Quantity and Quality of Mind

Table 1

I had to relate the graphic in the last post to the four ways multiple-choice tests can be scored when students pick the questions to report what they know and can do. This is not an efficient way to do standardized testing.

It is a way to promote student development from passive pupil to self-correcting scholar; the basis for high standardized test scores.

Table 1 points out respective pass/fail scores (red box) for the four quantity to quality ratios. The 60% cut point was used in my quantity and quality scoring.

Students voted to value quantity and quality equally. This removed a variable between traditional scoring of marks influenced by their luck on test day; and quantity and quality scoring of marks influenced by their judgment of what they already did know and could do, and of what they had yet to learn: know and understand.

It was also important not to present something that new students would see as a barrier to switching from luck to reason. As is, it took until the third bi-weekly test in each semester for over 90% of students in a class to make the change in scoring and several more weeks to change study habits (bicameral to introspective mind, see previous post).

Chart 1

Chart 1 graphs the above table. It shows the quality vectors for a score of 60%. A traditional test would require a minimum of 30 right marks.

Quantity and quality scoring requires a minimum of 10 right marks added to a perfect 50% value for self-judgment. This rarely happened out of over 3,000 students.

The standard of 90%, set for high risk exams (nuclear power operators, police, and doctors), starts with a 75% value for judgment. You better know what you are doing before you act, or ask questions, or do not answer.

With the active start score (75%) set higher than the cut point (60%) there would be no incentive to mark anything on such a test. A game rule is needed: A minimum of 10 questions must be selected [(75%-60%)/(75%/50 counts) = 10 counts] to include the 60% cut point.

The chart points out that any cut point can be reached from any starting score. Then create a test bank of items with difficulties in the 20s, 40s, 60s and 80s.

Deliver the test over the Internet starting with a question from the 40s or 60s. A test, starting with a few items averaging at 60% difficulty, followed by 10 more items near 60%, may stop and call you a winner at 60%. The test stops when answering more questions is expected to not make a change in the score.

The test is efficient. It takes the least time with the fewest questions. It can dynamically cruise across the four, on paper, static levels to only deliver a few questions that match each student’s preparation instead of presenting a test booklet of a 100 questions.

We will never know what you actually know. But you know enough. We will know that your performance is a near perfect match to the average scores of a select group of individuals that you are believed to be a good fit. This works for graduation, job placement and entrance exams.

It works for high quality students; who may only attend class on test days. Low quality students need a teacher to attend to specific problems.

The Internet statistics are based on all the students tested. Classroom, teacher created test, statistics are based only on that one class. The paper and pencil methods we found so effective are now in the past. The bicameral/introspective mind theory hints at why they worked.