Monday, August 3, 2015

Leadership vs. Advanced Placement

How nice to see the Philadelphia Inquirer finally running an article on the best science and STEM school in city, as opposed to the science leadership school that gets all the local buzz and national attention. And how nice to see this school (yes, J's former high school) finally get some monetary recognition from the Philadelphia School Partnership:
Carver High School for Engineering and Science, which is expanding to serve 120 seventh and eighth graders in September, has been awarded $200,000 from the Philadelphia School Partnership, officials announced Thursday.

That's on top of a $147,000 grant that PSP, a deep-pocketed nonprofit, already awarded to Carver to fund planning for its middle school.

The newest award will support more planning as the school develops at 16th and West Norris Streets, principal Ted Domers said.

"There's a void of meaningful STEM [science, technology, engineering, and math] education in the city and across the country," Domers said. "We think this is an opportunity to be doing something that no one else is doing."
Carver's middle-school students will take engineering and computer science classes from the moment they walk in the door. They'll study algebra as eighth graders. Eventually, that will mean more advanced classes for them as high schoolers.

"The only reason our kids can't accelerate quicker is because we can't expose them quickly enough," Domers said.

Going forward, there's no reason a sophomore Carver student won't be able to take a class like Advanced Placement computer science, Domers said.
Mr. Domers, who, I'm pretty sure, is the best principal in the entire Philadelphia school district, is absolutely right that no other Philadelphia public school is doing this. With a largely low-SES population, with much less selective admissions than its leadership school counterpart, Carver High School for Engineering and Science has been achieving much higher scores on math, science, and computer science AP tests.

Perhaps next year Arne Duncan will invite Mr. Domers, rather than the science leadership leaders, to the "Principals at ED" program that, in the words of the earlier Inquirer article, "brings groups of highly innovative and successful principals from across the country to the Education Department to learn more about federal programs and to share experiences from their jobs as school leaders."

Saturday, August 1, 2015

Don't dwell on the concepts; use them to build things

About a year ago, Elizabeth Green published a piece in the New York Times magazine entitled Why Do Americans Stink at Math? Just a couple of months ago, the Notices of the American Math Society published some reactions to her piece. And I, in turn, have some reactions to what's in some of these reactions--in particle to Bill Jacob's discussion of how teachers should promote conceptual understanding:

Imagine a third-grade class being asked, "How many legs on there on three spiders?" Children who draw three spiders may first count the legs, but the context can elicit many strategies. Three groups of eight legs can e viewed as six groups of four when four legs are drawn on each side of a spider and viewed as a unit. A row of three spiders could be viewed as having two rows of twelve legs (top and bottom), or the legs could be counted as twelve pairs. A skilled teacher can pull from various groupings of the legs a spatial understanding of why the equivalence of 8 × 3 = 4 × 6 = 2 × 12 = 12 × 2 arises, beyond merely having the same value.
Jacobs also writes about the virtues of emphasizing how subtraction can be thought of as "difference on a number line" so that later students will understand why slope can be expressed as (y1 - y0) / (x1 - x0):
Learners who only understand subtraction as removal and not as difference in a measurement context will miss the meaning of (y1 - y0) and (x1 - x0) in the slope expression.
Both of these concepts--the different multiplicative groupings that produce highly divisible numbers like 24; and the fact that subtraction represents not just removal but measurement differences--strike me as relatively easy to grasp in isolation, even for third graders. In other words, they seem like the kinds of concepts that, like function and slope, are relatively easy to understand in and of themselves, especially when presented concretely, as Jacobs is advocating.

What's challenging about representing slope as (y1 - y0) / (x1 - x0), I'm pretty sure, isn't the concept of subtraction as measurement difference, but the symbolic abstraction involved in the algebraic expression.

And what's challenging about different multiplicative equivalences like 8 × 3 = 4 × 6 = 2 × 12 = 12 × 2 is remembering that you can use them to as tools to quickly simplify complex expressions.

These and other concepts are like some of the simple building blocks of computer programming--like div and mod and lists and arrays--or, for that matter, the simple building blocks of engineering--like levers and pulleys and valves and gears. All these are simple concepts in and of themselves, but very powerful tools for solving complex problems--especially when understood abstractly. The challenge is to figure out when and how to use them.

Thursday, July 30, 2015

Math problems of the week: Common Core-inspired 4th grade test questions

From the Smarter Balanced Assessments, a Common Core-inspired, standardized test consortium now consisting of about 12 states: the next three problems on the sample 4th grade practice test.





