A University Professor Writes: "There Is Something Wrong In American Secondary Education

April 8, 2008--See update--I owe an apology to the Angry Professor, who writes the blog A Gentleman's C.

The professor blogs at A Gentleman's C, and describes herself as follows:

I am a tenured faculty member at a large state university. My teaching efforts primarily consist of delivering statistics lectures to social science majors. These experiences have colored my perspective somewhat.

In the post that follows, the blogger is writing about her experiences grading essays written by high-school students for a competitive scholarship, which require high SAT/ACT scores for eligibility. This year, she was judging essays written in the history category. She found about only 2% to be thoughtful and well-written.

I should have made abundantly clear that the phrase "Something like, say, the wheel" was the professor's replacement phrase for the actual question. The replacement phrase was used to protect the anonymity of the students' responses.

I also should have made more clear that I found the value in the post to be in the comments.

The students were asked to describe what life would be like today if something critical to modern society had never been invented. Something like, say, the wheel. Here is a little sample of what the kids had to say:

• "History is a very valuable topic to today's society."
• "The wheel should never have been invented in order to benefit society."
  
• "Thousands of people would strew together creating uncertainty and disorder."
• "Without the wheel, all of mankind would have been and would be vastly effected."
• "The industrial revolution began with the invention of the wheel in 15th century Europe."

Go read the comments, as well.

Connecticut's Curriculum Standards Revision

The State Dept of Ed website has draft curriculum standards posted. If you are a Conn parent or educator, you might want to take a look at what they are doing. I haven't looked through these things carefully, but I want to get the links up here. The letter accompanying the draft standards invites feedback. I don't see why only educators should have fun with this, so please do take a look. The standards will be in draft form until December 2007.

Draft Connecticut Pre-K through 8 Math Standards

Draft Connecticut Pre-K through 8 English Language Standards

There is a Feed Back Form for both draft standards here.

The biggest change to the standards is the inclusion of "grade level expectations." These are fairly specific and are a big improvement over the old standards. For example, in 2nd grade, students should be able to order simple fractions, tell time to the 1/2 hour, and know the calendar months in order.

The standards are clear. They may not be very high, but they are at least clear.

But there are still too many standards. The mile wide inch deep criticism is even more apparent when you look at each of the tasks to be mastered along the way. Still too much pattern recognition, probability, and graphing in the earliest grades and not enough emphasis on automaticity with basic math facts and fluency with fractions, decimals, and percents in later elementary grades. It's there, but there's no focus and no sense of what is most critical. Because of the sheer number of standards and expectations, how is a teacher or school to wade through them all? If they give equal emphasis to everything, they will not master anything.

So a mixed bag, but a step in the right direction. If you have the time to look at these things, you might consider downloading the feedback form and e-mailing it in to the State Dept of Ed.

After all, how often does anybody in education ask for your input?

Tom Loveless on automaticity

Question from Alison Corner, Principal, Pawtucketville Memorial, Lowell MA:

Their is alot of emphasis in K-4 on teaching math as a problem solving exercise. How would you recommend incorporating teaching computation skills for automaticity?

Tom Loveless:

Some lessons have to be devoted to computation alone, including why procedures work. Automaticity involves both accuracy and speed so I would stress both in memorizing basic facts in addition, subtraction, multiplication, and division and in the use of algorithms.

The State of Math Standards - transcript

I don't know how I managed to remember automaticity (which I have in theory been trying to achieve with C.), but forget speed.

Actually, I do know how: my years of ABA, when Jimmy and Andrew worked to a 90% criterion for mastery, dominated my memory of what mastery meant.

One year in KUMON ("speed and accuracy") wasn't enough to overwrite 4 years of ABA, or however many it was....

how to determine fluency for an individual child

An adult-to-child proportional formula can also be helpful in setting performance aims. Measures are first taken of the student’s tool skills rate and the rates at which a competent adult performs both the tool skill and the target math skill.^* The tool skill for answering math facts is writing random numbers without solving any problems. This fast-as-you-can number writing rate provides a ceiling for the fastest rate at which answers to math facts can be produced. The proportion obtained by dividing the adult’s performance rate on the target math skill by his or her tool skill rate is then multiplied by the student’s tool skill rate. The resulting figure is the fluency aim for the student. For example, if the adult solves math facts at a rate of 60 correct answers per minute and can write 120 random numbers per minute, his or her target skill to tool skill proportion is .5 (60 divided by 120). Based on the adult-child proportional formula, the fluency aim for a student whose tool skill rate is 80 would be set at 40 correct answers per minute (80 times 0.5). Providing direct and repeated practice on the relevant tool skills may be an effective way of improving the overall fluency of some children. Alternative modes of response, such as answering orally, should also be considered for children who exhibit very slow writing or poor fine motor control.

source:
Do Your Students Really Know Their Math Facts: Using Daily Time Trials to Build Fluency (pdf file)
by April D. Miller and William L. Heward
p 134
Intervention in School and Clinic, Volume 28, Number 2, November 1992

Effects of sequential 1-minute trials with and without inter-trial feedback and self-correction on general and special education students' fluency with math facts
(abstract)



^* tool skills; component skills; composite skills - see speed test

speed test

The precision teaching folks distinguish amongst:

• tool skills - how many digits can a student read or write per minute
• component skills - how many simple addition problems student can solve per minute
• composite skills
  

After discovering that C. can solve only 50 simple addition problems in 60 seconds when he should be able to do between 70 and 90, I decided to find out how fast he can write digits.

