Core-Plus Mathematics: Course 1, Unit 1, Lesson 3 Review
Another lesson, another pretentious title: “Tools for Studying Patterns of Change”. The chapter starts with three simple expressions that the book calls “rules”. One of these expressions represents a well-known formula for average speed, but for some reason speed is identified with letter s instead of v or u commonly used in physics, and a numerical constant is used in place of distance.
Investigation 1: Communicating with Symbols
The textbook tries to show how to formalize word problems — that is, to represent statements made in natural language with mathematical symbols and operations — but does it awkwardly. For example, it tries to pursue students to recall formulas for calculating perimeter and area of rectangle by drawing a box:
A rectangle has right angles, and its opposite sides are congruent. This fact is not shown on the picture, which is a major faux pas for a mathematics textbook.
The mistake is not repeated with the picture of a right triangle, where the right angle is correctly marked. But the book is afraid to call its sides AC and BC as legs and the side AB as hypotenuse, instead calling hypotenuse a “side opposite the right angle”.
Then it asks, “what is the minimum number of ruler measurements you would need in order to find both the perimeter and area of any right triangle?” assuming that you know about Pythagorean theorem. At this point the book haven’t provided a formula for the area of right triangle, does it expect the students to figure it out themselves? Granted, it is rather simple, just half of a rectangle really, but we already know how little this book thinks about the intellectual level of its readers.
Then comes the gem of this section: “What is the minimum number of measurements you would need in order to find both the perimeter and the area of any nonright triangle? What measurements will meet that condition?”
Does the book really expect students to know Heron’s formula? Or maybe the authors expect students to derive this formula by themselves?
Well, this section is one big piece of joy. Let us move to the next section.
Investigation 2: Quick tables, Graphs and Solutions
This chapter returns back to the first lesson about bungee jumping. It says that “The rule I = p(50 — p) predicts daily bungee jump income at Five Star Amusement Park,” where I means income. But what they say next is truly frightening: “Sometimes you can answer questions like these by doing some simple arithmetic calculations. In other cases, calculators and computers provide useful tools for the work.” This is the credo of Core-Plus course in one paragraph. This course does not appreciate what is called analytic solution, where you can work out the dependency between variables in symbolic form, the Core-Plus rather wants you to figure out an answer either by trial and error like a 16-century carpenter, or by using “powerful tools” like calculators and computers.
And this is what they are doing. Instead of solving a quadratic equation in symbolic form, they show how a calculator solves it for you. Granted, the particular equation they “solve” on a calculator is more complex that the original one, because they target for 500 dollars income, so it has an extra term.
Nevertheless, instead of explaining a generic formula for finding roots of quadratic function the books asks students to pull out their graphing calculators, which will do it for them. And the authors have the nerve calling their textbook a mathematics course! Then in the pullout titled “Summarize the mathematics” they proudly proclaim that in this investigation, “you developed skill in use of calculator or computer tools to study relations between variables.” Unbelievable!
Investigation 3: The Shapes of Algebra
“As you work on the explorations of this investigation, look for answers to this question” — this rhymes almost like bad hip-hop.
In this section the textbook pries open the curtain behind the functions you’ve seen before but did not know what they are called and neither how to find their roots — linear, quadratic, reciprocal, exponential — and shows how their graphs look like. And… and that is it.
The book does not even care to call these graphs a line, a parabola or a hyperbola, because these words may be too confusing, and why do need them anyway? Just use your fucking graphing calculators.
In the homework section (applications, connections, reflections), the book presents graphs of the four above function types and asks you to map each graph to a function. No, you do not need to solve anything, just connect a shape to a symbolic form. This is a 9th grade math book, ladies and gentlemen.
If you were SOL doing previous exercises calculating circumference and area of a circle or finding perimeter and area of a triangle, finally the book gives you the relevant formulas, rejoice! No Heron’s formula though. If you could not derive it yourself, then you are just too stupid for this book. Measure these angles then, just apply a protractor, read the number and get your hard-earned C.
In the next lesson:
- Finally, a definition of a function (an incomplete one though);
- An advertisement of spreadsheets, computer algebra systems, and graphing calculators;
- Pull out some numbers out of your butt and then explain why you chose those numbers and not some other.
