Our Tax Dollars at Work

Well, the new year has come, and it’s time to start gathering up receipts and thinking about tax forms.

Would you like to know that our tax dollars are doing good in the world? The National Science Foundation has spent many millions developing and promoting “reform” math textbooks, with encouragement from the U.S. Department of Education. Surely our public schools will now rise out of the doldrums and surge ahead in mathematical achievement, right?

Try for yourself this problem from one of the more famous/infamous of the reform math textbooks:

Can you find the slope and y-intercept of this equation?

10 = x – 2.5

And then check out this editorial[editorial has disappeared] at edspresso.com. You’ll be amazed at the answer!

Update: Checking on back-links, I discovered that this page had gone AWOL, so I’ll give you the “answer” from the teacher’s manual. The “slope” is 1 and the “y-intercept” is -2.5, according to Connected Math. Unfortunately, this equation actually describes a vertical line (undefined slope) at x=12.5 (never touches the y-axis).

Doesn’t bode well for “CMP helps students and teachers develop understanding of important mathematical concepts…”

5 thoughts on “Our Tax Dollars at Work

  1. I suppose I should point out, for my less-mathy readers, that the “solution” given by the math textbook quoted in this article is totally wrong. The equation

    10 = x – 2.5

    is the same as saying that

    x = 12.5

    If you put this equation on a graph, it makes a vertical line and NEVER intercepts the y-axis. It could only intercept the y-axis if x could be zero. That is what the y-axis is: the place where x is zero. But if x is 12.5, then it can never be zero.

    Also, vertical lines have an undefined slope. To try to calculate the slope of a vertical line, one would have to divide by zero. You can’t divide by zero—it is mathematical nonsense. There is no such animal.

  2. Whew… glad you put the real answer out here.. I came up with what your answer is (there is no Y-axis)..
    The article that you cited was quite interesting reading and sadly it doesn’t just stop at the mathematics subjects.. the textbooks used in schools have unbelievable historical mistakes and misinterpretations as well.. what kids are learning in government school is riddled with misinformation – so it isn’t surprising what most government schools are turning out.

  3. Naah. Not so bad.

    I remember someone’s horror when I told them I learned History from Mr. Peabody’s Way-Back Machine on the Bullwinkle and Rocky Cartoon Show.

    He didn’t understand that it taught me about taking all sources with a grain of salt and (the beginning of) what it meant to search out and compare (and rank) multiple sources for information.

    Having stuff obviously wrong in your learning materials does a lot of good.

  4. Having stuff obviously wrong may train students not to trust everything they read in print, which is a valuable lesson. But this error isn’t obviously wrong except to people who already know math—which doesn’t include the 7th grade students or, unfortunately, many of their teachers.

  5. True. Wasn’t talking so much about that error as the general discussion about how bad the Textbooks are. After spending what they spent.

    But, while occasional errors can be useful in the way I mentioned, the more errors the less useful the Text.

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