Making Curriculum Complexity Visible and Actionable
Vignon Oussa and Uma Shama · Bridgewater State University
October 14, 2026 · 4:30–5:15 p.m. · Discovery
Open the HTML in a current browser. The slides and local demonstrations work offline. Space or Right Arrow reveals the next point. PageDown advances a slide. N shows or hides the current notes. T opens the contents. Show all reveals every point on the current slide. Resources opens the appendix directory. Print opens the browser print dialog. External resource links require internet access.
The deck has 44 main slides, including 11 optional detail slides, plus six appendix slides. Core mode follows 33 main slides and includes all audience activities. Use the timed facilitation plan below for the 45-minute event. Full mode is for later exploration or a longer workshop. Open Contents and choose Core talk; full mode remains the default for independent browsing. Printing includes every slide. Core slide numbers: 1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 18, 20, 22, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44.
Use Core mode for the conference. Full mode retains optional background and teaching illustrations for later reading. The opening is intentionally brief so participants can choose concepts from their disciplines and track them as mathematics examples are presented.
| Elapsed time | Segment |
|---|---|
| 0–3 minutes | Welcome and four-tool overview |
| 3–6 minutes | Choose concepts from your discipline |
| 6–13 minutes | Concept Analyzer: preparation and downstream ideas |
| 13–18 minutes | Program Analyzer: course pathways |
| 18–25 minutes | Curriculum Mapper, including a one-minute reflection |
| 25–36 minutes | Worked transfer case, including a one-minute reflection |
| 36–40 minutes | Faculty review, pilot, and acknowledgments |
| 40–45 minutes | Discussion using participants’ concepts |
These allocations include the writing and comparison pauses. Keep the transfer block within its eleven minutes; show the approved scenario and one change if time permits. Begin synthesis by minute 36 and discussion by minute 40.
At slide 5, pause for three minutes: 90 seconds to write 3–5 concepts from one familiar course, 60 seconds to share with a neighbor, and 30 seconds to circle one concept. Ask participants to keep that list beside them and annotate it as the mathematics examples unfold. Their list is provisional, not an approved canonical inventory.
During Concept Analyzer, give about 30 seconds to add a prerequisite and a later idea. During Program Analyzer, give about 30 seconds to name an introducing course and a later course that relies on it. These checkpoints are included in the tool blocks.
At slide 27, allow one minute to sketch a provisional 0–3 row and identify needed evidence. At slide 38, allow one minute to identify incoming evidence, depth, and an essential omission. Use 45 seconds of individual annotation and 15 seconds of neighbor comparison for each pause. Avoid extended report-outs until the final five-minute discussion.
Open the printable audience concept tracker. Participants can use their own paper instead. The tracker is blank and is not collected by the plugin.
The demonstrations have local fallback examples, so the talk can continue without opening the live apps.
The supplied email and concept-first explanation, the event listing, the full curriculum-map page, the operations hub, and nine additional relevant pages or app entry points were reviewed. The companion workbooks, CSVs, course archive, program states, transfer paper, example syllabus, and available assurance documentation were inspected. App descriptions and saved examples were used as sources; this review did not exercise every live app feature.
Three public tutorial videos were successfully downloaded for inspection, but the narration-summary service could not accept the video batch after two attempts. The newer Concept Analyzer video link returned a sharing page instead of downloadable media. Video narration was not transcribed or independently verified. The presentation uses the written walkthroughs and companion source files, and keeps the public tutorial links available for follow-up.
Keep the fictional evidence packet, canonical dictionary, and local map conceptually separate. An exact phrase supports concept presence, while the near match requires added assignment evidence. Scores use local levels; they do not establish incoming depth. Overlap alone leaves two candidates tied. The tutorial’s declared local-level tie-breaker favors Applied Vector. Missing Green’s and Stokes’ theorems explain why the broader Multivariable course needs additional review. Even the highest-ranked candidate requires evidence for its level-3 expectations and institutional policy review.
The worked case and added course-attempt counts are synthetic. Source workbook excerpts retain their original values. Supplemental examples are marked in Contents with a gold border and can be skipped in Core mode. All cases are teaching demonstrations, not institutional results.
