feat: course sequencing insights and high-risk gateway course identification

[William-Hill]

Overview

The PRD identifies gateway course bottlenecks — particularly in math and English — as a leading predictor of non-retention. Currently, the ML pipeline generates gateway_math_probability and gateway_english_probability per student, but there is no course-level view that surfaces which sequences or combinations are highest-risk.

Background

From the PRD problem statement:

"Gateway course bottlenecks — particularly in math and English — are a leading predictor of non-retention, but course-level risk is not surfaced in existing tools."

The pipeline also generates low_gpa_probability per student and there is a course_predictions table (or equivalent course-level data) that could be aggregated.

Requirements

New page or section: Course Insights

Gateway course risk summary

• Table or chart showing gateway math and English pass rates by cohort year
• Flag courses where gateway_math_probability or gateway_english_probability is below a threshold (e.g., avg < 0.50)

High-risk course sequences (DFWI)

• Query course_predictions (or the course CSV) to find course combinations with high D/F/W/I rates
• Surface top 10 highest-risk sequences as a static table
• Columns: subject area, course code, cohort, DFWI rate, avg gateway risk score

Readiness vs. gateway outcome correlation

• Chart: readiness score tier (High / Medium / Low) vs. gateway math/English pass rate
• Shows whether the readiness score is predictive of gateway success

API

• GET /api/insights/gateway — aggregated gateway risk stats (avg probability, pass rate) by cohort and subject
• GET /api/insights/dfwi — top DFWI course sequences with risk scores

Navigation

• Add a "Course Insights" link in the dashboard header (or as a tab under the main dashboard)

Acceptance Criteria

• Gateway math and English pass rate by cohort is visible
• Highest-risk course sequences surfaced (top 10)
• Chart correlating readiness tier to gateway pass rate
• Accessible to Faculty and Advisor roles
• No individual student GUID exposed in course-level aggregates

Notes

• The student_level_with_predictions table has gateway_math_probability and gateway_english_probability per student — these can be aggregated by cohort for the gateway summary
• See PRD §2 (Problem Statement), §6 (Institutional Requirements), and FR4 (Dashboard Requirements)

[William-Hill]

Superseded by #85 and implemented in PR #87.