Highest combined risk
0.869
MATH 162 — high DWF, rising trend, largest impact
Executive view
The program has two immediate performance priorities and one structural leverage point.
The analysis is designed to help reviewers move from raw course-level data to a focused set of questions for validation, discussion, and action.
Research and demonstration use only
The metrics in this example are illustrative. They should not be used to infer course quality, instructor effectiveness, or departmental performance without validated institutional context and stakeholder review.
Highest recent DWF
48.5%
MATH 401 — persistent upper-division concern
Primary structural hub
6
MATH 202 — downstream courses directly dependent
Data quality exceptions
2
Metadata cleanup and one consistency mismatch
What leaders should notice
Four essential findings01
MATH 162 is the clearest near-term review priority.
Its recent weighted DWF is 40.6%, up 13.1 percentage points, with the largest estimated enrollment impact.
02
MATH 401 shows a persistent upper-division readiness issue.
The recent weighted DWF is 48.5%, essentially unchanged from the prior period.
03
MATH 202 is the program’s strongest leverage point.
It feeds six downstream courses, so readiness and corequisite policy decisions can affect multiple pathways.
04
The data is usable, but not yet fully publication-ready.
Course titles and offered-term metadata need cleanup, and a reference to MATH 325 should be reconciled.
Combined risk profile
Illustrative 0–1 scoreDecision brief: Begin with a section-level diagnostic for MATH 162, pair it with a readiness-alignment review for MATH 401, and treat MATH 202 policy or support changes as a high-leverage system intervention rather than an isolated course adjustment.
Trustworthiness
Data quality and analysis rules
The report distinguishes between validated records, neutral omissions, and issues that should be corrected before operational use.
Integrity checks
7 checksCourse records12 unique course codesPass
Dependency endpointsAll source and target codes are validPass
Dependency typesOnly prerequisite and corequisite linksPass
DWF course mappingAll outcome rows map to known coursesPass
Saved node positionsEmpty; analysis is unaffectedNeutral
Course metadataMATH 303/340/341 need titles and offered termsCleanup
Context note consistencyMATH 325 is referenced but absent from the modelReview
Analytic settings
Transparent assumptions| Track | bs_math_baseline |
|---|---|
| State components | COURSES, EDGES, DWF, optional NODE_POS, and META |
| Minimum enrollment | 30 students for trend screening |
| Seasonality | Like-term comparison enabled; summer terms excluded from trend estimates |
| High DWF screen | Approximately 25% or higher |
| Rising DWF screen | Increase of approximately 5 percentage points or more |
| High impact screen | DWF × enrollment of 25 or more |
| High combined risk | Illustrative score of approximately 0.70 or higher |
Curriculum architecture
Program flow and dependency structure
The map shows a single entry point, a compact intermediate spine, and a broad upper-division fan-out centered on MATH 202.
Prerequisite
Corequisite
Structural hub
Structural interpretation: MATH 202 has an out-degree of six and is the central fan-out hub. Because the maximum upstream depth is only about three, disruptions in the early sequence can reach upper-division access quickly.
Student outcomes
DWF performance and enrollment impact
Rates are presented with trend direction and estimated impact so that high percentages are not considered separately from the number of students affected.
| Course | Band | Recent DWF | Prior DWF | Change | Latest term | Impact | Interpretation |
|---|---|---|---|---|---|---|---|
| MATH 162 | Very high | 40.6% | 27.5% | ↑ 13.1 pts | 2025S (n=353) | 185 | Rising, very high impact |
| MATH 401 | Very high | 48.5% | 48.4% | → 0.1 pts | 2025S (n=114) | 70 | Persistent, high impact |
| MATH 180 | High | 25.9% | 21.6% | → 4.3 pts | 2025S (n=218) | 75 | Above threshold, high impact |
| MATH 202 | Moderate | 23.6% | 18.5% | ↑ 5.1 pts | 2025S (n=67) | 12 | Rising; monitor closely |
| MATH 261 | Moderate | 21.6% | 15.8% | ↑ 5.8 pts | 2025S (n=135) | 18 | Rising; mid-sequence watch |
| MATH 408 | Moderate | 22.2% | 17.6% | → 4.6 pts | 2025S (n=101) | 42 | Meaningful enrollment impact |
| MATH 416 | Low | 15.7% | 18.2% | ↓ 2.5 pts | 2025S (n=102) | 18 | Improving |
| MATH 340 | Very low | 0.5% | — | — | 2024S (n=120) | ≈0 | Very low observed DWF |
| MATH 341 | Very low | 2.7% | — | — | 2024F (n=64) | ≈0 | Very low observed DWF |
Caution: Small-enrollment terms can produce unstable rates. Trend interpretations should prioritize adequately sized sections and be reviewed alongside local context.
Integrated model
Combined risk ranking
The example score combines performance, trend, estimated impact, and structural importance to support triage—not to replace professional judgment.
1
MATH 162High DWF • rising trend • largest impact • high centrality
0.869
2
MATH 401Very high DWF • high impact • critical upper-division course
0.696
3
MATH 180Above-threshold DWF • high impact • feeds core hub
0.496
4
MATH 161Single entry point • broad reach • moderate impact
0.439
5
MATH 202Primary fan-out hub • moderate but rising DWF
0.357
6
MATH 408Moderate DWF • meaningful impact
0.334
7
MATH 261Rising DWF • mid-level structural importance
0.315
8
MATH 301Rising DWF • moderate impact
0.315
From insight to action
Recommended next steps
Each action is framed as a disciplined inquiry that can be assigned, investigated, and brought back to stakeholders with evidence.
1
Conduct a MATH 162 diagnostic review
Examine section-level variation, modality, assessment structure, prerequisite readiness, repeat patterns, and student support usage.
2
Align readiness expectations for MATH 401
Compare prerequisite outcomes with the proof and analysis demands of the course; consider a diagnostic or bridge intervention.
3
Review the MATH 202 corequisite model
Clarify concurrency rules, placement expectations, support structures, and whether readiness gaps are amplified at the program’s primary hub.
4
Resolve metadata and model inconsistencies
Add complete titles and offered terms for MATH 303/340/341 and reconcile the MATH 325 reference before the next reporting cycle.
Technical appendix
Detailed structural metrics
The appendix preserves the analytic detail for reviewers who need to audit or reproduce the interpretation.
Course role classification and graph metrics
| Course | In-degree | Out-degree | Upstream depth | Downstream reach | Role |
|---|---|---|---|---|---|
| MATH 161 | 0 | 2 | 0 | 11 | Entry |
| MATH 162 | 1 | 2 | 1 | 9 | Intermediate |
| MATH 180 | 1 | 1 | 1 | 7 | Intermediate |
| MATH 202 | 2 | 6 | 2 | 6 | Intermediate hub |
| MATH 261 | 1 | 3 | 2 | 3 | Intermediate |
| MATH 301 | 1 | 0 | 3 | 0 | Terminal |
| MATH 303 | 1 | 0 | 3 | 0 | Terminal |
| MATH 340 | 1 | 0 | 3 | 0 | Terminal |
| MATH 341 | 1 | 0 | 3 | 0 | Terminal |
| MATH 401 | 2 | 0 | 3 | 0 | Terminal |
| MATH 408 | 2 | 0 | 3 | 0 | Terminal |
| MATH 416 | 1 | 0 | 3 | 0 | Terminal |
Interpretation guidance
This example report is a screening and conversation-support tool. A high score indicates a course or policy area that deserves contextual investigation; it does not establish a cause. Operational decisions should incorporate section-level data, curricular intent, instructor and student perspectives, scheduling constraints, modality, transfer patterns, and other institutional evidence.