All for the good of the children--and their brave new century

The largest textbook company in the world has teamed up with the 16th largest school system in the US--and one of the highest performing ones--to boost students' futures even more by teaching them 21st century skills.

You can read all this partnership in a paper by an Associate Research Scientist at Pearson by the name of Emily Lai, entitled “Creating Curriculum-Embedded, Performance-Based Assessments for Measuring 21st Century Skills in K-5 Students” and published by the American Educational Research Association.

The partnership between Pearson Publishing and the Montgomery County (Maryland) Public Schools, notes Lai, began in 2010 “with the goal of developing Pearson Forward, a digital curriculum featuring embedded assessment and professional development resources,” centered around 21st century skills.

21st century skills, explains Lai, include the following:

Critical thinking (encompassing analysis, synthsis and evaluation), creativity (encompassing fluency, flexibility, originality, and elaboration), collaboration, metacognition, motivation, and intellectual risk taking.

These, she assures us, have been operationalized based on a thorough literature review, which appears, from Lai’s bibliography, to be based predominantly on publications by education journals.

So important are these skills, Lai explains, that they will be assessed every 9 weeks during a 3 week period, each one in the course of 1-2 class periods, through Pearson’s Performance Based Assessment, (a variety of “embedded assessment,” or assessment that is “seamless with instruction”). Assessment tools include “holistic” rubrics, checklists, and student self-ratings. The 8 assessment tasks (assigned every 9 weeks) include “open-ended or ill-structured tasks,” tasks embedded in “authentic, real-world contexts,” and strategies for “making student thinking and reasoning visible.” The goal of all this assessment? “Tracking progress to predict success in post-secondary education.”

As Lai notes:

Each of the skills targeted in the curriculum entails both cognitive and noncognitive or affective components… Cognitive components of these constructs include knowledge and strategies, whereas noncognitive components include attitudes, traits, and dispositions.

Different assessment tasks target different 21st century skills. A task assessing intellectual risk-taking might look at whether, when a student is given a particular reading task, he or she chooses a story that is already familiar to them, or one that isn’t, since:

choice of unfamiliar story [is] arguably more of an intellectual risk than the choice of a familiar story.

Tasks assessing motivation similarly vary by subject (after all, different kids are more or less motivated in different subjects). Pearson’s task for assessing motivation in reading is:

a task that paired a teacher observation tool designed to capture students’ use of strategic behaviors with a student self-rating tool designed to capture more affective aspects of motivation, such as the student’s interest, self-efficacy, and goal orientation.

Tasks assessing metacognition might include open tasks that

allow students to decide what relevant information to use or how to use the information to solve the problem,” as opposed to “closed” tasks that “are characterized by more teacher control and structure.

Such tasks should also make student thinking and reasoning visible, which is

typically accomplished by embedding some sort of informal teacher-student interview into the assessment.

For example, during a ramp-construction project:

Students were encouraged to share their thinking with teammates as they worked together. We provided a set of interview questions for the teachers to pose to individual students as they worked:

How is it going?

What are you doing right now?

Why did you decide to build the ramp this way?

What is working well about your ramp?

What would you change about your ramp?  

As Lai notes:

Using this tool, teachers could observe the extent to which students were able to share their thinking and explain their ideas to others, both key indicators of metacognition at the Kindergarten level.

A task that measures “creativity” could be a time-limited response to a prompt:

We point out aspects of tasks that should not be varied, such as the time provided to students to respond to prompts (when assessing the creativity indicator of fluency, for example)

The most important 21st century skill, of course, is collaboration, and Lai’s proposals here are commensurately elaborate. A task assessing collaboration might involve:

Ill-structured tasks that cannot be solved by a single, competent group member… Ill-structured problems are those with no clearly defined parameters, no clear solution strategies, and either more than one correct solution, or multiple ways of arriving at an acceptable solution.

Collaboration-assessing tasks might also involve time constraints that make it impossible for one person to complete the task:

For example, to assess collaboration in math, teams of 2nd -grade students were required to design and create a mosaic using multi-colored tiles and then to devise and implement a method for representing the data on tile color by creating a graphical depiction of it (e.g., a bar graph showing the number of tiles of each color used to create the mosaic). 

