Protect a regular time.
Sessions were designed to meet on the same days and at the same times during the school day. Local schedules ranged from 25–60 minutes, two to five times each week.
← All case studiesMath learning.
Denver Public Schools · Math · 2022–23
Math learning.
A steadier routine.
In its second full year with Denver Public Schools, Cignition brought live small-group math tutoring to 21 schools. The work paired a consistent school-day routine with weekly conversations about students, instruction, and implementation.
- Program window
- 2022–23 · Ten-month school-year program
- Delivery
- Live virtual small-group math tutoring
- Actual average ratio
- 3.6 students per tutor
- Local schedules
- 25–60 minutes · Two to five times weekly
The routine
Consistency was part
of the design.
The partnership began with a spring pilot in 2020–21, followed by full programs in 2021–22 and 2022–23. The second full year brought the routine—and the information needed to review it—into sharper focus.
Make the group workable.
The program targeted four students per tutor to support collaborative learning. The actual average ratio was 3.6:1, reflecting local logistics.
Review the work together.
Weekly meetings with school leaders brought current data into conversations about implementation and classroom alignment. The report says 95% of participating schools attended these check-ins.
“Working with Cignition has been first-rate.”
Quoted in the original 2022–23 case study
Participation & tutoring time
A stronger routine.
Time still mattered.
The report compares participation across the two full program years. Those comparisons helped the team review scheduling, student challenges, and the conditions around learning.
Average attendance
Share of scheduled sessions students attended.
2021–2264.2%
2022–2377.5%
Tutor-rated engagement
Average of perseverance, active listening, and discussion ratings.
2021–2274.2%
2022–2382.3%
Report, page 13 · Both bars use a 0–100% scale.
Learning measures
Two measures.
Read each on its own terms.
Tutor observations and diagnostic scores provide different views of learning. Explore how each varied across the report’s implementation-benchmark groups.
Benchmarks used in these charts
- 70%+ attendance
- 80%+ tutor-rated engagement
- 25+ contact hours
Students meeting all three benchmarks
77.3%Average Standards Progress.
The average final tutor-rated score across standards students worked on. It is not a state-test proficiency rate or a pre/post gain.
Denver 2022–23 · Formal report, page 18
Average Standards Progress (%)
100%75%50%25%0%
36.9%
0benchmarks63.4%
1benchmark69.0%
2benchmarks77.3%
3benchmarksNumber of implementation benchmarks met
View the exact values
| Student group | Average result |
|---|---|
| 0 benchmarks met | 36.9% |
| 1 benchmark met | 63.4% |
| 2 benchmarks met | 69.0% |
| 3 benchmarks met | 77.3% |
Tutors considered the answer, the student’s process, and their explanation. Each standard used the student’s final session rating.
Students meeting all three benchmarks
15.0ppAverage diagnostic gain.
The average difference between pre- and post-diagnostic percent-correct scores, expressed in percentage points. These results describe students with paired diagnostic records.
Denver 2022–23 · Formal report, page 23
Average absolute gain (percentage points)
20151050
2.4 pp
0benchmarks9.5 pp
1benchmark13.0 pp
2benchmarks15.0 pp
3benchmarksNumber of implementation benchmarks met
View the exact values
| Student group | Average result |
|---|---|
| 0 benchmarks met | 2.4 pp |
| 1 benchmark met | 9.5 pp |
| 2 benchmarks met | 13.0 pp |
| 3 benchmarks met | 15.0 pp |
The report says 30.6% of enrolled students did not complete a diagnostic series. The diagnostic results do not represent every enrolled student.
These are comparisons among different students in the 2022–23 program. They do not establish that meeting a benchmark caused a higher result. Read the measurement notes
At Place Bridge Academy
The classroom view
belongs in the story.
A teacher’s perspective adds context to the numbers. The original Denver case study featured Meg Cypress reflecting on the learning she saw.
“In the second year of the program, I can see a deeper conceptual understanding in the kids.”
Meg Cypress5th Grade Teacher and Senior Team Lead
Place Bridge Academy
2019 Colorado Teacher of the Year
Place Bridge Academy
2019 Colorado Teacher of the Year
Historical perspective from the 2022–23 case study; one educator’s experience.
A closer look at tutoring and student learning at Place Bridge Academy.
95.0%Student feedback
Report, pages 6 & 12
Positive student survey responses.
The report’s overall average across questions on tutor relationships, collaboration, understanding, and perseverance. “Positive” included Strongly Agree and Somewhat Agree.
Report, pages 6 & 12
Read the evidence
Clear definitions.
A useful comparison.
Understand the measures, the benchmark groups, and the limits of what this program’s data can tell us.
Denver Public Schools · 2022–23Program-aligned math measures, alongside school instruction.
How did Standards Progress work?
Tutors rated understanding using three levels: Complete Understanding (1.0), Partial Understanding (0.5), and No Understanding (0.0). They considered the process and explanation as well as the answer. Standards could be addressed across multiple sessions; the final session’s rating was used for that standard. The average score is a different measure from a pre/post diagnostic gain or state-test proficiency.
How did the diagnostic series measure gain?
The program used multiple-choice questions drawn from the math standards students were expected to address. Absolute gain is the post-diagnostic percentage correct minus the pre-diagnostic percentage correct. A 15.0-point gain means 15.0 percentage points, not a 15% relative increase. School logistics and absences affected assessment completion; 30.6% of enrolled students did not complete a series.
Why does this page use a 25-hour benchmark?
The formal report’s comparison charts define the three benchmarks as at least 70% attendance, at least 80% tutor-rated engagement, and at least 25 contact hours. The original school-year design target was 50 hours, or 25 per semester. A design target and an analysis threshold answer different questions. This case study uses the report’s 25-hour definition for the results shown.
What else changed between the two years?
In the report’s comparison table, average attendance moved from 64.2% to 77.5%, and tutor-rated engagement from 74.2% to 82.3%. The share of students improving on at least ten standards moved from 31.0% to 47.0%. These figures describe different program years, not one identical student cohort or a controlled test of a single change.
What can these results tell us?
They describe the 2022–23 implementation and relationships between participation, tutoring time, and recorded learning measures. Students and schools differed, and school instruction continued alongside tutoring. The comparisons do not isolate tutoring’s effect or establish that meeting a benchmark caused a higher result. The subgroup charts do not provide counts for each group, so the result should not be treated as a forecast for another program.
More of the story
Look back.
Then plan forward.
Explore the earlier Denver year, or the program decisions that shape a Cignition implementation today.
From Denver’s experience to your school
Start with a routine
your school can sustain.
Talk through your students’ needs, the instruction already in place, and the time your team can protect for learning.