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Denver Public Schools · Math · 2021–22

Built to grow.
Shaped with schools.

Denver’s first full year of Cignition tutoring grew from an initial launch at three schools to a district implementation serving 1,069 students. Local needs shaped the schedules. Weekly conversations helped the partnership adapt.

Follow the rolloutRead the data report
Program window
2021–22 · Eight-month school-year program
Delivery
Live virtual math tutoring
Group design
Target 4:1 student-to-tutor ratio
Paired diagnostic sample
374 students · Report, page 8

The rollout

Grow the reach.
Keep listening locally.

Following spring and summer pilots in 2021, the partnership moved into its first full school year. Schools had different priorities and schedules, so implementation took more than one form.

  1. October 4, 2021 · Launch201

    students. Three schools.

    The starting point for the school-year rollout.

  2. By March 2022 · Expansion1,069

    students. Nineteen schools.

    The program expanded across elementary, middle, and high school settings.

  3. End-of-year review

    Turn experience into the next design.

    Weekly data review, school feedback, and delivery experience informed plans for the following year.

One partnership. Different school needs.

01

Inside the math classroom.

Some schools used tutoring as part of differentiated grade-level instruction. Content was developed from Denver’s scope and sequence, with room for schools to realign it.

02

A schedule that fit the setting.

Implementations included before- and after-school sessions as well as school-day tutoring. Session lengths ranged from 25 to 90 minutes.

03

A regular review with people.

School staff, district leaders, and Cignition met weekly to examine key metrics, discuss progress, and adapt the work. Schools received weekly updates and access to program data.

Rollout milestones: original case study. Program design: report, pages 4–6.

Brittany Miller
“Cignition has been open to growing their program as interest increases and is conscientious in their alignment to our district’s curriculum and assessments.”
Brittany Miller, Ph.D.Senior Director, Expanded Academic Learning
Historical title from the original case study

Diagnostic results

A closer look
at the paired records.

The report includes pre- and post-diagnostic results for 374 students. These program-aligned math measures offer one view of learning during the school year.

Across the paired-diagnostic group

12.1pp

Average absolute gain.

The change in average percent-correct score, expressed in percentage points. These results describe students who completed both diagnostics.

374students with paired records
of 1,069 students served

Formal report, page 8.

From pre- to post-diagnostic.

Average percent correct · Paired records, n = 374

Pre-diagnostic30.7%
Post-diagnostic42.8%
+12.1 percentage points42.8% − 30.7%

Formal report, Figure 3.1, page 8 · 0–100% scale.

The paired-record groups, by school level.

Different students and grade levels; these figures are not a ranking of programs.

Elementary

Grades 4–5 · 183 paired records
13.6pp

Middle

Grades 6–8 · 148 paired records
10.5pp

High

Grades 9–12 · 43 paired records
12.3pp

These are pre/post observations from the implementation. They do not isolate tutoring’s effect from school instruction or other differences.

Program benchmarks

The group you choose
changes the question.

Denver and Cignition reviewed attendance, engagement, and contact time each week. Explore the share meeting each benchmark in two different groups.

1,069 enrolled students

Share meeting each benchmark.

Attendance70% or more of sessions
49.3%
Engagement80% or higher tutor rating
53.4%
Contact time36 or more hours
19.5%

Formal report, pages 9–10 · Each bar uses a 0–100% scale.

Compare the exact values
Benchmark attainment · Report, Figure 3.2, pages 9–10
BenchmarkAll enrolled
n = 1,069		≥10-point gain
n = 179
Attendance70% or more of sessions49.3%87.7%
Engagement80% or higher tutor rating53.4%68.7%
Contact time36 or more hours19.5%53.6%
36 hours

A target needs room in the schedule.

The contact-time goal was 36 hours. Median potential contact time across implementations was 32 hours; median actual contact time for individual students was 30 hours. The report distinguishes program design from delivered time.

Report, page 5

The groups differ in size and composition. Their comparisons show relationships in the recorded data; they do not establish causality.

School perspectives

The reporting mattered.
So did the relationship.

The original case study captured district leaders’ perspectives on adapting the program and making its information useful for schools.

“Cignition has been so responsive and it has actually been a PARTNERSHIP. Everyone has been seeking to improve.”
Bridgett Bird
Bridgett BirdSenior Manager of Academic Program and Planning
Denver Public Schools
Visibility

Make the information usable.

Weekly updates and reporting tools brought the view from the district down to schools and individual students.

“We got better and better at sharing that data with schools.”
Adaptation

Build with the people doing the work.

Feedback from schools shaped content selection, reporting, and communication priorities for the next year.

Quotations and titles are historical, from the original 2021–22 case study. They describe individual leaders’ experiences.

Student perspectives

What students said
about learning math.

The report’s survey adds a different view of the experience. These are response shares—not diagnostic gains or a measured change in confidence.

97.1%

“I can learn math if I work hard.”

Very True or Somewhat True
94.3%

“I am better now at math than I was at the beginning of the year.”

Very True or Somewhat True
96.6%

“I can persevere through challenging material.”

Very True or Somewhat True
94.7%

“I am proud of my math understanding.”

Very True or Somewhat True

All-student survey figures · Formal report, Figure 3.3, page 11. Weekly survey items began March 7, 2022; the report does not state a response count for this chart.

Read the evidence

Keep the context
with the numbers.

Who was measured, how the groups were defined, and what the comparisons can—and cannot—tell us.

Denver Public Schools · 2021–22
Grades 4–12 · Program-aligned math diagnostics
Who is included in the diagnostic results?

The report includes 374 students with paired pre- and post-diagnostic results: 183 in elementary school, 148 in middle school, and 43 in high school. The program served 1,069 individual students. Different implementation models meant not every student received both diagnostics, so these results describe the paired-record group—not every enrolled student.

What does a 12.1-point gain mean?

The report’s average pre-diagnostic score was 30.7% correct and its average post-diagnostic score was 42.8% correct. The difference is 12.1 percentage points. It is not a 12.1% relative increase, a state-test proficiency rate, or a comparison against an untreated control group.

How should the benchmark comparison be read?

The first view uses all 1,069 enrolled students. The second uses the 179 students who achieved at least a 10-percentage-point diagnostic gain. The bars show the share of each group meeting an attendance, engagement, or contact-time benchmark. For example, 87.7% of the students reaching the gain threshold also met the attendance benchmark. Reversing that statement would describe a different statistic.

What does the 19.4-point result describe?

Among students measured with paired diagnostics, those meeting all three program criteria—at least 70% attendance, at least 80% tutor-rated engagement, and at least 36 contact hours—had an average absolute gain of 19.4 percentage points. The report does not give that subgroup’s size. The comparison is observational; it does not isolate the effect of tutoring or of any single benchmark.

What should we know about the student survey?

The survey asked students to rate statements as Very True, Somewhat True, or Not True. The figures shown combine Very True and Somewhat True responses for all students in Figure 3.3. They describe response shares, not measured diagnostic gains or a before-and-after confidence change. Survey questions changed during the program, with the weekly items beginning March 7, 2022.

Why do some counts differ on the older page?

The original web page lists 272 groups at its March rollout milestone. The formal report lists 338 groups for the program and 1,069 individual students. Some students enrolled in multiple classes, so the report’s grade-division enrollment counts total more than its individual student count. This page uses 1,069 for students served and keeps the rollout milestones separate from the formal report’s diagnostic sample.

From one district’s story to your setting

Build around your students.
Plan with your schools.

Start with local needs, the time available for instruction, and the information your team needs to keep improving.

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