File:KozoNoteBook20.jpeg

Fragment of the student work on algebra found in the Note book by Koso Okudaira.

This is assumed to be exercise or a control quiz on elementary algebra written by Kozo.

Mistake by Kozo
The document reveals the mistake by Kozo:

The sample

$~ m^3+n^2-mn-m^2n^2$

seems to be transformed with error. This error is mentioned by the teacher (or examiner) with red diagonal slash-like line.

Mistake by the Teacher
The document seems to reveal also some mistakes by the teacher.

Sample $73\times 67=(70+3)(70-3)=70^2-3^2=4900-9=4891$ seems to be transformed correctly; but the Teacher marks it with diagonal line. Perhaps, the the Teacher dislikes the dirt: some stroke-out writing appear before the correct answer.

Sample $\sqrt{x^2-6x+9}$ seems to be transformed with error.

First, the expression $x\pm 3$ is suggested.

Then, the $+$ is stroke-out; so, finally, the partially-correct expression $x\!-\!3$ is suggested.

However, generally, the suggested expression is wrong. In order to see it, it is sufficient to consider case $x\!=\!0$; the initial expression gives $\sqrt{9}=3$, while the suggested expression gives $-3$.

Perhaps, the correct simplification of the initial expression should be

$\pm(x-3)$

where symbol $+$ or $-$ should be chosen dependently on value of $x$, or on the choice of branch of the square root, if not only the principal branch is assumed.

This fault is not revealed by the Teacher; the answer is marked with red loop, in the same way, as the correct answers.

Not only Kozo
Faults by teachers are not specific for Japan. In other countries, and, in particular, in the USSR, teachers show high dogmatism and make serious errors; some examples are suggested in article Уроки (In Russian).

Errors by teachers seem to be unavoidable; however, each error should be mentioned as soon as possible, and late is better than never. The specification and discussion may help to reduce number of similar errors in future. For this reason, the image above is loaded into TORI.