• Kindergarten and first graders mastering the lower/higher addition/subtraction facts and reading numbers in the hundreds of trillions (fifteen-digit numbers).
• Second graders mastering all multiplication facts and long division.
• Fifth graders mastering “seventh grade math.”
• Fifth and sixth grade classes in the most disadvantaged communities outperforming ninth graders on statewide algebra exams.
• We have consistently delivered HUGE GAINS in math scores.

OUR PHILOSOPHY
Copyright © Professor B Enterprises, Inc., 1999

What was your experience in elementary and middle school mathematics? Did you experience it as connected and flowing like a story, or as disconnected and fragmented? Throughout my thirty years of national and international staff development presentations, the vast majority (by far) of my audiences concur regarding the utterly frustrating disconnection and fragmentation of the content they experienced in what was referred to as “mathematics.” Was it mathematics?

Well, mathematics is the academic area that studies structures for their own sake, and to build a structure, whether it be physical (like a building) or mental (like a story you know) you must connect the pieces (fragments) in a specific way. In fact, when you tell a story you heard a long time ago, you become aware that you are mentally building its structure, from “scratch,” if you are alert enough to perceive that the connections keep “popping up” as you go. At no point do you see the whole story ahead of you. If they did not pop up, you would not be able to verbalize the flow (the structure) of the story. Clearly, we recall stories by means of reconstruction of connections, not memorization. Our methodology permits learners to retain mathematics in the same way. Now do you see the contradiction? The disconnection and fragmentation of content you experienced in elementary to middle school and beyond was, in fact (by definition), the very opposite of math.

The prefix “anti” has such meanings as “against”, “the opposite of”, “preventing” or “counteracting”. So in order to eliminate the confusion caused by giving the same name to something and its opposite, I hope the time has finally arrived to accurately rename that disconnected, fragmented content as “anti-math.” Anti-math deactivates learners’ natural gift for perceiving and receiving the structures within mathematics, the very academic area that studies structures (by placing large intervals of time between connected math concepts and skills). It is an absolute nuisance to mathematics education. So what was it that you “hated” or were not “good at”? It was not math; it was anti-math!

If two people tell the same story, their words are different (and also different from the original version) but the events are the same and are recalled in the same sequence. Hence there is no intentional and laborious memorization of words, as in the learning of a poem. What children effortlessly (naturally) perceive, receive and retain from a story, therefore, is the structured connection and flow of its events: its internal contextual dynamics of relationships. If I say the words “woods”, “wolf”, “grandma”, they are likely to immediately reactivate, after all these years, a structured dynamics of relationships entitled “Little Red Riding Hood”. This is the genius in virtually all children for learning mathematics. Our methodology activates this universal genius for mastery learning of math by ensuring that children experience it the same way they experience stories: as connected and flowing. Similar to their experiences with stories, children will then learn and retain math without memorization or remediation: two of the major pillars of conventional mathematics education. Professor B methodology will enable this nation to produce home-grown brains, rather than import them. This is an urgent necessity in these perilous times.

In numerous instances, contemporary math education, in spite of claims to the contrary (“we adhere to NCTM standards”), provides no alternative to children, during their impressionable years, besides memorization of facts and “steps” for getting answers. It presents a curriculum that fails to deliver an enormous number of arithmetical connections. This unnatural way of forcing children to function in a desperate and futile attempt to “learn” mathematics is precisely the training necessary for transforming the vast majority of children into non-thinkers and, consequently, poor problem solvers (see the article on our website entitled, “Memorization Is a Nuisance to Elementary Mathematics Education”). If the “honor students” they produce can only do the mechanical “steps” to get the answers, but are not exposed to the reasons why they work, then the honor status is an illusion. Where is the mathematics? It’s in the structured meanings and understandings that are bypassed by steps (for getting answers). Conditioned by these mechanical procedures, these students will “pay the piper” when faced with high school or college mathematics which challenges them to structure meanings and understandings. A few recover; the vast majority falters.

IMPLICATIONS FOR MATHEMATICS EDUCATION
Copyright © Professor B Enterprises, Inc., 1999

The rapid assimilation of a story by young children is not merely an example of “accelerated learning”; it is the result of a natural, even unintentional, activation of a gift to all of humanity. Children can similarly experience a natural assimilation of mathematics providing parents’ and teachers’ verbalizations permit them to perceive its structures.

We are not proponents of “accelerated math.” This phrase usually implies that youngsters are being forced to learn mathematics at a pace beyond their abilities. However, we are proponents of activating children’s natural ways of learning math. When this is done, they cannot avoid learning faster. Is this accelerated learning? No, it is natural learning! In spite of the fact that many college students struggle through four semesters of a foreign language without learning to speak it, no one regards three year old children as accelerated learners when they converse in a language that was foreign to them at birth. Disputes regarding accelerated learning justifiably arise in the context of forcing children to learn math unnaturally. The issue does not (or should not) arise in the context of enabling them to learn math naturally, even if second graders are learning “third grade math.”

