Thursday, August 27, 2015

Math problems of the week: 5th grade Common Core-inspired test questions vs. Singapore Math

I. A sample end-of-5th grade test question from Pennsylvania's revised PSSA tests.

Note: The state doesn't publicize what percentage correct is necessary for a score of "proficient" or "advanced," but rumor has it that it's significantly below the 80% benchmark set by the Singapore Math placement tests.




II. From the Singapore Math 5A placement test, for which 80% correct says you're ready for the second half of the fifth grade curriculum:


III. Extra Credit

Compare the problems in terms of (1) how well defined the questions are and (2) how obvious the first steps are.

First hint: How well defined is "1/3 of a bowl of rice"?

Second hint: In which problem is the first arithmetic operation immediately obvious, and in which one do you need first to devise an overall strategy?

Tuesday, August 25, 2015

21st century humanities majors

In my post below, I discussed what I think are the most job-relevant communication and collaborative skills. Boiled down a bit differently, they are:

(1) attending to and understanding directions
(2) being competent enough to fulfill them
(3) getting your own points across clearly.

It is these skills--rather than the more social aspects of communication and working together--that are in increasingly short supply.

And all three of them relate, in part, to something over which there's been a lot of handwringing recently: the value of a liberal arts education. What with the decline in the numbers of humanities majors, and, in particular, of English and literature majors, along with all the forces out there "disrupting" traditional education, more and more people are wondering what, if anything is being lost.

Here's my answer. Fewer humanities majors, and fewer traditional (reading and analytical writing-based) humanities classes, means fewer students reading significant quantities of challenging prose, writing significant numbers of analytical essays, and getting significant amounts of feedback on their reading and writing skills. What's being lost, in other words, are

(1) careful reading skills, including the ability to sustain attention while reading
(2) writing skills, including the ability to make clear points and coherent arguments

There relate directly to the workplace skills deficiencies I note above.

In addition, as far as literature majors in particular are concerned, there is some reason to think that reading, discussing, and analyzing literature fine-tunes empathy and ethical reasoning. Reading--especially in nonfiction-intensive courses like history--also substantially enhances general knowledge. Empathy, ethical reasoning, and general knowledge, in turn, probably enhance performance in a whole variety of vocations, including 21st century jobs.

Ironically, some people think that college needs to be rethought in light of how much today's jobs are changing. We never know which specific skills are going to be important in the future, so we should focus on more general ones like flexibility, creativity, grit, and team work. But I'm guessing that most jobs still require the ability to follow complex directions and get your points across clearly: indeed, these are some of the most general, generalizable skills there are.

If these skills are so important, why are so many students defecting from the departments that, traditionally, have fostered them the most? Perhaps students are ill-informed about what the humanities can offer them, assuming that the more "pre-professional" majors--business, communications, interactive media?--provide more relevant vocational training. Or perhaps the humanities departments themselves are at fault: perhaps, as I've suggested earlier, they are no longer focused on informational content, complex characters, ethical subtleties, or, most importantly, on developing students' reading, writing, and analytical skills.

Sunday, August 23, 2015

The importance of communicating well and working well with others

In an earlier post on HR departments and hiring, I considered whether it's ever appropriate to discriminate against people on the basis of personality:

Should corporations never discriminate against people on the basis of personality? Ironically, the personality type that thrives best in interviews--particularly the informal ones that are so popular today--is the type that is potentially the most toxic of all: the narcissistic, manipulating backstabber who charms his superiors, undermines his equals, and takes credit for the work of his underlings, advancing through the corporation and undermining morale and productivity. 
Given just how toxic the psychopathic employee can be for the workplace, one can appreciate how important it is to consider personality and social behavior. The problem, though, is that people often conflate two different types of socially problematic personalities:

(1) jerks
(2) people who mean well--or at least don't mean ill--but are socially awkward.

Personality does matter, but the aspect that matters most is decency, not charm.

In reading the comments on my earlier post, I've realized that two other general factors that seem important in making hiring decisions can be bifurcated in similar ways.

Anonymous/bj writes:
the ability to communicate and work with others is being shown to be an important part of successful performance of many jobs, including the ones that include significant technical skills.
As with personality, so, too, with the ability to communicate and the ability to work with others. Each has a more social aspect, and a more job-relevant aspect. For the former:

(1) conversational skills; being fun to talk to
(2) content-based communication skills: understanding directions, getting your points across clearly.

