Friday, January 31, 2014

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

I. One of the last percentage problem sets in the 6th grade Everyday Math Student Math Journal, Volume 1, p. 157 [click to enlarge]:

II. One of the last percentage problem sets in the 6th grade Singapore Math Primary Mathematics Workbook 6A (volume 1), pp. 64-65  [click to enlarge]:

III. Extra Credit
Contrast the number of steps needed to solve the Everyday Math problems vs. the Singapore Math problems.

Which students are more likely to be able to solve the other students' problem set: the Everyday Math students, or the Singapore Math students?

Wednesday, January 29, 2014

And the silver bullet du jour is...

First it was Constructivism and child-centered discovery learning, then it was Grit and Social Emotional Learning, now it's Recess. This, apparently, is what we need more of in order to raise test scores. After all, it's "The Secret Behind Finland's Super Smart Kids."

Somehow I missed this piece (it dates to this past September), but I really should have mentioned it the last time I brought up Finland, just two weeks ago, in connection with those Finnish exchange students. One of them, remember, was shocked at the easiness of an American algebra test and at how poorly his classmates did on it. The other one was astounded at how undemanding the history tests were, at how little homework the students did, and at the in-class projects, which were mostly "glue this to the poster for an hour." She had to repeat that year of high school when she returned to Finland. Who knew that it was recess that put her and her compatriot at such an advantage vis a vis her American counterparts?

I'm all for American children getting a lot more time to run around outside than they do now.  Our kids need many more breaks, and should be going outside and exerting themselves even when (shudders!) the temperature drops below freezing or there's snow on the ground and their teachers would prefer to supervise them indoors while they play board games and computer games or watch movies.

But I hadn't realized that what leads to teachers giving harder algebra tests and students doing better on them, and to students taking homework more seriously, and to teachers assigning more essays and less bubble-filling and poster-gluing, is recess.

Perhaps if we--or any country, really (Finland, after all, has been slipping lately in international rankings)--want to totally maximize student achievement, we could completely replace class time with recess. That would, at the very least, eradicate those in-class poster-gluing projects.

Monday, January 27, 2014

When final exams should trump “formative” assessments

One current trend in K12 is a growing aversion to summative assessments like final exams. At the very least, many US educators feel, summative assessments shouldn’t be, as they are in many other countries, the major determiners of course grades. Here in America, of course, essays, lab reports, and other homework assignments have long figured significantly in course grades—and reasonably so—for most subjects. But what about a highly cumulative subject that doesn’t (or shouldn’t) involve essays, research projects, and lab reports? I’m thinking, of course, of math.

Here, arguably, stellar performance on the final should override everything else. For imagine a student who hasn’t turned in a single homework assignment and/or has performed poorly on earlier tests and quizzes. Now suppose that student gets almost everything right on a well-constructed, comprehensive, cumulative final. Then shouldn’t s/he should get an A in the course rather than the B, C, or D to which those earlier “formative” assessments drag him down?

This idea, naturally, won’t resonate with many of today’s educators—trained as they are to favor process and portfolios and other, supposedly more authentic, “formative” assessments, and to lavish students with partial credit and “points for trying.” Along with those multiple “entry points” that are supposed to welcome multiple “learning styles,” surely there should be multiple ways to demonstrate mastery?

But mastery is an end result; not a process. And, in a subject like math, a comprehensive, cumulative final exam is the ultimate measure of that mastery at that crucial end point, i.e., the course’s conclusion. In the spirit of multiple learning styles (or multiple learning strategies), therefore, shouldn’t we allow multiple pathways, not all of which involve turning in assignments and studying for quizzes, to attaining mastery by the end of the course?

Saturday, January 25, 2014

Teachers should submit syllabi instead of daily lesson plans!

It's been a long time since I've taught in the K12 classroom, and things were quite different back in the late 1980s. Were I still teaching K12 today, I'm guessing that one of the things I'd like the least about the job would be having to submit my daily lesson plans for my principal's approval. The more so in this day and age of edujargaon, "The student will be able to" goals, and, worse, the growing requirement that every lesson plan be explicitly mapped to one or more Common Core goal--goals like "Analyze how complex characters (e.g., those with multiple or conflicting motivations) develop over the course of a text, interact with other characters, and advance the plot or develop the theme."

