kitchen table math, the sequel: 21st century

Friday, May 25, 2007

21st century

Assessment in the Age of Innovation
By Charles Fadel, Margaret Honey, & Shelley Pasnik
EDUCATION WEEK
Published in Print: May 23, 2007

Within the past 50 years, we’ve seen our country move from an industrial economy to an information-based economy. Now, early in the 21st century, it appears we are shifting to an innovation-based economy, [ed.: evidence, please] one that requires what the psychologist Robert J. Sternberg calls “successful intelligence,”*(pdf file) a three-point foundation of analytical, practical, and creative skills. In other words, the measure of success in today’s economy is not just what you know, but how you use that to imagine new ways to get work done, solve problems, or create new knowledge. This innovation-based environment calls for substantially new forms of assessment, and therein lies a major hurdle for schools, especially American schools, trying to prepare students for this new century.

American students today are largely evaluated based on their factual knowledge. A recent study by Robert C. Pianta and his colleagues at the University of Virginia’s Center for Advanced Study of Teaching and Learning found that the average 5th grader received five times as much instruction in basic skills as instruction focused on problem-solving or reasoning. ....


So there's hope.


wrong about the rim


* Naturally Robert Sternberg's "What Is an Expert Student?" appears to have been the sole article handed out to our curriculum committee a couple of years back: This article suggests that conventional methods of teaching may, at best, create pseudo-experts—students whose expertise, to the extent they have it, does not mirror the expertise needed for realworld thinking inside or outside of the academic disciplines schools normally teach. It is suggested that teaching for “successful intelligence” may help in the creation of future experts. It is further suggested that we may wish to start teaching students to think wisely, not just well..... [ed: yes, good idea, Bob. Staff the schools with 25 year old novice teachers and tell them to teach wisely, not just well. see where that gets you.]

8 comments:

Ben Calvin said...

...the measure of success in today’s economy is not just what you know, but how you use that to imagine new ways to get work done, solve problems, or create new knowledge.

Yes. Well. Fulton, Edison, Samuel Morse etc. never "imagine(d) new ways to get work done, solve problems, or create new knowledge when we were back in the industrial age, did they.

Barry Garelick said...

The mythology of creativity, critical thinking and higher order thinking skills as originating from the ill-conceived problems that mask as math education in this country continues to pervade. There was an article in the Washington Post about a contingent of educators from Singapore who visited a school in Loudon County in the DC suburbs, ostensibly on a tour to see how the US education system enhances such creativity. Buried deep in the article was this gem that refutes this belief:

"In 2005, a report commissioned by the U.S. Education Department compared math teaching in the United States and Singapore. It found that U.S. texts place less emphasis on understanding math concepts in depth and that U.S. teachers are less likely to clearly understand the subject. William Schmidt, a Michigan State University education professor, said the United States could learn a lot from Singapore. He said the success of scientists here owes more to a business and cultural environment that rewards risk-taking than to the U.S. education system." (emphasis added).

One way to catch people in this canard is if they tout the creativity of US business as evidence that we do something right in our education system, point out that such creativity has spanned 200 years, including the years when math was taught in a "rote" fashion.

Pianta's study in Science Magazine adds so-called "evidence" that we bore our students to death. So how come we're still creative in business, Dr. Pianta? Actually, I asked Dr. Pianta some other questions about his "study". I asked how he differentiated between the teaching of "basic math skills" and "problem solving/reasoning". I asked how he evaluated time spent on each, particularly if a classroom used Saxon Math whose problem sets are typically a mixture of straight math computation and word problems.

I wrote a letter to Science which they declined to publish but he did write a response which they gave to me. In my letter I asked:

"Pianta’s article does not explain how he differentiates between “basic math skills” and “problem solving and reasoning skills. Such a definition would lend some additional understanding to the study. For example, by "basic computation" does he mean problems such as 4+ 5 = ?. Would a variant of this, such as 4 + n = 9, qualify as “basic computation” or “problem solving”? What would he consider the following: "A boy gives away 5 marbles and has 4 left. How many did he start with? Did he observe any classes that used the Saxon Math texts? Those texts require students to work about 30 or so problems, some of which are straight computation and others are like the word problems. How would he describe working with such texts in terms of tallying how much time is spent on computation versus problem solving?"

He replies (in part):

