The American Institute for the Improvement of
MAthematics LEarning and Instruction

The MALEI Mission: Through mathematics, to provide scientific leadership for the progressive improvement of instructional and learning practices, with emphasis on the personal educational health of the individual.

Generating scientific knowledge:
The Institute pursues its mission through two avenues, as follows. One is to create and disseminate scientific knowledge about personal mathematical health, and about how the quality and effectiveness of learning and instruction in mathematics can be improved in that regard. Personal educational health is all about how the individual learner's functional personal intelligence compares with immediate and imminent needs for it. The presently germinating science of mathematics instructology ... rooted in several, well established, associated sciences ... stujdies how the processes of instruction guide development of the learners' functional mathematical intelligence. The Institute's pursuits in that area focus on the healthy instructional guidance of healthy mathematical learning. After substantial advances are achieved in the arena of mathematical learning, similar progress surely will be made in many diverse areas of human learning.

Cultivating a scientific community:
The second avenue is through catalyzing the advent of that science ... by promoting and facilitating similar pursuits by other scientists. The Institute's own scientific achievements can set a pace. But inspiring other scientists to engage in similar pursuits requires: (1) providing them with an initial system of research tools that will enable them to contribute to scientific progress in the area of personal mathematical health; (2) providing them with an ongoing demonstration that, and how, scientific R&D in that area can visibly be of great educational benefit for very large populations; and (3) ensuring that they have the occassions and mechanisms for effectively communicating with each other in this particular context. At this time, MALEI's roles in facitilating professional communications are limited to providing website services, and hosting small forums in connection with regional or natrional professional conventions.

Investigations of Mathematics-Learning Distress (MLD):
The Institute's special focus on personal mathematical health stems from the nation's educational dilemma. The quality and effectiveness of American education

In the field of mathematics instructology, as with any other area of human psychology, scientific progress happens most readilythrough researching the causes, preventions, and remedies of specific diseases. The Institute's focus on personal mathematical health is motivated by the nationwide epidemic of Mathematics-Learning Distress (MLD: dismay, frustration, alienation, anxiety, fear, depression, phobia, suppression, etc.). Learning is a mental process, and as a learning-inhibitor and conststraint on mental self-management, tne MLD syndrome is a special aspect of poor mental health.

Childhood victims of strong MLD normally continue to be math-suppressed throughout adult life, commonly suffering adverse effects of the affliction. The present estimate is that more than half of all working-age Americans would immediately become "math distressed" if suddenly compelled to learn mathematics beyond what they already studied. Half of American college entrants suffer that plight.

Classical instructological research ... about instructional practices with classes of students ... cannot determine the causes, remedies, cujres or preventatives for MLD. Although MLD often can be reduced by various kinds of clinical attitude-counseling, it can be prevented, minimized, or cured only through healthy math-instructive experiences. Scientific research about MLD thus sheds much light onto the relative healthi-ness of

The MLD sydrome results from unhealthy childhood experiences with unhealthy scholastic curricular instructruction in mathematics. But throuhgout adult life, its adverse residual effects can contiunue to undermine personal well-being. .

Just why so many humans have so much trouble with curricular mathematics ... and how such maladies can be prevented, overcome, or cured ... cannot be determined through

For an ongoing demonstration, the Institute's MALEI Mathematical Learning Clinic is focusing its scientific R&D activities toward nurturing a video-based program of alternative community education in basic-literacy mathematics. MALEI's research tool will be shared primarily through its websites.

Scholastic educators presently make instructional decisions about who should learn what, and how, with essentially no scientific guidance about what kinds of curricular experiences are healthy for the students, themselves. The science of psychomathematics (emerging since the 1950's) can disclose much about what is healthy for learners to know (or not), in what circumstances ... and much about healthy ways of learning it.The more inclusive science of mathematics instructology likewise discloses much about healthy and unhealthy practices of mathematics instruction. As yet, neither of those sciences has become strong enough to substantially impact scholastic practices.

The MALEI Clinic's mathematics instructional service program specializes in the prevention, detection, reduction, and prevention of MLD. For such purposes, the Clinic heavily relies on eductive modes of instruction ... which also is how competent clinical psychotherapy works. Learners' responses to eductive instruction also provide scientifically reliable case-study data peratining to educational practices in mathematics.

Many of MALEI's scientific advances in health-oriented mathematics instructology stem from case-studies of clinical proceedings with client victims of MLD. However, no science can stop with the collection of data. The function of any science is to

THEORIZE!

