More Saxonisms from 1982-1996, Author’s Notes, Media Excerpts
On teaching methods: “Educators cannot teach students to reason; they can hope only to provide students with the skills to reason. Prevailing math teaching methods fail to do that.”
“Beautiful explanations do not lead to understanding.”
On measuring success in math education: “Three measurable and understood criteria: 1) higher percentages of students enrolling in advanced mathematics and science classes; 2) lower percentages enrolling in watered-down mathematics; 3) high percentage passing college board exams.”
On teaching “creativity”: “I do not believe that challenge [word] problems stimulate thinking in other than the most gifted… I believe that overemphasis on challenge problems is one of the primary reasons that so many students avoid math. They have been challenged beyond their ability to cope and this makes them angry.
“Creativity can be discouraged or encouraged, but “creativity” cannot be taught.
“Creativity can be…enabled by giving a firm foundation on which students can stand as they reach for higher concepts, and by teaching productive thought patterns and devising practice problems that permit the student to review fundamental concepts from new perspectives…”
On teaching problem solving: “[This] is a process of concept recognition and concept application. Problem solving is therefore the application of previously learned concepts. The ‘art’ of problem solving cannot be taught. You grasp an abstraction almost by osmosis through long-term exposure. You can’t put your hand on it. That’s the reason we call it an abstraction.”
On teaching “critical thinking”: “The use of productive thought patterns can be taught, but the act of ‘critical thinking’ cannot be taught.”
(Author’s note: The following articles were published after Saxon’s death. They show he was correct about the push for “critical thinking” too early.)
Critical thinking takes place in the prefrontal cortex of the brain. That part of the frontal lobe begins to develop around the time a child is in middle school. The end of that brain development is about age 25. See Peter Lorain, “Brain Development in Young Adolescents, Good News for Middle School Teachers,” National Education Association, http://www.nea.org/tools/16653.htm. “Adolescents are moving from concrete to abstract thinking and to the beginnings of metacognition (the active monitoring and regulation of thinking processes). They are developing skills in deductive reasoning, problem solving, and generalizing …This period of brain growth marks the beginning of a person’s ability to do problem solving, think critically, plan, and control impulses.” Also see Margaret Semrud-Clikeman, University of Minnesota Medical School, “Research in Brain Function and Learning, The importance of matching instruction to a child’s maturity level.” American Psychological Association, 2016. “Instruction that is above or below the maturity level of a child’s brain is not only inappropriate, it can also lead to behavior problems in your classroom. Inappropriate behaviors — such as avoidance, challenging authority and aggression towards other students — can be explained by a failure to match instruction to the brain maturity of your students.” Then see Gwen Dewar, Parenting Science.com, “Teaching critical thinking: An evidence-based guide,” October 2012. “Perhaps the most effective way to foster critical thinking skills is to teach those skills. Explicitly. (Abrami et al 2008). “Studies suggest that students become remarkably better problem-solvers when we teach them to • analyze analogies • create categories and classify items appropriately • identify relevant information • construct and recognize valid deductive arguments • test hypotheses • recognize common reasoning fallacies • distinguish between evidence and interpretations of evidence.)
On proof of results: “Mathematics is an arena of proof, but mathematics education seems to be an arena of well-intentioned but totally unproven guesses. The guesses are implemented and will be forced into American schools, not because they work, but because they were…recommended by a committee whose credentials are supposedly impeccable. There is an advantage to this method, for there is no one to blame if the guesses lead to disaster. There seems to be a tacit understanding that we are all in this together and that there will be no pointing fingers if it doesn’t work.”
On the (NCTM) not proving its “visions” and “premises” (1989): “It is difficult to find words to describe my outrage at a document which proposes that we implement a totally radical and untested change in math pedagogy whose implementation document admits it is a pig in a poke and more pie in the sky. Americans may be naïve, but they would have to be stark raving crazy to let their schools implement this untested and poorly conceived change in direction in math education…I believe that proven results are more important than their premises and visions.”
On ideology: “To be dogmatic is one thing, but to be so wrong that it prevents others from trying to end the disaster is totally inexcusable.”
On the need for practice: “There’s nothing wrong with students or teachers. If students get enough practice, they can learn… Don Shula and Vince Lombardi insist that [football] players practice the fundamentals because they must be total masters of those fundamental skills. But the present math books are unsure what the fundamental skills are.”
