • CCSS.ELA-LITERACY.RL.8.3 Analyze how particular lines of dialogue or incidents in a story or drama propel the action, reveal aspects of a character, or provoke a decision.
And, for grades 11-12
  • CCSS.ELA-LITERACY.RL.11-12.2 Determine two or more themes or central ideas of a text and analyze their development over the course of the text, including how they interact and build on one another to produce a complex account; provide an objective summary of the text.
  • CCSS.ELA-LITERACY.RL.11-12.6 Analyze a case in which grasping a point of view requires distinguishing what is directly stated in a text from what is really meant (e.g., satire, sarcasm, irony, or understatement).
  • CCSS.ELA-LITERACY.RL.11-12.7 Analyze multiple interpretations of a story, drama, or poem (e.g., recorded or live production of a play or recorded novel or poetry), evaluating how each version interprets the source text. (Include at least one play by Shakespeare and one play by an American dramatist.)
So, if we want autistic students to graduate from high school, what are the appropriate accommodations?

Saturday, July 19, 2014

Modern English as a foreign language

While there will always be readers, and there will always be teachers who assign the classics, I wonder how many of today’s kids are still engaging on a regular basis with the archaic constructions that permeate the older classics. I’m speaking, not just of archaic vocabulary (relatively easy to look up), but of archaic syntax. Even if we restrict ourselves, as schools long have tended to, to “Modern English”  (which dates back to the year 1550), there are still a number of syntactic constructions we no longer find in the majority of the texts that today’s young readers encounter. I wrote about some of these earlier, but have collected a few more since.

Some constructions may simply bog readers down and/or baffle them:

1.”of a” plus time expression to express habitual time:

“of a night” (at night); “of an evening” (in the evening); “of a Sunday morning” (Saturday morning)

“..she had her cap on, which he had never seen her in before when he came of an evening.” (Adam Bede)

2. “that” for “so that”:

Let us die that we may live

3. “as” for the relative conjunction “that”:

"those as sleep and think not on their sins." (The Merry Wives of Windsor)

4. “were” for “would be,” with “that” for “if:

“It were better for him that a millstone were hanged about his neck, and he cast into the sea, than that he should offend one of these little ones.” (King James Bible)

5. “but” for “that” plus “wouldn’t”:

“There is no good man in any line but I call to my standard” (My Book House retelling of Robinhood)

6. Inversions: of subject and verb; of object and verb; of adjectives and nouns:

“On her head sang its war-song wild”. (My Book House retelling of Beowulf)

“For them the gracious Duncan have I murther’d” (Macbeth)

7. Nonrestrictive relative clauses shifted away from the definite nouns that modify:

“My lair is empty that was full when this moon was new” (The Jungle Book)

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Some instances of archaic syntax may not merely baffle today’s kids, but lead them astray:

8. “Should” for “would”:

“I should have asked you to lunch with me even if you hadn't upset the vase so clumsily.” (Screenplay to Rebecca)

Here, one might think that the speaker is expressing an obligation to have lunch.

“You want to know if I can suggest any motive as to why Mrs. de Winter should have taken her life?” (Screenplay to Rebecca)

Here, one might think that the question at hand is why there was an obligation for Mrs. de Winter to take her life.

9. “had” for “would have”:

“So had life ended for Beowulf.” (My Book House retelling of Beowulf)

One might think Beowolf actually died.

10. “Though” for “even if”:

“Though ye gave me a thousand pounds, yet would I never sign the lease” (My Book House retelling of Beowulf)

One might think that the speaker actually did receive a thousand pounds.

As I noted earlier, even now things are a-changin’: “before”, “beside,” and “about” are losing their spatial meanings (“in front of,” “next to,” “around”), making sentences like “She stood before the crowd of people about the grounds beside the lake” not as readily understood as they once were.

Whether these archaisms merely confuse contemporary readers, or actually lead them astray, cumulatively, they make pre-20th century classics (e.g., Shakespeare, Dickens, Dumas, and James) increasingly inaccessible.

No wonder so many English classes now accompany the written classics with the growing number of movie versions that Hollywood is so eagerly churning out. Although, as we see from the screenplay for Rebecca (1940), it's hard to completely escape archaisms unless one sticks to relatively recent movies. Which I'm guessing is pretty much what today's K12 English teachers are doing.

