PROFOUND (reflections) BY CRISMIL MANSUETO

"Oh no! creating a blog?!? That is hard"-- These words flashed on my thoughts when I first heard our professor instructing us to create our own blogs. Nevertheless, i was challenged since it's my first time to do such activity. Meanwhile; when i first searched the information on how to do blogging, I was never wrong with my prognostications: it is indeed very exciting yet a tough task. I thought I might not able to do it well but trying it will never cause something harmful to me. As i went through many searches and exploring many things on the net to integrate our subject to the useful sources; I realized that as a student who belongs to this 21st century, our access to education must also be on the level of highly innovated industry. The fact that it's a click away, it also helps the students to learn more things that could not be learned on the four-corner classroom. Thought it's difficult for some reasons, learning it could make us more knowledgeable rather than ignorant. Lastly, I am very thankful that Prof. Ava Robles is our professor, because of her intellectual ideas and principles about education that she had shared to us; we became integrated as students of this new generation as her imparted wisdoms reached the depths of our “brains”. :)

SELECTING METHODS of ASSESSMENT

There is a wealth of assessment methods used in higher education to assess students' achievements, but how to choose?

The primary goal is to choose a method which most effectively assesses the objectives of the unit of study. In addition, choice of assessment methods should be aligned with the overall aims of the program, and may include the development of disciplinary skills (such as critical evaluation or problem solving) and support the development of vocational competencies (such as particular communication or team skills.)
Hence, when choosing assessment items, it is useful to have one eye on the immediate task of assessing student learning in a particular unit of study, and another eye on the broader aims of the program and the qualities of the graduating student. Ideally this is something you do with your academic colleagues so there is a planned assessment strategy across a program.
When considering assessment methods, it is particularly useful to think first about what qualities or abilities you are seeking to engender in the learners. Nightingale et al (1996) provide eight broad categories of learning outcomes which are listed below. Within each category some suitable methods are suggested.

1. Thinking critically and making judgements

(Developing arguments, reflecting, evaluating, assessing, judging)

• Essay
• Report
• Journal
• Letter of Advice to .... (about policy, public health matters .....)
• Present a case for an interest group
• Prepare a committee briefing paper for a specific meeting
• Book review (or article) for a particular journal
• Write a newspaper article for a foreign newspaper
• Comment on an article's theoretical perspective

2. Solving problems and developing plans

(Identifying problems, posing problems, defining problems, analysing data, reviewing, designing experiments, planning, applying information)

• Problem scenario
• Group Work
• Work-based problem
• Prepare a committee of enquiry report
• Draft a research bid to a realistic brief
• Analyse a case
• Conference paper (or notes for a conference paper plus annotated bibliography)

3. Performing procedures and demonstrating techniques

(Computation, taking readings, using equipment, following laboratory procedures, following protocols, carrying out instructions)

• Demonstration
• Role Play
• Make a video (write script and produce/make a video)
• Produce a poster
• Lab report
• Prepare an illustrated manual on using the equipment, for a particular audience
• Observation of real or simulated professional practice

4. Managing and developing oneself

(Working co-operatively, working independently, learning independently, being self-directed, managing time, managing tasks, organising)

• Journal
• Portfolio
• Learning Contract
• Group work

5. Accessing and managing information

(Researching, investigating, interpreting, organising information, reviewing and paraphrasing information, collecting data, searching and managing information sources, observing and interpreting)

• Annotated bibliography
• Project
• Dissertation
• Applied task
• Applied problem

6. Demonstrating knowledge and understanding

(Recalling, describing, reporting, recounting, recognising, identifying, relating & interrelating)

• Written examination
• Oral examination
• Essay
• Report
• Comment on the accuracy of a set of records
• Devise an encyclopaedia entry
• Produce an A - Z of ...
• Write an answer to a client's question
• Short answer questions: True/False/ Multiple Choice Questions (paper-based or computer-aided-assessment)

7. Designing, creating, performing

(Imagining, visualising, designing, producing, creating, innovating, performing)