Use the facilitated Core route for this 45-minute session. Opening 0–3 minutes; concept-selection activity 3–6; Concept Analyzer 6–13; Program Analyzer 13–18; Curriculum Mapper 18–25; Transfer 25–36; faculty review, pilot, and acknowledgments 36–40; discussion 40–45. All activities are included in these allocations. Move quickly through familiar background. At minute 36, leave the transfer section and begin synthesis. Full mode retains optional background and technical examples for later reading. Choose Core talk in Contents or use route=core in the WordPress shortcode. The original source examples and their scope labels remain in place.
Optional background for the Full route. In the 45-minute Core route, move directly to the shared concept principle and four-tool overview. Ask the audience to think of a point where students experience friction in their own curriculum. The session description emphasizes prerequisites, gateway courses, transfer pathways, advising, and timely graduation. Frame these as questions COMPASS can help investigate. The material supplied for this presentation does not establish an effect on retention or graduation, so avoid presenting those outcomes as demonstrated benefits.
Opening: explain this principle in about 45 seconds. The audience will supply concepts from their own disciplines immediately after the four-tool overview. Use the central principle from your explanation: concepts are the basic components of a curriculum. A course is more than an unordered list because relationships and depth also matter. The concept inventory provides a common basis for the four tools. In another discipline, the comparable units might be skills, competencies, or clearly bounded disciplinary ideas. Adapt the vocabulary while preserving the structure.
Opening: give each tool’s question in one sentence, then move into the three-minute audience activity. The cover, concept principle, and this overview together occupy the first three minutes. Give the audience the complete suite before discussing individual tools. Each tool can be useful independently. A reviewed concept inventory feeds the map, and the reviewed map supplies the local vocabulary for transfer matching. Program structure adds the pathways needed to interpret coverage along routes students actually take. The numbered order here follows the concept-first narrative rather than the ordering of sections in the operations hub.
Pause the presentation for three minutes. Allow 90 seconds for individual writing, 60 seconds to share with a neighbor, and 30 seconds to choose one concept and return. Ask for learning ideas rather than course titles. Participants may use concepts, skills, or competencies appropriate to their discipline. This is a provisional working list, not an approved canonical dictionary. Say: As we use mathematics, keep your own circled concept in view and ask how each tool would apply to it. A printable audience tracker is linked from the presentation and included in the plugin. Do not collect participants’ lists.
Optional background for the Full route. In the 45-minute Core route, move directly to the shared concept principle and four-tool overview. Explain the two interfaces described in your project materials. The public hub recommends static evidence followed by AI interpretation. The concept and map tutorials also illustrate AI-assisted drafting before faculty revision. Both routes require review. Describe the customized GPTs as configured for their COMPASS tasks rather than claiming model fine-tuning. The public directory lists static Concept, Program, and Mapping tools, while the Course Transfer entry links to a GPT and protocol. Do not imply that this review verified a separate public static Transfer interface.
Audience checkpoint: allow about 30 seconds for participants to add one prerequisite and one later idea to their own list. Include this within the seven-minute Concept Analyzer block. The matrix convention is important: the row is the concept being taught, and the column is the prerequisite. If B requires A, the entry in row B and column A is 1 and the graph arrow runs from A to B. The app also distinguishes 0 for no direct relation, 0.5 for co-dependence, and ? for uncertainty. Those values describe relationships and must not be confused with the separate 0–3 curriculum coverage rubric.
Walk through row U, column F: a 1 says foundations support substitution. Read row P, column U and row T, column U in the same way. These selected relations reproduce edges in the source review matrix; the four-node illustration omits other direct edges and concepts. Zero means no direct edge in this illustration, not a statement that ideas are unrelated.
This diagram displays seven of the workbook’s fourteen concepts and seven selected strict prerequisite edges. Other concepts and bypass edges remain in the full matrix. Click a node to highlight its descendants in the displayed excerpt. Start with integration foundations, then show how substitution branches into integration by parts and trigonometric integrals before convergence and power series. The excerpt illustrates propagation and is not a complete teaching plan. The accompanying full matrix contains 37 strict prerequisite edges.
