Howard Gardner Community Charter: math

The shaded band is this school's normal range. If nothing about how it works changes, nearly every future year should land inside it. Zero means the typical student just meets the state standard. The small numbers under the years are how many students were tested.

Measured against the grade bars

The state's math test uses one scale for every grade, so a score means the same thing in grade 3 as in grade 8.

3rd The average 3rd grader scores 40 points under the grade 3 bar. 2396 vs. 2436.
4th The average 4th grader scores 47 points under the grade 4 bar. 2438 vs. 2485.
5th The average 5th grader scores 36 points under the grade 4 bar. 2449 vs. 2485. The 5th-grade bar is 2528.
6th The average 6th grader scores 20 points under the grade 4 bar. 2465 vs. 2485. The 6th-grade bar is 2552.
7th The average 7th grader scores just under the grade 6 bar. 2551 vs. 2552. The 7th-grade bar is 2567.
8th The average 8th grader scores 11 points under the grade 5 bar. 2517 vs. 2528. The 8th-grade bar is 2586.

2019 results. "Meets standard" is the state's mark for being on track for that grade.

Step 1 · Each year's result

For each grade tested, take the average (mean) scale score from the California Department of Education's results file, and subtract the lowest score that counts as "Standard Met" for that grade. That is the grade's distance from standard. Weight each grade by its share of the students tested, then add the grades up. Grades where the state hides the average because ten or fewer students tested are left out entirely.

2015 from sb_ca2015_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	70,539	2393.5	− 2436	−42.5	× 23 / 119	−8.2
4	70,541	2414.3	− 2485	−70.7	× 22 / 119	−13.1
5	70,543	2458.0	− 2528	−70	× 24 / 119	−14.1
6	70,545	2448.4	− 2552	−103.6	× 15 / 119	−13.1
7	70,547	2428.4	− 2567	−138.6	× 14 / 119	−16.3
8	70,549	2446.5	− 2586	−139.5	× 21 / 119	−24.6
Sum, rounded to a whole point						−89

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	65,372	2420.3	− 2436	−15.7	× 21 / 134	−2.5
4	65,373	2479.9	− 2485	−5.1	× 27 / 134	−1
5	65,375	2475.0	− 2528	−53	× 30 / 134	−11.9
6	65,378	2499.9	− 2552	−52.1	× 21 / 134	−8.2
7	65,380	2501.5	− 2567	−65.5	× 22 / 134	−10.8
8	65,381	2514.8	− 2586	−71.2	× 13 / 134	−6.9
Sum, rounded to a whole point						−41

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,180	2400.1	− 2436	−35.9	× 28 / 153	−6.6
4	67,181	2477.0	− 2485	−8	× 22 / 153	−1.2
5	67,183	2514.7	− 2528	−13.3	× 21 / 153	−1.8
6	67,186	2502.3	− 2552	−49.7	× 29 / 153	−9.4
7	67,187	2560.6	− 2567	−6.4	× 30 / 153	−1.3
8	67,189	2518.2	− 2586	−67.8	× 23 / 153	−10.2
Sum, rounded to a whole point						−30

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,276	2407.9	− 2436	−28.1	× 21 / 148	−4
4	67,277	2471.4	− 2485	−13.6	× 27 / 148	−2.5
5	67,280	2506.7	− 2528	−21.3	× 21 / 148	−3
6	67,281	2564.1	− 2552	12.1	× 21 / 148	1.7
7	67,284	2521.9	− 2567	−45.1	× 29 / 148	−8.8
8	67,285	2509.0	− 2586	−77	× 29 / 148	−15.1
Sum, rounded to a whole point						−32

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	67,777	2396.4	− 2436	−39.6	× 20 / 158	−5
4	67,778	2437.8	− 2485	−47.2	× 19 / 158	−5.7
5	67,779	2449.1	− 2528	−78.9	× 29 / 158	−14.5
6	67,780	2465.0	− 2552	−87	× 29 / 158	−16
7	67,781	2550.9	− 2567	−16.1	× 31 / 158	−3.2
8	67,782	2516.8	− 2586	−69.2	× 30 / 158	−13.1
Sum, rounded to a whole point						−57

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −89, −41, −30, −32, −57 → −49.8
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 48 · 2016→2017: 11 · 2017→2018: 2 · 2018→2019: 25 → average 21.5
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 21.5 × 2.66 = 57.2. Upper limit 7.4, lower limit −107.

Why 2.66? It is the standard factor from quality control, the work of Walter Shewhart and W. Edwards Deming. It turns "how much the result typically changes in a year" into "how far it can wander by chance alone".

Step 3 · Free or reduced-price meals

The share of enrolled students eligible for free or reduced-price meals. From 2014–15, 2015–16, 2016–17, 2017–18, 2018–19, 2020–21.