• Portfolio
• Performance
• Presentation
• Hypothetical
• Projects

8. Communicating

(One and two-way communication; communication within a group, verbal, written and non-verbal communication. Arguing, describing, advocating, interviewing, negotiating, presenting; using specific written forms)

• Written presentation (essay, report, reflective paper etc.)
• Oral presentation
• Group work
• Discussion/debate/role play
• Participate in a 'Court of Enquiry'
• Presentation to camera
• Observation of real or simulated professional practice

Variety in assessment

It is interesting to note that the eight learning outcomes listed above would be broadly expected of any graduating learner from a higher education program. Yet, when choosing assessment items, we tend to stay with the known or the 'tried and true methods', because they seem to have the ring of academic respectability, or possibly because it was the way we were assessed as undergraduates ourselves.
From learners' perspectives, however, it often seems as if we are turning them into 'essay producing machines' or 'examination junkies'. When choosing methods it is important to offer variety to learners in the way they demonstrate their learning, and to help them to develop a well-rounded set of abilities by the time they graduate.

References

• Nightingale, P., Te Wiata, I.T., Toohey, S., Ryan, G., Hughes, C., Magin, D. (1996) Assessing Learning in Universities Professional Development Centre, University of New South Wales, Australia.

REFLECTIONS:


REACTION:
At first, we were very curious when we heard about doing blogs. Most of us are new in doing such activity. At the first activity, most of the group members had a hard time opening, doing blogs and most especially following our blogs. but as we became more familiar with this, we realized that doing this will enhance us and will be more informed about technology. we had more learning and deeper understanding on how to easily access to some useful informations. Moreover, this activity gave us a the enthusiasm to be more updated to technology. as a conclusion, i could say that blog is a very good way to practice our writing and typing skills as a preparation for our more demanding future.

my secret journey in my life

In this activity it was hard for me to do things that i did not know.i was shy to asking my group that i did not know how to put video and images in our blog.i want to say sorry to our leader because i did not do my part as a member of this group.

Assessing Products

      Many of the difficulties met in assessing interpersonal relationships and performances are also encountered when we attempt to measure the quality of student products. Among the most prominent considerations are factors like physical effort required to construct measures, complexity, administrative difficulties, and questions of validity and scoring. While it is true that many products have physical dimensions that may be measured, like size, weight, number of errors and color, a number of qualitative dimensions are also needs to be assessed. Such dimensions may include flavor of the cake, the composition of painting or the neatness of handwriting. Thus, judging the aesthetic qualities of a product is more difficult than assessing its physical properties and attributes.

Process and product are intimately related. The decision to focus on products or process or both rests on the responses of the following questions.

1.   Are the steps involved in arriving at the product either indeterminate or covert?

2.   Are the important characteristics of the product apparent, and can they be measured accurately and objectively?

3.   Is the effectiveness of the performance to be discerned in the product itself?

4.   Is there a sample product available to use as a scale?

5.   Is evaluation of the procedures leading to the product impractical?

If the answer to each of the foregoing questions is “yes”, the teacher can focus assessment on product evaluation.

Products can easily be assessed by the careful use of rating scales and checklist. Nonetheless, the usefulness of any product assessment will depend on the accuracy with which its distinctive features have been defined and delineated.

Assessing the Quality of an Artistic Product. Assessment is in the artistic and aesthetic areas of human activity are quite difficult. The problem posed by the wide variety of relevant factors is compounded by the subjective nature of aesthetic standards. Nevertheless, the assessment task can be approached systematically and directly through the use of a rating scale.

The following is an example of a rating scale for assessing the quality of an artistic product and for evaluating a specific food product.

A SAMPLE RATING SCALE FOR ASSESSING FREEHAND ART DRAWING

CATEGORIES	A	B	C	D
1.   Drawing (A) Accuracy of proportion of suitability of distortion (B) Relationships of proportion (C) Stability of subjects (D) Ease of interpretation
2.   Composition (A) Balance (B) Rhythm (C) Spatial relations (D) Textural interest
3.   Fell foe Medium (A) Line Quality (B) Tone Quality
4.   Subject Matter (A) Interest (B) Arrangement
Key to Variations: A = aspects add materiality to the excellence of the picture B = aspects noteworthy, but there is room for improvement at this level C = aspect not well utilized D = drawing shows no regard foe aspect being judged

Assessing Food Products. In assessing food products, there is a need to consider both physical and aesthetic qualities which will be rated. Through the use of a rating scale, a teacher can gather qualitative data which can be used in confirming more traditional information derived from test scores.