Explain metrics in plain language. A high-reach concept can affect many later concepts. A bridge can matter even if it has fewer descendants. A long chain places constraints on pacing. A topological order satisfies stated prerequisite relationships, but several valid orders may exist. It does not prove that one teaching sequence is pedagogically optimal. Cycles require faculty review or a defensible jointly taught block before claiming a strict order.
The bars show downstream reach computed from the current workbook matrix, counting each reachable concept once. The top values are integration foundations 11, substitution 10, integration by parts 7, and trigonometric integrals 7. Sequences and limits reaches 3. The workbook Analytics sheet labels itself a baseline snapshot and contains values inconsistent with this matrix, including substitution reach 3. This chart uses the recomputed values. Metrics describe the supplied model, not measured student weakness.
Both rows respect F before U and U before P and T, with P and T before I in this selected illustration. Either branch can be taught first. A third row violates preparation by placing integration by parts before substitution. A topological order is feasible, not automatically optimal. Define the objective—time, spaced review, cognitive load, or readiness—and examine co-dependent blocks and instructional constraints.
Distinguish a gateway concept from a gateway assessment. The concept marks an important dependency. The assessment supplies evidence about students’ readiness. For example, check integration setup and substitution before later integration applications, or sequence and series foundations before convergence tests. These are proposed instructional uses, not validated placement rules. Assessment design, timing, grading, and remediation remain faculty decisions.
A student may follow a substitution procedure without recognizing when it applies. The example assessment therefore asks students to choose and justify a method, carry it out, and interpret the result. A weakness triggers targeted review before a more demanding topic. Downstream reach helps select where a diagnostic could matter, but a structural count does not establish an assessment cut score or make high-stakes gateway exams mandatory.
Audience checkpoint: allow about 30 seconds for participants to name the first course teaching their concept and a later course relying on that preparation. Include this within the five-minute Program Analyzer block. Move from concepts to courses while retaining the same graph idea. Program graphs require more than arrows: prerequisite groups may mean A and B, or A or B. Co-requisites and concurrent enrollment need explicit treatment. Course offering patterns affect whether a mathematically valid sequence fits a real schedule. Use structural findings to guide program review and advising questions. They do not, on their own, explain student outcomes.
These course relationships come from program.json in the University of Vignon tutorial archive. The diagram shows a seven-course excerpt, not the complete thirteen-course program. Algebra and Trigonometry precede Calculus I but are outside this excerpt. Linear Algebra also has earlier prerequisites outside the excerpt. In the archive, Real Analysis requires Calculus II and Abstract Algebra together. Differential Geometry requires Multivariable Calculus and Linear Algebra together. The two incoming edges at those destinations represent AND requirements. Click a course to trace downstream effects.
Two incoming arrows alone can hide catalog logic. This example contrasts requiring both Calculus II and Linear Algebra with accepting either course. Under AND, delaying either blocks eligibility; under OR, the other route can satisfy the rule. Co-requisites additionally permit simultaneous enrollment under local rules. Program analytics should preserve these distinctions as well as course availability, credits, and minimum grades.
DWF commonly refers to D grades, withdrawals, and failures, but the institution must define the numerator and denominator consistently. Use aggregated course records with specified terms and sample sizes. A structurally important course with a high DWF rate deserves attention, but the combination does not establish causality or blame. Compare rates fairly and investigate preparation, course access, assessment design, advising, and other local explanations. No institutional DWF dataset was supplied for this presentation.
The toy denominator counts eligible graded or withdrawal attempts in the same period, including repeated attempts according to the declared local rule. Course A has 36 D/W/F outcomes among 120 attempts, or 30%; B has 6 among 40, or 15%. A also reaches five later courses in a fictional graph. This combination justifies investigating A. It does not establish that A causes later attrition. Check denominator rules, course sections, student preparation, grading policies, term comparability, and uncertainty before comparing actual rates. Define institutional treatment of withdrawals, incompletes, and repeats explicitly.