Thursday, July 17, 2014

Math problems of the week: 5th grade Investigations vs. Singapore Math

Chart reading versus estimation: large numbers in Investigations vs. Singapore Math.


I. An early problem set involving large numbers in the 5th grade TERC/Investigations Student Activity Book, from Unit 3 of the book [click to enlarge]:

































II. A continuation of the first first problem set involving addition and subtraction (and multiplication and division) of multiples of ten from large numbers in the 5th grade Singapore Math Primary Mathematics 5A Workbook, from Unit 1 of the book [click to enlarge]:
































III. Extra Credit:Is chart reading a 21st century skill?






Tuesday, July 15, 2014

Conversations on the Rifle Range 4: The Rifle Range and What the Hell Am I Going to Do Now?

Barry Garelick, who wrote various letters under the name Huck Finn and which were published here is at work writing what will become "Conversations on the Rifle Range". This will be a documentation of his experiences teaching math as a long-term substitute. OILF proudly presents episode number four:



When it comes to teaching math, I am a drill instructor. I say this without apology. I believe that practice is essential in mathematics; it results in automaticity which ultimately allows students to take on increasingly complex tasks. It is part and parcel to the much ballyhooed concept of “understanding”. Yes, I put this word in quotes.

I am also the equivalent of a rifle range instructor. I’ve never served in the military but from what I’ve heard, in basic training the instructors on the rifle range are not the drill instructors that wreak havoc on the recruits. According to a friend who served, on the rifle range the instructors were very patient, talked in quiet tones and gave the recruits advice and encouragement in learning how to shoot their rifle. I imagine that this might be a safeguard to prevent any kind of mayhem on the rifle range if the drill instructors were within range of loaded rifles in the hands of the recruits they harass on a continual basis. But that is only my conjecture.

Out of necessity, I start out as drill instructor. Prior to the start of any class, when confronted with a sea of faces, people talking, not wanting to start class (particularly true of my 6th period class), my lesson plan disappears from my mind to be replaced with this solitary and recurring question: “What the hell am I going to do now?” I then revert to a technique I learned when I was student teaching. Clipboard in hand, I stand at the front of the room and shout: “In your seats and homework out, please!” This technique serves two purposes. It gives me the illusion that I am in control. Secondly, it tells the students what to do, and even if they don’t do it, they at least know what it is they should be doing.

My routine after that is something I’ve seen written up in articles that decry the traditional classroom for its dull, staid, predictable and uninspiring drills. It is also something that I have heard people say will disappear once Common Core kicks in full tilt. Thus, I am a vanishing breed soon to be relegated to the world of buggy whips, slide rules, 8-track tape players, and well-written math textbooks. While I check in homework, they are to work on the warm up questions that I have on the screen. We go through the warm-ups, I put up the answers to the homework, answer any questions they may have on the homework and then embark on the lesson.

My rifle range instruction occurs at mostly when I circulate around the room after I assign the problems they are to work on. The conversations can be personal as well as instructive, and it is a time for me to get to know them. My second period class is algebra, 1 second year. This means that the students have passed the first year of the 2-year sequence of algebra 1—most of them anyway—and are older and somewhat more mature and well behaved than the first year students.

In this class I had about six football players on the junior varsity team, almost all of them struggling with the material. I was working on solving systems of linear equations. The chapter started out by solving by graphing—always a frustrating topic because the main intent of the lesson, it seems, is to show how inaccurate and unreliable graphing is as a means of solving equations. I suppose it’s also to show that the solution of a system of equations exists at the point of intersection. And then there are the typical “real world” problems that describe two health club plans or two long distance plans, or any two plans that involve 1) a membership fee (which translates to the y-intercept) and 2) a monthly, weekly, or daily rate (which translates to the slope) and asks at what point (days, weeks, or months) will the plans cost the same. I have nothing against such problems but, like most problems in Holt Algebra, little is ever varied so that once you learn how to solve one such problem, you’ve solved them all. As it was, many of my students were struggling even with basic types of non-word problems.

During one of my rifle range tours, one girl in that class, worried about a quiz upcoming in the next week, asked “Will the quiz have any division on it?”

“You mean will you have to know how to divide? Yes, of course,” I said. She looked crestfallen. “I mean, it won’t have a lot but can you divide things like 24 by 8 and things like that?”

