## Scientific Method in the Reconstruction of Ninth-grade Mathematics: A Complete Report of the Investigation of the Illinois Committee on Standardization of Ninth-grade Mathematics, 1913-1918 |

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Page 90 - VIII on the course of study. b) If the fault in an undifferentiated teaching emphasis is that the teacher does not know which are the difficult operations (and many teachers have written the present writers after giving standardized tests that it was the first time in their lives that they had ever known specifically which are the most difficult operations), the suggestion as to the remedy is simple and direct. The use of standardized tests can be made to lead to a detailed and helpful classification...

Page 19 - In the last half of the second year and the first half of the third, t May be taken in either year. ious experience with geometry, and (3) the proximity to college. The few schools that report this subject in the second year do so in order to make the work in algebra continuous. Solid geometry is placed in the third year in some schools because of its sequential relation...

Page 39 - And I would advise you, my Pupils, to pursue a Regular Course of Academical Studies in some Measure according to the Order of this Catalogue. And in the First Year to Study principally the Tongues, Arithmetic and Algebra; the Second, Logic, Rhetoric and Geometry; the Third, Mathematics and Natural Philosophy; and the Fourth, Ethics and Divinity.

Page 31 - to develop In the pupil the ability to use Intelligently the most powerful devices of quantitative thinking : the equation, the formula, and the 9raph.

Page 91 - ... exponents, signs, etc. Test 2: Evaluation or substitution. Relatively few errors are made in this operation. Of the most frequent it will be noted that nearly one-third are due to squaring the product of literal factors instead of the one factor designated by the exponent. Thus the evaluation of ab* is many times more difficult than 2ab.

Page 165 - For example, she may base a series of pertinent questions on thermometer readings at different times, or at different places at the same time.

Page 76 - Denver at average speed of 40 miles an. hour, takes 3 hours longer to make the run than one running at 45 miles an hour. What is the distance from Chicago to Denver? 80 If a cistern can be filled by one pipe in x minutes and emptied by another in x+5 minutes, what part of the cisternful runs in one minute if both pipes are open?

Page 92 - — 2c" at all, or, when his attention is immediately on the division of 12 by the coefficient of x, the sign drops from his mind. Following in frequency comes the ever-present arithmetical difficulty. Other errors of lesser difficulty are : error in signs in division, eg...

Page 94 - But the greatest difficulty encountered in learning to handle the operation is that of recognizing the necessity of continuing the process of factoring until the prime factors have been found. At the root of the matter, however, is the development of an attitude of distributing attention between two equally important things, namely, finding the monomial factor and continuing the factoring until the prime factors are found. Students are outstandingly weak with this particular type of manipulation....

Page 76 - ... 60 A father 54 years old has a son aged 9 years. In how many years will the age of the father be just 4 times that of the son?