Information Age Education
   Issue Number 59
February, 2011   

This free Information Age Education Newsletter is written by David Moursund and Bob Sylwester, and produced by Ken Loge. The newsletter is one component of the Information Age Education project. See http://iae-pedia.org/ and the end of this newsletter.

The Information Age Education web site now includes a blog. Access the blog and comment on blog entries at http://i-a-e.org/iae-blog.html.

You may find the following blog entry to be particularly interesting: Creating academic standards that that may be inappropriate and unattainable.

"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 skills.

Veridical Problems. The 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?

Adaptive Problems. Adaptive 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 students.


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 constitutionally correct.

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.


Suggestions

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 issues.

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.

Examples. 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 that should 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.


References

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.



About Information Age Education, Inc.

Information Age Education is a non-profit organization dedicated to improving education for learners of all ages throughout the world. Current IAE activities include a Wiki with address http://IAE-pedia.org, a Website containing free books and articles at http://I-A-E.org, a Blog at http://i-a-e.org/iae-blog.html, and the free newsletter you are now reading.

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