I recently wrote an open message to my congressman, Scott Peters, urging him to reject the proposed rewrite of the Elementary and Secondary Education Act. In it I said, “When fads like “new math”, “phonics only” or “whole word” came along, they infected many jurisdictions but not a majority of the country. As their weaknesses manifested, these fads were abandoned before serious damage occurred.” Federally centered power would end that protection from bad policy. After reading this post, Professor Larry Lawrence invited me to lunch to discuss “new math.”

I met Larry briefly in Chicago at the April NPE conference. I knew he lived in Carlsbad, California less than 30 miles north of my San Diego home. I was intrigued by his proposal to get together and discuss the “Zen of teaching math.” So I agreed to meet him at a spot between our homes.

Larry has been called a “consummate teacher of math” and has a significant pedigree. After graduating from Morningside High School in Inglewood, California, Larry did his undergraduate work at Occidental College where he was a classmate of star quarterback, Jack Kemp. Barack Obama also attended Occidental. When finished there, Larry went on to Columbia University’s Teacher’s College pursuing a Masters degree.

It was at Columbia that Larry was introduced to a more profound grasp of the principles of mathematics and how students can successfully develop mathematical thinking. In 1958, almost 30 years before California’s 1985 adoption of “teaching for understanding” also referred to as “new math”, Larry was learning from the movement’s fathers. (1)

Referring to the 1985 adoption of “teaching for understanding” Elizabeth Green tells us in her book __Building A+ Better Teacher__, “… the California teachers were struggling to understand students’ ideas, figure out what the students needed to know, and then use that information to respond.” (2) Larry and I agreed that this was the essential weakness with “teaching for understand” – the elementary school teachers did not have the training to do it.

On day one of his first math class at Columbia (Advance Algebra), the teacher gave an instruction for an assignment that stumped Larry. He went throughout the dorm asking everyone he could find to explain to him what “one to one correspondence” meant. No one knew! In 1958, few people apprehended the fundamental principles of mathematics.

Larry also brought along a prompt from his professor. I have shared the setup here:

Arithmetic by mail: Stan Brown had a pen pal, Al Moore, who lived in Alaska. Stan and Al corresponded quite frequently. Stan liked to receive letters from Al because he wrote about interesting things like hunting and fishing and prospecting for gold. Al enjoyed hearing about the things Stan did, especially about school, for Al had had very little opportunity to attend school. One day, Al wrote to ask if Stan would mind teaching him some arithmetic. Stan agreed but decided he needed to know how much Al already knew. So, in his next letter to Al he included a simple test, and asked Al to write in the answers and to return the test to him. Al sent the test back immediately; he said it was very easy and asked Stan to send some harder questions next time.

Take 2 away from 21. 1

What is half of 3? ͻ

Add 5 to 7. 57

Does 2 x 4 ½ equal 9? No

Which is larger, .000065 or .25? .000065

How many times does 3 go into 8? Twice

How many times does 9 go into 99? Twice

Which is larger, 3 or 23? 23

What is a number smaller than 4? 4 (written smaller)

What is a number larger than 4? 4 (written larger)

Some of Al’s reasoning follows.

Anyone can see that 3 goes into 8 twice, and pretty neatly too, without any 2 left over. You put 3 into 8 the regular way and then you turn another 3 around and put it in on the other side of the 8.

In question 4, you don’t even need a ruler to tell that 2 x 4 ½ is different from 9.

In question 8, 23 is larger than 3 because 23 already has a 3 in it and a 2 added on in front.

Larry was an early adopter of “new math” when in 1959 he returned to Morningside High School to teach mathematics. Since taking that decision, he has dedicated his life to improving education in California. In the early 1960’s, Larry may have been the first California teacher to teach calculus in high school.

His career includes a stint at UCLA working in the lab school then known as Seeds. In 1975, he received his doctorate from UCLA and went on to work as director of curriculum for the Turlock School District. He also served as the principal of an elementary school in Upland California. In 1982, he returned to UCLA to again work in the lab school training elementary school teachers how to teach mathematics.

Larry’s story is also the story of education reform gone wrong. There are many Larry Lawrence’s out there who have dedicated their lives to understanding teaching and learning. They are a treasure. They have both theoretical knowledge and practical experience, but as Elizabeth Green reports (and then praises) people like Doug Lemov and Stacy Boyd purposefully shunned people like Larry when they formulated their “no excuses” charter school movement and embraced pedagogy spiced with “disruption.”

Larry told me that in 1993 he got involved with developing a charter school. The lab school at UCLA was having a difficult time surviving and they decided to become a charter. In retrospect, Larry says that was a mistake because on the whole, charters are damaging the public education system. Whether they are good or bad, “charters harm public education.”

It was a wonderful lunch at a second floor corner table overlooking the Pacific Ocean. The drive from La Jolla along old highway 101 to the Ki restaurant in Cardiff by the Sea is among the most breathtakingly beautiful drives in America. The restaurant Larry chose had a wide variety of; wraps, smoothies, tofu dishes and teas. The staff knew Larry by name. I had the cheeseburger.

- Green, Elizabeth.
__Building A+ Better Teacher__, W.W. Norton & Company New York and London, ©2014 by Elizabeth Green – page 102 - Ibid. page 105

“…the elementary school teachers did not have the training to do it.”

This a real problem, and it is also true of many teachers up to grade 8 at least.

One has to find some fault with the teacher training, as even if BA’s in math take up teaching in elementary school their grasp of the relationships between math and reality is frequently poor.

I have done numerous posts on basic ideas, but I fell that readers do not always get the point.

This one went down fairly well:

https://howardat58.wordpress.com/2015/02/03/commutative-distributive-illustrative-ly/

ps. The gravatar is me as Dr. Coppelius