In rating students based on these collaboration tasks, teachers should consider:

the quality of the completed group work project… the student’s ability to work respectfully and productively with others, and the student’s self-reported collaboration skills and contribution to the group.

As well as:

factors related to students’ use of helping behaviors (e.g., communicating respectfully, soliciting diverse opinions).

Citing a 1995 article written by N. M. Webb and published in Educational Evaluation and Policy Analysis, Lai writes:

As Webb explains, assessments that occur in group contexts can fulfill several different purposes. For example, teachers may wish to determine how much a student can learn from collaborating with others, whether a group of students can complete a product together, or whether individual students can communicate respectfully with teammates. Group processes that support one goal may not support another goal. For example, if the goal is to measure a student’s ability to learn from collaboration, then group processes such as co-construction of ideas, identification of conflict, giving and receiving elaborated help, and equality of participation should all be encouraged. In contrast, if the goal of group assessment is to determine whether a group can successfully complete a task on time, then group processes that facilitate student learning, such as trying to ensure equal participation among all group members, may be counterproductive. In this case, it will be more efficient to use processes that maximize group productivity, even if they minimize learning opportunities. Such processes might include letting the most competent student in the group perform most of the work. 

All of this, of course, is for the sake of the children--as the emphases on assessment (as opposed to instruction and remediation) and on predicting (as opposed to influencing) who will be successful in post-secondary education make abundantly clear.

In other words, in no way is it about multi-million dollar backroom deals between powerful companies and school boards that shut out all meaningful input from parents and traffic in educational buzz words and double speak. And in no way is it about branding half-baked assessment tools as “Pearson Forward Performance Based Assessment” tools and then associating them with a famously high performing school district whose current reputation lends them credibility (however much their relentless deployment--every nine weeks over a three week period,1-2 class periods for each 21st century skill--might help diminish this reputation in the future).

The child-centered classroom vs. the child-friendly classroom, II

Another thing I’ve noticed in my classroom observations is how, especially with primary school students, the more child-centered the class discussions, the more children tune out.Young children are often long-winded, inarticulate, unfocused, and slow to get to the point. Many of them routinely raise their hands before they’ve formulated a response. Soon their classmates are fidgeting and talking amongst themselves, losing the current thread and, along with it, the ability to say something relevant when it’s their turn.

Countrary to some people’s intuitions, then, the way to keep young kids engaged in a whole-class activity is to minimize their airtime, to interrupt and redirect them frequently, and, generally, to control the conversation tightly enough to keep things on track and moving swiftly.

It is, of course, the youngest children whose combination of short attention spans and unfocused, long-winded responses require the tightest teacher control. But I saw a similar need while in college and grad school seminars. After all, over-eager students who think they have something important to say that all of us should listen to at great length aren’t specific to primary school. I’ll never forget how frustrated I was with one particular professor who exerted so little control over the graduate student windbags that by the end of the 10-week quarter we were two weeks behind where we should have been. He was a brilliant scholar, highly articulate and full of revelations, and it was him I had signed up to listen to, not my fellow classmates.

Were people to bother asking students what they prefer, I wonder what sorts of students would say they prefer student-centered discussions to teacher-centered ones.

The child-centered classroom vs. the child-friendly classroom

I’ve been spending a little more time in schools lately, and have formed a few more impressions of child-centered classrooms--particularly of those in which students sit in pods facing one another rather than the teacher. I’ve written earlier about how seating students in pods makes it hard for them--particularly those facing away from the teacher--to focus on the teacher or any material that is being presented to them in the front of the classroom. I’ve also written about how pods can be arenas for the sort of subtle bullying that is particularly difficult for teachers to detect and discourage. And I’ve also written about how when students often opt to arrange themselves in rows rather than pods.

What I’ve noticed most recently is how much more disruptive behavior results when students are facing one another rather than forward. In particular, the temptation to talk to, mouth words at, exchange glances with, and otherwise interact with the peers you’re sitting next to and across from, even when the teacher requests your attention, is extremely high. This not only disrupts learning; it can also lead to a lot more angry yelling by the more frustrated teachers--some of whom would perhaps prefer to arrange the desks differently, if only their principals would allow it.

