Book Reviews 514
Mathematics Carrousel 514 ©1999
Breton, G. et al.
Instructional Package
Les Éditions CEC inc. , Wilson & Lafleur Ltée
| Approved components |
Pages |
Student's Textbooks (2)
Teacher's Guides (2) ©2000 |
459
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This one of the better written works in the Carrousel series. It is the
or one of the most professional. The flaws in it are few and minor in comparison
to the other Guy Breton co-authored works (translated into English) for
secondary II to IV mathematics in Quebec.
But when I looked at the content wondered how it was of services to the
students. The topics covered well provide a means to review and improve exact
arithmetic skills with whole numbers and fractions, but I do not see how the
student futures will otherwise benefit from the MEQ selection of topics. These
students would be better served by an exposure to consumer mathematics. See my
suggestions for secondary III mathematics.
Mathematics Carrousel Secondary V, 514, Books 1, Guy
Breton, Eric Breton and Mathieu Dufour, 1999, ISBN
2-89127-467-9
Notes on Book 1.
- On page 2, bottom, a box introduces the word experiment without any
explanation of its connection to probability. It says "An
experiment is considered to be random if none of its possible outcomes can
be predicted with certainty." We can imagine experiments or
situations in which none of the possible outcomes can be predicted because
of ignorance.
- On page 3, the text mentions the Montreal Casino without condemning
it.
- On page 4, the text uses the phrase real probability for the first
time as an alternative to theoretical probability. Yet I wonder if students
reading skills are sufficient to catch that significance.
- The page 5 statement "As the number of repetitions increases,
the ratio of the number of favourable outcomes to the total number of trials
approaches the theoretical or real probability" represents
a mathematical hope not a fact.
- On page 7, the text mentions slot machines without condemning them.
- On page 12, the text says outcomes are given by n-tuples but the first
example of n-tuples appears on page 24 in example 5. There we see outcomes
represented by ordered pairs, that is 2-tuples. A precise mathematical
definition of an n-tuple appears to be missing before pages and between
pages 12 and 24. The wordy indication of what is a n-tuple on page 12 may be
precise but some extra explanation of what it means would have been optimal.
- On page 21, the text says "The last two situations", meaning
examples, "confirm the following two properties." I found
the confirmation hard to understand. More in the first property, the text
says "The probability of an event corresponds to the the sum of
probabilities of the outcomes it contains". Here is a first
instance of Books 1 and 2 using the phrase correspond to instead of
the clearer phrase such as is given by.
- On page 39, the text says "Mathematical expectation provides data on
the long-term outcome of random experiments". The word information
would have been more appropriate that the word data. The word data
according my copy of the Collins Dictionary of Mathematics (www.collins.co.uk,
ISBN 0-00-710295-x) refers to "the information, usual numerical values,
gathered from an experiments, observation, survey or other
study". Mathematical expectation is a theoretical construct
rather than a statistical one as indicated by the conventional use of
the word data.
- On page 43, the text use the words corresponds to and not the words
given by. The next statement about theoretical
probability should be reworded to indicate the limiting value of the
experimental or theoretical probability, if it exists, should equal any or
the theoretical probability for the case at hand. At very least the
words limiting value should replace the word value in
this definition or summary of what is a theoretical probability.
- After an example, Page 71 indicates "A graph is a representation of
the relationships that exists between the elements of a set". The
concept of a graph being a set of relations is a bit abstract for my liking.
I prefer the more concrete viewpoint that a graph is a collection of
vertices and edges which can be use to represent situations.
The top of Page 72 gives a more precise account of what was
meant or hinted at in page 71. But the purple box in which includes that
precise account is offers many more graph theory concepts, which I feel
would be best put a summary after a longer exposition. I expect
the student trying to read ahead of the current position in a course would
have difficulty with the density and order of information in the box on page
72.
- The solution of graph-base optimization problems involves trial and
error. I did not see an explicit statement in the text book of that
aspect of the optimization problems. That non-deterministic,
trial and error, approach to graph-based optimization problems
will be new to many students.
