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Mathematical Science Teachers, Postsecondary

SOC 25-1022.00Job Zone 5 · Extensive Preparationv.26.05

Context coveredThis framework covers the full instructional, curricular, assessment, and mentorship responsibilities of postsecondary mathematical science teachers across emerging through advanced career stages in university and college settings.

Sources:O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.SkillsCrosswalkSkillsCrosswalk — O*NET enrichment + adjacency index. Opens in new tab.
Emerging
Entry / Apprentice
  1. Undergraduate course lectures — prepare and deliver introductory presentations on topics such as calculus or linear algebra under the guidance of a supervising faculty mentor in a university classroom setting.
  2. Examination materials — compile and administer assessments for lower-division mathematics courses using departmentally approved templates and rubrics under faculty supervision.
  3. Student work — evaluate and grade routine homework assignments and quizzes using provided answer keys and grading guidelines in a postsecondary instructional context.
  4. Course syllabi and handouts — prepare standard course materials by adapting existing departmental templates for use in an introductory undergraduate mathematics course.
  5. Student attendance and grade records — maintain accurate logs using university learning management systems under the procedural guidance of senior faculty.
  6. Classroom discussions — initiate and facilitate structured student exchanges on foundational mathematical concepts by following discussion protocols established by the course coordinator.
  7. Office hours — maintain regularly scheduled sessions to provide academic guidance to undergraduate students in a university mathematics department.
  8. Mathematical reasoning problems — apply deductive and inductive reasoning to explain standard proof techniques to students encountering formal mathematics for the first time.
  9. Analytical software tools — use course-approved platforms such as MATLAB or Mathematica to demonstrate mathematical concepts during scheduled laboratory or recitation sessions.
  10. Active listening and social awareness — observe student comprehension signals during lectures and adjust pacing or examples in response, under the mentorship of experienced instructors.
Developing
Mid-level / Established
  1. Lecture series for undergraduate and introductory graduate courses — design and deliver coherent instructional sequences on topics such as differential equations and discrete mathematics with reduced supervisory oversight.
  2. Examinations and assessments — compile, administer, and grade course-level evaluations independently, applying consistent grading criteria aligned with course learning objectives in a postsecondary mathematics department.
  3. Student assignments and papers — evaluate written mathematical work with attention to rigor, notation, and logical structure across multiple course sections in a university setting.
  4. Course materials — revise and update syllabi, problem sets, and supplementary handouts based on student performance data and emerging pedagogical best practices.
  5. Curricula review — participate in departmental curriculum evaluation meetings, offering evidence-based suggestions for improving content sequencing and instructional methods.
  6. Student records — manage and maintain complete and compliant attendance, grade, and advising records using university database and scheduling systems with minimal administrative support.
  7. Classroom discussion facilitation — moderate mathematically rigorous Socratic dialogues that develop students' critical thinking and proof-writing skills in an upper-division course environment.
  8. Complex problem-solving instruction — guide students through multi-step, non-routine mathematical problems by applying learning strategies tailored to diverse student preparation levels.
  9. Word processing and spreadsheet software — produce professionally formatted course documents, grade books, and student progress reports independently for departmental records.
  10. Time management planning — coordinate teaching responsibilities, office hours, grading deadlines, and research obligations across a full semester course load in a research-active university.
Proficient
Senior / Expert IC