Keep this explanation to about 48 seconds within the seven-minute mapping block. Use one example or observation and move on. Translate the earlier phrase pairwise orthogonal into curricular language: distinct, nonredundant concepts with clearly agreed boundaries. Orthogonal does not mean independent or unrelated in the prerequisite graph. Concepts may have strong dependencies while retaining distinct definitions. The map tutorial illustrates reconciling derivative rules with differentiation rules only after faculty confirm matching scope. The aim is to prevent double counting, preserve meaningful differences, and support comparisons across courses.
A partial derivative and the instruction to differentiate with respect to x while holding y fixed describe the same concept in this illustrative dictionary. A gradient is a distinct vector assembled from partial derivatives. The concepts can be nonredundant while remaining connected by dependencies. Interpret mutually orthogonal in the original brief as a demand for distinct, agreed boundaries; literal statistical or mathematical independence is not required.
Ask participants to keep their circled concept in view while you explain the 0–3 rubric. They will sketch their own row in the timed reflection after the alignment slide. Keep this explanation to about 54 seconds within the seven-minute mapping block. Use one example or observation and move on. Explain the four ordered categories. Zero means no teaching recorded in the approved course map. One indicates introduction, two development, and three an independent mastery target at the department’s standard. These are ordinal categories rather than equal units of learning. A three records an intended standard and assessment opportunities, not proof that every student reached it. In working records, an unknown entry is not interchangeable with zero.
Read each column as a progressively deeper course expectation. A code of 3 is a mastery target; it is not proof that every enrolled student mastered the concept. Faculty should agree on the task, independence, complexity, and assessment evidence before coding the map. Levels are ordered categories, and using them as scoring weights is a declared convention.
Keep this explanation to about 96 seconds within the seven-minute mapping block. Use one example or observation and move on. This table is an unchanged selection of five rows and six course columns from the expanded University of Vignon workbook. It is separate from the page’s smaller twenty-concept interactive example. Click a row to examine it across these selected courses. The complete workbook contains 883 canonical rows and thirteen course columns. Its metadata says atomic concepts inherit levels from broader source topics, so those levels are tutorial assumptions requiring validation before use in a real department. Course columns here are a display convention, not a semester schedule.
Use the controls to compare three hypothetical patterns on a chosen five-course route. The gradual pattern 1,1,2,2,3 provides repeated teaching opportunities. An isolated introduction raises a reinforcement question. A first recorded appearance at mastery raises a preparation question. These are design questions, not universal defects. Some specialized concepts need fewer appearances, prior learning may explain an abrupt start, and a later lower value describes course teaching depth rather than loss of student knowledge.
Keep this explanation to about 54 seconds within the seven-minute mapping block. Use one example or observation and move on. The Program Map Alignment guide describes comparing an upstream Course A with downstream Course B and exporting coverage. Use that comparison to connect individual faculty decisions with a program-level conversation. Concept naming mismatches can produce apparent gaps, so verify vocabulary before interpreting. Examine every route students may take. Coverage in an optional elective does not guarantee that all students receive that preparation.
Pause for one minute within the seven-minute Curriculum Mapper block: 45 seconds to annotate the audience tracker and 15 seconds to compare with a neighbor. Use the concept participants circled at the beginning. Treat their codes as working hypotheses to check against course evidence. A mastery target is not evidence of every student’s attainment. Take at most one brief response before moving to transfer.
Course C expects independent use of partial derivatives, but the route initially records only an introduction in A and no teaching in B. Faculty first inspect the syllabi and assessment evidence. If B already develops the concept, correct the record. If it does not, consider adding relevant practice and assessment in B and then revise the approved map. The suggested 1,2,3 pattern is an illustrative design choice, not an automatic requirement or a change to the source workbook.
Tell the audience to track the evidence needed for their own circled concept as the eight-step mathematics case unfolds. A one-minute reflection follows the case. Explain the course-as-concept-set idea from your introduction. A title alone is inadequate for equivalency decisions. The incoming syllabus supports a mapped concept set, and the local map provides the receiving course profiles. Near matches require justification. Unmapped topics remain visible but do not silently enter the official scoring universe. Reviewers retain missing local content and extra incoming topics in the diagnostics. A strong ranking is a candidate recommendation rather than an award of credit.