“Oh yes,” she said, looking relieved. “It’s just the double and triple digit division I have a hard time with.” For some reason I didn’t find this very assuring.

My fourth and sixth period classes were also a mixture of abilities. Some students asked more questions than others. In sixth period it was Elisa, the girl who told me she had trouble with math. I found out she lived with her aunt, and had just moved from Colorado. She had had a tough time with math in Colorado and said she developed a stomach ulcer because of her last math class. The teacher wouldn’t answer any of her questions. Maria, a Mexican girl, was another who asked many questions and, like Elisa, said her previous teachers in math didn’t answer her questions. I don’t know if their teachers were of the philosophy that less teaching means more learning but both expressed gratitude to me for answering their questions.

Although I would explain the concept behind the problem, in most cases it always came down to telling students the procedures. Maria, for example, asked me how to solve -7 -3. “Maria, if you lost 7 dollars and then lost 3 more how much have you lost?”

“Ten dollars” she said, counting on her fingers.

“OK. So what you’re really doing is adding two negatives. It’s really (-7) + (-3).” I showed this on a number line.

“So if you have two negative numbers, you just add them and put a minus sign in front?” she asked.

I found myself thinking “What the hell do I do now?”

I answered her question, shakily and guiltily confident in my belief that procedural fluency leads to understanding. “Yes,” I told her. “That’s what you do.”

And that’s what she did.

Sunday, July 13, 2014

The view from 10,000 feet: Superintendents and the Common Core

Kids, parents, and teachers are frustrated by the Common Core, but, as a recent article by Education Week reports, superintendents generally support it.

A survey of more than 500 district superintendents and administrators from 48 states [conducted by American Association of School Administrators] shows that most of the local K-12 leaders are firmly behind the Common Core State Standards.
... 
The AASA survey finds that 93 percent of the superintendents say the new standards are more rigorous and will better prepare students for success after high school. In all, 78 percent of those surveyed believe the education community specifically supports the standards.
Among the other "notable findings" that Edweek highlights is this one:
73 percent of those surveyed by AASA believe that the fight between supporters and opponents is actually hindering implementation of the standards.
I'm not exactly sure what makes this finding notable, but I'd say it's reason, not for concern, but for hope.

Friday, July 11, 2014

Math problems of the week: 5th grade Investigations vs. Singapore Math

I. The second multiplication problem set in the 5th grade (TERC) Investigations Student Activity Book, Unit 1: "Number Puzzles and Multiplication Towers," p. 10 [click to enlarge]:


II. The second multiplication problem set in the 5th grade Singapore Math Primary Mathematics 5A Workbook, Unit 1: "Whole Numbers", p. 16 [click to enlarge]:

III. Extra Credit:

What grade should/will an Investigations student get if they leave their assignment blank because their parents saw to it that they learned all their multiplication "combinations" over the summer?

Wednesday, July 9, 2014

Common Core Math: Is it wrong to want to know which way is right?

The latest New York Times article on the Common Core State Standards begins with a refreshing acknowledgment of the frustrations that the Common Core has been causing among those most directly affected by it. The article opens with a description of a mother who, because of "the methods that are being used for teaching math under the Common Core,” plans to home-school her four children:

Ms. Nelams said she did not recognize the approaches her children, ages 7 to 10, were being asked to use on math work sheets. They were frustrated by the pictures, dots and sheer number of steps needed to solve some problems. Her husband, who is a pipe designer for petroleum products at an engineering firm, once had to watch a YouTube video before he could help their fifth-grade son with his division homework.
“They say this is rigorous because it teaches them higher thinking,” Ms. Nelams said. “But it just looks tedious.”
The article also mentions
viral postings online that ridicule math homework in which students are asked to critique a phantom child’s thinking or engage in numerous steps, along with mockery from comedians including Louis C. K. and Stephen Colbert.
But then the Times proceeds to regurgitate the Common Core's tired rationale:
The new instructional approach in math seeks to help children understand and use it as a problem-solving tool instead of teaching them merely to repeat formulas over and over. They are also being asked to apply concepts to real-life situations and explain their reasoning.
When did math students ever repeat formulas over and over again? And when did students ever not apply concepts to real-life situations? And when did “explain your reasoning,” ubiquitous to American Reform math and rare everywhere else, become the one, one-size-fits all path towards, and the one, one-size-fits measure of, conceptual understanding?