  1. Graduate and upper-division undergraduate lectures — autonomously design and deliver advanced instruction on topics such as real analysis, abstract algebra, or topology, adapting content to diverse learner backgrounds in a doctoral-granting department.
  2. Comprehensive assessment systems — independently develop, administer, and evaluate a full suite of examinations, projects, and written papers that measure both procedural fluency and mathematical reasoning in a postsecondary context.
  3. Non-routine student work — assess and provide substantive written feedback on graduate-level proofs, theses chapters, and research expositions, applying expert judgment about mathematical validity and communication quality.
  4. Curriculum design and revision — independently lead the planning, evaluation, and revision of course content and instructional methods for a mathematics program sequence, incorporating current disciplinary and pedagogical research.
  5. Interdisciplinary course materials — develop innovative syllabi and handouts that integrate computational tools, real-world applications, and primary literature to enhance student engagement and disciplinary depth.
  6. Student academic advising — provide sustained mentorship and guidance to undergraduate and graduate students during office hours and advising sessions, supporting degree planning and research development in a university mathematics department.
  7. Classroom discourse management — facilitate high-level seminar discussions that require students to construct, critique, and refine mathematical arguments autonomously in graduate-level course environments.
  8. Learning strategy differentiation — apply evidence-based instructional approaches to address varied levels of mathematical preparation and learning needs across a heterogeneous student population.
  9. Analytical and scientific software integration — incorporate tools such as Mathematica, R, or Python seamlessly into course delivery and assessment to support computational mathematics pedagogy.
  10. Systems evaluation — assess the effectiveness of instructional methods and course structures by analyzing student performance trends and implementing data-informed improvements across a full academic year.
Advanced
Lead / Principal / Executive
  1. Mathematics program curriculum — lead the comprehensive design, evaluation, and reform of undergraduate and graduate mathematics curricula at the departmental or college level, aligning content with national standards and institutional strategic goals.
  2. Faculty instructional development — mentor junior faculty and graduate teaching assistants in evidence-based pedagogical methods, providing structured feedback on teaching practice within a university mathematics department.
  3. Examination and assessment policy — establish departmental standards and policies for assessment design, grading equity, and academic integrity across all course levels and instructors.
  4. Scholarly course materials and textbooks — author or edit advanced instructional resources, including textbooks, open-access course notes, and problem sets, that contribute to the broader mathematical education community.
  5. Graduate student mentorship — direct the academic and professional development of doctoral students, overseeing dissertation research, qualifying examinations, and career preparation in a research-intensive postsecondary environment.
  6. Institutional curriculum governance — represent the mathematics department on university curriculum committees, advocating for program priorities and leading cross-disciplinary course articulation and policy decisions.
  7. High-level classroom discourse — design and model transformative seminar and lecture formats that cultivate independent mathematical inquiry and scholarly habits of mind among advanced graduate students.
  8. Strategic advising and outreach — build advising frameworks and student-support initiatives that improve retention and degree completion across the mathematics program, coordinating with institutional student success offices.
  9. Technology and learning environment strategy — lead departmental adoption of analytical software platforms, online learning tools, and database systems to modernize mathematics instruction at scale.
  10. Disciplinary leadership and knowledge dissemination — present pedagogical and mathematical research at national conferences, publish in peer-reviewed venues, and serve in editorial or leadership roles that advance the field of mathematical science education.