All names, profiles, excerpts, and decisions in this case are synthetic. The syllabus explicitly lists partial derivatives, double and triple integrals, and vector fields. It also says work done along a path, which could involve line integrals but needs clarification. Coordinate geometry is an extra topic outside this small local dictionary. No evidence of Green’s or Stokes’ theorem appears in the packet. The absence is an evidence gap, not a claim that an actual instructor never taught it.
C1, C2, and C3 are accepted on explicit topic evidence. C4 is initially pending because the phrase work along a path could be informal. For the baseline example, a reviewer obtains an assignment explicitly asking students to evaluate a line integral and approves C4. Thus A={C1,C2,C3,C4}. Coordinate geometry remains in the unmapped evidence record and does not silently enter the scoring universe. Confidence labels are qualitative review statuses, not probabilities.
Use the three synthetic local columns. Multivariable Calculus teaches C1–C6, while Applied Vector Calculus teaches C1–C4. Calculus II teaches C7 within this deliberately small universe. Zeros denote no recorded teaching in that course. Levels in the candidate columns are local teaching targets; they do not establish incoming mastery. The dictionary is restricted for explanation; a real review uses the complete approved concept inventory. No values here replace the downloaded curriculum workbook.
The incoming set is C1 through C4. Both Multivariable and Applied Vector overlap on all four concepts. Sum the four local coverage levels: 2+2+2+2=8 and 2+2+3+3=10. Calculus II contributes zero because C7 is outside A. The tutorial’s lexicographic policy selects Applied Vector. This is local depth-weighted shared coverage, not a measurement of incoming depth. The protocol paper also formalizes maximizing overlap and maximizing general weighted scores separately; state the chosen policy rather than treating these policies as identical.
The two courses share the same four incoming concepts, so their overlap scores tie. The local-level tie-breaker favors Applied Vector by two points. Under overlap alone, both courses would remain tied. Do not report a match percentage of 100% as proof of full equivalency: the calculation uses a reduced dictionary and ignores incoming depth, assessment quality, credits, and institutional policy.
Multivariable expects Green’s and Stokes’ theorems, but neither has evidence in the packet. Applied Vector has no uncovered concepts in the toy dictionary, yet its level-3 expectations for vector fields and line integrals still need incoming assessment evidence. Calculus II expects sequences and series, which are not supported. Coordinate geometry is additional incoming content outside the toy canonical universe. These diagnostics make the recommendation intelligible and prevent coverage alone from being mistaken for equivalency.
The approved case accepts C1 through C4. The strict case withholds the near-match C4: scores become 3,7 for Applied Vector and 3,6 for Multivariable. The limited-evidence case accepts only C1 and C2, producing a tie at 2,4. Remove all concepts to show that no supported candidate can be recommended. A zero-overlap score produces no supported match even if all candidates tie. These scenarios illustrate extraction sensitivity; they are not the formal stability bound in the paper.
The illustrative memo records the evidence packet, dictionary/map version, mapping approval, candidate scores, gaps, and unresolved requests. The recommendation is provisional: obtain assessment evidence for vector fields and line integrals, then apply local credits, minimum-grade, and equivalency policies. The committee may approve equivalency, identify a bridge requirement if policy permits, select another outcome, or decline. No student credit is awarded by the demonstration.
Pause for one minute within the eleven-minute Transfer block: 45 seconds to write and 15 seconds to compare with a neighbor. Ask participants to translate the evidence workflow to their own discipline using their original circled concept. They do not need a completed curriculum map or a numerical ranking during this activity. Reinforce the distinction between concept presence, demonstrated depth, and an authorized equivalency decision. Reserve broad report-outs for the final discussion.
Return to the consistent boundary across all four tools. Deterministic calculations can be reproducible while inputs still require correction. AI can draft a readable narrative while faculty retain responsibility for the interpretation. Keep a versioned record of source files, approved definitions, reviewers, and the final rationale. This is the basis for an auditable process and for revisiting decisions when curricula change.
