Assessing the Mathematics Major

1
Assessing the Mathematics Major

• MathFest 2003
• Donna Flint
• Dan Kemp
• Department of Mathematics and Statistics
• South Dakota State University

2
Profile of SDSU

• Largest of five State Universities in South
  Dakota
• 10,000 Students
• About 70 mathematics majors
• 15-20 graduates per year- about half seeking
  teaching certification (long term average)
• 17 full time faculty

3
History of Assessment of Math Graduates at SDSU

• 1980s read 15 articles / write reaction papers
• 1990s added departmental competency test
• 1996 senior seminar course (response to
  University assessment requirement)
• 2002 revamping senior seminar (to align with
  mission statement and collect assessment
  information)

4
Departmental Learning Objectives

• Demonstrate competence in all core areas of
  undergraduate mathematics.
• Use contemporary mathematical and presentation
  software and technology.
• Apply research methods to mathematical problems.
• Communicate clearly and succinctly in writing in
  the discipline.
• Articulate complex ideas to an audience.
• Reflect on learning experiences over an extended
  period of time period to identify areas for
  further learning.
• (Extracted from Departmental Goals)

5
Senior Seminar Course

• One credit course (meets once a week)
• Major research paper (evaluated by faculty)
• Presentation of research paper (evaluated by
  faculty)
• Student portfolio

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During Semester

• To help prepare for paper and presentation
• Read journal article (Reaction paper)
• Calculus modeling problem (word process results)
• Short paper about major field or mathematics
  career
• Faculty talks / outside speaker

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Research Paper

• Survey of a single topic (careful with topic)
• Must include one proof
• Need not be original work
• 8-12 pages of content
• Weekly meetings with paper advisor
• Evaluated by volunteer faculty members
• Pamphlet available with directions and tips

8
Scale for research paper assessment

• 7 Excellent has no mathematical errors may
  need some minor re-wording
• 6 Very Good needs minor revisions in a few
  places
• 5 Good needs minor revisions sporadically
  throughout paper
• 4 Satisfactory minor revisions needed
  throughout the paper
• 3 Poor needs major revisions in a few places
• 2 Very Poor needs major revisions
  sporadically throughout paper
• 1 Unsatisfactory paper has little or no merit

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Sample Paper Assessment Document

• Math 490 Senior Seminar
  Spring 2003
• Research Paper
•  
• Student _________________ Faculty Reviewer
  __________________ Paper grade ____________
•  
• You are assessing a senior Mathematics Major
  students research paper. This paper was written
  with the supervision of a Mathematics Faculty
  member. You should assess the paper based on the
  following criteria using the scale as described
  on the attached memo. Learning objectives are
  listed in brackets. Please add additional
  comments on the back of this sheet.
•  
• Presentation
•  
• How well written is the report (e.g., correct
  grammar, spelling, etc.)? 4
• 1 2 3 4 5 6 7
•  
• How effectively does the student use
  graphics/figures (e.g. placement, neatness,
  etc.)? 2,4
• 1 2 3 4 5 6 7
•  
• How effectively does the student use examples to
  clarify points made in the paper? 4
• 1 2 3 4 5 6 7
•  

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Further Criteria for Research Paper Technical
Aspects of the Report
Scale (1-7) How well does the student 4.
explain the purpose of the project? 4 5.
explain the history of the project? 3,4 6.
explain the mathematics needed for this
problem? 3,4 7. use and cite both print and
electronic sources? 3 (Note numbers in
brackets are learning objectives)
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Further Criteria for Research Paper Mathematics/S
tatistics
Scale (1-7) How well does the student 8.
explore the topic in depth? 1,3 9. make
accurate math/stat statements? 1,3 10. justify
the math/stat statements? 1,3,4 11. use
notation? 1,3,4 12. demonstrate that he/she
understands the mathematics/statistics
involved? 1,4,5
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Sample Student Summary
Questions 1-3 Presentation (organization/writing)
Questions 4-7 Technical Report (explanations,
sources) Questions 8-11 Mathematics/Statistics
(notation, justification) Question 12 Overall
(impression of students understanding)
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Summary of Research Paper Data 2002-2003
Senior Seminar Class (Fall-4 students Spring- 2
students) Average faculty responses
(1-7) Learning Objective Average
Score Fall Spring 1 (competence)
5.47 4.97 2 (technology)
5.64 6 3 (apply research methods)
5.50 5.18 4 (communicate in writing)
5.54 5.39 5 (communicate verbally)
N/A N/A 6 (reflect on learning experiences)
N/A N/A
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Student Presentation