AI-at-Work Competency Framework

Sources:Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab.Jadhav & Danve, 2026Skill Automation Feasibility Index — Jadhav & Danve, 2026 (arXiv:2604.06906). Opens in new tab.WEF Skills TaxonomyWEF Skills Taxonomy 2021 — Building a Common Language for Skills at Work. Opens in new tab.
Subscriber feature

Authoritative source data identified for 998 occupations

How a worker at each mastery level uses, directs, and evaluates AI tools in this occupation. Each statement cites its evidence inline; click a citation chip to verify the source.

Emerging
  1. AI-assisted problem set drafting — uses an AI tool to generate initial homework problems and practice exercises for standard topics such as calculus or linear algebra, then reviews each item for mathematical correctness before distribution Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
  2. Lecture note scaffolding — prompts an AI assistant to outline lecture structures for undergraduate courses, then fills in rigorous mathematical derivations and proofs by hand Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab. WEF Skills TaxonomyWEF Skills Taxonomy 2021 — Building a Common Language for Skills at Work. Opens in new tab..
Developing
  1. Exam compilation support — delegates first-draft question generation for quizzes and exams to an AI tool, then edits items to match course learning objectives and verifies solution accuracy independently Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab. Jadhav & Danve, 2026Skill Automation Feasibility Index — Jadhav & Danve, 2026 (arXiv:2604.06906). Opens in new tab..
  2. Grading rubric construction — directs an AI assistant to draft scoring rubrics for written assignments and proofs, then refines criteria to reflect disciplinary standards and pedagogical intent Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
  3. Attendance and grade record automation — uses AI-enabled administrative tools to organize and reconcile student attendance logs and grade entries, reserving judgment calls on borderline cases for personal review Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
Proficient
  1. Syllabus and course material production — orchestrates AI-generated drafts of syllabi, handouts, and reading guides across multiple courses simultaneously, applying critical evaluation to ensure mathematical rigor and alignment with program outcomes Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab. WEF Skills TaxonomyWEF Skills Taxonomy 2021 — Building a Common Language for Skills at Work. Opens in new tab..
  2. Formative feedback acceleration — hands off batches of student written work to an AI tool for preliminary error-pattern identification, then synthesizes the output into targeted, instructor-authored feedback that addresses conceptual misunderstandings Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab. Jadhav & Danve, 2026Skill Automation Feasibility Index — Jadhav & Danve, 2026 (arXiv:2604.06906). Opens in new tab..
  3. Differential equations and discrete mathematics explanation generation — directs an AI assistant to produce multiple alternative explanations or worked examples for high-difficulty topics, selecting and adapting the most pedagogically effective versions for classroom delivery Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
  4. Research literature synthesis — tasks an AI tool with summarizing relevant mathematical literature or pedagogical research, then critically appraises the summaries against primary sources before incorporating findings into course design Jadhav & Danve, 2026Skill Automation Feasibility Index — Jadhav & Danve, 2026 (arXiv:2604.06906). Opens in new tab. WEF Skills TaxonomyWEF Skills Taxonomy 2021 — Building a Common Language for Skills at Work. Opens in new tab..
Advanced
  1. Curriculum-level AI workflow design — architects department-wide protocols for AI-assisted course development, specifying where AI tools augment content creation versus where instructor mathematical expertise remains the sole authority, and trains junior faculty in responsible adoption Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab. WEF Skills TaxonomyWEF Skills Taxonomy 2021 — Building a Common Language for Skills at Work. Opens in new tab..
  2. High-autonomy task boundary governance — evaluates which instructional tasks—such as proof verification, graduate student mentorship, and original mathematical exposition—fall outside safe AI delegation given the occupation's Q1 displacement-risk profile, and communicates these boundaries explicitly in teaching practice Jadhav & Danve, 2026Skill Automation Feasibility Index — Jadhav & Danve, 2026 (arXiv:2604.06906). Opens in new tab. Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab..
  3. AI-mediated adaptive assessment design — engineers assessment pipelines in which AI tools generate, randomize, and provide immediate feedback on problem sets at scale, while the instructor retains authorship of learning objectives, difficulty calibration, and academic integrity standards Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab. WEF Skills TaxonomyWEF Skills Taxonomy 2021 — Building a Common Language for Skills at Work. Opens in new tab..
  4. Critical evaluation of AI mathematical output — systematically audits AI-generated solutions, proofs, and explanations for logical errors and notational inconsistencies, modeling this verification process for students as a transferable epistemic practice in mathematical reasoning Jadhav & Danve, 2026Skill Automation Feasibility Index — Jadhav & Danve, 2026 (arXiv:2604.06906). Opens in new tab..
Evidence pack
AEI usage
Task observations: 5107
Augment share: 95%
Time saved: 83%
AI autonomy: 3.04
SAFI positioning
Top skill: Mathematics
Score: 73.2 / 100
Quadrant: Q1_high_displacement_risk
precision: exact
WEF cluster
Human-Technology Interaction
human_technology_interaction
Sources:Anthropic Economic IndexAnthropic Economic Index — release_2026_03_24. Opens in new tab.WEF Skills TaxonomyWEF Skills Taxonomy 2021 — Building a Common Language for Skills at Work. Opens in new tab.Jadhav & Danve, 2026Skill Automation Feasibility Index — Jadhav & Danve, 2026 (arXiv:2604.06906). Opens in new tab.

Pathsmith Durable Skills Framework

Sources:Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Subscriber feature

Ten durable-skill domains mapped to four proficiency/role levels for each occupation. Each statement is aligned to the Pathsmith taxonomy, derived from trusted grounding data and mapped to occupation-specific O*NET tasks and skills.