We have made reference to kindergarteners learning to read fifteen-digit numbers, second graders mastering long division and fifth to sixth graders outperforming ninth graders on state-wide algebra exams. If you look at our strategies for teaching the reading of large numbers to young learners (visit our website at www.profb.com), you may be convinced that the tradition of starting with one-digit numbers in first grade and gradually getting up to seven-digit numbers in fifth grade actually prevents children from perceiving the structure of our number system. The fact that kindergarteners only need fifteen minutes to learn to read any fifteen-digit number is the most significant testimony that our strategies permit them to learn it naturally. The traditional “bring down” approach is such an unnatural way of doing long division that the majority of sixth graders in this nation cannot do it; all that learners can do to survive it is to desperately memorize “the steps”; even those college educated adults in this nation who can do it are not able to explain the steps; and the vast majority of us who can do it took a rather long time to finally “get it.” Look at our strategy on our website and, although you may not have understood long division throughout your entire life, you will understand it (and be able to explain it) in a few minutes. That you can understand in ten minutes what you may not have understood for your entire life is strong testimony regarding the natural learning that our long division strategy permits. This is how second graders learn long division without stress.

There are those who claim that boys are better at math than girls. We agree that under those circumstances where youngsters are forced to learn unnaturally and boys are carefully and deliberately socialized toward academic success, boys will be “better.” But the same sources, that claim superiority for boys in math, inform us that girls have superior verbal intelligence. Who, then, will have the advantage for learning math when teachers’ verbalizations consistently permit youngsters to learn naturally?

PROFESSOR B IMPLICATIONS FOR “DO OR DIE” TESTING: NO CHILD WILL BE LEFT BEHIND
Copyright © Professor B Enterprises, Inc., 1999

We contend that a major reason for this nation’s mediocrity in mathematics education is the training of elementary school teachers, by our teacher-training institutions and math programs, to engage and condition the unnatural learner in their students. Unnatural learners are those who memorize to retain mathematical information: the addition, subtraction, multiplication, division facts and the “steps” for all the arithmetical processes and algorithms involving whole numbers, fractions, decimals and percents. Even when they get correct answers, they cannot explain reasons for any of the steps. They are conditioned to attempting the recall of virtually all mathematical information through memory.

On the other hand, our math program enables teachers to nurture and engage the natural learner in children. Natural learners retain mathematical information in the same way they retain the content of a story: they perceive and recall structures (the connection and flow within content). Traditional verbalizations of math content PREVENT learners’ perception of structure in mathematics.

The untruthful or meaningless statements of a false witness may totally deactivate a detective’s gift for perceiving connections among clues in order to solve a crime. Such statements can confuse our minds when we are trying to make sense of some information or solve a problem. Our gift may permit us to perceive some connections, but untruths or meaningless statements can cause a great deal of mental discombobulation that prevents us from achieving the satisfaction of a solution. We are all familiar with this mental sensation. We call it confusion. This is the mental sensation we experience when our gift for perceiving structure has been deactivated.

It will not require “rocket science” to reveal the fact that the traditional verbalization of virtually every arithmetical process and algorithm involving whole numbers, fractions, decimals and percents consist entirely of either untruthful or meaningless statements! If this is true, then the reason why the vast majority of learners are poor math students, in spite of their natural gift for learning mathematics, is now palpably clear!

Professor B mathematical verbalizations are all truthful and meaningful and, like the verbalization of a story, they permit learners’ instant perception of structures (the connection and flow within mathematical content), thereby activating children’s universal gift for learning mathematics. Hence, the learning of mathematics becomes as inevitable as the learning of a story.

Children’s learning of stories is certainly an example of “accelerated learning”. Their perception of structure is the basis for their acceleration in the learning of stories and mathematics. When structure is perceived in mathematics, it is virtually impossible to avoid accelerated learning. Hence, the natural learner is awesomely accelerated in comparison to the unnatural learner.

Another source of acceleration in mathematics education is the cumulative experience over a number of years, as natural learners are consistently permitted to experience connection and flow, and they continue to link new structures to those that have been previously mastered. Teachers who engage natural learners in mathematics have no concern about completing grade level curricula, because the acceleration enables them to teach content that is traditionally offered one or two years beyond grade level. Acceleration is also enhanced by the virtual elimination of remediation, when math content is naturally retained in the same way that perception of structures ensures children’s effortless retention of stories. Teachers will have an enormous amount of time for honing their students’ critical thinking skills by having them solve an enormous number of problems.

In spite of stringent accountability requirements enforced by “high-stakes” testing and other strategies like reductions in their class size, incentives for superintendents, principals and teachers, and so on, traditional staff development programs for mathematics can only barely and inconsistently yield “significant gains.” Certainly by now, after all these decades of massive fear and failure in math education (despite wave after wave of “reform”) the truth should finally be dawning on us: no matter how much we tweak or flog that dead horse (traditional mathematics staff development programs for teachers), it is totally incapable of delivering huge gains in math scores because its methodology deactivates rather than activates children’s universal gift for mastering mathematics.

Our data, our precedents and our philosophy substantiate our claim that we can lift the math scores in any school system from among the worst to among the first in two to three years. Allow us to state, in no uncertain terms, that we will deliver the highest levels of performance on the “do-or-die” exams without focusing on the tests themselves.

Finally, please be assured that, as staff developers, we do not require you to discontinue the use of your textbook adoption. Throughout our twenty-five years of staff development experience, we have supplemented and complemented almost all of the various textbook programs.

  Copyright © Professor B Enterprises, Inc., 2000