For the latter:

(1) getting along with people socially; behaving such that they enjoy your company
(2) understanding what your role is in a collaboration and being competent and conscientious enough to fulfill it.

The more job-relevant aspects of communication and working with others aren't trivial. A programmer on a software development team I was part of--someone who appeared to have gotten hired in part because he was a drinking buddy of one of the team leaders--set us back about a year (and many paychecks worth of funds) because it turned out he wasn't able to follow our directions or communicate what was confusing to him. I'm sure he was fun to hang out with after hours at bars. A lawyer friend of my regularly laments how her firm hires "team players" who don't pull their weight because, for all their Ivy League training, they're lacking in reading and writing skills.

Maybe I'm insufficiently "21st Century" in my thinking, but I'd take a decent, competent coworker who understands directions and can get his or her point across clearly, however socially awkwardly, over someone who's engaging to talk to and fun to be around but, like so many people these days, is a sloppy, inaccurate reader; an inarticulate writer; an inattentive listener; a poor follower of complex directions; and a lazy, responsibility-deflecting coworker--even if s/he isn't also a manipulative, backstabbing psychopath.

Friday, August 21, 2015

Math problem of the week: a 5th grade Common Core-inspired test question

A sample 5th grade test question from Pennsylvania's revised PSSA tests, which resulted in a huge drop in test scores test-wide.




[The correct answer is starred, and the incorrect answers have italicized annotations]

Extra Credit:

Compare this question's mathematical demands with its linguistic demands. Identity the dangling modifier, the ambiguity of "at the end," and the ambiguity of what "from the end of" and "combined" apply to.

Wednesday, August 19, 2015

Evaluators, cognitive flexibility, and insight

I noted in my last post that one group of professionals that really stands out as insulated from feedback are psychiatric evaluators--especially those who contract primarily, not with private customers, but with public agencies. Having this realization, I noted, helped take the sting out of J's most recent psych eval.

The most comprehensive one he's received so far, it was contracted by a state governmental agency that provides vocational guidance and placement services for adults with special needs. The evaluation finally landed in my inbox a few days ago.

Here are some of its highlights--with annotations:

In meeting with J, is was noted that he does have a bone conduction hearing device on the right side.
[He has a cochlear implant, which conducts sound to his auditory nerve and without which he would be completely deaf; bone conduction devices are for people with conductive hearing loss rather than complete deafness.]
..his overall affective level of response was somewhat odd, with his manner of interaction noted to be somewhat peculiar.
[Yup.] 
..he was somewhat gangly in his presentation.
[Right. He's skinny and 6'5''.] 
...he was found to have signifiant difficulties at times in readily understanding questions and/or statements that had been presented.
[Perhaps sometimes as a result of his deafness--especially if the evaluator was sitting closer to his left ear.] 
J overall was a rather limited to poor historian, unable to provide much in the way of significant background information.
[Or perhaps unwilling to. J generally prefers deceiving to informing.] 
J demonstrated a mild to moderate sense of impairment within the RBANS List Learning measure. Within they particular measure, a list of ten words had been read to J over 4 learning trials. After each trial was completed, J was asked to repeat back as many of the words he was able to recall.
[Perhaps confounded by hearing loss.] 
…a comparative level of weakness in his ability to effectively reason, plan, organize and engage in a degree of cognitive flexibility when working thought language based problem situations that are presented.
[The below-average receptive language skills common in autism are widely recognized among autism experts to confound any language-based assessment of non-language-specific skills--e.g.,  reasoning, planning, organizing, and cognitive flexibility.] 
There is no sense of insight or introspection that J displays, thus restricting his ability to effectively understand situations that he may encounter within his social/emotional environment and also with regard to his ability to then respond in a meaningful manner.
[It depends on his motivation. When it comes to ceiling fans, earning money, or avoiding detentions, J is a master manipulator--and a master impersonator of non-autistic individuals.] 
In looking at J, it is readily noted that he is presenting with personality factors that will likely impede his ability to effectively apply those strengths that he does possess.
This concluding remark is the real downer--contrasting starkly with J's last school-based evaluation, which concluded with remarks about how essential it is that J's talents not go untapped.

But I remind myself of the confounding factors of deafness, receptive language deficits, and motivation--and of the fact that the school-based evaluation, while far less comprehensive, was conducted by an in-house professional who has built-in opportunities to get feedback outside the office setting and see how his predictions pan out over time.

