Assessmentin’the’Departmentof’ Mathemacs’and’Computer ......Coverage’ • 1.’All’math’courses,’spec.’1611,’2711,’3912,’CSAS’1114’ • 2.’All’math’courses,’spec.’1611,’2813,’3515,’3815

Assessment in the Department of Mathema1cs and Computer Science

An ongoing effort

In this era of powerful applica1ons and diverse students, a prime concern of mathema1cs departments must be to protect the core of mathema1cal culture: the value and validity of careful reasoning, of precise defini1on, and close argument. This is an ac1vity that is most highly cul1vated in mathema1cs, but vital for the whole of society. -‐-‐Roger Howe, Yale University

Summary of Program Review, 2009

•  …the discussion of the major itself is uninformed by a sense of what students are learning and how skill proficiencies can be improved.


•  There is a brief discussion of student advising in the self study, and a discussion about post gradua1on careers, but liPle about skills taught and whether students find them useful.


•  Student sa1sfac1on is measured by alumni academic achievement, career achievement, test results, capstone projects, porQolios and interviews. The external math reviewer, Dr. Linda Lesniak of Drew University, specifically cites student sa1sfac1on as a strength of this program.


•  The Mathema1cs curriculum seems consistent with disciplinary norms and best prac1ces at compe1tor schools.

Department Retreat, June 2011

•  The purpose of this retreat is to look at our current mathema1cs major course of study and to determine what changes need to be made in light of recent developments in the field as well as the College of Arts and Sciences.

Sta1s1cs ≠ Mathema1cs

Required Intro

•  Calculus I,II,III •  Int. Discrete •  Founda1ons •  Lin Alg.

•  Calculus I,II,III •  Int. Discrete/proof •  [Symbolic Logic—PHIL1204]

•  [CSAS 1114] •  4 credit prob/stat (NEW)

•  Lin Alg.

Required Advanced

•  Abstract Alg I •  -‐Analysis I •  -‐Junior Seminar •  + at least one of Alg or Analysis II

•  Abstract Alg MATH3815 •  Analysis MATH3515 •  Junior Seminar (3 credit) MATH3912

•  MATH 3626 Applied Matrices (to cover OR, stochas1c matrices Systems of DE, Numerical Analysis)

Upper Level Elec1ve

•  4 courses at the 3000 level or above, which must include a 2-‐part sequence. (among the courses: DE, Numerical analysis, Sta1s1cs, Number theory, Geometry, History of Mathema1cs)

•  4 courses at the 3000 level or above

•  MATH3815 Algebra •  MATH 4815 Advanced Topics in Algebra

•  Prerequisites for all courses en1tled “Advanced Topics” will be the course in the sequence immediately preceding it

Departmental Honors

•  Comple1on of 3 sequences, two of which are Alg and Analysis

•  4092 seminar •  3.3 in all courses 3000 and above

•  Comple1on of one sequence in either Analysis or Algebra

•  4092 seminar •  3.3 in all courses 3000 and above

Math Major Learning Objec1ves •  “Learned Socie1es”: MAA, AMS, CUPM,NCTM •  St. Olaf: •  Mathema'cs Major ,Intended Learning Outcomes •  Students will demonstrate: •  the ability to understand and write mathema1cal proofs. •  the ability to use appropriate technology to assist in the

learning and inves1ga1on of mathema1cs. •  apprecia1on of mathema1cs as a crea1ve endeavor. •  the ability to use mathema1cs as a tool that can be used to

solve problems in disciplinary and interdisciplinary selngs. •  the ability to effec1vely communicate mathema1cs and other

quan1ta1ve ideas in wriPen and oral forms.

Outcomes of a mathema1cs major

•  1. Knowledge of Problem Solving. – Students know, understand and apply the process of mathema1cal problem solving.


•  2. Knowledge of Reasoning and Proof. – Students reason, construct, and evaluate mathema1cal arguments and develop as apprecia1on for mathema1cal rigor and inquiry.


•  3. Knowledge of Mathema1cal Communica1on. – Students communicate their mathema1cal thinking orally and in wri1ng to peers, faculty and others.


•  4. Knowledge of Mathema1cal Connec1ons. –  Students recognize, use, and make connec1ons between and among mathema1cal ideas and in contexts outside mathema1cs to build mathema1cal understanding.


•  5.Knowledge of Technology. – Students can employ technology appropriately for doing mathema1cs.


•  6. Knowledge of Number and Opera1ons. – Students demonstrate computa1onal proficiency, including a conceptual understanding of numbers, ways of represen1ng number, rela1onships among number and number systems, and the meaning of opera1ons.


•  7.Knowledge of Algebra. – Students demonstrate a computa1onal and conceptual understanding of the axioma1c structure of vector spaces, groups, rings and fields.


•  8. Knowledge of Geometries. – Students use spa1al visualiza1on and geometric modeling to explore and analyze geometric shapes, structures, and their proper1es.


•  9. Knowledge of Analysis. –  Students demonstrate a computa1onal and conceptual understanding of limit, con1nuity, differen1a1on, and integra1on and gain a thorough background in techniques and applica1on of analysis and the mathema1cal idea of the infinite.


•  10. Knowledge of Discrete Mathema1cs. – Students apply the fundamental ideas of discrete mathema1cs in the formula1on and solu1on of problems.


