Mathematics education
National and international organisations regularly hold conferences and publish literature in order to improve mathematics education.
[citation needed] In most cases, formal education was only available to male children with sufficiently high status, wealth, or caste.
[1] Historians of Mesopotamia have confirmed that use of the Pythagorean rule dates back to the Old Babylonian Empire (20th–16th centuries BC) and that it was being taught in scribal schools over one thousand years before the birth of Pythagoras.
In the Middle Ages, the academic status of mathematics declined, because it was strongly associated with trade and commerce, and considered somewhat un-Christian.
Basic numeracy skills, such as the ability to tell the time, count money, and carry out simple arithmetic, became essential in this new urban lifestyle.
Main events in this development include the following: Midway through the twentieth century, the cultural impact of the "electronic age" (McLuhan) was also taken up by educational theory and the teaching of mathematics.
[28] At high school level in most of the US, algebra, geometry, and analysis (pre-calculus and calculus) are taught as separate courses in different years.
Even in these cases, however, several "mathematics" options may be offered, selected based on the student's intended studies post high school.
Thus, a science-oriented curriculum typically overlaps the first year of university mathematics, and includes differential calculus and trigonometry at age 16–17 and integral calculus, complex numbers, analytic geometry, exponential and logarithmic functions, and infinite series in their final year of secondary school; Probability and statistics are similarly often taught.
Mathematics majors study additional other areas within pure mathematics—and often in applied mathematics—with the requirement of specified advanced courses in analysis and modern algebra.
Specific topics are taught within other courses: for example, civil engineers may be required to study fluid mechanics,[29] and "math for computer science" might include graph theory, permutation, probability, and formal mathematical proofs.
[30] Pure and applied math degrees often include modules in probability theory or mathematical statistics, as well as stochastic processes.
Business mathematics is usually limited to introductory calculus and (sometimes) matrix calculations; economics programs additionally cover optimization, often differential equations and linear algebra, and sometimes analysis.
Throughout most of history, standards for mathematics education were set locally, by individual schools or teachers, depending on the levels of achievement that were relevant to, realistic for, and considered socially appropriate for their pupils.
[37] PISA has repeated this assessment every three years to provide comparable data, helping to guide global education to better prepare youth for future economies.
There have been many ramifications following the results of triennial PISA assessments due to implicit and explicit responses of stakeholders, which have led to education reform and policy change.
Quantitative research includes studies that use inferential statistics to answer specific questions, such as whether a certain teaching method gives significantly better results than the status quo.
[48][49] In other disciplines concerned with human subjects—like biomedicine, psychology, and policy evaluation—controlled, randomized experiments remain the preferred method of evaluating treatments.
[49] On the other hand, many scholars in educational schools have argued against increasing the number of randomized experiments, often because of philosophical objections, such as the ethical difficulty of randomly assigning students to various treatments when the effects of such treatments are not yet known to be effective,[52] or the difficulty of assuring rigid control of the independent variable in fluid, real school settings.