Monday, August 17, 2015

Feedback loops: it's not just students who need them

Many jobs have built-in feed-back loops. You produce lousy work, and you get negative critiques and poor sales. You interact poorly with customers, and you get indignant reactions and diminishing patronage. Online reviews of all sorts of professionals are proliferating around the internet--from doctors to realtors to carpet cleaners to college professors.

So jobs that lack feed-back loops really stand out now. One of them, I recently realized, is psychiatric evaluation. Conducting and writing up evaluations, for some psychotherapists, is their main occupation. In the absence of follow-up treatments or longitudinal tracking, these people receive no information about the accuracy of their prognostications. Most insulated from feedback are those evaluators who contract primarily, not with private customers (who might vote with their feet), but with public agencies (which tend toward inertia and cronyism). Having this realization helped take the sting out of J's most recent psych eval. But more on that in my next post.

Certain key pockets of the education sector also lack feedback loops. Take admissions departments. However carefully and comprehensively they review applicants, how often do they receive feedback, years later, about how particular acceptances or rejections panned out? How often do they hear about accepted applicants who failed out, were kicked out, or who tormented their classmates and professors? Whenever a problematic student comes along who lacks basic reading skills, basic writing skills and or a basic work ethic, or makes extravagant excuses, unreasonable demands, and nasty accusations (the kinds of things that often accompany being severely lazy or under-skilled), or who cheats their way through assignments (ditto), I wish there were official channels for reporting back to the admissions committee. In the worst cases, when I find myself and others spending dozens of hours on a single problematic student, I wish the admissions department were required to dip into its budget and reimburse us for at least some of our extra time.

On the flip side, how often do admissions departments hear about rejected applicants who thrived elsewhere and made great contributions later on in life?

Then there are K12 classroom teachers. While the occasional K12 teacher gets reviewed on sites like ratemyteachers.com, most aren't, and even if they were, there's little opportunity to for students/parents to vote with their feet. And while testing and other assessments take up huge chunks of class time, how often do they function as meaningful, teacher-directed feedback? Standardized tests scores provide only a couple of quantitative data points (e.g., general scores for reading, writing, and math), even these measurements are only as reliable as the (often problematic) tests themselves are. As for the potentially more granular and meaningful class-specific assessments, many schools and teachers seem to treat these exclusively as feedback for students and parents, and not as feedback that might motivate adjustments to teaching practices. On one occasion at our local school, for example, a near 90% failure rate on an in-class science test resulted, not in the science teacher considering that maybe she should reteach the lesson in a different way, but in her sending out an blast email to parents complaining about how badly their children did and how they clearly hadn't studied hard enough.

This last example is giving me some feedback: I'm realizing now that I need to reformulate what I'm suggesting here. It's not enough to have a feedback loop; there also needs to be some built-in motivation to actually pay attention to that feedback and make appropriate adjustments.

Saturday, August 15, 2015

Conceptual structures vs. learning conceptual structures = not homomorphic


It's become an obsession. Everywhere I look now, I see cases where people dwell on basic concepts that are relatively easy to understand in isolation and challenging only within complex situations.  Time and again I wish that instructors would move on more quickly and save time for the more complicated applications that lie ahead.

Typically, this concept-dwelling happens at the beginning of a course or unit and takes up the first couple of classes. For example, in an MIT OpenCourseware course on basic chemistry that I'm having J sit through in preparation for Chem 101 in college, the instructor begins with an overly long discussion of what's known about the basic structure of atoms. While she asks the students whether they've ever had plum pudding, I think about the challenging problems that lie ahead and the time that could have been reserved for working through some of these in class.

The problem, I think, is a combination of the difficulty that many instructors have remembering what it's like to be the student, and the default assumption that the conceptual structure of a given subject maps neatly onto to the process of learning that subject. What's foundational to a subject, in other words, may not be the same as what's foundational to learning that subject. Now I don't remember much at all about chemistry. But I'd venture to guess that, while learning the structure of atoms is part of what's foundational to learning chemistry, but there are a number of other key concepts that are also foundational to learning chemistry, and more time-consuming to master (including, for example, some basic algebra).

Another fallacy that afflicts introductory classes is a sort of ontogeny recapitulates phylogeny assumption. This is the idea that the history of the field's development over time maps onto the student's personal trajectory of understanding it. But while the history of the various notions of elementary particles is interesting in and of itself (a great topic for a history of science class), it probably doesn't replicate the student's own developing understanding of elementary particles, and going over that history may or may not actually facilitate that understanding.

Of course, all of these are empirical questions that could be addressed by applying the foundational concepts of yet another field--in new and complex ways.