Mark Twain Elementary: 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 6.

All students

3rd The average 3rd grader meets the grade 3 bar. 2462 vs. 2436.
4th The average 4th grader scores just under the grade 4 bar. 2484 vs. 2485.
5th The average 5th grader scores 19 points under the grade 5 bar. 2509 vs. 2528.
6th The average 6th grader scores 21 points under the grade 6 bar. 2531 vs. 2552.

Students fluent in English

Math with English out of the way. Includes students who have only ever spoken English.

Grade bars 3rd 110 students Meets the grade 3 bar.

English learners

Students leave this group as they become fluent, so its average stays low even where they learn well.

Grade bars 3rd 12 students 48 points under the grade 3 bar.

the group's average that grade's own bar the distance between

2026 results. "Meets standard" is the state's mark for being on track for that grade. The state leaves out any group of ten students or fewer, so a grade may be missing from the charts.

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	58,011	2448.9	− 2436	12.9	× 156 / 612	3.3
4	58,013	2483.8	− 2485	−1.2	× 162 / 612	−0.3
5	58,015	2504.1	− 2528	−23.9	× 149 / 612	−5.8
6	58,017	2548.5	− 2552	−3.5	× 145 / 612	−0.8
Sum, rounded to a whole point						−4

2016 from sb_ca2016_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	53,846	2469.7	− 2436	33.7	× 159 / 623	8.6
4	53,847	2477.3	− 2485	−7.7	× 154 / 623	−1.9
5	53,850	2494.3	− 2528	−33.7	× 156 / 623	−8.4
6	53,852	2562.7	− 2552	10.7	× 154 / 623	2.6
Sum, rounded to a whole point						1

2017 from sb_ca2017_1_csv_v2.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	55,409	2461.3	− 2436	25.3	× 165 / 673	6.2
4	55,410	2496.1	− 2485	11.1	× 169 / 673	2.8
5	55,412	2496.5	− 2528	−31.5	× 170 / 673	−8
6	55,414	2556.0	− 2552	4	× 169 / 673	1
Sum, rounded to a whole point						2

2018 from sb_ca2018_1_csv_v3.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	55,501	2449.2	− 2436	13.2	× 158 / 667	3.1
4	55,504	2494.2	− 2485	9.2	× 171 / 667	2.4
5	55,506	2514.2	− 2528	−13.8	× 163 / 667	−3.4
6	55,507	2552.0	− 2552	0	× 175 / 667	0
Sum, rounded to a whole point						2

2019 from sb_ca2019_1_csv_v4.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	55,763	2453.5	− 2436	17.5	× 132 / 623	3.7
4	55,764	2491.0	− 2485	6	× 154 / 623	1.5
5	55,765	2517.3	− 2528	−10.7	× 178 / 623	−3.1
6	55,766	2563.7	− 2552	11.7	× 159 / 623	3
Sum, rounded to a whole point						5

2022 from sb_ca2022_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	55,821	2436.6	− 2436	0.6	× 137 / 539	0.2
4	55,822	2482.9	− 2485	−2.1	× 148 / 539	−0.6
5	55,823	2501.5	− 2528	−26.5	× 138 / 539	−6.8
6	55,824	2538.2	− 2552	−13.8	× 116 / 539	−3
Sum, rounded to a whole point						−10

2023 from sb_ca2023_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	55,774	2444.7	− 2436	8.7	× 132 / 577	2
4	55,775	2487.4	− 2485	2.4	× 149 / 577	0.6
5	55,776	2500.0	− 2528	−28	× 147 / 577	−7.1
6	55,777	2535.3	− 2552	−16.7	× 149 / 577	−4.3
Sum, rounded to a whole point						−9

2024 from sb_ca2024_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	55,650	2444.3	− 2436	8.3	× 154 / 599	2.1
4	55,651	2493.5	− 2485	8.5	× 147 / 599	2.1
5	55,652	2511.4	− 2528	−16.6	× 146 / 599	−4
6	55,653	2526.0	− 2552	−26	× 152 / 599	−6.6
Sum, rounded to a whole point						−6

2025 from sb_ca2025_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	55,408	2431.3	− 2436	−4.7	× 159 / 612	−1.2
4	55,409	2484.7	− 2485	−0.3	× 151 / 612	−0.1
5	55,410	2515.0	− 2528	−13	× 146 / 612	−3.1
6	55,411	2529.3	− 2552	−22.7	× 156 / 612	−5.8
Sum, rounded to a whole point						−10

2026 from sb_ca2026_1_csv_v1.zip

Grade	Line in file	Average score	Standard Met	Distance	Students	Weighted
3	55,321	2461.7	− 2436	25.7	× 122 / 582	5.4
4	55,322	2484.0	− 2485	−1	× 157 / 582	−0.3
5	55,323	2509.0	− 2528	−19	× 152 / 582	−5
6	55,324	2530.7	− 2552	−21.3	× 151 / 582	−5.5
Sum, rounded to a whole point						−5

Step 2 · The average and the normal range

Average: add the yearly results and divide by how many there are. −4, 1, 2, 2, 5, −10, −9, −6, −10, −5 → −3.4
Typical year-to-year change: how far the result moved from each year to the next, ignoring up or down. 2015→2016: 5 · 2016→2017: 1 · 2017→2018: 0 · 2018→2019: 3 · 2019→2022: 15 · 2022→2023: 1 · 2023→2024: 3 · 2024→2025: 4 · 2025→2026: 5 → average 4.1
Normal range: multiply the typical change by 2.66, then add it to the average and subtract it. 4.1 × 2.66 = 10.9. Upper limit 7.5, lower limit −14.3.

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".

Years with no result (no state tests were given in spring 2020) are skipped: the year-to-year change runs from the last year with a result to the next one.

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, 2021–22, 2022–23, 2023–24, 2024–25, 2025–26.