1Communication11 statements
Emerging
  1. Mathematical vocabulary introduction — uses standard notation and terminology when presenting foundational concepts such as limits or basic algebra to entry-level undergraduate audiences Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Lecture preparation basics — drafts simple explanations and worked examples for course handouts under faculty supervision O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Developing
  1. Concept explanation calibration — adjusts verbal explanations of topics such as linear algebra or differential equations based on observed student comprehension during class Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Discussion facilitation — poses structured questions to initiate and sustain productive classroom dialogue about mathematical reasoning and proof strategies O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Written feedback delivery — provides written comments on student assignments that identify specific errors in logic or computation and suggest corrective approaches Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Applying
  1. Lecture delivery — prepares and delivers coherent, sequenced lectures on advanced topics such as discrete mathematics or real analysis to undergraduate and graduate audiences with clarity and appropriate rigor O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Syllabus and course document communication — authors syllabi, assignment descriptions, and rubrics that precisely convey expectations, grading criteria, and mathematical scope O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Office hour advising — elicits student confusion through active listening and responds with targeted explanations tailored to individual mathematical background Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Exceeding
  1. Cross-audience mathematical communication — translates complex graduate-level research topics into accessible presentations for diverse audiences including undergraduates, interdisciplinary colleagues, and public stakeholders Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Curriculum communication leadership — leads faculty discussions to align course communication standards and mathematical writing expectations across a department's course sequence O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Scholarly writing mentorship — guides graduate students in communicating original mathematical findings through rigorous proof writing and academic publication preparation Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
2Leadership10 statements
Emerging
  1. Classroom initiative — takes responsibility for managing basic classroom logistics such as distributing materials and recording attendance without prompting Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Peer support modeling — volunteers to demonstrate problem-solving approaches to fellow graduate teaching assistants during pedagogical training Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Curriculum contribution — proposes revisions to homework assignments or course materials based on observed student performance and disciplinary updates O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Student academic guidance — proactively identifies struggling students during office hours and directs them toward appropriate support resources Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Applying
  1. Course ownership — independently plans, evaluates, and revises course content, instructional methods, and assessment instruments for assigned undergraduate or graduate mathematics courses O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Undergraduate research direction — assigns and oversees independent mathematical investigations for advanced undergraduates, providing structured feedback and milestone accountability Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Committee participation — contributes substantively to departmental curriculum committees by evaluating course proposals and recommending changes to mathematical program requirements O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Exceeding
  1. Departmental program leadership — leads the design or overhaul of a mathematics concentration, graduate program, or interdisciplinary mathematics initiative, coordinating faculty roles and learning outcomes Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Doctoral mentorship — takes sustained responsibility for shaping the intellectual development, research trajectory, and professional readiness of doctoral students in mathematics Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Institutional mathematics advocacy — represents the mathematical sciences faculty in institutional governance, advocating for resource allocation and curricular standards that elevate disciplinary quality Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
3Metacognition9 statements
Emerging
  1. Teaching self-reflection — identifies specific moments in a lecture where student engagement dropped and connects those moments to gaps in one's own instructional preparation Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Learning strategy awareness — recognizes which mathematical topics require more personal review before teaching and allocates preparation time accordingly Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Instructional approach monitoring — tracks which pedagogical techniques produce stronger student performance on exams and adjusts mid-semester instructional strategies in response Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Mathematical knowledge gap identification — diagnoses areas of personal content expertise that require deepening prior to teaching new or advanced course topics Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Applying
  1. Pedagogical strategy evaluation — systematically reviews student outcome data across multiple semesters to evaluate the effectiveness of one's own instructional methods and revises curricula accordingly Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Research-teaching integration reflection — consciously monitors how one's active research agenda informs and enriches classroom examples and problem selection Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. Assessment design self-review — critiques one's own examination and rubric designs for alignment with stated learning objectives before administering them to students Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Exceeding
  1. Scholarly teaching inquiry — conducts formal self-study of one's own teaching effectiveness using student performance evidence and peer observation, publishing or presenting findings to improve mathematics pedagogy broadly Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Mentored metacognitive modeling — explicitly teaches doctoral and advanced undergraduate students to monitor their own mathematical reasoning processes and identify productive versus unproductive problem-solving strategies Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
4Critical Thinking11 statements
Emerging
  1. Proof verification — checks student-submitted proofs for logical validity and identifies specific steps where reasoning breaks down Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Assumption identification — recognizes implicit assumptions embedded in textbook problem statements and highlights them during introductory course instruction Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Examination design analysis — evaluates proposed exam problems for mathematical correctness, appropriate difficulty distribution, and alignment with course learning objectives Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Student reasoning diagnosis — analyzes patterns of error across a class's submitted work to determine whether misconceptions are computational, conceptual, or procedural in origin Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Curricular evidence evaluation — assesses competing textbook options or instructional approaches using evidence from peer-reviewed mathematics education research Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Applying
