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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.

This MALEI site is continually under development
Your suggestions and inquiries are welcomed.
Send e-mail to office@malei.org Subject: MALEI site .

The MALEI Institute is an Oklahoma chartered, Tulsa-based, not-for-profit 501(c)(3) organization, so functioning in the areas of scientific research in support of the nation's educational efforts. Its annual reports to the IRS presently are provided through form 990-N.

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The Institute's work of bringing science to bear on improving American educational practices in mathematics is supported through contributions from the general public, from its individuals and families, and from its communities and organizations concerned with the nation's struggle to adequately educate its members.

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The institute's scientific leadership is of the kind often expected of university academic departments:

  • advancing scientific knowledge;
  • disseminating scientific knowledge to appropriate academic and public communities;
  • demonstrating the scientific and practical public benefits of so advancing and disseminating scientific knowledge;
  • promoting and facilitating the engagement of other scientists and organizations in such scientific activities.

The Institute is unique with regard for its scientific mode of contributing to the progressive improvement of educational practices:

  • Focus on Mathematics: MALEI focuses on practices pertaining to learning and instruction exclusively in mathematics. [Click here to access the rationale for that choice.]

  • Professional Mathematics: MALEI invokes a professional meaning of the term, "mathematics." It refers to specialized arts and products of learning through critical personal reasoning about precisely described entities. That is how mankind advances its mathematical knowledge. The kind of mathematics on which MALEI focuses is not a consensus of how professionals view mathematics. Rather, it describes what mathematicians actually do, and how it is done ... even by preschoolers and lay persons. Thus, MALEI focuses on the kind of "mathematics" on which science, industry, the workplace, and family-life relies (often unknowingly so) ... which is not the same meaning that the public popularly gleans from scholastic curricular instruction under the same title. Within the settings of educational practices, the distinction between professional and popular meanings of "mathematics" manifests as the difference between the mathematical learning of mathematical information, and the non-mathematical learning of part of the same information.[Click here to access a comparison and contrast between popular and professional perceptions of mathematics .].

  • Mathematical Intelligence: MALEI attends learning and instruction with regard for how their processes affect the development of functional personal intelligence, rather than focusing on the acquisition, storage, retrieval, of data and data-processing routines. [Click here to access an abbreviated description of functional personal mathematical intelligence and its internal development within the human mind].

  • Mathematical Health: MALEI proceeds through humanitarian concerns about the states and development of the individual learner's own functional personal mathematical intelligence, rather than through socioeconomic concerns or curricular dogmas. The Institute's context for its investigations into whatever mathematics the individual should know (and whatever is better avoided) is the individual's readiness to effectively deal with immediate and imminent demands and opportunities as presented by the learner's present and projected situations ... what MALEI calls "personal educational health in mathematics." [Click here to access a short orientation to personal mathematical health ].

  • Educational Practices: MALEI's attends educational practices with regard for the healthiness and unhealthiness of their effects on the learner. That distinction manifests in the ("barometric") degree to which those practices contribute to the escalation of MLD (Mathematics-Learning Distress) within the learner, or contribute toward the prevention or reduction of MLD. [Click here to access an overview of MLD: math anxiety, fear, depression, phobia, etc.].

  • Clinical Research: MALEI researches the healthiness of mathematics educational practices through its clinical case-studies. MLD escalates when learners cannot adequately make mathematical "common sense" of things they are being required to learn. So, the MALEI Mathematical Learning Clinic is conducted within the broader framework of the Institute's, (MACS) Project for Teaching and Learning Mathematics As Common Sense (to the learners, themselves). That title allows the public to perceive the essence of the Project's mission. The Project's more definitive academic title directly discloses how "common sense" and personal mathematical comprehension depend on the mathematical learning of mathematics. [Click here to access an overview of The MALEI Clinic or of its MACS Project .]

  • Mathematical Comprehension: MALEI regards the learning of mathematics as being a psychological evolution of the individual learner. Over time, the learner's functional mathematical intelligence transits from its earlier achieved developmental states, to its later developmental states. The state-transition of its evolving mathematical intelligence is the crux of the recently evolving scientific psychology of personal mathematical comprehension. It perceives personal mathematical intelligence as being the ownership, use, and developmental processes of (what amounts to) personal mathematical "theories" about all kinds of things, in varying degrees of refinement and consciousness.[Click here to access an overview of theoristic mathematical comprehension.]

  • Mathematical-Learning Lattice: MALEI invokes a dual model of the mathematical learner's state-transition. The learner's instantaneous internal state of mathematical intelligence is a highly structured "body" of knowledge and processes, and it continually changes its contents and shapes. But on the lattice of all possible developmental states of such intelligence, each state also is a single "point" During the learner's state-transition evolution, that "point" moves along the learning-lattice. It traces out a path-of-progress much like how a nautical, aerial, or space vessel continually changes its position. [Click here to access an overview of the mathematical-learning lattice.]

  • Mathematical-Learning Space: MALEI uses "theoristic" images of the mathematical learner, with regard for whatever personal mathematical theories that learner owns and is progressively developing. The nature of that technology calls for mathematical research to determine just what mathematical theories are accessible for the learner to achieve. Those accessible theories constitute the "territory" over which the learner can grow. Of special importance for mathematical health are the mathematical theories that enable the learner to mathematically comprehend the topics attended by the core-curriculum in mathematics. Those are where malcomprehension escalates MLD. [Click here to access an overview of the mathematical foundations of core-curricular mathematics.]

  • Mathematical Knowledge for Teachers' Education (MKTE): MALEI's mathematical research discloses that, in order for students to mathematically comprehend the topics that are normally attended by the core-curriculum in mathematics, they are mathematically required to own and intuitively invoke very many mathematical "points" that are not commonly aired by the present curriculum. Curricular omission of those cognitive prerequisites reduces the healthiness of curricular studies. Also missing are many supplementary, non-prerequisite math-points whose ownership by students greatly facilitates their mathematical learning of the usual curricular topics. All curricular teachers of mathematics need access to the mathematical foundations of core-curricular mathematics. [Click here to view an orientation to MKTE.]

  • Mathematical Instructology: MALEI's clinical research is the empirical aspect of its scientific research into the instructional guidance of learning. [Historically, instructology (the study of instruction) has been very non-scientific. MALEI's own theory of mathematics instructology is not only scientific. It even is grounded to a mathematical model of how instruction guides mathematical learning.] As the mathematical learner transits along its mathematical-learning lattice, the instructor strives to navigate the state-transition progress path so that it will approach some instructor-acceptable goal-state. In the process, the critically minded instructor necessarily engages is the (STAGML) State-Transition Analysis and Guidance of Mathematical Learning. MALEI's scientific version of STAGML is a learning-management adaptation of numerous elements from the managerial sciences of operations research. [Click here to view an orientation to STAGML methods .]


     > Director: Prof. Clyde Greeno; greeno@malei.org

     > Location: Tulsa, Oklahoma: East side;
                        offices not accessible to the general public; visitations or meetings by appointment
                        clinical facilities on 31st St. near Garnett Rd.

     > USPS address: P.O. Box 54845, Tulsa, OK, 74155-0854

     > Telephone: 918-836-6284

     > e-mail: office@malei.org


© July, 2013, by  C. L. Greeno and The MALEI Mathematics Institute.    All rights reserved.