•  11. Knowledge of Data Analysis, Sta1s1cs and Probability. – Students demonstrate an understanding of concepts and prac1ces related to data analysis, sta1s1cs, and probability.

Coverage •  1. All math courses, spec. 1611, 2711, 3912, CSAS 1114 •  2. All math courses, spec. 1611, 2813, 3515, 3815, 3912, PHIL 1204 2711, 3111, 3912, CSAS 1114 •  3. All Fresh/Soph courses, spec. 3111, 3411, 3513, 3514, 3611,

3612, 3626, 3711, 3614, 4512, 4712, CSAS 1114, PHIL 1204 •  4. All Fresh/Soph courses, spec. 3514, 3611, 3513, 3411, CSAS 1114 •  1611, 3111, 3815, 3813, 4512, 3513 •  2813, 3815, 3626, 4816 •  1511, 2511, 3911, 3626, 4512, 4911 •  1501, 1511, 2511, 3515, 3514, 4512, 4516, 4911 •  1611, 2711, 3612, 3614, 3411 •  2711, 3711

Outcomes addressed 1.  All math courses, spec. 1611, 2711, 3912, CSAS 1114 2.  All math courses, spec. 1611, 2813, 3515, 3815, 3912, PHIL 1204 3.  2711, 3111, 3912, CSAS 1114 4.  All Fresh/Soph courses, spec. 3111, 3411, 3513, 3514, 3611, 3612,

3626, 3711, 3614, 4512, 4712, CSAS 1114, PHIL 1204 5.  All Fresh/Soph courses, spec. 3514, 3611, 3513, 3411, CSAS 1114 6.  1611, 3111, 3815, 3813, 4512, 3513 7.  2813, 3815, 3626, 4816 8.  1511, 2511, 3911, 3626, 4512, 4911 9.  1501, 1511, 2511, 3515, 3514, 4512, 4516, 4911 10.  1611, 2711, 3612, 3614, 3411 11.  2711, 3711

Department Retreat, June 2012

•  The purpose of this retreat is to look at our current mathema1cs major course of study and to determine what changes need to be made in light of recent developments in the field as well as the College of Arts and Sciences.

•  “Learned Socie1es”: MAA, AMS, CUPM,NCTM •  Established assessment project

Course Objec1ves: MATH 2711 •  Students will demonstrate a knowledge of the key concepts in

combinatorics, probability and sta1s1cs covered in the text, lectures, or supplements, and be able to apply these in a variety of situa1ons.

•  Students will apply basic sta1s1cal analysis and elementary calculus, integrated with the principles and distribu1ons presented in the class, to the problems of probability and sta1s1cal modeling.

•  Students will analyze data from various applica1ons in exploring inferen1al sta1s1cs. They will perform calcula1ons by hand as well as with sopware. Applica1ons may be taken from texts, the literature, on-‐line resources, or student-‐generated data.

Course Objec1ves: MATH 2711 (cont.) •  Students will pursue an extended inves1ga1on of at least one

sta1s1cal ques1on, and present wriPen conclusions using proper sta1s1cal terminology and good technical style, incorpora1ng appropriate forms of data visualiza1on (charts, tables, graphics, etc.). This inves1ga1on may be based on data from the instructor, external sources, or student-‐generated research projects.

•  Students will iden1fy ethical issues that may arise in acquiring and using sta1s1cal informa1on, and demonstrate an ability to discuss these in a cri1cal way.

Department Retreat, June 2013 •  Discussion of Assessment Project for 2012-‐2014 –  2. Knowledge of Reasoning and Proof.

•  Students reason, construct, and evaluate mathema1cal arguments and develop as apprecia1on for mathema1cal rigor and inquiry.

–  3. Knowledge of Mathema1cal Communica1on. •  Students communicate their mathema1cal thinking orally and in wri1ng to peers, faculty and others.

•  Crea1on of our own assessment forms for oral and wriPen work

Data •  In 2013, the retreat focused on the analysis of the assessment project for the year. It is a two year project.

•  – We used three separate courses:

•  Fall, 2012 MATH 3515 (Analysis I)-‐-‐wriPen work from final exam; (proof of result not seen before in the course) Math 3511.pdf

•  Spring, 2013 MATH 3912 (Junior Seminar)-‐-‐(a) Petersheim poster presenta1ons; Spring, 2013 MATH 3912 (Junior Seminar)-‐-‐(b) Oral Presenta1on to department; Spring 2013 MATH 4912 (Senior Project )-‐-‐1 student, oral presenta1on [department used assessment tool from Petersheim

•  Spring, 2013 MATH 3912 (Junior Seminar)-‐-‐(c) Paper wriPen by class has been accepted for publica1on by Graph Theory Notes of NY. Jr Sem GTN paper.pdf

Outcomes

•  It is the opinion of the department that student performance in standard #2 was en1rely sa1sfactory. While high-‐achieving students performed as expected, the dept. was par1cularly impressed by the improvement in the students who had not previously dis1nguished themselves.

Con1nua1on

•  MATH 3815 •  Junior Seminar •  Senior Projects

Documents

Assessmentin’the’Departmentof’ Mathemacs’and’Computer ......Coverage’ • 1.’All’math’courses,’spec.’1611,’2711,’3912,’CSAS’1114’ • 2.’All’math’courses,’spec.’1611,’2813,’3515,’3815