Barcharts, Inc Algebra Part 1

Ottimo per l’ottimo anno

A clear and concise summary

(I was looking for a highly portable item for my algebra students.)Like most materials for beginners, this ‘study guide’ blockades the way to deepening cognition by ignoring ambiguity, by conflating meanings, and by sloppiness of presentation. It even contains one outright error.details:Under NOTATION, they ignore the ambiguity of ‘last element’, and they fail to mention the possibility of a set ‘with no first element’ (e.g., {..., -3, -2, -1, 0}, although later in the guide they use the concept.Under OPERATIONS, they say “making sure not to write any element more than once’, giving the impression that this is a rule of the same importance as not dividing by zero. Actually, not writing an element more than once is not a mathematical rule at all, but merely a formatting rule. They miss the opportunity of emphasizing the fact that a set is defined purely in terms of membership by failing to give an example such as {3, 5, 7} = {7, 7, 5, 3, 3}.Under SETS OF NUMBERS, they say, “the sets of Real numbers and Imaginary numbers have no elements in common”, but the way that they have defined Imaginary numbers includes 0 as an imaginary number, and so the sets of Real numbers and Imaginary numbers DO have an element in common, namely, 0. (This is the ‘outright error’ mentioned above.)Under PROPERTIES OF REAL NUMBERS, they say, “If c is not equal to 0 and c is greater than 0”. Saying merely, “If c is greater than 0” is sufficient, and adding the preface that they do, about c not being equal to 0, gives the wrong impression to beginners that such a preface is necessary. (Ditto for “If c is not equal to 0 and c is less than 0”.)The heading OPERATIONS OF REAL NUMBERS should be OPERATIONS ON REAL NUMBERS. (The real numbers are not performing operations; WE are.)Under COMPLEX NUMBERS, they say, “The conjugate of the complex number -2 + 12i is -3 – 12i. True, but the connection to what is being described, “Divide complex numbers by rationalizing the denominator. The answer is complete when there is no radical expression or i in the denominator and the answer is in simplest form.” is far from clear to a beginner.*******Besides the above, there are a number of even lesser glitches, or non-standard renderings, that I will not attempt to detail here.Note: Because this review venue does not support special symbols, I have spelled out the special symbols used in the guide, when quoting from the guide (such as ‘If c is not equal to 0’).cf:“Low quality of teaching is not readily detected by the lay mind.”-- W. D. Lewis(in ‘Principles of secondary education’, edited by Paul Monroe)

I have been teaching for over 20 years in grades K-2. This year I was thrust into 5th grade 5 weeks into the year of virtual learning. I am so glad I purchased these Quick Study guides, as they have saved my hide more than once.

Every parent & student should have this going thru Jr high & high school ranks. It helps with the little steps you may have forgot about. I picked up all levels since I have kids in pre algebra, algebra, & these guides are a GodSend. GET EM ALL FOR THE PRICE. Worth every penny!!