When armchair education experts conflate child-centered with child-friendly, they’re failing to apply a child-centered approach to their thinking. In particular, they’re failing to imagine what it’s like to sit facing the side or the back of your classroom opposite classmates who distract or bother you all day long, “guided” by a teacher who yells much more frequently that he or she might have in the teacher-centered alternative that no longer appeals to the experts.

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]:

Stacking, regrouping, and corrupting the children, II

Rumor has it that a principal at a local school that uses Investigations Math has recently been making surprise visits to classrooms and demanding who knows how to add and subtract numbers via "stacking." (Stacking, which Investigations mentions reluctantly in passing and resists teaching to mastery, is that old fashioned method of arranging numbers one on top of the other before adding, subtracting, or multiplying them, and then "borrowing" or "carrying"--aka "regrouping"--from one column to the next.)

Since this principal has, for years, been a stalwart defender of the use of Investigations at her school, this was a bit of a surprise not just for the students, but also to their parents--especially the many who dislike Investigations. Some--including one who has set up an after school math program to teach stacking and other things that Investigations fails to teach--are now hoping that the principal is having second thoughts about Investigations (in spite of what the school's math consultant has said against stacking).

The specific surprise visit I heard about involved a 3rd grade class. Here a particularly brave girl who'd attended the after school enrichment program and knew how to stack volunteered to go up to the board and do so. She proceeded to stack, subtract, and get the correct answer.

What's unclear is what the principal made of this--or, for that matter, what her intentions were in the first place. While it's possible she's been having second thoughts about the curriculum, it's also possible she was simply fishing for confirmation that her kids can stack. That would give her a ready response the next time someone claimed that Investigations doesn't teach this. 

In general, the proliferation of Investigations in the greater Philadelphia area has been a boon to those running after school math programs. (One told me she really should have named her program "Thank You, Investigations.") But the symbiosis between Investigations schools and after school math programs is more dynamic than it might first appear. The more parents resort to after school math remediation, the more students (in spite of Investigations) learn math, and the easier it is for Investigations proponents to claim that Investigations is working--further entrenching both Investigations and after school math remediation. 

A "left-brain" take on misbehavior and discomfort

In the largely right-brain world of pop psychology, harking back at least to Freud, most afflictions would seem to have a socio-emotional source. In particular, misbehavior results from anger, poor emotional self-regulation, social insecurity, or a craving for attention. Distress when routines change results from fear of novelty and uncertainty. A desire for black and white categories results from a discomfort with ambiguity. The remedies, too, are social and emotion-based. If you’re upset about something, talk it out and process it emotionally.

Too often people ignore the possibility of cognitive causes and remedies. Misbehavior, for example, is often the result of cognitive disengagement, aka boredom. That’s why it occurs disproportionately when kids are waiting: waiting in line, waiting for a transition to end and a new activity to begin, or waiting for a long-winded classmate to finish talking.

Irritation when routines change, as I’ve noted earlier, can likewise have a cognitive source. Whenever someone puts your salt and baking powder containers in the wrong place, or changes the user interface on Windows or Blogger, you’re forced to relearn the boring, tedious stuff you’d earlier been able to automate, your mind no longer free to wander to more interesting places.

When you suddenly discover that a system of categories is more complicated than you thought it was, your heart may sink not because you’re emotionally uncomfortable with ambiguity, but because messy categories are much more of a cognitive pain in the neck to learn.

When you read the latest reports about how a nonhuman species supposedly communicates via nouns, verbs, and productive syntax, your failure to embrace these conclusions may not be because you feel threatened by the notion that humanity isn't as unique and privileged as you thought it was, but because of what you know about language, cultural transmission, and common misunderstandings about grammar.

Even when the cause is emotional the remedy may be cognitive. If I find myself brooding or unproductively anxious, I’ll seek out an intellectually engaging book or article to distract me, finding greater solace in Malcolm Gladwell, Steven Pinker, Jared Diamond, Matt Ridley, or Nancy Minshew than I would hashing things out with a therapist.

Math problems of the week: traditional vs. IMP trigonometry

The first 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 first two pages of the first trigonometry chapter in A Second Course in Algebra (published in 1937), pp.393-394 [click to enlarge]:

II. The first two pages of the first trigonometry chapter in Interactive High School Mathematics Math Program Year 4, pp. 4-5 [click to enlarge]: