DNSM Program Outcomes

A Discussion

College Math Program Outcomes

After looking at material from the Mathematical Association of America, the American Mathematical Association of Two Year Colleges, the National Council of Teachers of Mathematics, I have tentatively come up with this proposed list of program level outcomes for the college level math courses at the College of Micronesia-FSM.

Program Outcomes
Students will be able to:
1. define arithmetic, algebraic, geometric, spatial, and statistical concepts
2. calculate arithmetic, algebraic, geometric, spatial, and statistical quantities using appropriate technology.
3. estimate arithmetic, algebraic, geometric, spatial, and statistical solutions
4. solve arithmetic, algebraic, geometric, spatial, and statistical expressions, equations, functions, and problems using appropriate technology.
5. represent mathematical information numerically, symbolically, graphically, verbally, and visually using appropriate technology.
6. develop mathematical and statistical models such as formulas, functions, graphs, tables, and schematics using appropriate technology.
7. interpret mathematical and statistical models such as formulas, functions, graphs, tables, and schematics, drawing conclusions and making inferences based on those models.
8. explore mathematical systems utilizing rich experiences that encourage independent, nontrivial, constructive exploration in mathematics.
9. communicate mathematical thoughts and ideas clearly and concisely to others in the oral and written form.

The above material is color coded in the online web page version using the following coding:
Crimson is the action, meant to be interpreted broadly and generally with the intent of subsuming many related action words.
Indigo is the mathematical field descriptors meant to indicate some of the fields in which the outcome is to be applied. These listings should not be taken as limiting.
Dark green is the target object of the action
Saddle brown is the condition under which the action is to be performed.

Let me begin by noting that this document presumes prior knowledge of the following four documents: http://shark.comfsm.fm/~dleeling/department/slorevolution.html
http://shark.comfsm.fm/~dleeling/department/slorevolution_ii.html
http://shark.comfsm.fm/~dleeling/department/slorevolution_iii.html
http://shark.comfsm.fm/~dleeling/department/systemwidecompetencies.html

These program level outcomes will appear where we used to list general objectives on our outlines. These outcomes only apply to college level math courses, although some of them may also be applicable to developmental math courses. Each courses does not need to use and meet all of these program outcomes. Different courses will likely serve different subsets of the above superset.

Notice that my discussion of Type I and II outcomes has shelved. Turns out the Type I outcomes were never really true student learning outcomes in the first place, but were rather indicators. I still hold that the institution may have outcomes that utilize Type I indicators such as "The institution will maintain a reasonable faculty to student ratio." I continue to maintain that this is a worthy and valid learning outcome. It happens to be measured by an indicator, but it is still an outcome. There exists the opinion that the bulk of these will be measured out of the Director of Research and Planning's office.

Please bear in mind that these program outcomes are PROPOSED. With this note I am soliciting discussion on the the outcomes.

MS/ED 110 Math for Teachers I

To help frame this discussion, I am going to take a look at what happens to outlines with this model. I will start with the first of the proposed MS/ED 110 Math for Teachers year long course outlines. This is part of a plan to take MS/ED 110 into the fourth year education program as a year long integrated content and methods course.

Below is a section of the current proposed outline:

Course Objectives

General: The student will:
1. Develop a firm understanding and background in mathematics topics that are taught in the elementary levels
2. Improve skills in planning mathematics instruction by utilizing the Pacific Standards for Mathematics
3. Learn mathematics constructively through the appropriate use of manipulatives, models, and diagrams
4. Be able to convey mathematical thoughts and ideas clearly and concisely to others in the oral and written form
5. Acquire confidence in using mathematics meaningfully and be able to apply mathematics thinking and modeling to solve problems that arise in other disciplines
Specific: The student will be able to
1. Select and apply a variety of strategies to solve multi-step problems; including making a table, chart or list, drawing pictures, making a model, and comparing with previous experience
2. Apply algebraic methods to solve a variety of real-world and mathematical problems
3. Use patterns and functions to represent and solve problems
4. Develop number sense for whole numbers and their four fundamental operations.
5. Model and explain the processes of addition, subtraction, multiplication, and division and describe the relationship between them
6. Identify, model, and label simple fractions. Describe and define them as the part-to-whole concept, the division concept, and the ratio concept
7. Use, explain, and define the rules of divisibility, prime and composite numbers, multiples, and order of operations
8. Develop and apply number theory concepts (e.g., primes and composite factors and multiples,) in real-world and mathematical problem situations
9. Describe, extend, analyze, and create a wide variety of patterns
10. Recognize, describe, and use properties of the real number system.
11. Describe and use a variety of estimation strategies including rounding to the appropriate place value, multiplying by powers of 10, and using front-end estimation to check the reasonableness of solutions
12. Describe and model the relationship of fractions: to decimals, percents, ratios, and proportions
13. Model counting, adding, and subtracting in different base systems
14. Organize and communicate mathematical problem solving strategies and solutions to problems.

