For people who want to learn or teach mathematics on the basis of reason …
Ever since, back in 1978, Tobias' Overcoming Math Anxiety became a best seller, I have wondered what the fuss was all about as things seemed obvious enough to me.
Up until, say, 1950, mathematics had been taught to only a minority of people and for only one purpose: to maintain a managerial class, e.g. engineers, scientists, etc for whom mathematics was a tool to be acquired but also administrators, physicians, etc for whom it was just a screening device to be overcome. In neither case was there any incentive to teach mathematics other than by passing along mathematics as formulated by the mathematicians who had created it: the students who could make it would be annointed to the managerial class and those who couldn't would serve in the lower ranks and all would be as it had always been and therefore as it should be.
Naturally enough, though, the general public began to see education as a means for social advancement and business to realize that here was a way to externalize its training costs i.e. to pass them to the taxpayers rather than to the customers. In both cases, mathematics continued to be seen as a barrier. Thus, that people really should dislike mathematics, be afraid of it and/or resent it was certainly not surprising. The trouble was that by now the people were getting to be many which is why Tobias' book sold so well. But, quite unperturbed, the teaching profession continued to think in terms of what they daintly call "innate ability". As for math anxiety, you the teacher need only say a few soothing words, let the anxious student take the exams in a reassuring environment and you will have done all you could. Obviously, the profession has a built-in incentive to see all mathematics as being difficult and, consequently, just to see "math anxiety" as an epiphenomenon, a natural occurrence when people are trying to do something that most are not good enough to do, that most should not really even attemnpt: We the teachers made it and that sets us apart!This "intrinsic difficulty of all mathematics" is taken so much for granted that, to my knowledge, nobody has ever tried to document it. But then, of course, there is absolutely no need whatsoever to present mathematics as formulated by mathematicians. If, naturally enough, mathematicians formulated mathematics for their own purposes as research mathematicians, nothing ever said that this was the formulation best suited to beginners. And it clearly is not inherently difficult: Mathematics all the way up to and including the "mathematics of change", AKA the Differential Calculus, can demonstrably be formulated so as to remain mathematically correct as well as become politically correct, namely within reach of everybody.
So, I have always thought that the prime responsability for "math anxiety" was with a profession unwilling to even consider the possibility that it might be a clue that there is something drastically and fundamentally wrong with what it is teaching. And, unable to argue much further than that there is nothing inherently difficult to mathematics up to and including Differential Calculus, I decided long ago to leave it at that and to keep working on designing mathematics courses "for the rest of us".
Much to my surprise, though, a text was posted on Aug 13, 2009 on several lists, mathedcc, mathspin, ncsm-members, ctyc-developmental-math, that thoroughly dealt with the issue. I was ready to steal parts of the last two paragraphs but the author kindly gave me permission to reproduce the complete text here with just a few sentences edited out as relevant only to the list on which the text had been originally posted.
Mathematics-Learning Distress: Clinical Insights into Curricular Causes of "Math Anxiety"
"Math anxiety" is a curricular learning disease -- adversely afflicting millions of American students and adults, and caused largely by maladies in the mathematics curriculum. Careful studies of its dangers, symptoms, causes, treatments, cures and preventions shed much light on what is wrong with the American curriculum in mathematics and on how it can be radically improved.
Within the field of clinical psychology, the definition of "anxiety" is relatively clear. The condition typically focuses on anticipation about the possible dangers of suffering potentially adverse effects from situations/events over which one has inadequate abilities to control the challenges or the outcomes. [It sometimes is described as "fear that there might be something to fear" ... as with, "Oops, maybe I won't get to class on time."] But presenting a viable meaning for "math anxiety" requires attending a few particulars.
In popular discourse (and in most educators' discourse) the "math anxiety" phrase is quite loosely used in reference to any one of a broad spectrum of somewhat diverse conditions of varying intensity. More careful attention ... as we must give in the MALEI Mathematical Learning Clinic ... reveals a progressive curricular (MLD) syndrome of Mathematics-Learning Distress -- many of whose stages have been loosely called "math anxiety".
Invariably, MLD is contracted during the school/college years, in connection with curricular demands for learning. The "anxiety" actually develops through past, present, and future curricular expectations for learning. But because unknowing students commonly misinterpret the causes, they commonly develop anxieties about any mathematics that remotely looks like what they encountered in mathematics classrooms. The resulting anxiety, normally carried over into adult life, is genuinely about (that kind of) mathematics But in the curricular context, the distress is more accurately viewed through the psychomathematics of mathematical learning.