  1. Advanced problem construction — designs original examination problems and assignments that require students to synthesize multiple mathematical concepts and demonstrate non-routine reasoning Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Research hypothesis evaluation — applies rigorous analytical criteria to evaluate the validity of mathematical conjectures within one's own or students' research projects Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Pedagogical method critique — evaluates existing course delivery approaches by comparing student learning outcomes against established benchmarks and identifies causal explanations for performance gaps Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Exceeding
  1. Original theorem development — formulates and rigorously establishes new mathematical results through systematic analysis of existing proofs, identification of generalizable patterns, and formal verification Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Graduate research evaluation — critically assesses doctoral dissertation chapters and conference papers for logical rigor, methodological soundness, and contribution to the mathematical literature Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Field-level curriculum critique — leads departmental or national disciplinary conversations that challenge prevailing curricular assumptions and argue for evidence-based reforms in postsecondary mathematics education Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
5Collaboration10 statements
Emerging
  1. Co-instruction support — assists a lead faculty member in preparing course materials and grading for a shared course section, responding to feedback on task quality Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Departmental norm adoption — participates in shared grading calibration sessions to align one's evaluative standards with department-wide rubrics Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Developing
  1. Co-authorship contribution — contributes substantively to a jointly authored mathematical paper or grant proposal by producing assigned sections and integrating feedback from collaborators Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Interdisciplinary coordination — works with faculty in statistics, engineering, or physics departments to align mathematical prerequisites and shared course content Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Study group facilitation — designs and moderates structured collaborative problem-solving sessions that distribute mathematical reasoning responsibilities among student participants Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Applying
  1. Research team coordination — manages collaborative mathematical research projects involving graduate students and peer faculty, ensuring equitable contribution and timely progress toward shared publication goals Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Curriculum committee collaboration — works with departmental colleagues to collectively revise program learning outcomes, course sequencing, and assessment policies for the mathematics curriculum O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Cross-institutional partnership — collaborates with faculty at peer institutions on joint research, dual course offerings, or shared professional development initiatives in mathematical sciences Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Exceeding
  1. Research consortium leadership — builds and sustains multi-institutional or international mathematical research collaborations, navigating diverse disciplinary perspectives and allocating intellectual contributions equitably Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Doctoral cohort community building — structures graduate program environments so that doctoral students in mathematics collaborate productively on seminars, peer review, and joint projects rather than competing in isolation Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
6Character9 statements
Emerging
  1. Academic integrity modeling — enforces course academic honesty policies consistently and explains the mathematical community's standards for original work to students Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Attendance and record accuracy — maintains accurate student attendance and grade records in compliance with institutional requirements without error or delay O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Developing
  1. Equitable grading practice — applies assessment rubrics consistently across all student submissions, correcting one's own errors promptly and transparently when grading mistakes are identified Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Professional reliability — meets all course preparation deadlines, returns graded work within stated timelines, and honors all scheduled office hour commitments Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Applying
  1. Ethical research conduct — upholds standards for mathematical proof attribution, data integrity in applied mathematics research, and honest reporting of results in publications and presentations Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Inclusive classroom accountability — takes responsibility for identifying and addressing exclusionary dynamics in mathematical learning environments, including differential treatment of students by background or identity Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Transparent assessment communication — discloses grading criteria and learning objectives fully to students before assessments and provides honest, actionable performance feedback afterward Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Exceeding
  1. Disciplinary ethics leadership — shapes departmental or professional association standards for academic integrity, authorship ethics, and equitable access in postsecondary mathematics Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Mentorship accountability — takes explicit personal responsibility for the professional and ethical development of doctoral advisees, including modeling principled conduct in research disputes or publication decisions Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
7Creativity9 statements
Emerging
  1. Novel example construction — generates original worked examples that connect standard course content such as calculus or statistics to students' familiar real-world contexts Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Alternative explanation generation — invents a second or third approach to explaining a concept when the standard textbook explanation produces student confusion Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Developing
  1. Creative problem design — authors non-routine homework problems that require students to combine techniques from multiple mathematical topics rather than apply a single memorized procedure Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Pedagogical experimentation — pilots unconventional instructional formats such as inquiry-based learning or flipped lecture models in a mathematics course and evaluates their effect Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Applying
  1. Original course development — designs a new elective or graduate seminar around an emerging or underrepresented area of mathematics, creating all materials, sequencing, and assessments from scratch Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Mathematical research innovation — pursues original research questions by generating novel proof strategies or mathematical frameworks that extend or challenge established disciplinary knowledge Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Interdisciplinary problem formulation — constructs mathematical models or research questions that bridge the mathematical sciences with other fields such as biology, economics, or computer science Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Exceeding