. Nothing could more catalytic than an ongoing demonstration that, and of how, science can greatly help to alleviate the nation's educational dilemma with mathematics. Such a demonstration must be a highly visible program of education in mathematics, one that clearly provides some kinds of solutions for some educational problems which the nation regards as serious. Although the MALEI Mission is not one of providing educational services for the public, illustrative demonstration educational programs must be the primary catalyst for accelerating nationwide advent of the science.

Learning is a psychological process of mental growth by continually structuring information, within. It is a natural part of living. Without doing it, no human can long survive. It might or might not modify the learner's external actions or behaviors. It might or might not be in response to others' wishes for the learner to acquire that information. Although man has made important beginnings in the scientific psychology of human learning, it has yet to contribute much toward improving educational practices. MALEI's role it to help bridge that gap.

In mathematics, classical educational research has strongly focused on how well school students perform tasks that are taught by teachers. But in the last few decades, increasing attention has been given to "cognition" and "conceptual understanding". The growing field of psychomathematics now is congealing around the scientific psychology of personal mathematical comprehension. As yet, very few mathematics educators have been exposed to that science. That is part of the gap that MALEI strives to bridge.

Any science of instruction must be based on an underlying science of learning ... but also must reach far above that base. Instructology is the field that studies how instruction works. Its philosophic beginnings date back centuries. It is a major area of concern and activity among education professors. But even the field of mathematics instructology presently does not function from a scientific foundation. As a result, mathematics teachers, curriculum developers, and teacher-educators cannot yet be educated with a scientifically reliable theory of mathematics instruction. That is another part of the gap that MALEI strives to bridge.

As applied in practice, the science necessarily is about learning and instruction in whatever mathematics the learner "should" own. Curricular mathematics educators continue to quarrel over divergent opinions about the whats and hows of scholastic education in mathematics. The net effect has been that the American core-curriculum has produced an adult population almost half of whom do not have mathematical literacy at the age-12 level ... and the majority of whom are fearful of mathematics. Childhood encounters with American "school math" commonly are so negative that the scholastic curriculum actually undermines personal mental health of many millions of adults. The prevailing curriculum is woefully unhealthy for most students ... which explains MALEI's focus on personal educational health.

The science of mathematics instructology cannot accommodate curricular disputes that lead to widespread tragedy. But it can emerge through accepting "the medical perspective" ... which focuses on the well being of individual persons. Learning is a very personal psychological process; functional personal intelligence is a very personal psychological state; and personal educational health is a special aspect of personal mental health. The arena of personal mathematical health is wide open to scientific research and development ... and is a realistic and viable context for advancing the science of mathematics instructology.

The practices of medical and mental health care are arts that are grounded to scientific foundations. The instructional guidance of learning likewise is an art, and it dates back to the beginnings of mankind. It might or might not be done for projecting , into the learner, some information that already is held by the instructor. It might or might not be done through the encoding/decoding processes of linguistic communications.

However, the function of instruction always is to affect the learner's information processing structures. The instructor targets some information which the instructor intends for the learner to acquire, and strives to navigate the learner's growth, so that it acquires that information. That information might or might not already be held by the instructor. either way, instruction always is a learning-management endeavor. The science of learning-guidance lies within the operations-research arena of the managerial sciences ... which is one reason why educators have been unable to find it.

Moreover, intentional instruction invariably relies on the instructor's presumptions about how learning happens. The instructor might or might not actually consider how learning does or might happen within the learner. But if the effectiveness or healthiness of instruction is of serious interest, instruction must be done within the context of anticipation of how the learner might respond. In that way, instruction necessarily is its own kind of applied psychology, invoked for the purpose of learning-management.

Every bona fide science has two essential components ... scientific theories about whatever is being attended, and empirical investigations that motivate and corroborate the evolution of those theories. The MALEI theory of mathematics instructology invokes a mathematical (STAGML) model of learning-management ... the State-Transition Analysis and Guidance of Mathematical Learning. In keeping with a health-oriented perspective, MALEI's empirical medium is its mathematical learning clinic. As in the fields of medical and mental health, clinical R&D proceeds through clinical casework with individual patients ... mostly patients who arrive with moderate-to-severe afflictions. The casework prompts advancement of the STAGML theory, and also corroborates the theory.

Early results from the MALEI Clinic revealed that the conditions popularly known as "math anxiety" and "math fear" and "math blues" and "math phobia" are but various phases of a single syndrome. MALEI calls it Mathematics-Learning Distress (MLD) because it is contracted only during studenthood ... although its adverse effects on adult life often are lifelong and quite severe. The distress, itself, is not truly with the mathematics, but with students' difficulties in trying to learn the math from how it is presented by the American scholastic curriculum. When the same topics are presented in more natural ways, the distress is prevented or overcome.

