Elsewhere, it has been claimed that in some schools mathematics has been taught by tutors with only a GCSE in the subject themselves due to an acute shortage of professional maths teachers.
These gaps, when compared with the standard deviation of schools' mathematics mean scores, are considered large.
Table 2 shows the regression coefficient of the different instructional modes used in mathematics classrooms on schools' mathematics mean scores in low-, medium-, and high-achieving countries (in bold in the table).
In this regard, I prefer to assess the meaning of the regression coefficient by comparing its size to the standard deviation of the distribution of the schools' mathematics and science mean scores in each group of countries.
Figure 3 demonstrates the differential relationship between "students working out problems on their own," a practice that reflects more student-centered constructivist modes of instruction, and schools' mathematics mean scores.
Commonly in secondary schools' mathematics education, the real numbers are constructed by defining a number using an integer followed by a radix point and an infinite sequence written out as a string to represent the fractional part of any given real number.