  1. Field-advancing mathematical contribution — produces published original mathematical research that introduces new methods, theorems, or conceptual frameworks adopted by other researchers in the discipline Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Curricular innovation leadership — leads the creation of a distinctive pedagogical approach, course sequence, or program model in mathematics education that is adopted or cited by peer institutions Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
8Growth Mindset9 statements
Emerging
  1. Instructional feedback reception — accepts critical observations from course evaluations or peer reviewers without defensiveness and identifies one actionable improvement to implement in the next course offering Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Mathematical challenge engagement — voluntarily explores mathematical problems outside one's existing expertise as part of ongoing professional learning Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Teaching practice iteration — revises course delivery approaches between semesters based on student performance data and peer feedback rather than defaulting to identical methods Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Research persistence — maintains sustained engagement with an unresolved mathematical proof or research problem through periods of repeated failed attempts, documenting what each approach revealed Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Applying
  1. Growth mindset instruction — explicitly teaches students to interpret mathematical struggle as a productive part of the learning process rather than evidence of inability, embedding this into course design and feedback language Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Professional development commitment — pursues pedagogical training, research conferences, and new mathematical learning opportunities consistently across career stages, not only when required Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  3. Curricular adaptation after failure — analyzes courses or programs that produced poor student outcomes without assigning blame, isolates root instructional causes, and rebuilds course structure accordingly Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Exceeding
  1. Discipline-level learning culture shaping — establishes departmental norms that celebrate intellectual risk-taking, normalize mathematical difficulty, and reward iterative improvement in student and faculty work alike Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Mentorship through setback — guides doctoral students through dissertation failures, rejected papers, and negative peer reviews by modeling constructive response patterns and sustaining their belief in eventual mastery Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
9Mindfulness9 statements
Emerging
  1. Classroom attention management — notices when personal cognitive load from simultaneous teaching demands such as pacing, student questions, and board work is degrading lecture quality, and pauses to reset Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Student affect recognition — observes signs of frustration or disengagement in individual students during class and adjusts the instructional moment intentionally rather than continuing without response Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Office hour presence — gives full and undivided attention during student advising sessions, setting aside research or administrative distractions to engage genuinely with the student's mathematical difficulty Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Grading emotional regulation — approaches the evaluation of poorly executed student work with measured, non-reactive feedback that focuses on learning rather than disappointment Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Applying
  1. Intentional pacing in instruction — monitors the cognitive load of a lecture in real time, inserting deliberate pauses, checks for understanding, and transitions to prevent student overload during complex mathematical derivations Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Conflict de-escalation in academic settings — responds to grade disputes or academic integrity allegations with calm, structured communication that prevents escalation and preserves the student relationship Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. Research focus discipline — manages attention deliberately during mathematical research sessions, recognizing and redirecting unproductive cognitive patterns such as circular reasoning or premature conclusion Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Exceeding
  1. Mindful mentorship leadership — models and explicitly cultivates present-moment awareness and emotional regulation practices within the graduate student community, particularly during high-stakes events such as dissertation defenses or job searches Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Intentional course redesign — enters curricular revision processes with deliberate suspension of prior assumptions about what works, attending fully to new evidence before committing to instructional changes Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
10Fortitude9 statements
Emerging
  1. Difficult class management — continues to deliver instruction effectively on days when student participation is low, technology fails, or classroom dynamics are challenging Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Research frustration tolerance — persists with a mathematical problem through initial confusion and unsuccessful solution attempts without abandoning the inquiry prematurely Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
Developing
  1. Negative evaluation response — uses critical end-of-semester student evaluations as diagnostic information rather than as reasons to reduce instructional ambition or avoid challenging topics Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Grant rejection resilience — resubmits revised research proposals after funding rejections, incorporating reviewer feedback without abandoning the research agenda Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Applying
  1. Sustained research perseverance — pursues a long-term mathematical research program across multiple years of incremental progress, peer skepticism, or publication setbacks without abandoning the intellectual direction Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
  2. Institutional adversity navigation — maintains high standards for teaching and research through periods of departmental resource cuts, enrollment pressures, or institutional restructuring Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  3. High-stakes student advocacy — persists in advocating for a student's academic needs or thesis defense readiness even when departmental or institutional resistance is encountered Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Exceeding
  1. Career-spanning intellectual courage — pursues unconventional or unfashionable mathematical research directions despite limited initial recognition, maintaining rigorous standards and ultimately contributing lasting disciplinary value Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.
  2. Crisis teaching leadership — sustains coherent, high-quality mathematical instruction and student support through major institutional disruptions such as pandemic-era transitions, department reorganizations, or sustained budget crises, while simultaneously supporting faculty colleagues Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab. O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
Sources:Pathsmith Durable SkillsPathsmith Durable Skills Framework — America Succeeds + CompTIA. Opens in new tab.O*NET v30.2O*NET Resource Center — Occupational Information Network, v30.2 (Sept 2025). Opens in new tab.
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O*NET enrichment · skillscrosswalk.com