An example of a rating scale for assessing a specific food product, like waffles, is presented below:

FOOD SCORE CARD FOR WAFFLES

CATEGORIES			SCORE
1.   appearance	irregular shape	Regular shape
2.   color	Dark brown or pale	Uniform golden brown
3.   moisture content	Soggy interior or too dry	Slightly moist interior
4.   tenderness	Tough or hard	Tender; crisp crust
5.   lightness	Heavy	light
6.   taste	Too sweet of flat	Pleasing flavor
rate on a scale from 1 to 3 (1 = lowest; 3 = highest)

Oral Exams

Oral exams are similar to an oral supply or completion items where the test taker completes or supplies an answer for a question or series of questions posed by a test giver. The oral exam is a potentially useful technique.

          Some principles of oral examinations are cited below (Fiztpatrick & Morrison, 1999).

1.   Use oral examinations only for the purposes for which they are best suited

2.   Prepare in advance a detailed outline of materials to be sampled in the examination event to the extent of writing questions which will be asked.

3.   Determine in advance how records of student performance will be kept and what weights will be assigned to various factors.

4.   Keep questioning relevant to the purposes of the course or program.

5.   Word questions in such a way that the students can see the point of the question with minimum difficulty.

6.   Where several examiners are involved, make each one responsible for questions on a specified part of full examination.

7.   Judge students on the basis of their performance precisely defined not in terms of a generalized impression of their total appearance.

8.   Use both general and specific questions but do so in some logical order.

9.   Pose questions which students with the training which has preceded a particular examination can reasonably be expected to know.

10.                Do not spend a disproportionate time probing for the answer to one question. If the first several questions do not elicit the desired response, move on to some other matter.

11.                Develop some facility with several basic techniques for successful oral examination creating a friendly atmosphere, asking questions, and recording responses.

12.                Make a written record of the student’s performance at the time it is given. Do it without disturbing the student or disrupting the flow of the examination.

13.                Allow students ample time to think through and make responses to questions.

14.                Avoid arguing with the student. Let the student make the most of it as it is his show.

REFERENCES

Evertson, C.M & JL Green (1992). Handbook of research on Teaching. New York: Macmillan Book Company.

Fritzpatrick, R & EJ Morrison (1999). Performance and Product Evaluation. New York: Macmillan Book Company.

Gronlund, NE & RL Linn (1990). Measurement and Evaluation in Teaching. New York: Macmillan Book Company.

Payne, DA (2003). Measuring and evaluating Educational Outcomes. New York: Macmillan Book Company

Shertzer, B & JD Linden (2000). Fundamentals of Individual Appraisal. Boston: Houghton Mifflin Book Company.

Stiggins, RJ (1997). Evaluating Students by Classroom Observation. San Francisco: Jossey-Bass Publishers

Webb, EJ. Unobstrusive Measures. Nonreative Rerearch in the Social Sciences. Chicago: Rand McNally Publishing.

Mean, Median, Mode, and Range

Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all.

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.

The "range" is just the difference between the largest and smallest values.

• Find the mean, median, mode, and range for the following list of values:
13, 18, 13, 14, 13, 16, 14, 21, 13

The mean is the usual average, so:
(13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15
Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers. The median is the middle value, so I'll have to rewrite the list in order:
13, 13, 13, 13, 14, 14, 16, 18, 21
There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number:
13, 13, 13, 13, 14, 14, 16, 18, 21
So the median is 14.   Copyright © Elizabeth Stapel 2004-2011 All Rights Reserved The mode is the number that is repeated more often than any other, so 13 is the mode. The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8.
mean: 15 median: 14 mode: 13range: 8

Note: The formula for the place to find the median is "( [the number of data points] + 1) ÷ 2", but you don't have to use this formula. You can just count in from both ends of the list until you meet in the middle, if you prefer. Either way will work.