• Based on Paper (after comments from faculty)
• PowerPoint is used (already know how to use- and
  cleverly!)
• 25-30 minutes with 10 minutes for questions
• Attended by faculty and students
• Evaluated by volunteer faculty members

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Criteria for Student Presentation

• 7- excellent ready for presentation at a
  conference
• 6-Very good needs refinement
• 5- Good needs 1-2 minor changes
• 4- Satisfactoryneeds 3-5 minor changes
• 3- Poor needs 1-2 major changes
• 2- Very Poor needs 3-5 major changes
• 1- Unsatisfactory little or no merit

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Evaluation Criteriafor Student Presentation

• How well did the student
• 1. explain the purpose 5
• 2. organize the material 5
• 3. make use of technology 2
• 4. present themselves (voice, delivery) 5
• 5. answer questions 5
• 6. communicate his/her understanding 1,3,5
• 7. develop the mathematics 3,5
• 8. demonstrate that he/she understands the
  mathematics involved 1,4,5

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Summary of Student Presentation Data

• Senior Seminar Class (Fall-4 students Spring- 2
  students)
• Average faculty responses (1-7)
• Learning Objective
• Fall Spring
• 1 (competence) 5.81 4.18
• 2 (technology)
  6.10 6.64
• 3 (apply research methods) 5.71 4.32
• 4 (communicate in writing) N/A
  N/A
• 5 (communicate verbally) 5.92 5.32
• 6 (reflect on learning experiences) N/A N/A

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Student Portfolio

• Compiled by student
• For each item included, student must include a
  paragraph explaining how that item illustrates
  the requirement
• Evaluated by two faculty members
• Used by Department Head in exit interview
• Returned to student upon request

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Portfolio Expectations- Competence

• Calculus 1,4
• Linear Algebra 1,4
• 3 other upper level courses 1,4
• ability to write a correct and clear proof
  1,4
• use of mathematical software 2,4

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Portfolio expectations Reflection

• Example of test on which they did well (and why)
  4,6
• Example of test on which they did poorly (and
  why) 4,6
• Summary of extra-curricular activities 6
• Essay written as a sophomore- plans for academic
  career 6
• Essay written as senior- reflecting on career as
  student 6
• Essay written as senior- how student will use
  mathematics training or discuss student teaching
  experience 6

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Portfolio Expectations Other

• Revised Research Paper 3,4
• Current Resume 4
• Letter of Application for Job 4
• Letter from cooperating teacher (if seeking
  certification) 6
• Evaluation of the Mathematics Program 6

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Scale for Portfolio Evaluation

• 4- excellent (good choice/thoughts insightful)
• 3- good (good choice/needs more reflection)
• 2- poor (poor choice/very little or no
  reflection)
• 1- not included

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Summary of Portfolio Data

• Senior Seminar Class (Fall-4 students Spring- 2
  students)
• Average faculty responses (1-4)
• Learning Objective
• Fall Spring
• 1 (competence)
  3.69 3.958
• 2 (technology) 4 4
• 3 (apply research methods) 4 3.5
• 4 (communicate in writing) 3.76
  3.833
• 5 (communicate verbally) N/A N/A
• 6 (reflect on learning experiences)
  3.78 3.958

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Thoughts on Data

• Need more data (only two semesters- 6 students-
  next semester we have 10 students registered)
• Averages look good no evidence of a need to
  change

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Recommendations

• Students need more time to write paper and
  develop presentation
• Need more consistency in how students work with
  their advisors
• More consistency in evaluation needed train
  reviewers

26
Open Questions

• How can we involve faculty more and still
  maintain consistency?
• Calculus and Linear Algebra are what we decided
  to call core areas. Should technical ability
  in the core be assessed?

27
Thank you

• Thanks to MAA, NSF, and organizers of the SAUM
  Workshops for the opportunity explore assessment
  with guidance and with peers.
• Thanks to participants in the SAUM workshop for
  new ideas
• Thanks to SDSU Department of Mathematics and
  Statistics for encouragement and participation in
  assessment activities
• donna_flint_at_sdstate.edu
• daniel_kemp_at_sdstate.edu