Math Rubrics and Portfolio

Mathematics Rubrics

The performance assessment that promotes authentic and alternative assessment needs to design a scoring device because a performance assessment does not have an answer key in a sense that a multiple choice test does. A good set of scoring guidelines or ‘rubric’ provide a way to make the judgment fair and sound. It can be done by setting forth a set of precisely defined criteria or guidelines that are properly shared to students, their families, and the school teachers, which will be used to judge student’s work.

Herman, Aschbacher, and Winters (1992) stressed that a good scoring rubric will help teachers define excellence and plan how to help students achieve it, communicate to students what constitutes excellence and how to evaluate their own work, communicate goals and results to parents and others, help teachers and other raters be accurate, unbiased and consistent in scoring, and document the procedures used in making the important judgment about students. Thus, a scoring rubric is very useful and helpful. What make the scoring rubric useful are the several components which include one or more dimensions on which performance is rated, definitions and examples that illustrate the attributes being measured and a rating scale for each dimension. Ideally, a good scoring rubric contains examples of student’s work that fall at each level of the rating scale. A rubric with two or more separate scales is called an analytic rubric. This contrasts with a scoring rubric that uses a single scale that yields a global or holistic rating. Holistic scoring is often more efficient, but analytical scoring systems generally provide more detailed information that may be useful in planning and improving instruction, learning tasks and
activities, and communicating with students. Hence, a mathematics teacher must examine first these two rubrics and think about which would provide him with better diagnostic information to use in planning instruction, and also provide the students with the clearest feedback about their works and how to make their works better.

Mathematics Portfolio

In this era of performance assessment related to monitoring of students’ mastery of a core curriculum, and in response to DepEd Order No. 79, s. 2003 stressing the need for an assessment and evaluation system that truly reflects and reveals holistic information about students’ performance, portfolio can enhance the assessment process, support mathematics goals, encourage student, teacher and the parent reflection, and provide continuity in mathematics education.

A portfolio is a purposeful collection of student work that exhibits the student’s efforts, progress and achievements in one or more areas of the curriculum. The collection must include the student’s participation in selecting contents, criteria for selection, criteria for judging merits and evidence of a student’s self-reflection. It should represent a collection of student’s best work or best effort, student’s selected samples of work experiences related to outcomes being assessed, and documents according to growth and development toward mastering identified outcomes (Paulson, Paulson and Meyer, 1991).

Basically, portfolio is a record of student’s works – a type of elaborate grade book that contains not just scores, notes on progress or percents of correct answers, but also the work on which the scores and notes are based.
Rubrics and Portfolio Assessment in Mathematics
According to Paulson, Paulson and Meyer (1991), “Portfolios offer a way of assessing students’ learning that is different from traditional methods. Portfolio assessment provides the teacher, students and parents an opportunity to observe students in a broader context: taking risks, developing creative solutions, and learning to make judgments.”

Portfolio assessment is a multi-faceted process characterized by the following recurrent qualities:

  • It is continuous and ongoing, providing both formative and summative opportunities for monitoring students’ progress toward achieving essential outcomes.
  • It is multi-dimensional, i.e., reflecting a wide variety of artefacts and processes reflecting various aspects of students’ learning processes.
  • It provides a collaborative reflection, including ways for students to reflect about their own thinking processes and meta-cognitive introspection as they monitor their own comprehension, reflect upon their approaches to problem-solving and decision-making, and observe their emerging understanding of subjects and skills.

As the school year progresses, students and teacher can work together to identify especially significant or important artifacts and processes to be captured in portfolio. Additionally, they can work collaboratively to determine grades and scores to be assigned. Rules and scoring keys in rubrics must be designed for a variety of portfolio components.

Guidelines for Portfolio Entries

The following guidelines will be used for selecting entries in the assessment portfolio. The assessment portfolio will be due one week before the final test. A complete portfolio contains the following:

  • A complete table of contents
  • A cover letter
  • At least five entries reflective of the topics studied and the activities completed

Instructions for the cover letter

Write a cover letter to go with your portfolio. Include with your cover letter
a. what math topics you studied
b. what you learned
c. why you choose each item for your portfolio
d. how do you think you progressed in these areas:

  1. working with others
  2. presenting your work to the class
  3. writing about and describing your thought processes

Guidelines for the Selection of Five Entries

The following are the portfolio materials:

a. Journal Entry

Every week, you will be asked to write your impressions on the lesson for the week. Include as entry in your journal the lesson which, you think, is interesting and which you learned new, or the lesson which you got stuck or did not understand fully.

b. Debugging

Include a problem from one of your quizzes or homework that you did not complete or did not answer correctly, but which you realized later how it should have been done. Include a correct solution and an explanation of why it works and what you think of it. Also include your false or incomplete start.

c. One Special Project (Mathematics problem and solution)

Describe the procedure and difficulties you encountered in making the project. Cite the usefulness or its application.

d. Best Work

Include a test or quiz that you think shows your best work for each quarter period.

e. Critique’s Corner

A group or individual student will be asked to present a project to the class. You will be asked to grade the presentation. Comment on the presentation of the topic must be clear, which contains what you have learned from what was presented.

Criteria for a Finished Portfolio

The following are the criteria for a finished portfolio:

  • Thoughtfulness (including evidence of students’ monitoring of their own comprehension, metacognitive reflection, and productive habits of mind)
  • Growth and development in relationship to key curriculum expectancies and indicators
  • Understanding and application of key processes
  • Completeness
  • Correctness
  • Appropriateness of products and processes presented
  • Diversity of entries (e.g., use of multiple formats to demonstrate achievement of designated performance standards)

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