The monitoring by higher authorities of daily lesson plans seems like little more than a means to disempower teachers and make sure that they are following to the letter all those problematic new pedagogic principles--e.g., of Reform Math, Writer's Workshop, group activities, and, now, the Common Core.

Instead of daily lesson plans, what teachers should turn in, once per semester instead of once per day, are course syllabi. Yes, syllabi, as in what college professors give out to students, and what those students take into account when considering whether to take particular courses.

K12, of course, is different, but there is one really good reason for K12 teachers to submit syllabi also. Only recently did it occur to me, though: i.e., only after news about a move in Pennsylvania to mandate instruction about the Holocaust. This move, in turn, was inspired by recent surveys revealing just how little Pennsylvania's top college students are about the holocaust in particular, and the 20th century in general. (I was reminded of all this just the other day, after hearing this story, on Philadelphia public radio's Newsworks program.)

As I wrote in my earlier post about this, the best way to teach about the Holocaust is not as a disembodied "Holocaust appreciation" unit, but within its place in world history:

Pennsylvania already mandates world history, and the approved world history textbooks, not so surprisingly, do cover the Holocaust. So perhaps instead the state could stipulate that teachers not skip entire chapters in world history textbooks.
Having teachers turn in a syllabus at the beginning of each semester, and making sure they stick to it, is one way to accomplish this. Having them turn in daily, piecemeal lesson plans isn't--no matter how many TSWBAT, CCS-aligned goals they contain.

Thursday, January 23, 2014

Math problems of the week: 4th grade Investigations vs. Singapore Math

I. A 4th grade  (TERC) Investigations homework assignment, assigned in late November:

II. From a similar point in the 4th grade Singapore Math Curriculum (Primary Mathematics 4A):

III. Extra Credit:

Neither traditional math, nor Singapore Math, spell out shortcuts as explicitly Investigations does ("Can you use the first problem to help you solve the second problem?"). Instead, students of traditional math and Singapore Math discover these tricks on their own. Which is better, child-centered discovery of ad hoc shortcuts, or more explicit hints via teachers, worksheets, and other authoritative entities?

Tuesday, January 21, 2014

Mistaking “communication” for language… and shortchanging those with language impairments

I wrote earlier about how we Americans view grammar as rote and dry and largely dispensable. When it comes to that warm, fuzzy, alternative to grammar, namely language, we make similarly wrong-headed but contrasting assumptions. “The language of dance”—or of music, or of art—we see language as involving anything remotely communicative. Dog owners claim that their pets understand English; students of language acquisition, that the cries of newborns exemplify early language, and students of autism, that nonverbal individuals who click on buttons displaying pictures and keywords are ipso facto using language.

But all sorts of things are communicative without involving intentional communication. A clock communicates the time; rings on a tree communicate how old it is; even a rock dropped into a dark well is “communicative”: how long it takes to say “plop” tells you how deep the well is. A newborn who cries when she is hungry may be no more intentionally communicative than a clock or a tree or a rock; her cry may simply be an innate, reflexive response to hunger that happens to communicate something to knowing adults. When a dog runs to the door when you say “Do you want to go on a walk?” it probably isn’t parsing the question into subject and predicate and/or calling up the word definitions from long term memory; rather, it’s responding to a holistic sound pattern.

So, when a nonverbal autistic child pushes the “drink” button on a keyboard, how do we know whether he understands the definition of “drink,” and/or has conceived the intention of communicating to others? Perhaps, after months of therapeutic “conditioning,” he is simply performing an act (a click on a particular button) that he associates with a particular consequence (getting something to drink).

Nor is even intentional communication a sufficient condition for language. For what’s truly special about language is that we can use it to refer to things out in the real world and express ideas about them. Coffee tables, coffee, the hypothesis that drinking coffee may help prevent Parkinson’s disease or extend life, the question of what it would mean to leave forever. Whether the language is English or Igbo or Navaho, and whether that language is spoken or signed or written, there is no limit to what it can be used to refer to and what it can express about that referent.

The arts are different. As expressive as Mozart’s Piano Concerto in D Minor is, neither its composer nor its performer is intentionally referring to anything other than to music (or sound) itself, and any “ideas” the composer, the piece, or the performer expresses are purely musical. Anything else evoked in our heads, or hearts, is a product of our own personal associations and sensitivities to the music.