• Find the mean, median, mode, and range for the following list of values:
1, 2, 4, 7

The mean is the usual average: (1 + 2 + 4 + 7) ÷ 4 = 14 ÷ 4 = 3.5 The median is the middle number. In this example, the numbers are already listed in numerical order, so I don't have to rewrite the list. But there is no "middle" number, because there are an even number of numbers. In this case, the median is the mean (the usual average) of the middle two values: (2 + 4) ÷ 2 = 6 ÷ 2 = 3 The mode is the number that is repeated most often, but all the numbers appear only once. Then there is no mode. The largest value is 7, the smallest is 1, and their difference is 6, so the range is 6.
mean: 3.5 median: 3 mode: none range: 6

The list values were whole numbers, but the mean was a decimal value. Getting a decimal value for the mean (or for the median, if you have an even number of data points) is perfectly okay; don't round your answers to try to match the format of the other numbers.

• Find the mean, median, mode, and range for the following list of values:
 8, 9, 10, 10, 10, 11, 11, 11, 12, 13

The mean is the usual average:
(8 + 9 + 10 + 10 + 10 + 11 + 11 + 11 + 12 + 13) ÷ 10 = 105 ÷ 10 = 10.5
The median is the middle value. In a list of ten values, that will be the (10 + 1) ÷ 2 = 5.5th value; that is, I'll need to average the fifth and sixth numbers to find the median:
(10 + 11) ÷ 2 = 21 ÷ 2 = 10.5
The mode is the number repeated most often. This list has two values that are repeated three times. The largest value is 13 and the smallest is 8, so the range is 13 – 8 = 5.
mean: 10.5 median: 10.5 modes: 10 and 11range: 5

While unusual, it can happen that two of the averages (the mean and the median, in this case) will have the same value.

Note: Depending on your text or your instructor, the above data set may be viewed as having no mode (rather than two modes), since no single solitary number was repeated more often than any other. I've seen books that go either way; there doesn't seem to be a consensus on the "right" definition of "mode" in the above case. So if you're not certain how you should answer the "mode" part of the above example, ask your instructor before the next test.

About the only hard part of finding the mean, median, and mode is keeping straight which "average" is which. Just remember the following:

mean: regular meaning of "average" median: middle value mode: most often

(In the above, I've used the term "average" rather casually. The technical definition of "average" is the arithmetic mean: adding up the values and then dividing by the number of values. Since you're probably more familiar with the concept of "average" than with "measure of central tendency", I used the more comfortable term.)

---

• A student has gotten the following grades on his tests: 87, 95, 76, and 88. He wants an 85 or better overall. What is the minimum grade he must get on the last test in order to achieve that average?
The unknown score is "x". Then the desired average is:
(87 + 95 + 76 + 88 + x) ÷ 5 = 85
Multiplying through by 5 and simplifying, I get:
87 + 95 + 76 + 88 + x = 425                       346 + x = 425                                 x = 79 He needs to get at least a 79 on the last test.

Student Assessment Through Portfolios

                                                By: Alan P. Knoerr and Michael A. McDonald

Reflective portfolios help students assess their own growth. Project portfolios identify their interests and tackle more ambitious assignments.

Background and Purpose

We discuss our use of portfolio assessment in undergraduate mathematics at Occidental College, a small, residential liberal arts college with strong sciences and a diverse student body. Portfolios are concrete and somewhat personal expressions of growth and development. The following elements, abstracted from artist portfolios, are common to all portfolios and, taken together, distinguish them from other assessment tools:

* work of high quality,
* accumulated over time,
* chosen (in part) by the student.

These defining features also indicate assessment goals for which portfolios are appropriate.

Our use of portfolios is an outgrowth of more than six years of curricular and pedagogical reform in our department. We focus here on two types of portfolios — reflective portfolios and project portfolios — which we use in some second-year and upper-division courses. We also describe how we integrate portfolios with other types of assessment.

