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I. Problem and method of investigation.-The reliability of the school's estimate of the accomplishment and progress of pupils is of large practical importance. For, after all, the marks or grades attached to a pupil's work are the tangible measure of the result of his attainments, and constitute the chief basis for the determination of essential administrative problems of the school, such as transfer, promotion, retardation, elimination, and admission to higher institutions; to say nothing of the problem of the influence of these marks or grades upon the moral attitude of the pupil toward the school, education, and even life. The recent studies of grades have emphatically directed our attention to the wide variation and the utter absence of standards in the assignment of values. Dearborn pointed out in his investigation' the large inequalities in the standards of grading employed by different teachers. Of two instructors in the same department one gave 43 per cent of his students the grade of "excellent" and to none the grade of "failure," whereas the other gave to none of his students the grade of "excellent" and to 14 per cent the grade of "failure." The wide difference in this instance is no doubt due in part to a difference in the students and in the nature of the work, but largely to a difference in the standards of marking.In order to determine precisely the personal equation in evaluating the work of pupils, it is necessary to eliminate all other causes of variation. The mere comparison of marks assigned by different teachers to their classes will not reveal this personal factor stripped of the other variable elements, such as difference in amount and kind of work covered by the class, emphasis upon different topics, 'W. F. Dearborn, School and University Grades (Bulletin of the University of Wisconsin, No. 368), p. 57. 442This content downloaded from 054.245

QUESTIONS Choose 8, including one selected from 4, 6, and 8. I. Two triangles having the three sides of one equal, respectively, to the three sides of the other, etc. Prove. 2. Prove that every point in the bisector of an angle is equally distant from the sides of the angle. 3. An angle formed by two intersecting chords is measured by, etc. Prove. 4. If the middle points of two opposite sides of a quadrilateral be joined to the middle points of the diagonals, the joining lines form a parallelogram. 5. To construct a mean proportional to two given lines. Explain fully. 6. AM is a chord of a circle, xy is a diameter perpendicular to AN and intersecting AM at 0. XO is io in. and ax is 20 in. Find the diameter of the circle. 7. The ratio of the areas of two similar triangles is equal to, etc. Prove. 8. Find the area of a right triangle whose hypotenuse is i ft. 8 in. and one of whose legs is I ft. 9. The sum of the interior angles of a triangle is equal to, etc. Prove. io. If two circles are tangent, and two secants are drawn through the point of contact, the chords joining the intersections of the secants and the circumferences are parallel.

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