by Bill Lauritzen
I received my bachelors degree from the Air Force Academy in 1973, and shortly thereafter received my masters degree in Industrial Psychology/Ergonomics. I worked in the Air Force as a Human Performance Engineer.
After leaving the AF, I tried many jobs, none of which interested me, in 1982, I began to substitute teach for the LA Unified School District and later the Glendale Unified School District. This gave me time to pursue other interests, but also, I had in the back of my mind that I would study education. I concentrated more than 50% of my time on teaching mathematics, as I felt that teaching this subject would minimize personal bias, so that nature of the mind and learning could be more easily seen.
1) Through teaching and substitute teaching, I intimately interacted with over 85 different schools, some 600 classrooms, and approximately 60,000 students over a 18 year period. By contrast, the average teacher may only interact with only one or two schools, a few classrooms, and about 3,000 students over the course of their career.
2) I always explained any words the students didn’t understand and linked the lesson to the real world whenever possible.
3) I talked with mentor teachers and regular teachers to see which methods they found most effective.
4) I explored that various methods of teaching that I observed, to see which was the most effective.
1) Subjective: I relied on feedback and comments from the students for information about their teachers and methods of teaching, as well as about my own teaching.
2) Objective: By concentrating on teaching mathematics (about 50% of the time), in which the answer is precise, it was clear when the student was learning or not.
Interaction time by grade level:
English proficient 60%
English limited 40%
Los Angeles USD: Secondary: Arroyo Seco, Audubon, Bancroft, Belmont, Belmont Continuation, Belvedere, Berendo, Boyle Heights, Burbank, Burroughs, Center for Enriched Studies, Central High School, Dorsey, Downtown Business Magnet, Eagle Rock, East LA Occupational Center, El Sereno, Emerson, Fairfax, Franklin, Abram Friedman, Garfield, Griffith, Hollenbeck, Hollywood, Irving, King, Le Conte, Lincoln, Los Angeles, Marshall, Marlton, Metropolitan Skills Center, Mid City Alternative, Mount Vernon, Nightengale, Palisades, Palms, Revere, Roosevelt, Stevenson, University, Venice, Virgil, Wilson, West Hollywood Opportunity Center, Westside Alternative.
Glendale USD: Elementary: Balboa, Cerritos, Columbus, Edison, Fremont, Glenoaks, Keppel, La Cresenta, Mann, Marshall, Mountain Avenue, Muir, Verdugo Woodlands, R.D. White. Secondary: Roosevelt, Rosemont, Toll, Wilson, Hoover, Glendale, Cresenta Valley.
Private Schools: Southwestern Academy
Public Adult Schools: Hollywood Adult School
Private Adult Schools: Transwestern Institute, BSN Institute
Kachina Charter School, Arizona
1. Most students fail algebra because they never learned fractions.
2. Most students fail to grasp fractions because they haven’t had enough practical or hands-on experience with fractions.
3. Most students fail geometry because they never had hands-on experience with protractors or compasses. Also, they are taught in difficult Greek and Latin nomenclature.
4. Most teachers are uncomfortable using protractors and compasses in the classroom.
5. Early arithmetic skills should be done on an abacus for a more hands-on approach.
Long-term: Our base ten Hindu-Arabic system may hinder mathematical comprehension as well as having a negative affect on society. See my paper, “Versatile Numbers--Versatile Economics,” and also my video, “Numbers of the Future.” Math classes should teach prime numbers as well as highly composite numbers (versatile numbers).
1. There is a major mismatch in English between sound and spelling. National spelling reform is needed. Every year a special commission should pick several words and revise the spelling to make them match how they sound.