Reflective Portfolios. In a reflective portfolio, students choose from a wide range of completed work using carefully specified criteria. They are asked to explicitly consider their progress over the length of the course, so early work which is flawed may nonetheless be included to illustrate how far the student has progressed. A reflective portfolio helps students assess their own growth.

The collection of portfolios can also help a teacher reflect on the strengths and weaknesses of the course. It can point out strong links made by the students, and indicate struggles and successes students had with different topics in the course. It can further open the window to student attitudes and feelings.

Project Portfolios. Project portfolios are one component of a "professional evaluation" model of assessment [1, 2]. The other components are "licensing exams" for basic skills, small but open-ended "exploration" projects, and targeted "reflective writing" assignments. These different components, modeled on activities engaged in by professionals who use and create mathematics, have been chosen to help students develop a more mature approach to their study of mathematics.

Students choose projects from lists provided for each unit of the course. Completed projects are included in their project portfolio. This method of assessment helps students identify their interests, produce work of high quality, and tackle more ambitious assignments which may take several weeks to complete. Collecting work from the entire course encourages students to look beyond the next test or quiz.

Method I. Reflective Portfolios

To increase students' self-awareness of how their understanding has developed requires that information about this understanding be collected by the students as the course progresses. Keeping a journal for the course is a useful supplement to the usual homework, classwork, quizzes, and tests. For example, in a real analysis course, students are asked to make a journal entry two or three times each week as they, among other possibilities: reflect on their readings or problem sets, discuss difficulties or successes in the course, clarify or connect concepts within this course or with those in other courses, or reflect on their feelings toward this course or mathematics in general. The teacher collects and responds to the journals on a regular basis.

Near the end of the semester, students are asked to prepare a reflective portfolio. The assignment says:

The purpose of this portfolio assignment is to allow you to highlight your own selections of your work and give an analysis of them in your own words. I will focus on two specific things in evaluating your portfolio: (1) an understanding of some key concepts in real analysis and (2) a self-awareness of your journey (where you started from, where you went, and where you are now).

Select three pieces of work from this semester to include in your portfolio. These pieces can include journal writing, homework assignments, tests, class worksheets, class notes, computer experiments, or any other pieces of work you have produced in this class. Your analysis should explain your reasons for picking these pieces. As examples, you might consider a selection which shows the development of your understanding of one key concept, or a selection which shows your growing appreciation of and proficiency with formal proofs, or a selection which shows your connection of two or more key concepts.

The most important part of the portfolio is your reflection on why you chose the pieces you did, how they show your understanding of some key concept(s), and how they show a self-awareness of your journey through this class. You should definitely write more than one paragraph but no more than five pages. The portfolio is 5% of your final grade.

Method II. Project Portfolios

The project portfolio corresponds to papers and other completed projects a professional would include in his or her curriculum vitae. Two sorts of themes are used for projects in a multivariable calculus course with a linear algebra prerequisite. For example, "Vector Spaces of Polynomials" concerns fundamental ideas of the course, while "Optimization in Physics" is a special topic for students with particular interests. All students are required to complete certain projects, while in other cases they choose from several topics. Here is an example of a portfolio project assignment.

Vector Spaces of Polynomials. What properties define a vector space over R? Let P3 denote the space of polynomials over R of degree less than or equal to three. Show that P3 is a vector space over R with natural definitions for "vector addition" and "scalar multiplication." Find a basis for P3 and show how to find the coordinate representation of a polynomial in P3 relative to this basis. Show that "differentiation" is a linear transformation from P3 to P2, where P2 is the space of polynomials over R of degree less than or equal to 2. Find a matrix representation for this transformation relative to bases of your choice for the input space P3 and the output space P2. To check your work, first multiply the coordinate representation of a general polynomial p(x) in P3 by your matrix representation. Then compare this result with the coordinate representation of its derivative, p´(x). Discuss what you learned from this project. In particular, has this project changed how you think about vector spaces, and if so, in what way?

Project reports must include: a cover page with a title, author's name, and an abstract; clear statements of problems solved, along with their solutions; a discussion of what was learned and its relevance to the course; acknowledgement of any assistance; and a list of references. Reports are usually between five and ten pages long. They are evaluated on both mathematical content and quality of presentation. First and final drafts are used, especially early in the course when students are learning what these projects entail.