The Times also cites employers, who “are increasingly asking for workers who can think critically”:
Employers “want a generation of people who can think and reason and can construct an argument,” said Steven Leinwand, a researcher for the American Institutes of Research.
But if there’s even one employer out there who (a) is looking for mathematically competent employees and (b) has taking a close look at a representative sample of Common Core-inspired math assignments (as compared with traditional math assignments), I have never seen him or her cited anywhere.

Citing global tests like the TIMSS and PISA, in which American children lag behind those in other developed countries, the Times also claims that “traditional ways of teaching math have yielded lackluster results.” The Times does not mention that many of America’s current students grew up, not with traditional math, but with Reform Math, and that the countries that outperform us in math have eschewed our types of reforms in favor of more traditional ways of teaching math.

Having carefully omitted these facts, the Times proceeds on to argument by authority:
The [Common Core] guidelines are based on research that shows that students taught conceptually retain the math they learn. And many longtime math teachers, including those in organizations like the National Council of Teachers of Mathematics and the National Council of Supervisors of Mathematics, have championed the standards. …
Math experts say learning different approaches helps students develop problem-solving skills beyond math.
Do these math experts include (a) any actual mathematicians who have looked at representative samples of Common Core-inspired math assignments or (b) anyone who has conducted or reviewed studies that actually address this question empirically?

As for the not-at-all-surprising claim that “students taught conceptually retain the math they learn,” this does not support Common Core-inspired math in particular. Traditional math also teaches conceptually.

The Times cites one authority in particular, Linda M. Gojak, the former president of the National Council of Teachers of Math:
“I taught math very much like the Common Core for many years.When parents would question it, my response was ‘Just hang in there with me,’ and at the end of the year they would come and say this was the best year their kids had in math.”
For what it’s worth, I’ve never met a single parent who has said that. But given how much Reform Math has watered down the actual math, it’s easy to imagine that some of the least mathematically inclined children experience their first year in Reform Math as their “best year in math.”

The Times ends up suggesting that most of the frustrations amount to growing pains—the pains of a transition to a whole new curriculum, or as one superintendent puts it, “a shift for an entire society.”

The article notes that, besides the issues of winning over skeptical parents,
textbooks and other materials have not yet caught up with the new standards, and educators unaccustomed to learning or teaching more conceptually are sometimes getting tongue-tied when explaining new methodologies.
Frederick Hess, directory of education policy studies for the American Enterprise Institute, puts it better:
“It is incredibly easy for these new instructional approaches to look good on paper or to work well in pilot classrooms in the hands of highly skilled experts and then to turn into mushy, lazy confusing goop as it spreads out to classrooms and textbooks.”
To its credit, the Times article, besides including Hess among its authorities, acknowledges that certain subpopulations may have particular problems with Common Core-inspired math:
Some educators said that with the Common Core’s focus on questioning lines of reasoning and explaining answers, the new methods were particularly challenging for students with learning disabilities, or those who struggle orally or with writing.
“To make a student feel like they’re not good at math because they can’t explain something that to them seems incredibly obvious clearly isn’t good for the student,” said W. Stephen Wilson, a math professor at Johns Hopkins University.
(It's refreshing to see an actual math professor cited here.)

Besides the language impaired, there are the mathematically gifted:
Some parents of children who have typically excelled at math find the curriculum laboriously slow.
In Slidell, an affluent suburb of New Orleans, Jane Stenstrom is concerned that her daughter, who was assigned to a class for gifted students as a third grader last year, did not progress quickly enough.
“For the advanced classes, it’s restricting them from being able to move forward,” Ms. Stenstrom said one recent afternoon.
Her daughter, Anna Grace, 9, said she grew frustrated “having to draw all those little tiny dots.”
“Sometimes I had to draw 42 or 32 little dots, sometimes more,” she said, adding that being asked to provide multiple solutions to a problem could be confusing. “I wanted to know which way was right and which way was wrong.”
Surely some people will see this child, however gifted, as overly rigid in her mathematical reasoning and problem solving skills. But here's my take: when it comes to mathematics, (or, for that matter, engineering, accounting, pharmaceuticals, surgery, piloting airplanes, operating machinery, or, dare I even say it, educating our children), "wanting to know which way is right" is a pretty reasonable desire--especially when it comes to one of the Common Core's main obsessions: all those "real-life situations."