Follow partial derivatives through the four tools. The concept graph locates its preparation; the program graph identifies required course routes; the map locates teaching depth; the transfer case compares incoming evidence against those expectations. If incoming evidence is weak, the review can identify where reinforcement belongs. None of these relations by itself measures attainment or demonstrates an effect on student outcomes.
Offer a feasible adoption path consistent with the hub’s onboarding guidance. Select strategically important courses rather than mapping an entire institution at once. Agree on concept granularity and coding criteria, collect syllabi and assessment evidence, and assign an owner for updates. The outputs should include reviewed concept matrices, a program graph, a curriculum map, and one documented review case. Expand after the pilot exposes data and workflow issues.
Separate proposed evaluation measures from results. The supplied material contains examples, documentation, and mathematical assurance materials, but no causal evaluation of student-success outcomes. A local pilot could measure inter-rater agreement, completion and review time, unresolved mapping issues, and usefulness for faculty and advisors. Later evaluation of outcome changes needs an appropriate design and consideration of competing explanations. Invite collaboration on that research rather than claiming demonstrated effects.
Acknowledge Bridgewater State University’s Academic Innovation Fund, InnovateBSU, Academic Innovation Project Grant AY 2025–2026. The funded project is Leveraging AI for Curriculum Mapping and Analytics to Enhance Academic Foundations at BSU. These contributor roles follow the public operations hub and your supplied email. Distinguish development and maintenance responsibilities from the other contributions without diminishing their importance.
Reserve the final five minutes for discussion, 40–45 minutes into the session. Invite participants to refer to their own lists and compare the mathematics examples with their disciplines. Take two or three brief examples and discuss a concrete first review question. If time is short, ask everyone to write one next step and invite a final question. The Project hub and Resources controls provide follow-up materials.
Use this slide if the audience asks how the graph is encoded. Diagonal cells are excluded. Do not use dependency values as coverage levels. Co-dependence is symmetric in the static app and can produce jointly taught blocks. A prerequisite-respecting sequence of blocks requires acyclicity of the strict relation between blocks.
This formula captures the alternative described in the original brief. The table uses the same incoming set C1–C4 and local profiles from the worked case. Declare concept weights C1–C4=1, C5–C6=3, C7=2. Multivariable has two missing concepts, C5 and C6, for distance 6. Applied Vector has no set mismatch, so distance 0. Calculus II has four extra incoming concepts and one missing local concept, C7, giving 6. Unmapped coordinate geometry remains outside the toy canonical universe. Unlike the tutorial tie-breaker, these weights attach to concepts rather than local coverage levels. The rules can differ: with equal weights, let A={a,b}, course B={a,b,c,d,e}, and course C={a,c}. Overlap favors B by 2 versus 1, while symmetric-difference distance favors C by 2 versus 3. Confirm any deployment of this alternative before describing it as the current public implementation.
The public program archive’s independent scope statement explicitly limits its certification: it does not establish end-to-end interface conformance, empirical truth, causality, or appropriateness of thresholds. Concept documents distinguish proved mathematics from illustrative numeric columns and curricular assumptions. The transfer paper separates extraction from matching and policy. These are summaries of the supplied archives, not a new Lean build or independent certification performed for this presentation. Avoid saying the entire app or GPT is formally verified.
The curriculum workbook contains four sheets: Curriculum Map, Legend & Method, Atomic Concept Audit, and Coverage Summary. Its method decomposes 130 source topics and propagates their levels to atomic labels. The downloadable course archive contains thirteen course records plus synonyms and program metadata. The compact web example differs from the large workbook and should never be presented as its complete contents. The linked incoming syllabus is an old public Berkeley Multivariable Calculus example, not an incoming student’s current transfer record.
These links give the audience the public static apps, specialized assistants, and written tutorials. The static Transfer app was not separately exposed by the current directory. Linked resources may require an account or change after preparation. The presentation itself and its local demonstrations have no external library dependencies. The original template is preserved separately and was not edited.
The source list records the workbook, course archive, transfer map and syllabus, protocol paper, and assurance archive used for this presentation. The webpages, workbook values, and selected archive documentation were inspected. Linked video review is documented in the presenter guide if a summary was available. Public tutorial examples do not constitute validated institutional outcomes.