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Source anchors that ground each statement

Related titles
Actuarial Science Professor · Actuarial Science Teacher · Adjunct Instructor · Adjunct Lecturer · Adjunct Mathematics Instructor · Adjunct Mathematics Professor (Adjunct Math Professor) · Adjunct Professor · Algebra Teacher · Assistant Professor · Associate Professor · Biometry Teacher · Biostatistics Professor
RAPIDS apprenticeships
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O*NET skills
MathematicsSpeakingInstructingReading ComprehensionActive ListeningCritical ThinkingLearning StrategiesMonitoringWritingActive LearningComplex Problem SolvingJudgment and Decision MakingSystems EvaluationTime ManagementSocial PerceptivenessCoordinationService Orientation
Knowledge domains
MathematicsEducation and TrainingEnglish LanguageComputers and Electronics
Abilities
Mathematical ReasoningOral ExpressionNumber FacilityOral ComprehensionDeductive ReasoningWritten ComprehensionSpeech ClarityWritten ExpressionInductive ReasoningNear Vision
Work styles
Intellectual CuriosityDependabilityAttention to DetailAchievement OrientationSocial OrientationIntegrity
Technology
Computer based training softwareData base user interface and query softwareCalendar and scheduling softwareWord processing softwareAnalytical or scientific softwareInformation retrieval or search softwareElectronic mail softwareOptical character reader OCR or scanning softwareSpreadsheet softwareOffice suite software
Tasks · seed anchors for statements
  1. Compile, administer, and grade examinations, or assign this work to others.
  2. Evaluate and grade students' class work, assignments, and papers.
  3. Prepare and deliver lectures to undergraduate or graduate students on topics such as linear algebra, differential equations, and discrete mathematics.
  4. Maintain student attendance records, grades, and other required records.
  5. Prepare course materials, such as syllabi, homework assignments, and handouts.
  6. Plan, evaluate, and revise curricula, course content, and course materials and methods of instruction.
  7. Maintain regularly scheduled office hours to advise and assist students.
  8. Initiate, facilitate, and moderate classroom discussions.
CIP education codes
13.131126.110227.010127.010227.010327.010427.010527.019927.030127.030427.030527.030627.039927.050127.050227.050327.059927.060127.999930.080130.500138.010252.1302

Sources: O*NET v30.2 (CC BY 4.0), SkillsCrosswalk.com, LER.me, Anthropic Economic Index, SAFI (Jadhav & Danve, 2026), WEF Skills Taxonomy 2021, Pathsmith Durable Skills Framework. © 2026 EBSCOed.