For the typical project, students will have one week to produce a first draft and another week to complete the final draft. Students may be working on two different projects in different stages at the same time. Allowing for test breaks and longer projects, a completed course portfolio will comprise seven to ten projects. Students draw on this portfolio as part of a self-assessment exercise at the end of the course.

Findings

The collection of reflective portfolios can serve as feedback of student mathematical understanding and growth through the course. It can sometimes also give us a glimpse of the joy of learning, and thus the joy of teaching. One student wrote:

Without hesitation I knew the selections I was going to analyze. I think one of the reasons why this worksheet and these two journal entries came to mind so quickly is because they reflect a major revelation I had in the course. Not often in my math classes have I felt so accomplished .... These selections represent something I figured out ON MY OWN! That's why they so prominently came to mind.

The first drafts of projects for the project portfolio are a rich source of information on how students are thinking about important topics being covered in the course. The final drafts reveal more clearly their depth of understanding and degree of mastery of mathematical language. We find that these projects help students achieve a better conceptual understanding of important aspects of the course and become more mature in presenting mathematical arguments. The discussion sections of their reports offer students some chance for reflection. For example, one student wrote the following in his report on vector spaces of polynomials:

I am fascinated to see how much we can deduce from an abstract space without being able to visualize it. While the concept of a polynomial vector space still amazes me it is very interesting to see how we can make this abstraction very tangible.

Use of Findings

Reflective portfolios document the development of mathematical knowledge and feelings about mathematics for each student in a particular course and class. This information has been used to realign class materials, spending greater time on or developing different materials for particularly difficult concepts. In addition, the evaluation of student journals throughout the semester allows for clarifying concepts which were not clearly understood. As an example, one student discussed an in-class worksheet on uniform continuity of a function f(x) and did not understand the role of x in the definition. Seeing this, class time was set aside to clarify this concept before more formal evaluation.

First drafts of project portfolios may highlight difficulties shared by many students and thus influence teaching while a course is in progress. Reflecting on completed portfolios can also lead to changing how we teach a course in the future. The projects themselves may be improved or replaced by new ones. Special topics which were previously presented to the entire class may be treated in optional projects, leaving more class time for fundamental ideas. These projects can also lead to more radical reorganization of a course. For example, one year a project on Fubini's Theorem revealed that students had trouble understanding elementary regions for iterated integrals. The next year we first developed line integrals, then introduced elementary regions through Green's Theorem before treating iterated integrals. Teaching these topics in this unusual order worked quite well.

Success Factors

The reflective portfolio, journal writing, and the project portfolio are all writing-intensive forms of assessment. Clarity, time and patience are required of both teachers and students in working with assignments like these which are unusual in mathematics courses.

The reflective portfolio is little more than a short paper at the end of the semester. The time is put in during the semester as the teacher reads and responds to the journals. Cycling through all the journals every few weeks is probably the most efficient and least burdensome way of handling them.

Some students enjoy reflective writing while others may feel awkward about it. In the real analysis class, for example, the female students used the journal more consistently and produced deeper reflections than did the males. Teachers must also allow for reflections which may not be consistent with the outcomes they desire.

Several techniques can make correcting first drafts of project portfolios more efficient and effective. Comments which apply to many reports for a given project can be compiled on a feedback sheet to which more specific comments may be added for individual students. Peer review will often improve the quality of written work. A conference with a student before his or her report is submitted may make a second draft unnecessary. Students often need to complete several projects before they fully appreciate the degree of thoroughness and clarity required in their reports. Sharing examples of good student work from previous years can help communicate these expectations.

References

[1] Knoerr, A.P. "A professional evaluation model for assessment." Joint Mathematics Meetings. San Diego, California: January 8-11, 1997.

[2] Knoerr, A.P. "Authentic assessment in mathematics: a professional evaluation model." Ninth Annual Lilly Conference on College Teaching — West, Lake Arrowhead, California: March 7-9, 1997.