Arguably there are better examples than music. Paintings, for example, are more plugged into the world out there, and can, in a sense, refer to coffee and coffee tables. But they, too, fall far short of the power of language to communicate arbitrary ideas—for example, the thought I’m expressing in this sentence. Math is a language of sorts, but it only expresses ideas about quantitative and spatial entities and relationships. Computer programs, though seemingly more expressive than math, live inside computers and don’t to refer to things in the real world, let alone express ideas about them.

How is all this relevant to education? Because nowhere is this misconception of language—as anything remotely expressive or communicative--more evident, and more problematic, than in the ed world. Wedded to the notion of Learning Styles, it has led to a debilitating complacency in language arts instruction, especially when it comes to kids with language delays or writing deficits. Combine the notion that art is a form of language with the notion that some kids are “visual” rather than “verbal” learners, and teachers can confidently assign dioramas rather than book reports, certain that students aren’t missing out on anything important, let alone in dire need of linguistic remediation. Or they can watch an autistic child doing complex math problems and celebrate the fact that his language is “the language of numbers”--without worrying too much about teaching him ours.

Finally, confusing the merely communicative with the intentionally so, and mere key words with full-fledged language, and teachers (and others) may fail to provide the necessary linguistic instruction (including grammar!) to help a “nonverbal” child move beyond the limited words, pictures, and pre-packaged phrases of the Dynavox, or PECS, or rudimentary "Signed English" either to a more open-ended communication device like a touchscreen or keypad that can express any possible English sentence, and/or to another true and fully expressive language like American Sign Language.

Sunday, January 19, 2014

Autism Diaries: Editing Cracker Barrel

It's not very often that I have an urge to edit Wikipedia. But every once in a while an article I assign for one of my classes contains minor errors or omissions that I'm tempted to fix. So, thinking things may be different this time, I push the "edit" button.

And once again, things aren't different, because I once again get the following message:

You are currently unable to edit Wikipedia.

You are still able to view pages, but you are not currently able to edit, move, or create them.
Editing from XX.XX.XX has been blocked (disabled) by Elockid for the following reason(s):
Wikipedia Checkuser.svg
CheckUser evidence has determined that this IP address or network has been used (not necessarily by you) to disrupt Wikipedia. It has been blocked from editing to prevent further abuse.
Once again, it would seem that a member of our household who is a bit more eager to edit Wikipedia than I am has gotten our IP address blacklisted. Hmm, who could that be?

"Why did we get blocked again?" I ask J. After the delete key episode, when we'd been banned for 6 months, wasn't he tired of not being able to ad important information about ceiling fans to all possibly relevant Wikipedia entries?

As it turned out, the problem this problem time was precisely J's zeal for adding fan information. He had gotten into, as he put it, "an edit war" with one of Wikipedia's senior editors--and the battlefield was none other than the Cracker Barrel entry.

The problem was that J kept adding helpful information about the fact that Cracker Barrels have ceilings fans, and the editor kept deleting it, telling him that it was irrelevant, and warning him not to put it back. And J, or so he told me, kept telling his editor that "Cracker Barrels do have ceiling fans; if you don't believe me, visit a Cracker Barrel and see for yourself!"

The Wikipedia editor, as you can see for yourself if you visit the Cracker Barrel entry, won the battle: there's not one reference to "ceiling fans" there.

But in the real world of the Old Country Store, Inc franchise, the truth is out there, in abundance. It's blowing the air around and making certain customers very happy: all you have to do is look up.

Friday, January 17, 2014

Math problems of the week: 4th grade Investigations vs. 1920s math

Multiplying by 10s: I. In 4th Grade Investigations Student Activity Book, "Multiplication Towers and Decimal Stories" unit, p. 42 [click to enlarge]:

II. In Hamilton's Essentials of Arithmetic, First Book, Chapter IV (first half of 4th grade), p. 144 [click to enlarge]:

III. Extra Credit

Which problem set involves more discovery-based learning and real-world applications?

Monday, January 13, 2014

Monday pop quiz!


1. Guess the diagnosis of the boy who completed this assignment.

2. What grade do you think he should get on it?

3. What grade do you think a neurotypical teacher might give him?

Saturday, January 11, 2014

What do foreign exchange students say about America's schools?

