kitchen table math, the sequel: how to fix a learning problem, calculus edition

Saturday, January 5, 2008

how to fix a learning problem, calculus edition

another palisadesk resource:

Tool skills are the most basic elements of more complex skills. For example, in order to build fluency in oral reading, one must be able to say sounds and words quickly. In order to build fluency in composition, one must be able to copy letters and words quickly. Although early studies in perceptual-motor learning demonstrated that fluency in task parts makes fluency on complex tasks that contain these parts easier to achieve (e.g., Gagne & Foster, 1949), it was not until the late 1960s that Eric Haughton studied such relations in education. Haughton (personal communication, August 1978) found that college students having trouble in calculus could improve their performance by building fluency on very basic elements, such as saying and writing numbers and math facts. Haughton (1971, 1972, 1980) reported that a program of tool skill building improved underachieving students' math performance to the level of their competent peers, whereas an arbitrary reward system, increasing the potency of consequences, and extensive practice in math at the students' grade levels all failed to improve their performance. Again, the presenting problem is not always the problem to solve.

source:
Breaking the Structuralist Barrier
Literacy and Numeracy With Fluency
Kent R. Johnson
T. V. Joe Layng
American Psychologist 1992 47(11) pp. 1475-1490

the presenting problem is not always the problem to solve


4 comments:

PaulaV said...

The incremental approach of Kumon is designed to build fluency in basic math skills. It worked wonders with my child.

By the way, I love the quote:

the presenting problem is not always the problem to solve.

I am printing it out for the fridge.

palisadesk said...

It's not going too far to say that the concept of missing "tool skills" (and the whole area of component/composite skill analysis) was a Eureka moment for me and revolutionized the way I looked at helping students learn. It has also been a concept that I have been able to share, successfully, with colleagues in a variety of settings. One recent example will suffice.

We have had many discussions about improving students' writing skills (especially at middle school level), and two years ago we brought in the local writing guru (very touchy-feely, all heart-no skills) for a half-day with the whole staff. Somehow I managed to escape this torture (they needed someone to supervise kids after all), but I saw the results, which were posted on charts all around the faculty lounge. One activity had been to brainstorm all the reasons children might not be proficient writers. They came up with 143, extensively elaborated.

Not one referred to any graphomotor skills -- holding pencil, making lines or circles on paper, tracing, etc. All were "higher order" things like organizational ability or "motivation." Typical solutions included using computer programs such as Inspiration, graphic organizers and so forth. All fine things but possibly not what the student needs.

Not long after, I was in a sixth grade class and the teacher wanted my opinion about a certain student's writing. She showed me a sample -- it resembled chicken tracks. "Does he need to do more brainstorming? Peer editing? Where should I start?" I looked at the barely legible scratches. "First find out how many tally marks he can make in 30 seconds, and double it," I said. She just looked at me. "What????"

"The average middle grade kid can make from 250-350 tally marks in a minute," I said."It's just making lines on paper (but legibly, in an organized pattern). See what his rate is. Then we can go from there. After all, if you want to write anything, you have to be able to make lines on paper, pretty automatically."

She thought it over. "OK," she said. "I can do that now!" Not long after, she flagged me down, very excited. "Look at this," she said. "J. could only do 28 tally marks in a minute, and he was doing his best -- I'm sure he was."

"So that tells us," I said, "that the FIRST thing we need to develop is tool skills for writing. His fluency is only 10% of the average. How long would you persist at something when everyone around you is not only better, but ten times better?" I shared info on tool skills and we put some things together. The student worked with a peer for a few minutes several times a day. The teacher found this a conceptual breakthrough for her. It was also enormously empowering to the student. He had something concrete to work on (in brief bursts) that he could see improvement in, that did not devalue his character, work ethic or intelligence. In fact his "higher level" processes were in pretty good shape. Brainstorming and organizing were not the problem -- it was graphomotor output.

Several of my peers have told me that this concept revolutionized their day-to- day approach to helping students with difficulties -- and to presenting new material as well. They think of what the "tool skills" involved might be and prepare resources to supplement their development for those kids who need it (and some always do).

Anonymous said...

Palisadesk,

It warms my heart to hear you say such things. To think that there really are teachers out there who get it is a great relief to those of us in the trenches.

We've been complaining around here about the goofy writing reforms for years.

Last summer, I discovered similar problems with my one son. He was simply uncomfortable with the act of writing: Holding the pencil, shaping the letters, etc., I was amazed that this could still happen in middle school. Like math facts, certain aspects of writing have to be automatic, and they were not.

But like you said, the complaints from teachers always involved "motivation," or worse, "maybe he isn't going to be a good writer and that's okay."

After a summer of writing up a storm (no computer help), he improved dramatically, but it was painstakingly slow at first.

One of his problems with me was that I expected basic punctuation, capitalization and the big one--legibility. Teachers seem to be giving passes on all of these things.

SusanS

PaulaV said...

How do you, as a parent, make suggestions to teachers without stepping on their toes? I would like my first grader to practice handwriting during center time. Writing in a journal is not helping him with graphomotor skills.

At home, he practices handwriting via Kumon...copying words and sentences. His handwriting is fine at home, but his classwork is illegible.

I've discussed this with his teacher on Friday and she suggested having him write in a journal at home. She mentioned that she was going to have to be tougher on the kids because she has noticed that they are turning in work that is not readable.

Should I or could I suggest to her that I would like him to work on copying sentences during center time?