On fads: “By asking math teachers of America to adopt the new list of fads (supported by NCTM and today’s progressives) without testing them, you will cause the gap between the advantaged and disadvantaged to widen…inner city schools are so bad they will do anything that you say so they can protect their rear ends.”
On focusing on concepts: “The ‘new mathers’ [1960’s] decided that just being able to work the problem did not suffice if the student did not ‘understand’ it first. So, the emphasis was shifted totally to understanding and ‘doing’ was ridiculed. It was acceptable for a student not to be able to work a problem if he understood the concept. When the scores began to decline and students began to bail out of math, it was dismaying to hear experts say that the teachers were to blame, or the students were to blame, or society was to blame. No one was saying that possibly the experts had made a mistake in recommending the decreed changes, or that the big book companies were unable to implement those changes effectively in their textbooks.”
On leadership failure: “Math educators have a fifty-year track record of abject failure in trying to produce effective math programs. Why should we believe or even consider the possibility that they [NCTM 1989 national standards] might succeed this time? Why should we subject the entire nation to another grand experiment [after the 1960’s “new math” failure and think Common Core now] when successful alternatives already exist? How many more generations of students are considered expendable as we search for effective ways to enable them to master mathematics?”
On speaking out: “I know I don’t make headway by speaking out this way, but I am determined to change this system of math education. Our math experts aren’t really experts; they have abdicated all claim to control by their behavior of the last 20 years.”
On his work: “I believe I’ll be proven right by 2015 or 2020.”
Sample press commentaries: Notice the dates of publication; think about today’s issues…
J’aime Adams, “How the Ol’ Boy Network Hurts Our Children—Why do bureaucrats denounce John Saxon for getting the results we all want?” Human Events, 1988. “…a canard is heard occasionally from Saxon opponents which, stripped of its pretty euphemisms and put crudely, is that Saxon is good for poor, dumb kids who need a lot of repetition, but not for smart, rich kids who don’t need to practice…The fact is there is a great deal of data showing that smart rich kids are running away from math and scientific careers right along with the poor…
“The general feeling among math educators who don’t like Saxon is that his books give only short retention gains in test-taking ability, but that he doesn’t give the students any overall understanding of broad concepts. There is no way to determine a student’s understanding of concepts without tests, and the simpler souls amongst us might be tempted to think that the student who makes a high score on his calculus exam just possibly may be further along the road of conceptual understanding than the kid who flunked.” (page 149)
Chester E. Finn, Jr., “Math Angles and Saxon,” National Review, 25 Nov 1988. “If Saxon is right, then a lot of people with fat reputations in the field must be wrong. Education barons don’t like to be wrong. They like even less to be told they are wrong. So long as state and local educators can be dissuaded from buying more of Saxon’s books, he can be shunned. After all, what really matters isn’t whether youngsters learn math. It’s whether the profession gains in stature and public acclaim in consequence of its efforts, however ill-conceived, to address the problems it may fairly be said to have created—all the while retaining control of the processes of diagnosis and solution. Isn’t that what an establishment is all about?” (page 152)
Chester E. Finn, Jr., “What if those [1989 NCTM] math standards are wrong?” Education Week, 20 Jan 1993. “Seldom has so profound a change in conventional wisdom and standard practice had such homage paid to it, so little resistance shown to its onrush, so few doubts raised about its underpinnings …Gov. Roy Romer of Colorado and U.S. Secretary of Education Lamar Alexander praise the standards repeatedly…We better hope the NCTM has got it right. If not, American education’s lemming-like rush to follow its lead could find us hurtling off a precipice… What happens to millions of children who receive prepackaged programs and their teachers are ‘told’ the ‘approved’ way to proceed?
“So long as many teachers are dependent in this way, it’s vital to ask of any new approach being thrust upon the education world whether it has been fully tested with students to ensure that it yields the desired results—and is not just being promoted because it appeals to grownups caught up in ideological battles. (page 112)
The Atlanta Journal/The Atlanta Constitution, quoting from Executive Editor Magazine, “Learning by heart is embraced anew,” 1 Nov 1992. “…a heretical yearning for ‘learning by heart’ was creeping across the land…relying on old-fashioned memorization and repetition. These efforts are initiated by teachers and meant to help students apply their learning of the real world. Proponents [Saxon supporters] don’t see this as a retreat into the past, but a post-modern appropriating of traditions for their effectiveness in the present.” (page 144)