To the extent that American education experts cite the countries that outperform ours on international tests, it's often to confirm their pre-established ideas about what works in education rather than to examine what's actually happening in foreign schools. Thus:

-overlooking the rigor that picks up in the later grades, they emphasize how formal education in Finland doesn't start until age 7.

-confusing homework load with homework rigor, they emphasize how students in Finland have much less homework than American students do, ignoring how much easier, if more time-consuming, American homework assignments are, and how many fewer extracurricular school activities (sports teams, marching bands, proms) Finnish students engage in.

-confusing rigorous research projects with the mushy, interdisciplinary, art-based sort that predominate in this country, they claim that Finnish education is based on American-style project based learning.

-confusing group work with whole class discussions, they conclude that Japanese students learn math in groups rather than in teacher-directed lessons.

-confusing a math education that focuses on rigorous math concepts with one that emphasizes language intensive word problems and trivial, if convoluted, applications of math to daily life, they claim that those countries that score highest on international tests use curricula more akin to American Reform Math than to traditional math.

--confusing truth with fiction, they suggest that countries in India and East Asia make more use of educational technology than we do.

Perhaps our best informants on how other countries actually compare are students who have studied in both American classrooms and classrooms abroad. Unfortunately, because America's foreign language instruction is so poor, comparatively few American exchange students are able to survive very long in foreign schools in non-Anglophone countries--ending up instead in English-language classrooms in international schools. So most of our eyewitnesses are foreign exchange students.

Some of these students are interviewed in Amanda Ripley's new book, The Smartest Kids in the World. I have yet to read the book, but have read a number of reviews, including this one by Joanna Daneman on Amazon, in which she cites one of Ripley's exchange students, a male high school student from Finland:

Having aced an algebra test, the student is completely flummoxed that anyone would fail it. "How could you NOT know this?"
...The Finnish student remarks that school seems like elementary school--a lot of making posters rather than intensive coursework.
An equally compelling informant from Finland appeared a few years ago in an article in the Wall Street Journal:
Finnish high-school senior Elina Lamponen... spent a year at Colon High School in Colon, Mich., where strict rules didn't translate into tougher lessons or dedicated students, Ms. Lamponen says. She would ask students whether they did their homework. They would reply: " 'Nah. So what'd you do last night?'" she recalls. History tests were often multiple choice. The rare essay question, she says, allowed very little space in which to write. In-class projects were largely "glue this to the poster for an hour," she says. Her Finnish high school forced Ms. Lamponen, a spiky-haired 19-year-old, to repeat the year when she returned.
Another source, via, is Felix, a UK exchange student attending an America high school:
The UK curriculum I think is harder, and stricter but probably a better education. But I prefer the American system for it's [sic] lenient style and how grades are determined by also your work ethic, while in UK it's based solely on the results you get on tests and assessments.
A community newspaper article about exchange students at a high school in Door County, Wisconsin cites a Chinese student as remarking that "math and science are super easy." And another community newspaper article about exchange students at a high school in Mille Lacs, Minnesota cites a German student as calling the American school system as "a lot easier" and a Taiwanese student who
agreed with her fellow exchange students that some subjects taught here are much easier than back home, such as math, but that others are more difficult.
One has to wonder how much of that extra difficulty comes simply from the linguistic challenges of reading and writing in high school-level English when it's not your native language--which is much less an issue in math than in other subjects.

Consistent with this, here's is more of what Finnish student Elina Lamponen says, this time on NPR's The Takeaway:
I had a bit of a culture shock at first there. It took me a couple of weeks to realize it at first – on the first courses I thought it would be really hard and difficult for me, but it was only because of the language. In a couple of weeks when I caught up in the language, it was fine and I was fine and then I really knew that I was far ahead. It was probably it was in math class where ... when they showed us what we were going to do and gave us homework and we did problems in class, I realized that I’d already done this a year or two ago. So I really got that it’s ... it’s not that difficult. So I had – the math course I took was Algebra 2 which was the hardest math class in the whole school, and then I knew everything on the tests and then I always got like 105% on the test because I just knew everything. The American students, they were really surprised how I could get 105 because they were struggling with the tests.
Interestingly, the big picture has long been known to the more rigorous of America's education researchers. Here's an excerpt from a 2001 study by the Brookings Institute:
Overwhelmingly, the foreign exchange students found U.S. classes easier than classes in their home countries. More than half, 56%, described the U.S. classes they attended as much easier and 29% as a little easier. In contrast, only 5% found U.S. classes much harder and 6% a little harder. Even considering that exchange students are excellent students, as noted above, while in the U.S. they usually attend above average schools and take the toughest classes that American high schools have to offer. Compared to the classes they are familiar with back home, which probably serve high achieving students, the American classes do not seem very rigorous.
This perception is widespread among students coming from our subsample of high scoring countries on TIMSS. The percentage of students describing American classes as much easier: Sweden 55%; Hong Kong, 60%; Japan, 61%; Russia, 67%; France, 73%. It’s clear that students from the highest achieving countries in Europe and Asia regard American high schools as less demanding.
So the facts have been out there for quite a long time. It's just that few of us Americans want to take note of them, much less to think very hard about what they imply.