"First, we did not code for the use of any specific instructional program, curriculum, or assessment tools. Because the study was so wide-ranging across many classrooms and districts, and because so many classrooms use a mixture of instructional programs and supplemental materials in a given content area, such as math, a decision was made that it was beyond the scope of the study to try and document such variation. So, we do not know whether Saxon Math was in use in nay classrooms.
Second, we did distinguish between a 'basic skills' focus and a focus on "analysis/inference and problem solving" in our codes of math activities. I summarize below the text describing these codes from the actual observation manual.
Teaching Basic Skills/Facts - The teacher's focus is on an isolated skill, the learning or reciting/remembering factual material, or when the goal is performance of a correct answer, including discussions where the questions are structured so that they lead to right or wrong answers. (HEAVEN FORBID; ed.) Another example would occur when the teacher may teach, step by step, a set of rules that can be applied in order to solve a problem. (SUCH AS IS DONE IN SINGAPORE? ed.) The teacher may lecture on a topic that focuses on facts, without engaging students in conversation or analysis. The instruction may assist students with memorizing facts or rules or practicing a skill they have learned. In math, and possibly other subjects, the teacher demonstrates only one strategy for solving a problem to obtain the one right answer. The focus is on correctness and performing individual skills.
Teaching Analysis/Inference/Application/Interpretation * The teaching involves students in some kind of critical thinking (e.g., analysis, inference, interpretation, synthesis, comparison, making predictions, drawing conclusions, critiquing) or application to the child's or others' lives that requires them to demonstrate understanding beyond memorized fact, rules, and procedures. Instruction may involve multiple representations (e.g., visual, verbal) or may embed skills in or make explicit connections to real-world applications. The teacher may encourage students to express and defend personal opinions or positions and the lesson or activity may foster students' original ideas or approaches to problems. The teacher may use open-ended questions and follow-up questions to encourage the children to continue exploring an idea or object.
More specifically, the teacher sometimes may ask a student to explain how she got the answer for a math problem, for example. The focus is on thinking and understanding.
The examples in Garelick's letter, assuming they are reflective of the rest of instruction coded in that 30-second interval, would be coded as "basic skills. (emphasis added)

Independent George said...

What do they mean by 'shifting' to an innovation-based economy? That was the entire thesis to 'The Wealth of Nations'.

Instructivist said...

This Dr. False Dichotomy should take a look at Wu's paper before he starts coding again.

BASIC SKILLS
VERSUS
CONCEPTUAL
UNDERSTANDING
A Bogus Dichotomy
in Mathematics Education

http://www.aft.org/pubs-reports/american_educator/fall99/wu.pdf

"The teacher may lecture on a topic that focuses on facts, without engaging students in conversation or analysis. The instruction may assist students with memorizing facts or rules or practicing a skill they have learned. In math, and possibly other subjects, the teacher demonstrates only one strategy for solving a problem to obtain the one right answer. The focus is on correctness and performing individual skills."

I cannot imagine a teacher who doesn't try to engage students in conversation or analysis or show multiple representations and approaches.

Even at a basic level like reducing fractions a teacher might present the GCF method and cancellation of prime numbers.

I love his one: "The teacher may encourage students to express and defend personal opinions or positions and the lesson or activity may foster students' original ideas or approaches to problems."

The personal opinion that I hear most often and that needs no encouragement is: "We've done this before." It's an ingrained attitude that is satisfied with scant familiarity and militates against mastery.

Catherine Johnson said...

What do they mean by 'shifting' to an innovation-based economy? That was the entire thesis to 'The Wealth of Nations'.

The level of ludicrosity (neologism alert!) is beyond words.

Ed was telling me that "century thinking" is a big part of human consciousness; people assume: New Century, New Everthing

Centuries are utterly arbitrary markers of time. There is no reason to think that the Information Age is now over, because the calendar moved from 1999 to 2000.

This is hooey.

More hooey.

From Cisco & Microsoft.

Catherine Johnson said...

It's worth reading the whole thing to see how bad it is.

My own district is now going to "have a community conversation" about the Strategic Plan.

The words "21st century skills" are prominently featured in all of the conversation topics we are apparently going to address.

Jeff Hetzel said...

Alexander Bell -- I want to invent a device so people can talk across great distances!

Sorry Alexander you will have to wait till the 21st century and the age of innovation we are currently in the industrial age.

Wright Brothers -- We want to invent the first powered flying machine!

Sorry Orville and Wilbur you will have to wait till the 21st century and the age of innovation we are currently in the industrial age.

Thomas Edison -- I want to invent (list to numerous to write out)!

Sorry Thomas you will have to wait till the 21st century and the age of innovation we are currently in the industrial age.

This is just stupid, we have been innovating for thousands of years, if we hadn't been we would still be in the caves.

Tracy said...

The teaching involves students in some kind of critical thinking (e.g., analysis, inference, interpretation, synthesis, comparison, making predictions, drawing conclusions, critiquing) or application to the child's or others' lives that requires them to demonstrate understanding beyond memorized fact, rules, and procedures. Instruction may involve multiple representations (e.g., visual, verbal) or may embed skills in or make explicit connections to real-world applications. The teacher may encourage students to express and defend personal opinions or positions and the lesson or activity may foster students' original ideas or approaches to problems. The teacher may use open-ended questions and follow-up questions to encourage the children to continue exploring an idea or object.
More specifically, the teacher sometimes may ask a student to explain how she got the answer for a math problem, for example. The focus is on thinking and understanding.


This is interesting, as I was required to do this regularly during school (explain how I got the answer to a problem), and when it came to calculus I just didn't understand why differentiating and setting to zero produced the right answer, regardless of whether you maximised or minimised it. The teacher had explained it in class, but it just seemed like a magic trick to me. But I wanted good grades on my schoolwork so I just memorised the explanation and restated it when appropriate for full marks.

Two years later it eventually dawned on me why differentiate-and-set-to-zero worked.

I was quite capable of memorising multiple representations and approaches to a problem too.

I doubt if this guy's tests can tell the difference between memorisation and understanding for a student with a good memory.

the lesson or activity may foster students' original ideas or approaches to problems

Any lesson or activity may foster students' original ideas or approaches to problems. Once a teacher has put information in the student's head, the teacehr has no more control over it.