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Population Explosion

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Technology Revolution

Population Explosion

Increased DENSITY

Information Rage

So many things to keep track of.

So many different ways we

keep track of them…

The logistical nightmare of it all …!

The Log of LogsMathematics Student Portfolio By Robert N. BakerInstructor of MathematicsNew Mexico State University, Grantsemail- [email protected] for AMATYC 2008 Washington, District of ColumbiaNovember 2008

Funk and Wagnall’s defines“log” as a noun, a

“record of the progress of an undertaking--usually technical in nature.”

Like learning mathematics !

So, how do we record progress …?

Laws of Nature

Job experiences & modern employers

Professional Standards: NCTM & AMATYC

Outcome Standards: UAS & NM Higher Ed.

indeed, through Accreditation processes

My own attempts to adapt Standards and student needs into practice to enhance traditional learning, humanely.

- 1905 Einstein: time-space continuum
Attempts to separate place from time have always distorted interpretations of reality, and always will.

- 1927 Heisenberg: uncertainty theorems
The more closely a measure informs us about position, the more it obfuscates trajectory, and vice versa.

- 1931 Gödel: incompleteness theorems
No set of axioms can fully explain a non-trivial system; there will always arise a truth that the system can not prove or predict.

By the 1930s, expanding American public school system adopted the INDUSTRIAL MODEL.

Alarmed mathematics educators responded:

George Polya: How to Solve It & Mathematical Discovery

Richard Currant and Herbert Robbins: What is Mathematics?

Mathematical problem solving in our dynamic world cannot be reduced to the static, discrete steps required by the assembly-line, mastery model.

They were ignored.

- 2004 & TIMMS suggests Polya and Courant were right.
- AMATYC and NCTM Standards finally insist:
Laws of the universe hold for people too!

Educational needs of community college students DO depend on both time and place.

“Traditional” pedagogy, its measures and assumptions

no longer suffice.

Through ≈ 1970: Mechanical, sensory

Could tinker and “figure it out”

In 2008: Electronic, abstract, symbolic

Must “read the instructions.”

Reasonable sometimes. Reducible to algorithm often. Seldom sensible…

The new “ Black Box” world

is not accessible

to the un-trained, to the un-equipped,

the illiterate.

U. Alaska president’s informal study 2000

Read and explain technical information

AMATYC and Georgia Transportation Dept 2001

Show up everyday

Learn from mistakes

“Every day you got to keep logs” said a worker on a water-drilling rig with a road-building crew.

(Overheard in Grants, NM on 26 June 2007. He provided example, shown here; a row for each “job,” in a 5-column table.)

- Apprenticeship includes training in system terminologies, reading charts for rigging and equipment. “They learn to look at a line, understandwhy it is built the way it is, and recognize the … range designed for each type and calculate their minimum …” (shades of Polya!)
- “Journeymen are gradually trained to do hot-line work. Meanwhile, they are busydocumenting daily activities.” The industry is changing pretty fast. With … devices and new loads coming online, you have to learn new stuff all the time.”

“Why adopt mathematics standards?...

- Increase quantitative literacy of all students
- Develop students ability to communicate mathematically.”

The 10% talented in mathematics/logic,

--assured by the normal curve, and

--traditional targets of math-ed in schools,

are no longer enough to meet modern society’s needs…

-- the “other” 90% also need mathematics, for employment and consumption

--and “algebra for all” diplomas and degrees

- Claim: Too many “good students” opt out of math and science as soon as possible.
- Why?
- The most significant contributing factors are the lacks of:
- Opportunity to develop facility
- with the language of the content

UAS Catalog“Student Outcome Goals: …Assignments and tasks will be embedded into the course objectives of many different courses at different level of the curricula to provide students the opportunity to learn and demonstrate mastery of these (6) competencies:Communication: …write, speak, read, and listen effectively for a variety of purposes…Quantitative Skills:…analytic and mathematical reasoning.. and quantitative problems…Information Literacy:…Identify…locate…analyze and evaluate…integrate and communicate…evaluate information, product and process.

UAS Catalog Cont.

Computer Usage: …skills range from basic abilities, to telecommunications….and electronic mail technologies.Professional Behavior:…is expected of college students…including responsibility, good work habits, ethical decision making, ...and successful human relations.Critical Thinking :… approach from multiple perspective…compare and contrast ideas and models, and willingness to take intellectual risks.Students’ skills in these six areas will be assessed periodically during their studies at UAS”

English faculty toutedportfolios

for outcome assessment

Not well-suited for technical studies: especially not the tradition

Proposition:

Adapt a great humanities tool for the hard sciences?

Toward a goal:

The Standards emphasize data …

Log the data relevant to students:

their grade, and process behind it.

Model for Grading Rubric for CCD and College Mathematics …

Your gradefor this class will be determined by your performance across

the four modes of assessment described below:

Preparation and Participation≥ 20%

Tests and Quizzes≤ 60%

All tests are “open portfolio”

Email writing or Other≥ 10%

Portfolio≥ 10%

*Note: Each component of this grading rubric is worth at least one full letter grade.

*Note: This grade does not include a component for “student’s innate abilities.”

Only student performance, as described herein, is considered in determining the final course grade.

- Daily work, table with chronologic listing of
- dates on which the class met,
- all assignments given on each date,
- check off attended class that day, or not
- assessment scores from that day .