Thursday, January 9, 2014

Math problems of the week: 4th grade 1920s Math vs. Everyday Math

I. The first fractions problem set in the first 4th grade chapter of Hamilton's Essentials of Arithmetic, published in 1920, pp. 176-177 [click to enlarge]:

II. The final fractions problems in the "Fractions and Their Uses" chapter of the 4th grade Everyday Math Student Math Journal, published in 2002, pp. 226-228 [click to enlarge]:

III. Extra Credit

What did traditional math students miss out on in not being asked for their meta-cognitive reflections?

Tuesday, January 7, 2014

The decline of the humanities, III

“If you want to be sure to learn a lot in college, major in math, science, or engineering rather than in the humanities.”

This was the advice I gave several years ago to my son, and, like so many of his peers, he is indeed pursuing a STEM field rather than English, history, or anthropology. But if college today was like college 30 years ago, I would not have given this advice.

As I’ve written earlier, pursuing the humanities potentially develops both life skills and vocational skills. Writing traditional, analytical essays and getting detailed feedback on them helps you refine your general writing skills, along with your ability to think clearly, analyze carefully, and argue coherently. Reading great literary and analytical works also refines your writing and thinking skills.

Then, of course, there’s the content of particular fields. Studying the past helps you better understand the issues of the present. Studying other political systems and cultures helps you better understand our own. Beyond this, engaging with other times and places, and with well-drawn fictional characters and imagined situations, helps you imagine other worlds, real and hypothetical, far removed from yours. It helps you conceive of other ways of living and being, and understand and empathize with people whose circumstances and/or personalities are vastly different from those closest to you.

But, with junior faculty time-strapped by the tenure treadmill, adjuncts time-strapped by the course load—or second jobs—they must bear in order to make ends meet, and much of the professoriate in general more interested in meta-analysis and intertextuality than in analysis and text construction, today’s college humanities courses are offering less and less training in straight-forward writing, analysis, and argumentation. And they’re offering less and less compelling material about other times, places, and peoples. Here, for example, is what Veryl Klinkenborg, in an NYTimes OpEd this past summer, has observed about writing:

