Corrective Arithmetic for Supervisors, Teachers, and Teacher-training Classes, Volume 1 |
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100 combinations 19 in grade Add Subtract Multiply adding amount of drill attention binations borrowing cards carrying causes cent cerning Chapter child Columbia University column addition common fractions compound multiplication connection correct answer correctly decade denominate numbers diagnosis difficulty disabilities divisor Educational Educational Psychology error studies estimating the quotient example exercises expected failure fundamentals of arithmetic given grade five grade four grade six grade three higher-decade additions involve bridging large number law of effect long division manner means mental method metic minuend number facts number four number of children Number six number three pay back practice material principles reasoning problems remainder response short division situation sort study of errors Subtract Multiply Divide subtraction combinations subtrahend taught textbooks Theisen things tion total number trouble type errors Wiscon Wisconsin wrong answers zero combinations
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Page 38 - Cent 1. Total failure to comprehend the problem 30 2. Procedure partly correct but with the omission of one or two essential elements 20 3. Ignorance of fundamental quantitative relations 10 Total ~60 4.
Page 154 - Wilson, GM A Survey of the Social and Business Usage of Arithmetic.
Page 47 - Multiply together the numerators for a new numerator, and the denominators for a new denominator.
Page 29 - Counts, GS, Arithmetic Tests and Studies in the Psychology of Arithmetic. Chicago: The University of Chicago Press, 1917.
Page 154 - Suzzallo, Henry. The teaching of primary arithmetic. A critical study of recent tendencies in method. With an introduction by David Eugene Smith.
Page 55 - In the second example the pupil is applying the rule for multiplication of decimals, and is pointing off as many places in the quotient as there are in the divisor and dividend taken together.
Page 11 - ... equals 5 is expected to respond correctly to 8 from 23, 8 from 33, 5 from 13, 45 from 53, and so on. Lastly, a child who is taught how much 7 times 8 are is supposed to respond correctly to 8 times 7, 56 divided by 7, 62 divided by 8, and the like. Thus we have been encouraged to believe that all our work is done when we have taught 180 facts — the 45 so-called " principal combinations " in addition, subtraction, multiplication, and division.
Page 65 - For one of the easier bonds, most facilitated by other bonds (such as 2X5 = 10, or 10 — 2 = 8, or the double bond 7= two 3s and 1 remainder) in the case of the median or average pupil, twelve practices in the week of first learning, supported by twenty-five practices during the two months following, and maintained by thirty practices well spread over the later periods should be enough. For the more gifted pupils lesser amounts down to six, twelve, and fifteen may suffice.
Page 82 - The children should all know the meaning of every word in every problem before they are asked to solve it. This means that every such word must be in the child's reading vocabulary. At least one fifth of the trouble which children have with reasoning problems is due to inability to read the problem.
Page 38 - Difficulties in column (higher-decade) addition. 4. Trouble in subtraction when a digit in the subtrahend is greater than the digit just above it in the minuend. 5. Interference between what is required and what is already known (harmful transfer). 6. Ignorance of the combinations in all of the processes. 7. Estimating the quotient in long division.