Core-Plus Mathematics: Course 1, Unit 2, Lesson 1 Review
Exploring distributions
You probably got tired from the solving quadratic equations on a graphing calculator, aren’t you? So the second unit changes gears to show you some fun tables and charts with data.
Investigation 1: Shapes of Distributions
The basic principles and techniques of analyzing data are much the same: make a plot of the data; describe its shape, center, and spread with numbers and words; and interpret your results in the context of the situation. If you have more than one distribution, compare them.
Right from the start the chapter suggests studying the “distribution” without defining what a distribution is. Ah, that’s self-evident, distribution, just a bunch of columns… or lines… or sectors… whatever, some things that stick up, or to the side, or all around. The more they stick, the bigger the value… or it is the frequency?
There are some juicy definitions that follow, like what is a “normal” distribution — it is one that looks like a hump. One hump — normal. Two humps — not normal. Actually, two-hump distribution is called “bimodal”, but you will find it only in the “On Your Own” section, twenty-something pages further.
Investigation 2: Measures of the Center
The measure of center that you are most familiar with is the mean (or average).
A proper definition of the mean comes several pages later, where the authors first humiliate the reader, practically accusing the student in forgetting terms supposedly explained earlier…
As you work on this investigation, think about this question: how do you decide whether to use the mean or median in summarizing a set of data?
…then they condescendingly “remind” the student:
Here, for your reference, are the definitions of the median and the mean.
And then the book shows this definition for the mean, which looks like a real piece of math in this otherwise very un-mathematical textbook:
This is not how you write textbooks! And then they lose steam, and provide a definition of the median in natural language:
The median is the midpoint of an ordered list of data — at least half the values are at or below the median and at least half are at or above it.
I am not sure how “at least half” clause works when both lower and higher values are mentioned. The definition from Wikipedia is much easier to understand:
The median of a finite list of numbers can be found by arranging all the numbers from smallest to greatest. If there is an odd number of numbers, the middle one is picked. If there is an even number of observations, then the median is usually defined to be the mean of the two middle values.
The textbook uses a very unconventional approach to integrate algebra and geometry under one cover. It says:
The term median is also used in geometry. A median of a triangle is the line segment joining a vertex to the midpoint of the opposite side.
Wow, a homonym, this is so rare.
Then the textbook switches to a familiar trope: tables and graphs. Um, sorry, not graphs — histograms. “Producing a graphical display is the first step toward understanding data”, claims the Core-Plus book. No need to try constructing this graph or histogram manually, “You can use data analysis software or a graphing calculator to produce histograms and other plots of data”, says the book and shows a pageful of nutritional info for a bunch of burger joints around the country.
Mode is mentioned in passing in the “On Your Own” section.
It is telling that as an example of a breakdown this chapter shows information about the takers of the GED test. The textbook says that people who have dropped out of the traditional school setting can “earn an equivalent to a high school diploma. A GED (General Educational Development Credential) is given to a person who passes a test for a course to complete high school credits.”
The textbook fails to mention that the GED has been created in the middle of the Second World War to help returning GIs find their way back in peaceful life, because most jobs required high school diploma. The textbook fails to mention that the test is not actually equivalent to four years of high school, and instead basically a reading and comprehension test, because one can infer answers from what is provided in the test itself. Well, except for math, but the math portion of GED is barely above middle school level. The third fact the textbook fails to mention is that despite that the GED is so primitive, only a third of the test takers pass the test.
The atrocious math skills of GED takers should be no surprise. Check out the skills the Core-Plus Math textbook expects from 9-graders:
Or this one:
This is it for this chapter. Stay tuned for the review of the next chapter, where you’ll learn about some statistical terms like box and whiskers and deviation from the mean.