- Weekly writing, table with chronologic listing of
i) the main topic of each e-mail ESSAY submission, ii) date submitted, and iii) the grade received.

* * * First experience with grade bookfor many education students, with

Math as a tool for humans, by humans.

- Experience with data and tables
- Enables student self-grading
- Back- up to instructor

- Complete compilation of assessment problems
i) all QUIZ and EXAM questions and problems,

ii) with a correct solution supplied for each.

- Table for “TOOLS of the TRADE”, with
i) a listing of each tool’s name,

ii) a description of the context for using the tool,

iii) an example for its use.

Mathematical tools include but are not limited to: symbols, formulas, algorithms, theorems, valuable facts, and contact information for each other.

- A listing of all VOCABULARY and abbreviations introduced in class and in the text.
Definitions and examples ok, but not required.

6)A comprehensive technology log which

i) gives the goal of each CALCULATOR USE

ii) gives commands and chains-of-commands associated with each use.

7) A compilation including one EXAMPLE of independent work from each section of the text (and written self-assessments, as assigned).

Service Learning Log: date, time, activity, supervisor initials

applies also to Community Service, Internships,

attendance and progress in self-paced settings, et al.

Daily Activity Report Log: compiled in chronologic order

applies to any lab setting requiring summary or report

? Differentiate symbols from tools and vocabulary?

? Other measures of progress?

Grading Sheet for Math 190 Portfolio,

1) Attend and participate

format (4 column table) ______

complete _____

Accessible________ Score ________

2) Q & E

originals _______

corrections _____

Accessible________ Score ________

3) Homework Samples

labeled ____difficulty _____

Accessible________

complete _______ Score ________

4) Tools

format (what, when, how) ____

complete _______

Accessible________ Score ________

5) Technology

format (use, commands) ____

complete _______

Accessible________ Score ________

6) Vocabulary List

complete _______

Accessible________ Score ________

7) Overall Presentation Score _______/5

Total _________

( out of 35 midterm, 95 final)

1. You recently took an “open portfolio” exam in this class. Answer the following questions regarding the usefulness of your portfolio as a tool for aiding your test-taking effort. Be specific, and please use complete sentences.

i) How did you find your portfolio helpful in taking this exam?

ii) Which of the logs in your portfolio did you access while you were taking this particular exam? What information did you seek in each?

iii) Given the portfolio as assigned, could yours have been more useful than it was?_______

iv) What can you do to make your portfolio more useful for the next exam?

For student: Reference center, now and later

Documentation to grease transfer credit

Self-reflection and assessment device

enables learning from mistakes

For Instructor: Back up, refresher, and overview

Concrete evidence of student involvement applied to critical thinking

For Program: Concrete, compact, comprehensive, adaptable and not an add-on.

Focused on traditional mathematical content,

students gain guided experience with:

Job Skills--documentation

Information and data literacy

Manipulation of information formats

Communications skills

Critical thinking

Professional behavior and Self-assessment

…and good study habits

I was told: “This year we assess Standard One in both your Math210 and Stat251 classes: ‘Display, analyze and interpret data.’

The HED restates … ‘Students should:

Discriminate among different types of data displays for the most effective presentation. LOG CONTENTS VARY

b. Draw conclusions from the data presented.

c. Analyze the implication of the conclusion to real life situations.’ SELF-GRADE WORKSHEET

Please convince me that your plan addresses these specific competencies.”

My response was already in place:

the log of logs is driven by data relevant to students.

for part a:

“The portfolio consists of organizing both quantitative and qualitative data, discrete and continuous data.

The qualitative data includes both categorical data (attended/not, for example) and judgment data (deciding which tools to include, for example).

Different logs contain different types of data, and thus require different compile and display formats.”

Alsoalready in place, “… students will interpret the data”

for parts b &c:

“Students are assigned to perform the self-grade evaluation several times each term.

They use these results--obtained from information they have compiled in their own portfolios--as feedback on their own efforts, and adjust according to their desired learning outcomes...

This is a very real situation for students, especially full-time students.”

In each realm you must compute the ratio of

the number of points you obtained to the total number of points possible.

(Your portfolio should contain all information needed to determine these ratios).

Tests and Quizzes: Your total / Possible total as a Percentage: ______

Portfolio: Your total / Possible total as a Percentage: ______

Other graded:Your total / Possible total as a Percentage: ______

Prepare & Participate: Your total / Possible total as a Percentage: ______

Weighted average: Fill in the blanks and compute.

Use above for your percentages; use syllabus to find the weight for each realm.

(T&Q %age) • (T&Q weight) + (P %age) • (P weight) + (Oth %age) • (Oth weight) + (P&P %age) • (P&P weight) = course %age

_____ • _____ + _____ • _____ + _____ • _____ + _____ • _____

= _______ + _______ + _______ + _______ = _________

Measuring Preparation & Participation approximately

Number of course meetings ____ • 3 = ____

Points possible from graded daily work: _____

Sum = total possible for P & P = _______

Your total from graded daily work: ______

Number of classes you attended: _____

Number of classes you arrived prepared for: _____

Number of classes you asked questions during: _____

Sum = your total for P & P = __________

Percentage (your total / total possible): ________

Keeping track of diverse forms of informationunderlies the search for patterns, in quantitative and qualitative data. Mathematics includesIntrinsic Beauty AND Usefulness