In the past few years, I’ve taught nonfiction writing to undergraduates and graduate students at Harvard, Yale, Bard, Pomona, Sarah Lawrence and Columbia’s Graduate School of Journalism. Each semester I hope, and fear, that I will have nothing to teach my students because they already know how to write. And each semester I discover, again, that they don’t.
They can assemble strings of jargon and generate clots of ventriloquistic syntax. They can meta-metastasize any thematic or ideological notion they happen upon. And they get good grades for doing just that. But as for writing clearly, simply, with attention and openness to their own thoughts and emotions and the world around them — no.
And here, in an OpEd in this past weekend’s Wall Street Journal, is what Heather Mac Donald has observed about literature courses:
Until 2011, students majoring in English at UCLA had to take one course in Chaucer, two in Shakespeare, and one in Milton —the cornerstones of English literature. Following a revolt of the junior faculty, however, during which it was announced that Shakespeare was part of the "Empire," UCLA junked these individual author requirements. It replaced them with a mandate that all English majors take a total of three courses in the following four areas: Gender, Race, Ethnicity, Disability and Sexuality Studies; Imperial, Transnational, and Postcolonial Studies; genre studies, interdisciplinary studies, and critical theory; or creative writing.
In other words, the UCLA faculty was now officially indifferent to whether an English major had ever read a word of Chaucer, Milton or Shakespeare, but the department was determined to expose students, according to the course catalog, to "alternative rubrics of gender, sexuality, race, and class."  
As Mac Donald notes:
Such defenestrations have happened elsewhere, and long before 2011. But the UCLA coup was particularly significant because the school's English department was one of the last champions of the historically informed study of great literature, uncorrupted by an ideological overlay. Precisely for that reason, it was the most popular English major in the country, enrolling a whopping 1,400 undergraduates.  
The corruption of the humanities, thus, extends far beyond UCLA:
The UCLA coup represents the characteristic academic traits of our time: narcissism, an obsession with victimhood, and a relentless determination to reduce the stunning complexity of the past to the shallow categories of identity and class politics. Sitting atop an entire civilization of aesthetic wonders, the contemporary academic wants only to study oppression, preferably his or her own, defined reductively according to gonads and melanin.
… It is no wonder, then, that we have been hearing of late that the humanities are in crisis. A recent Harvard report from a committee co-chaired by the school's premier postcolonial studies theorist, Homi Bhabha, lamented that 57% of incoming Harvard students who initially declare interest in a humanities major eventually change concentrations. Why may that be? Imagine an intending lit major who is assigned something by Professor Bhabha: "If the problematic 'closure' of textuality questions the totalization of national culture. . . ." How soon before that student concludes that a psychology major is more up his alley?
Contrast this with what the humanities could do for us:
They provide the thing that Faust sold his soul for: knowledge. It is knowledge of a particular kind, concerning what men have done and created over the ages.
The humanities are both a means to important ends:
The American Founders drew on an astonishingly wide range of historical sources and an appropriately jaundiced view of human nature to craft the world's most stable and free republic. They invoked lessons learned from the Greek city-states, the Carolingian Dynasty and the Ottoman Empire in the Constitution's defense. And they assumed that the new nation's citizens would themselves be versed in history and political philosophy.
And an end in themselves:
It is simply better to have escaped one's narrow, petty self and entered minds far more subtle and vast than one's own than never to have done so. The Renaissance philosopher Marsilio Ficino said that a man lives as many millennia as are embraced by his knowledge of history. One could add: A man lives as many different lives as are embraced by his encounters with literature, music and all the humanities and arts. These forms of expression allow us to see and feel things that we would otherwise never experience—society on a 19th-century Russian feudal estate, for example, or the perfect crystalline brooks and mossy shades of pastoral poetry, or the exquisite languor of a Chopin nocturne.
But how many of these things are seen and felt by today’s professional humanists? And how many of them will suspend their narrow and petty interests in order to give Mac Donald’s words the humanistic reading they deserve?

Sunday, January 5, 2014

Teacher of the year uses smartboards and hands-on group work!

In the course of my Comments of the Year bonanza, I got behind on the end-of-2013 news, including an article in the Philadelphia Inquirer on one of the winners of the 2013 Presidential Award for Excellence in Mathematics and Science Teaching, chosen by a panel of scientists, mathematicians, and educators. The winner in question is Jenn Basner, a third-grade teacher at Berlin Community School, who, along with the other 101 winners from around the country, received $10,000 from the National Science Foundation.

What makes Basner's teaching so prize-worthy?

First there's her use of smart boards. This, the Inquirer suggests, is the reason why Berlin Borough Superintendent Tony Trongone nominated her in the first place:

He was impressed by how she effectively used technology such as a smartboard to engage her entire class. 
"To do that every day takes a lot of passion and hard work for your craft," Trongone said. "She's the type of teacher I want my children to learn from."
But using a smartboard effectively was only the first step:
After she was nominated for the president's award in 2012, Basner had to complete a grueling application process. She wrote, created, and taught a math lesson on elapsed time, an important but difficult concept for third graders to grasp.
Just how difficult this concept gets is evident in the lesson's culminating assignment:
Students applied what they learned to determine if they arrived at the zoo at 9:30 a.m. and the field show was at 11 a.m., how much time did they have in between.
Luckily, Basner was able to come up with a truly creative and experiential way for students to solve this problem:
Using a hands-on approach as she typically does, Basner employed mini clocks and a fictional trip to the zoo to teach students how to compute elapsed time.
She also employed such innovations as watchfulness, reinforcement, and group activities:
To make sure they caught on, Basner had students work with each other and independently under her watchful eye. She followed up with reinforcement and enrichment in small group sessions.
Math, notably, hasn't been Basner's strongest subject. But, at least when it comes to Basner, this is a not a bug, but a feature:
While she was always a good student, Basner said, she had to work a little harder at math.  So when she sees that "aha moment" on her students' faces, she feels a sense of accomplishment. 
"I love that I am able to teach each student in my classroom something that he will use for the rest of his life," she said.
Speaking of elapsed time, the last time an Inquirer article about the Presidential Award caught my eye predates this blog by one year. So I didn't blog about it; instead, I put it in my book. You'll find a reference to on page 90,  in the opening paragraph to a section entitled "WHY DOES MY CHILD HATE SCHOOL MATH?".