Extra Credit

Discuss the various ways in which the emphasis on conceptual understanding and interpreting the thought processes of other "mathematical thinkers" undermines more challenging applications of procedures.

Tuesday, July 28, 2015

A test is only as good as its graders

A recent article in the New York Times raises yet another concern about the new Common Core tests: who exactly is grading them? This concern stems from the fact that these tests "put less stock in rote learning and memorization" and therefore require fewer multiple choice questions

and far more writing on topics like this one posed to elementary school students: Read a passage from a novel written in the first person, and a poem written in the third person, and describe how the poem might change if it were written in the first person.
The two big Common Core testing companies are Pearson and PARCC. For Pearson, according to the Times:
About three-quarters of the scorers work from home. Pearson recruited them through its own website, personal referrals, job fairs, Internet job search engines, local newspaper classified ads and even Craigslist and Facebook. About half of those who go through training do not ultimately get the job.
As for PARCC:
Parcc said that more than three-quarters of the scorers have at least one year of teaching experience, but that it does not have data on how many are currently working as classroom teachers. Some are retired teachers with extensive classroom experience, but one scorer in San Antonio, for example, had one year of teaching experience, 45 years ago.  
Compare this to the AP requirements:
For exams like the Advanced Placement tests given by the College Board, scorers must be current college professors or high school teachers who have at least three years of experience teaching the subject they are scoring.
Of course, much smaller numbers of students take the AP tests, thus fewer graders are needed, thus higher standards are possible.

But if the Common Core test questions really live up to claims about the high-level thought processes they measure, then surely we need measurably high-level thinkers grading them:
The new tests are much more complicated and nuanced than previous exams and require more from the scorers, said James W. Pellegrino, a professor of psychology at the University of Illinois at Chicago who serves on advisory boards for Parcc and Smarter Balanced. “You’re asking people still, even with the best of rubrics and evidence and training, to make judgments about complex forms of cognition,” Mr. Pellegrino said. “The more we go towards the kinds of interesting thinking and problems and situations that tend to be more about open-ended answers, the harder it is to get objective agreement in scoring.”
I've written earlier about the virtues of well-constructed multiple choice tests. This article highlights one of them.

Sunday, July 26, 2015

Why not teach Harry Potter?

It's not great literature, but it's better written, and surely more interesting, than the tedious realistic fiction that passes for literature in today's elementary schools.

On this, my latest round of education students have given me new insight.

First of all, it's taken as given that one key way to develop reading skills is by making personal connections. And, naturally, it's harder for students to make personal connections if the book takes place a long time ago, or far away, or in an imaginary or futuristic world.

More profoundly, it's taken as given that students aren't interested in books that they can't relate to their personal lives. Many of my students seem to deeply, deeply believe this.

They are willing to grant that realistic fiction is comparatively difficult for kids on the autistic spectrum: we discuss how such children often lack the necessary background knowledge to make sense of these stories, and how fantasy and science fiction level the playing field. But for all other "learners," they're certain, realistic fiction is not only best for learning, but what students prefer.

So what about Harry Potter, I ask. How can that be so popular?

Silence. Confusion. My students appeared never to have considered this question before.

Then one student finally said something about how they can't teach Harry Potter anyway because of concerns about schools endorsing witchcraft.

I looked that up and, as far as I can tell, only a few school districts have banned Harry Potter for that reason. Everywhere else, I'm guessing, it's all about real-life relevance. And the depressing notion that children are only interested in reading about slight variations on their own lives.

Another strike against fantasy and sci fi comes from the world of literary criticism, which prefers obscure, nonlinear, writerly prose to imagination and character-driven plots.

How many people, as a result are missing out on gems like this one--just published by my friend and colleague Stella Whiteman?

Friday, July 24, 2015

Math problems of the week: more Common Core-inspired 4th grade test questions

From the Smarter Balanced Assessments, a Common Core-inspired, standardized test consortium now consisting of about 12 states: the next three problems on the sample 4th grade practice test.




Extra Credit:

Discuss the 21st century challenges posed by these problems in terms of verbosity (problem 7), clarity (problem 8: the meaning of "gives each student 1 card"), and understanding the user interface as opposed to understanding addition with regrouping (problem 9).

Wednesday, July 22, 2015

Social-emotional studies

From the U.S. history book American Vision, the text used in Philadelphia's public high schools: