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Quebec High School Mathematics Education (English Version of)
his folder has a tree like structure. The child, same level and parent level webpages for this webpage follow.. More Links: 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 |
Curriculum Content ShrinkageWhile most students will not take calculus, preparing for calculus, the core skills and concepts it requires, provides focus for mathematics instruction which prepares for all arts, trades and disciplines needing mathematics. To that a second focus on consumer mathematics possibly in a course by itself could provide drill and practice, with explanation offered, of arithmetic, algebraic and geometry students may need in their daily lives buying and selling, and maintaining their homes. Developing the ability to follow methods, one step at a time, and one step after another, in a repeatable and reproducible manner is needed at home in cooking, in balancing a cheque book, in filling tax forms, in working at a fast food restaurant, in building or constructing or maintaining buildings and so far. In some subjects or field of work, creativity has to be discipline in favour of mastery methods carefully for the sake of repeatable and reproducible results. And in Quebec mathematics classrooms, secondary I to V, I have seen students having difficulty in evaluation expression involving whole numbers and fractions in a repeatable and reproducible way, independent of the students - a half-dozen different results may be offered by a class. The Quebec curriculum of the reforms in the 1990's for secondary II to V emphasizes at length and explicitly
While mathematics has many fine topics which students could learn, trying to lead students through too much leads to a loss or absence of a focus. Keep it simple. A clear focus, a simple message, is needed to retain or maintain the attention and will-to-learn in mathematics. Without a clear focus, the mathematics education become a lengthy formality. It is taught for the sake of employment and learnt for the sake of a high school teaching certificate. Doing less well may appeal to students and still give a solid base for calculus and for all arts, trades and disciplines needing mathematics. Quality is better than quantity for content in mathematics course design. Modes of Representation, Cut
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In secondary II, the full development of spatial sense (40% of the school year) as indicated in the first chapter of book 1, in accordance with the MEQ curriculum represent too much information. The coverage of similitude's is not needed in my opinion. I hope that the official curriculum of Quebec in the future will move most of spatial sense development to another course (drafting, art, drawing, crystals shapes) so that students are not alienated by a vast quantity of mathematics, intellectually appealing many senses, but context-free, long and pointless for most students.
Is secondary III mathematics time, well-spent? I say no. It provides marks but little or no preparation for secondary IV mathematics, save for a further unnecessary coverage of dilatation transformations. |
Secondary III mathematics emphasizes the study of linear functions and their use in the too lengthy discussion of direct, inverse, square and partial variation. Most of this is topic that could be treated in a lesson or two, or as aside, after students have mastered problem solving with linear equations in one or two unknowns.
The curriculum objectives for secondary I to V emphasize the develop of critical thinking with respect to the presentation, interpretation and collection of statistics. Critical thinking is the unifying theme. That connection is well put and well-written in one of Teachers Guide for the MEQ approved textbooks for Mathematics 436. But this emphasis on critical thinking is at odds with the practice in Quebec mathematics courses. With and without a calculator, students cannot do arithmetic in a repeatable and reproducible manner. Before we talk about developing critical thinking in statistics, students need to be taught how to follow arithmetic and logical lines of figuring in a repeatable and reproducible manner. That is a missing prerequisite.
The MEQ emphasis on critical thinking through statistics is not yet supported in secondary III to V by student inability to do arithmetic.. Critical thinking should be based on the ability to follow methods one step at a time and one after another with care and precision. Without that ability being emphasized, rational faculties of students lie dormant.
The objectives for Math 314 call for students to
Here students should understand that knowledge of the median, mode and range of a how a number or quantity is distributed provides a limited window on its behavior or distribution. Here many different distributions can have the same median, mode or range. This information can be used to contrast distributions and to highlight their differences. Knowledge of the latter by itself does not provide a full picture of the data, does not fully characterize the data.
The objectives for mathematics 416, 426 and 436 call for students to
Measures of position provide an internal ranking of data set and may be used to indicate the significance of scores. The Box and whisker plot provides a visual ways to view the distribution and dispersion of data. And in contrasting two sets of scores or numbers, Box and whisker plots can emphasize the difference in quantitative or qualitative manner. But many distribution may have the same or similar quartile distribution and hence the same or similar Box and Whisker plot visualization of the distribution's quartiles. But within each quarter or quartile, data distribution may vary greatly. Histograms with finer divisions of data may provide a clearer view of the similarity or differences.
In Mathematics 514 and 536, there are estimates of correlation coefficients based on rules which may be used but justified. That favors rote learning - the exposition and mastery of mathematical methods without any explanation why. It is nice to know, but not really necessary.
This course emphasizes
The whole course is full of material for students who typically do not a have good command of arithmetic or good command of fraction sense. The material here can be used to fine-tune and develop their fraction sense and skills, and their ability to apply formulas directly and indirectly. The discussion of optimization methods for graphs, weighted graphs, shows that deliberate trial and error may be required in some mathematical problems. That being said, this course fills the requirement for high school graduation but it not meet the needs of students for a practical command of mathematics in their daily lives and forthcoming careers.
As said above, developing the ability to follow methods, one step at a time, and one step after another, in a repeatable and reproducible manner is needed at home in cooking, in balancing a cheque book, in filling tax forms, in working at a fast food restaurant, in building or constructing or maintaining buildings and so far. In some subjects or field of work, creativity has to be discipline in favour of mastery methods carefully for the sake of repeatable and reproducible results.
Here are students, many of whom will become parents - later rather than sooner we hope. There is an opportunity in this course to talk about how to tutor young kids to develop a good primary school level comprehension of mathematics including place value, the explanation and justification of place value or decimal methods for addition, subtraction, multiplication, the development of fraction skills and sense, and how it important for algebra. See the Solving Linear Equations with Stick Diagrams = Fractions, Ratios, Rates, Proportions & Units areas of this site. Give these students the ideas that skills and concepts in primary school (and elsewhere) need to be develop in some sequence, cumulatively, one at time and one after another, with verification at step. That might improve their study skills. Talking about how to describe and propagate the reasoning in mathematics and the expectation of repeatable and reproducible results in arithmetic, algebra and geometry may raise the common understanding of mathematics and its logic.
This suggestion for Mathematics 514 into tutors could be appropriate for all students. The call in the current or forthcoming reform for better communication skills in general could be translated in to the view that a subject is not fully understood until a student can communicate its skills and concepts to others directly or indireclty.
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