Of learning and testing

Mindless testing of the young to improve K-12 education is the rage these days, at least in Ohio.  It is like measuring snakes with a straight edge.  Sure, you will get some numbers.  But are they meaningful?  This video about learning and passing tests from two species (crows and monkeys), should be an eye opener to those who have bet the educational farm on testing as the sole way to assess and improve education.  The big lesson:  Every child learns differently depending on his/her experiences.  The time for individualized testing, like personalized medicine,  has come.

Math by The Plug and Chug

   Math By The Plug and Chug Method

Many school students learn to do math by what I call the “plug and chug” method, where they mechanically perform calculations without really understanding what they are doing.    I formed this opinion based on my interaction with hundreds of college students, many of whom did not understand basic algebraic concepts.   While such a  mechanical approach might get many students  through state mandated standardized tests,   they are functionally “illiterate” when it comes to applying basic math to real life situations.  I provide two examples of this problem:  one, a personal experience involving  a 7th grader, and the other, rather shocking, involving a highly paid expert witness.

 Late last December, to test if a  7th grader understood percentages, I asked him this question: How many dollars will you have to give me, if you have $200 and you owe me 12% of that amount?  He could not answer that because he did not understand the concept that percentage is based on 100.  So, 6% means 6 every 100, to be proportionally adjusted for numbers smaller and larger than 100. For example, 6% of 50 and 200 would be 3 and 24 (oops, 12, thanks to a sharp-eyed reader) respectively (no calculator is needed).

Next, I asked him the same question amenable to the “plug and chug” method: Calculate 12% of $200. Using his calculator, he mechanically converted 12% in his mind to 0.12,  and multiplied it with 200 to give the correct answer of $24.

 The second example deals with an accident reconstruction expert who has trouble converting fractions to decimals. Given that the scaling factor   is 20 feet to an inch, he just could not convert 3 and 3 /16 inches  to the corresponding length in feet, using a calculator.   He kept saying that he needed formula sheets to do this straightforward calculation.

These examples emphasize the dire need to explain fundamental mathematical concepts, especially  early in students’ educational training.   Math teachers everywhere, please take note.


Even dumb kids from caveman days must have known this!

To Really Learn, Quit Studying and Take a Test

Finally, you are not alone, Galileo

Doors’ Morrison pardoned in indecent exposure case

Obscenity is time-dependent, like heliocentricity was in Galileo’s time.

Our kids lose again

Washington Schools Chancellor to Resign It appears that while Ms. Rhee was successful, she may have used an “iron-fist” to achieve her goals. Neglecting the Base. As a long term educator, I realize that, after decades of neglect, reform comes slow. Education involves the co-operation of three key stakeholders: students/parents, teachers and administrators. Unless all these parties are on the same page, reform will not succeed.

Easy math– Yes, if you also believe in free lunch, free money, . . .

Making Math Lessons as Easy as 1, Pause, 2, Pause …

The reporter failed to inform the reader what this SingaporeMath is all about, except that they go slow, focusing on one number at a time. The study of math is all about understanding the concepts; mostly math is taught in a “mechanical” way: Teaching a kid to get the correct answer, as in standardized tests. It is akin to a Pavlovian response- you fling the “frisbee”, and the dog “catches” it, without fail each time. I wonder if the dog understands what is involved. As a grad student, I took advanced differential equations more than 30 years ago. I felt like that dog: I aced my tests, but often did not understand or relate to the steps I took to get to the so called “correct” answer.