- On page 220, a disk is said to be a portion of the plane defined by a
circle. The reader should add bounded portion. A circle divides the
plane into two parts or portions, one bounded, its inside, and one
unbounded, its outside.
Mathematics Carrousel Secondary V, 514, Book 2, Guy
Breton, Eric Breton and Mathieu Dufour, 1999, ISBN 2-89127-467-7,
- Page 78 includes the sentence "Each variable studied can represent
different values". Are we referring the notion a letter representing a
number or quantity that may vary and when the latter varies, the letter
represent different values, one a time, one after another. I suspect here
that a variable refers to a number or quantity that may have or take
different values, each time its observed.
- Page 78 furthers says that "Characteristics that can vary are
known as statistical variables." There is no definition of what is a
characteristic in the text that I see. I suspect the text use of the
word characteristic means an observable number or quantity, for which we
collect data. That characteristic, that is observable number or quantity, in
varying while being observed provides a statistical variable and data for
use in calculating statistics.
- Page 79, I do not understand the sentences "We usually compare two
variables by associating two values of each case of a sample. This is how
two variables are related."
- Page 79 says a statistical relationship is created when the values of
two statistical variables are compared as ordered pairs. A more
objective or Platonic view of would say a statistical relation ship can be
represented or studied by forming order pairs of data from two
different statistical variables .
- On page 89, from the text, I do not understand the introduction of the
term statistical link and the hence the immediately following
definition or view of correlation. What the text means is unclear to me, a
possibly instructor of mathematic 514, and as instructor I would look for an
alternative means of introducing statistical links and the concept of
correlation. My remedy for my confusion about what the text is trying to say
would be to give students instruction on how to compute or estimate
correlation (coefficient) numerically and point how its values correspond to
the behavior of points in scatter plot. In mathematics, saying how to
compute a number or quantity defines it. I would skip the qualitative
discussion of correlation until I found an exposition I could understand.
- The Math Express on page 129 provides a review and summary of what has
been seen. It also adds a few new terms. The term multi-variable
distribution. But the textbook only discusses in depth two-variable
distribution and I have not noticed the phrase multi-variable distribution
elsewhere in the text.
- To the mathematician, a regression in statistics chooses coefficients in a
function or computation rule so that the rule gives a best fit to some
data. Linear regression in the plane is the process of finding the
best fitting straight line, what the text calls the regression line on page
146. The textbooks indication on pages 146 that a Linear Regression is
a statistical relation which is close to linear may describe the
objectives of linear regression but it differ from the concept that Linear
regression in the plane consists of fitting a straight line to a set
of data points or ordered pairs. The text or I need to be corrected.
- The pink box on page 186 says "The units for speed are the same as
those used for the distance and the time." I thought the units of speed
s = d/t were given by units of length over units of time.
- The LexiMath on page 210 gives a unique verbal explanation of absolute
value of a number x and indicates a change in coordinates is provided by variation
in x or y coordinates. The word variation in my mind is harder to
understand the word change.
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Quebec English Mathematics Education
A farce is a farce is a farce.
Area Intro
Copy Right Matters
Curriculum Cuts
Intermediate Objectives
MEQ Objectives
116 Textbooks
116 Objectives
116 Check List
116 Suggestions
216 Objectives
216 Check List
216 Book Review
216 Nonsense or BullShit
216 Suggestions
314 Objectives
314 Check List
314 Suggestions
416 Objectives
416 Check List
416 Suggestions
436 Objectives
436 Checklist
436 Suggestions
436 Book Reviews
436 Nonsense in
514 Objectives
514 Suggestions
514 Book Reviews
536 Objectives
536 Suggestions
536 Book Reviews
Area pages represent an effort to follow and understand the objectives of the
1997-2005, the prior reform, and the
text books required and used 1997-2005. In retrospect, the objectives and texts
in question
are too incoherent, too full of nonsense, for rational comprehension and for
service as a base for the current reform. A farce is a farce,
is a farce
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