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Moursund and Bob Sylwester, and produced by Ken Loge. The newsletter is
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"You don't drown by falling into the water; you drown by staying there." (Edwin Louis Cole; 1922–2002.)
Some problems are so complex that you have to be highly intelligent and
well-informed just to be undecided about them." (Laurence J. Peter;
author of The Peter Principle; 1919–1990.)
Assessing Student Achievement In Difficult To Assess Curricular Areas: Problem Solving
The two previous articles focused on difficulties associated with the
credible evaluation of social skills and the arts in K-12 school
settings. This article will focus on the assessment of problem solving
respected cognitive neuroscientist Elkhonon Goldberg suggests that our
brains confront two kinds of problem solving situations, veridical and
adaptive (2005). Veridical problems are factual, in that they are
clearly defined and have only a single correct response, such as 6 x 5
= 30 and Salem is the capital of Oregon. They are the essence of the
true/false dichotomy, in that the respondent’s preferences are
irrelevant. I may prefer that Eugene should be the capital of Oregon,
but it’s Salem. Some problems obviously have more than one correct
response, such as the different US and British spellings: program and
programme. It becomes a veridical problem if the question is: Is
program or programme the correct British spelling of the word?
problems allow for more than one acceptable response, and so adapt to
personal preferences and choices. They are the essence of such
dichotomies as right/wrong, fair/unfair, and appropriate/inappropriate.
We can question the wisdom and/or appropriateness of the choices that
others make about such things as clothing, investments, gifts, and
vacations, but individual respondents still get to make the subjective
decisions. So if the question is 'which spelling do you prefer, program
or programme?', either alternative is correct.
Consider the options on a menu. Four people at a restaurant table may
choose four completely different meals from the same menu. Diners may
encourage and/or discourage their friends from ordering specific items,
but they can’t make their fellow diners’ final decisions, or suggest
that any such decision is objectively bad. Menus include factual
information, such as price and ingredients, but a diner’s decision is
typically also based on other personal preference factors.
Evaluating problems that combine veridical and adaptive elements can
sometimes get a bit complicated. For example, consider the Pythagorean
theorem about the sides of a right triangle. This theorem has many
different correct proofs, and a competent math scholar can
differentiate between the correct and incorrect proofs. Consider this
question, however: “Among the following purported proofs of the
Pythagorean theorem, identify the correct ones. Among the correct
proofs, which one do you consider to be the most elegant
, and why?” The student can now be objectively graded on the veridical
correctness (identify the correct proofs), and subjectively evaluated on the adaptive
choice of elegance (which do you most prefer).
Similarly, suppose that a student is asked to write a critical essay on
an issue. Some elements of the essay such as spelling, grammar, and
“facts” fall into the veridical category, but much of what the teacher
is looking for falls into the adaptive area. If you have ever tried to
provide formative assessment and/or summative assessment on student
writing, you realize the difficulty of the challenge.
Problem Solving Practices and Issues
Current K-12 school assessment programs tend to focus on
veridical problem solving. One can make a case for this at the
elementary level, during which students are expected to master precise
language/arithmetic skills and the factual base of our culture.
Even when dealing with facts
however, it’s often enough to just get close to a precise fact. For
example, we could spell accommodate a half dozen different ways and
most people would still be able to read it without difficulty. Further,
much formerly memorized factual information is now readily available
via ubiquitous portable computerized sources, such as calculators,
search engines, and spell-checkers. Perhaps what 21st century students
really need is to develop a good personally-effective sense of when or
whether it’s better to memorize the factual information they’ll need to
solve potential problems, versus gaining expertise retrieving
information when needed.
Computer technology is making significant progress in being able to
solve veridical problems and answer veridical questions. See, for
example, Game of Jeopardy: Computer Versus Humans
or the Wolfram Alpha computational knowledge engine at http://www.wolframalpha.com/
. Such progress in computer technology is forcing educators to deal with the observation that increasingly, Two Brains (Human Plus Computer) Are Better Than One
In our work with students, teachers, parents, and politicians, we have
often run into discussions about teaching paper and pencil long
division versus the use of a handheld calculator. The basic question
often raised is, “But what if people don’t have ready access to a
calculator?” and the obvious response is “Well, what if they don’t have
paper and a pencil?”