I had him write the digits 0 - 9 over and over again as fast as he could for 60 seconds.

He wrote 110, 10 more than the performance standard the PT folks seem to use.

So we're going to be doing Saxon Fast Facts sheets, Books 7/6 and 8/7 (the Tests and Worksheets Bookets), until he's up to speed.

Literally.

I'm also starting both of us on Cursive Writing Skills from Megawords. His handwriting is horrific, as is his printing, and it's not getting better over time.


back to basics
speed test

back to basics

hmmm...

After reading this passage in Carl Binder's article Doesn't Everybody Need Fluency? (pdf file) I decided to give C. a speed test today.

[I]n regular classrooms we learned that students need to be able to write answers to between 70 and 90 simple addition problems per minute in order to be able to successfully and smoothly master arithmetic story problems. However, some students seemed to level off at around 20 or 30 problems per minute, and no amount of reward or encouragement seemed to help. Some of our colleagues (Starlin, 1971; Haughton, 1972) decided to check how many digits those students could read and write per minute—critical components of writing answers to problems. As you might guess, they were very slow, which held down their composite performance. With practice of the components on their own to the point of rapid accurate performance (for example, reading and writing digits at 100 per minute or more), students were able to progress smoothly toward competence on solving the written math problems.

70 problems per minute = 70 problems per 60 seconds

C. did two timed tests. The first was 50 problems; the second was 25.

70 problems/60 seconds = 50 problems/43 seconds

To meet this performance, standard he needed to write answers to 50 simple addition problems in 43 seconds. Right?

First test: 50 problems in 190 seconds.

yikes

After he was done, I took the same test & clocked in at 50 problems in 35 seconds without breaking a sweat. (Try it yourself. You'll see.)

I had C. try the test again. He cut his time in half, but he was still at 50 problems/66 seconds. He says he's tired & has a headache....but then again I'm tired, too, (albeit sans headache) not to mention old.

I'll have him take a third speed test tomorrow. If he's not down to 43 problems/50 seconds, I'll test his speed writing digits. Then, when I find out there's no way in h - e - double hockey sticks he can write 100 digits in 60 seconds, we will commence printing practice.

So.... we're back to handwriting. Yet another inconsequential non-21st century skill never, ever taught to mastery in our public schools!

bonus narrative: C. used cursive writing to label his Saxon percent ovals, leading me to the discovery that he's writing his f's wrong.

"I think you're writing your f's wrong."

"No I'm not! That's how you're supposed to write 'f'!"

I decided not to argue about it.

Let off the hook, C. stared at my cursive version of the letter "b" for a couple of seconds, then said, "I forgot how to write b's."

I decided not to argue about that, either.



simple addition worksheets online:

create & print whole number addition worksheets from aplusmath (best source - you can specify 50 problems)
free whole number addition worksheets from S&S Software
create & print addition worksheets
free math worksheets from tlsbooks
free math worksheets from math-drills.com

back to basics
speed test

first crack at editing exercise

re: eureka

wow

C. didn't have a clue how to proceed.

He only managed to cut one word:

Stunt people were around long before films. Even Shakespeare probably used them in fight scenes.

I thought "even" needed to stay put, but I see now that the transition is implied.

This is going to be hard for me, too.

Of course I'm wondering whether I'm starting at the top. Is there a simpler way into this kind of exercise?

I will mull.

Meanwhile, on the math front, C. did the Saxon Fast Facts Multiplication sheet - 64 1-digit multiplication problems - in 2 minutes 37 seconds, getting 100% correct. That seemed good (Saxon says the sheet should be done in less than 5 minutes) until I re-read this post:

[I]n regular classrooms we learned that students need to be able to write answers to between 70 and 90 simple addition problems per minute in order to be able to successfully and smoothly master arithmetic story problems.

More confusion. Each "simple" multiplication problem has a 2-digit answer, whereas most simple addition problems have 1-digit answers. I think.

Tomorrow I'm going to have him do 100 simple addition problems and see what's what.

If we have to practice writing digits, we will practice writing digits.

His handwriting is terrible. I came across some of his work from a couple of years ago and discovered there's been no improvement at all.

My efforts to afterschool handwriting, which I abandoned lo these many years ago, were an abject failure.


expert advice on teaching writing from Joanne Jacobs
eureka
more from Joanne Jacobs
doctor pion on writing a precis and critical reading
home writing program in place, for now