Friday, January 3, 2014

Math problems of the week: traditional vs. IMP trigonometry

The second in a series of posts comparing the introduction of trigonometry in traditional high school math vs. the Reform Math program Interactive Math Program.

I. The next two pages of the first trigonometry chapter in A Second Course in Algebra (published in 1937), pp.395-396 [click to enlarge]:

II. The next two pages of the first trigonometry chapter in Interactive High School Mathematics Math Program Year 4, pp. 6-7 [click to enlarge]:

Thursday, January 2, 2014

Ushering in the new year!

It was a pleasure for me to conclude '13 and begin '14 with my many favorites of this year's OILF comments. A pleasure, and also a great excuse to revisit and relearn many of the important facts and insights you all shared.

It seems fitting, then, to officially usher in this new year at OILF with a link to Barry Garelick's wonderful, just-released book, which outs him as the mysterious author of OILF's guest posts:

Letters from John Dewey/Letters from Huck Finn: A Look at Math Education from the Inside

It's available here both as a kindle and as a print book. Check it out now!

Wednesday, January 1, 2014

Favorite comments of '13, cont: TerriW and Evan

On Labels vs. Concepts, II: Why Piaget's followers underestimate and under-challenge America's students

TerriW said...
I am well-reminded of our experience transferring to a new swim lesson facility. At the beginning of the session, the new kids get a brief (and I mean *brief*!) minute with an instructor to assess their current level and place them in a class.

My 7 year old son -- already a little overwhelmed by our recent move and the intimidating new facility -- hopped into the water and was told: "Do a front switch!" and he just stared at them blankly.

So they put him in the class with the toddlers.

(You can probably imagine the rest of the story: he kept getting bumped back up as they realized he could already do everything but just didn't know their terminology. We were in three different classes within the first 40 minute class, and the whole thing ended in frustration and tears.) 
Evan said...
This reminds me of when I took my driving test and the instructor asked me to do a three-point turn. I stared blankly (out the windshield, because I didn't want him to see if he didn't need to) and asked, "Um, into this driveway?" Fortunately, he explained that you were supposed to do a three-point turn fully on the street - so I got my license after all. 

Favorite comments of '13, cont: kcab, Anonymous, Auntie Ann, C T and Deirdre Mundy

On The Testing Industrial Complex

kcab said...
My theory is that the problem was "Iowa" in the name. Identifying a test with a particular state makes it look specific to that state.
Anonymous said...
I can remember taking the ITBS in the '50's. Didn't take much time, there was no test-prep involved (other than 5 minutes on how to fill in the form).
Auntie Ann said...
We didn't take them in the 70's, but I remember calling the tests that we *did* take the "Iowa Test". It was a generic name for standardized tests back then.
C T said...
I homeschool in Colorado, which requires periodic testing with a nationally-normed test, so I have given my nine-year-old the ITBS. I don't think there's anything "wrong" with it. It seemed like a fair test of the stated skills and knowledge, and its results accurately reflected my child's weaknesses and strengths. It even helped me convince her that she really wasn't doing as well as she thought in math. She was SO dismayed when she ran out of time with over half the calculation questions left. Sometimes a kid needs to see how they measure up against the norm for their age group, even if it is an unpleasant dose of objective reality.
Deirdre Mundy said...
I imagine that 'what was wrong' was that the scores track way too closely to IQ.

At least, that was how it ended up when we used to take them as kids. They actually used them to screen for the GT program!

Also, they were low stress and fun. So they don't encourage teaching to the test....