MLD normally begins as (behavioral) dismay when the student first feels unable to learn to do what he or she feels expected (or self-expected) to do. From that stage, the syndrome can progressively worsen and increasingly inhibit personal progress through the mathematics curriculum. For some, MLD begins in kindergarten -- for some in graduate school -- but most commonly when first encountering long division, fractions, algebra, or calculus.
In the worst stages of MLD, the victim is afflicted with a learning disability in the form of a genuine phobia (sometimes manifesting as cold sweat and bodily tremors), about all challenges to learn mathematics-like information and procedures. Genuine math-learning phobia happens only with persons who feel strongly compelled to learn (or to know) what they just as strongly believe they cannot learn.
It presently appears that more than half of all Americans become moderate to severe victims of MLD before concluding their formal education. But since that usually manifests as avoidance of curricular mathematics courses (and as school/college dropouts), mathematics educators normally meet only captive, persistent, or non-afflicted students.
Withdrawal from mathematics does provide students with some immediate relief from the self-felt pressures. But it does not heal past psychological damages or provide fitness for future encounters. [For benefits of those kinds, some form of therapeutic instruction is required.]
The MLD syndrome is the student's response to the design and implementation of the mathematics curriculum. It is very much an "inside story".
Through successive curricular experiences, every student acquires self-sensed expectations that he or she "should" already know certain things ... and "should" be able learn whatever items are newly presented, from the ways in which they are presented. [The curriculum does not overtly educate students in how to learn mathematics. More often it covertly trains them in how to not learn, mathematically.]
The distress comes from the student's own awareness that his or her own knowledge or learning is not what that student feels is adequate (for his or her own purposes ... which might be wanting to satisfy others). The level of distress is heightened when the student actually tried to learn items which are not yet known -- or is failing to learn what now is being encountered. The subconscious mind is "an elephant"; it compiles such awarenesses within its internal personal mathematical history.
Moreover, the distress commonly is accelerated also because mathematics curricula normally are structured as developmental ladders. What can be learned at any step heavily depends on what then is known from earlier steps. Weaknesses in knowledge at lower levels undermines learning at higher levels. When each step is only partial learned, the learned portions become progressively smaller. So, scholastic success becomes increasingly difficult to achieve or sustain. Students' awareness of such increasing difficulty accelerates MLD.
Such is the exterior, "social performance" aspect of MLD. The curriculum so prescribes a path and mode of personal mathematical growth -- and induces expectations that students "should" use that mode, to follow that path. But in practice, the curriculum centers on expectations that students "should" be able to perform as directed by texts, by teachers, and especially by tests. The distress occurs when the student cannot readily perform as expected.
An evolving performance history of not meeting those supposed expectations -- or a sudden "crash" of abilities to keep up -- nurtures gradual or instantaneous escalation of MLD. But the student's scholastic performance is not a reliable indicator of the presence, state, or progress of MLD within the student.
The interior aspect of MLD is a matter of why students cannot perform as directed ... and of how they can be empowered for doing so. That is where MLD research sheds much light on how instructional productivity can be enhanced by progressively improving the curriculum.
All humans function through (conscious, pragmatic, or subconscious) development and application of their personal "theories" (if you prefer, "schemata") about whatever they encounter. We are "secure" about things that we firmly believe are adequately covered by "what we know" ... and "insecure" when suspecting that our theories are not adequate to cover our needs.
The students' curricular experiences with mathematics often are the primary media through which they develop their own, personally functional, mathematical theories. All students do so ... but how well their evolving theories mathematically comprehend the curriculum is quite another matter.
Students' malcomprehension of the mathematical theory enclosing the curriculum serves to progressively undermine their abilities to assimilate newly presented topics. The further the students go along a developmentally discontinuous curriculum, the more they must rely on merely memorizing things that are not commonsensible to them. Along the way, their mathematical comprehension gap progressively widens. So, their abilities to learn, mathematically, progressively deteriorates -- whether or not they are aware that it is happening.
When students sense that their evolving mathematical theories do not cover their needs for satisfactory performance in curricular courses, the students often take such mathematical inadequacy to mean that they lack in personal mathematical aptitude. Knowing educators would recognize that those students simply are under-prepared. But adequate preparation has many dimensions that are not attended by traditional curricula.
It almost never happens that students lack adequate personal mathematical aptitude. (Anyone who can achieve fluency with the English language has enough inborn mathematical potential to work as a professional in mathematics -- if prepared by the right kind of curricular experiences.) But students typically lack personal aptitude for mathematically digesting the present version of curricular mathematics into personal common sense ... a weakness that seems to be shared by most authors of mathematics textbooks.
Ironically, many MLD victims are so mathematical in how they think their ways through life, that they are totally confounded, distressed, and depressed by a curriculum which often makes no mathematical sense to them. Such students are not rare! What a waste! MLD research can shed much light on how to resolve that incongruity.