Appendix D: Further Discussion of Student Ages in EPGY

by Kalée Tock and Patrick Suppes

June 23, 2002

A table of student ages upon starting the EPGY curriculum at the given grade appears as Table 5 in the body of this study. It is interesting to compare these data to a table of student ages upon ending the EPGY curriculum for that grade. Table 1 shows these ages.

gradeaveragestd. devmaximum75 perc.median25 perc.minimunn
1
6.60
0.94
10.73
7.29
6.62
5.99
4.19
293
2
7.05
0.94
9.58
7.68
7.13
6.41
4.27
272
3
8.37
1.06
11.51
9.06
8.45
7.75
4.41
625
4
9.03
1.09
12.01
9.77
9.07
8.43
5.12
546
5
10.08
1.15
13.35
10.89
10.21
9.39
5.70
772
6
10.52
1.18
14.65
11.34
10.71
9.68
6.65
428
Table 1: Age upon ending the grade level

The average difference between student ages upon starting and ending each EPGY grade is shown in Table 2.

gradeaverage
(end age - start age)
1
0.11
2
0.16
3
0.25
4
0.34
5
0.34
6
0.23
Table 2: Average difference between end age and start age in years

As is clear from the tables, students typically spend only a few months working through any given grade in the program. This is drastically less time than would be spent in a traditional school. It follows that the longer a student spends in the program, the further ahead the student will become. However, this point is confounded by the fact that most students are at EPGY for only one or two terms. Table 3 shows numbers of students for whom age data are available with the numbers of EPGY courses they have completed, the average years ahead of a school curriculum they are upon starting the program, and the average years ahead of a school curriculum they are upon ending it. The years ahead are calculated based on a school year that begins September first and ends June first, and it is assumed that all students begin the first grade as soon as they are eligible to do so. Though policy varies considerably among the more than twenty-thousand school districts in the United States, we take 5.75 years old as the typical minimum age at which a student may begin the first grade.

number
of terms
years ahead
of school
at start
years ahead
of school
at end
number
of students
1
-0.87
-0.43
996
2
-1.02
0.20
562
3
-1.10
0.86
174
4
-1.29
1.56
53
5
-1.49
2.27
8
Table 3: Years ahead of school after terms in the EPGY curriculum

Notice that students typically start EPGY about a grade level below where they are in school. For the most part, this is due to the fact the EPGY grade levels are grouped together into courses composed of an odd and an even grade level. One EPGY course includes first and second grade, the next includes third and fourth grade, etc. It is recommended that students start with the odd grade of the sequence, regardless of their grade in school. This is because the EPGY courses cover topics like set theory and logic, which are typically not treated in comparable depth in school curriculum. Even students who do not start EPGY at the beginning of the odd grade level do start at the beginning of the even grade level. Because a student may start an EPGY course at any time during the school year, the student may have completed a considerable portion of the school year upon entering the program. In any case, despite the lower starting grades chosen by incoming EPGY students, the number of years by which they surpass their grade in school increases monatonically with the number of EPGY terms completed.