Under the new program outcomes system the outline might take on the following look:

Program Outcomes
Students will be able to:
1. define arithmetic, algebraic, geometric, spatial, and statistical concepts
2. estimate arithmetic, algebraic, geometric, spatial, and statistical solutions
3. solve arithmetic, algebraic, geometric, spatial, and statistical expressions, equations, functions, and problems using appropriate technology.
4. develop mathematical and statistical models such as formulas, functions, graphs, tables, and schematics using appropriate technology.
5. interpret mathematical and statistical models such as formulas, functions, graphs, tables, and schematics, drawing conclusions and making inferences based on those models.
6. explore mathematical systems utilizing rich experiences that encourage independent, nontrivial, constructive exploration in mathematics.
Course outcomes
Students will be able to:
1. define arithmetic, algebraic, geometric, spatial, and statistical concepts
  1. Develop number sense for whole numbers and their four fundamental operations.
  2. Use, explain, and define the rules of divisibility, prime and composite numbers, multiples, and order of operations
  3. Recognize, describe, and use properties of the real number system.
2. estimate arithmetic, algebraic, geometric, spatial, and statistical solutions
  1. Describe and use a variety of estimation strategies including rounding to the appropriate place value, multiplying by powers of 10, and using front-end estimation to check the reasonableness of solutions
3. solve arithmetic, algebraic, geometric, spatial, and statistical expressions, equations, functions, and problems using appropriate technology.
  1. Select and apply a variety of strategies to solve multi-step problems; including making a table, chart or list, drawing pictures, making a model, and comparing with previous experience
  2. Apply algebraic methods to solve a variety of real-world and mathematical problems
  3. Use patterns and functions to represent and solve problems
  4. Organize and communicate mathematical problem solving strategies and solutions to problems.
4. develop mathematical and statistical models such as formulas, functions, graphs, tables, and schematics using appropriate technology.
  1. Develop and apply number theory concepts (e.g., primes and composite factors and multiples,) in real-world and mathematical problem situations
  2. Describe and model the relationship of fractions: to decimals, percents, ratios, and proportions
  3. Model counting, adding, and subtracting in different base systems
5. interpret mathematical and statistical models such as formulas, functions, graphs, tables, and schematics, drawing conclusions and making inferences based on those models.
  1. Model and explain the processes of addition, subtraction, multiplication, and division and describe the relationship between them
  2. Identify, model, and label simple fractions. Describe and define them as the part-to-whole concept, the division concept, and the ratio concept
6. explore mathematical systems utilizing rich experiences that encourage independent, nontrivial, constructive exploration in mathematics.
  1. Describe, extend, analyze, and create a wide variety of patterns

Note that under the new format the program outcomes are restated in the course outcomes section. As a result, the program outcomes are measured by student attainment of the course outcomes given for each program outcome. If the specific course outcomes are met, then the program meta-outcome has been measured and met.

The above is a crude cut-and-paste of the old outline into the new format. I made some questionable choices as to which course outcome should be assigned to which program outcome. That, however, is not the point of this exercise. Later Yen-ti, Sue, and I will be trying to wrestle the current MS/ED 110 outline into the new format, but I expect we may have to rewrite either course outcomes or program outcomes to do this.

The key finding for me was that the new outline is far less comprehensible than the old. The new outline is terribly choppy and disorganized. The PE 101j outline, however, does not come across as being quite as choppy. This suggests to me that even well written SLO based outlines may need extensive rewriting before they can go into the new format. I can see a need for all kinds of redundancies in the outline for outcomes such as the current "Select and apply a variety of strategies to solve multi-step problems; including making a table, chart or list, drawing pictures, making a model, and comparing with previous experience." This outcome would have to be broken and redistributed under solve, interpret, and represent at the very least.

MS 150 Statistics

I am also redeveloping the MS 150 Statistics outline. At present it appears that all of the outcomes are under define, calculate, solve, and interpret, with the bulk of them under calculate and solve. Many of them read in the following manner: Students will be able to calculate a mean. Students will be able to calculate a sample standard deviation. I am also distinguishing [core] from peripheral, where core means the concept appears on the final examination.

The statistics outline, like the PE 101j outline, will also include a teacher intent section. This will include statements such as, Real-world data will be used where possible and practical. Sure, you could torque this around into a student learning outcome, Students will be able to use real-world data in the course, but it would corrupt the fact that the outcome is a teacher desire not a student competency.

I remain concerned about the choppiness, but hope that a careful rewrite might get around this inelegance. Another option would be to rewrite the program outcomes in search of a "non-choppy" set of program outcomes, but I think the program outcomes are somewhat constrained by MAA, NCTM, and AMATYC standards.

All of this is an enormously complex undertaking. In each area standards bodies will have to be consulted to ensure that our program outcomes are somewhat "sane" and connect to outcomes used at other colleges. I know the science outcomes will have to look at AAS' Project 2061, NSTA standards, and PREL Pacific Science standards. As I try to lead this effort as a division chair and tend to my other duties I find myself neglecting other areas. Such as producing a monthly report (a second month of no report!) and tending to my responsibilities as chair of Standard One of the self-study.