The primary cause of MLD is that the prevailing mathematics curricula make far too little common sense to the students, themselves. For, when victims of even very strong MLD are led to reason their own way through their troublesome topics, MLD is greatly reduced or even cured. It means that MLD is a curricular learning disease. Since most students become mild-to-severe victims of MLD before ending their curricular education, it is certain that the curriculum, itself, is quite unhealthy.

One important function of health-oriented scientific mathematics instructology is to surface the ills of America's low-sensibility curriculum, and to demonstrate how it can be upgraded. For such purposes, MALEI commissioned a special (MACS) Project for the Teaching and Learning of Mathematics As Common Sense (to the learners, themselves). The charge to that Project is to investigate how humans most naturally learn the major topics of core-curricular mathematics, why they don't, and what kind of demonstration educational programs (and related activities) can most effectively catalyze healthy changes in curricular mathematics instruction.

The MACS Project immediately took over operations of the MALEI Clinic, locally conducted some exploratory educational programs, and opened liaison with several national professional associations. One of the Clinic's major scientific findings was that a major cause of MLD is that the mathematics curriculum is wrought with mathematical weaknesses that greatly reduce its comprehensibility to students. As a result, MALEI is developing a mathematical "Encyclopedia" for nationwide professional use in repairing and strengthening the mathematical skeleton of the national curriculum.

A second clinical finding was that another major cause of MLD is the unnatural structure of most curricular instructional programs. From Grade 3 onward, students are routinely placed into math courses for which they are under-prepared ... and expected to keep pace with that course's learning schedule ... and "graded" according to how well they can and cannot do so. The MACS Project is developing and demonstrating alternative modes for student's progress ... and modes for supplementing courses, so that students are better able to keep pace.

A third finding was that mathematics is "commonsensible" to humans, only to the extent that they can internally construct the concepts and conclusions ... whether or not instructionally guided to do so. Those elements are internally organized into personal mathematical "theories." Such is the mathematical, natural, and healthy way of learning mathematics. Mankind's mathematical comprehension of anything consist of mathematical theories ... all of which began as very personal mathematical theories. All humans are born theorists, and much of their learning is done by theorizing. The current version of the American curriculum is not mathematically comprehensible to students who do not already know the material. So, students are forced to use non-sensible, irrational, non-mathematical ways to try to learn school mathematics. That is a direct route into the canyon of MLD.

Functional personal mathematical intelligence internally consists of personal mathematical theories ... and powers for learning by theorizing. The MACS Project is all about enabling and guiding humans to learn mathematics ... sensibly, rationally, naturally, and easily, by personally theorizing. The Project sometime is also called The Project for the Theoristic Learning of Mathematics. Its first step is clean up the mathematical foundations of the core-curriculum ... thus making it possible to make the curriculum mathematically commonsensible. Its next step is to activate a highly visible, Tulsa-area educational program that demonstrates the benefits and methods of making school-level mathematics fully commonsensible for all.

The STAGML theory is about the progressive development of the learner's functional personal mathematical intelligence ... and the instructional guidance, thereof. It is an adaptation of operations-research models to the psychological context of personal development in the mathematical arts. Its pertinence to the fields of personal mathematical health lies in the fact that the healthy, natural, easy way to learn mathematics is to learn it, mathematically.

The MALEI Institute is chartered in Oklahoma as a 501(c)(3) not-for-profit organization for conducting scientific educational research and providing educational services. Its headquarters has been in Tulsa, Oklahoma, since 1997. Due to the nature of its funding, MALEI has not been required to obtain an IRS certification number. Plans for alternative modes of funding call for IRS certification during 2012.

The original MALEI Institute was created in Hawaii, in 1980 ... where the native word, "male'i" literally means "toward enlightenment", and where the ancient Hawaiian goddess, Malei, watched over schools of parrot fish. Both contexts are suggestive of the Institute's orientation toward scientific educational research and service. Soon after publication of A Nation at Risk, MALEI operations were transported to Tulsa ... where the Institute was reincorporated in 1997.

Until 2012, there was no American precedent for the Institute's direct use of scientific clinical methods for purposes of accelerating national educational progress. Extensive explorations were needed for identifying the most viable means of doing so. In 2010, the Institute completed its thirteen year exploratory phase of operations, and began a three-year activation phase for becoming fully operational in 2014. Its present concentration is on applying clinical methods for purposes of generating non-curricular, alternative education programs for assisting math-fearing, math-illiterate adults to achieve basic-literacy levels of personal mathematical health. top

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