In an era in which it’s as easy to borrow a calculator as paper and
pencil, we believe it makes sense to go with the most appropriate
available technology. But perhaps for many it’s still not yet an
adaptive issue. Many people have strongly held beliefs about what they
believe is “the correct” instructional policy.
The same type of issue now exists for use of online computers. Adults
who have free choice routinely make such use of computers as they work
to solve problems and accomplish tasks. However, such computer use is
not allowed in most school-based, state, and national assessment of
Now, Back to the Assessment Question
Adults make most of the important adaptive decisions that young
children confront, but adolescents are moving towards an adult life in
which adaptive decisions will dominate. Their education should thus
focus more on helping them learn to make a well-reasoned choice among
acceptable alternatives. People typically don’t lose their job because
they don’t know the multiplication tables or that Salem is the capital
of Oregon, but rather because they can’t get along with their
co-workers, and/or they make inappropriate decisions.
Intelligent adaptive decision-making obviously involves having a good
command of the factual base of the current problem, but it also
requires a grasp of any moral/ethical issues implicit in the decision,
and empathy for the effects of their decision on others. It also
requires the realization that very intelligent people can disagree
about the resolution of personal and cultural issues. For example,
after carefully examining the factual base and relevant laws and
precedents implicit in a US Supreme Court case, the justices can (and
often do) come to a 5-4 decision on which of the two positions is
The best way for students to master adaptive problem solving skills is
to get them involved in adaptive decision-making throughout their K-12
schooling. The first of this series of three articles suggested that
students should participate in resolving many of the minor classroom
management issues that constantly occur. They should similarly help
plan and run such things as classroom parties and class projects.
Teachers should challenge teams of students with problems that have no
single correct answer, and then engage the class in a discussion of the
strengths and weaknesses of the various proposed solutions.
Such secondary school extra-curricular programs as interest clubs, the
school newspaper and Website, and athletics similarly provide many
opportunities for students to make adaptive decisions, and for the
faculty advisers and coaches to informally assess developing
competence. These experiences often also provide an especially good
training in learning how to assess cost/benefit ratios in developing
and administering budgets.
The two previous IAE Newsletter articles suggested that
assessment in these difficult-to-evaluate areas involves three
elements. The first two can be objectively assessed: (1) how well
students understand the elements of successful problem solving and (2)
what they believe to be the culturally appropriate choices when
confronted with moral and ethical dilemmas in adaptive problem solving.
The third element, which doesn’t lend itself to objective assessment,
involves the problem solving skills that students need when confronted
with real and/or simulated combined veridical and adaptive problems and
We believe that it’s possible for those who create state assessment
programs to develop fair, valid, and reliable assessment programs that
test K-12 students’ understanding of the central elements involved in
solving combined veridical and adaptive problems. In addition,
individual teachers can develop such assessment methods for use with
their own students.
. Such assessments could describe a problem and then ask students to:
- Identify the kind of factual information they would need to solve a
decision-making problem, and also to identify any moral/ethical issues
underlie the decision.
- Demonstrate skill in locating and effectively using both
computerized and non-computerized aids to dealing with the veridical and adaptive components of complex problems.
- Describe their resolution to an adaptive problem and explain why
they made the choice they made (the assessment isn’t about the
correctness of the students’ decisions, but rather on their ability to
explain how they arrived at their decisions).
Teachers can subjectively assess developing problem solving abilities
by carefully observing how individual students participate and
negotiate solutions to the kinds of real and simulated problems they
confront in both curricular and extra-curricular activities.
Finally, it’s certainly not going to be easy for educators to develop a
viable K-12 assessment program that incorporates social skills, the
arts, and problem solving, but to not make the effort is to incorrectly
suggest that these areas are irrelevant to a 21st century education.
Goldberg, E. (2005) The Paradox of Wisdom: How Your Mind Can Grow Stronger as Your Brain Grows Older. New York: Gotham Books.
Moursund, David (n.d.). Two Brains (Human Plus Computer) Are Better Than One. IAE-pedia. Retrieved 2/14/2011 from http://iae-pedia.org/Two_Brains_Are_Better_Than_One.
Moursund, David (2/8/2011). Game of Jeopardy: Computer Versus Humans. IAE Blog. Retrieved 2/14/2011 from http://i-a-e.org/iae-blog/game-of-jeopardy-computer-versus-humans.htm.
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