The Math Portfolio Protocol Developing Portfolios in the Math Classroom
This document includes the math departmentâ€™s basic guidelines for portfolios, some sample portfolio projects, and a sample portfolio rubric, all developed by various members of the IS 52 Math Department.
Mallol, Dania; Paumig, Cynthia; Pasco, Ernesto; Vilson, Jose IS 52, NYCDOE 1/25/2010
Math Portfolio G Guidelines A math portfolio contains samples o of a student's work that is collected over a given length of time. A good portfolio offers insights to a student's thinking, understanding, and mathematical problem-solving skills, an nd thus offers a picture of the student's pro ogress in math. Following are some sugge estions on how you can incorporate the use off portfolios in your math classroom: * Explain to your studentss what a portfolio is and how it will be used. * Provide students with po ortfolio folders / binders. They should be large enough to hold various kinds of work. * Portfolios may be one off two kinds: an assessment portfolio that shows s particular growth, or a work portfolio that con ntains various projects and activities. Gene erally, papers from the work portfolio are selected to g go into the assessment portfolio. * We generally want to have a sepa aration between a working folder with classs work and homework versus a portfolio which h has more comprehensive and detailed works that align with the standards. * While you may guide students in their selection of material for their portfoliios, they should be the judges of what actually goes in. For example, while we make portfolio tassks that are often uniform across the department, teachers can give students the option of picking a specific task so long as it aligns to the standard of th he task completed. * The material that goes into a portffolio should help the teacher and others to o understand how students see themselves in the learning of math. * Each assignment should have a ru ubric attached to it to demonstrate whether they've learned as well as appropriate feedback. * Many papers, activities, and proje ects are appropriate for inclusion in a porttfolio. Following are some suggestions: 1.
A table of contents
Solutions to difficult problem ms that detail problem-solving abilities
The use of mathematics in an nother discipline
Problems created by the student
An example of the student's group activity
A written report on a major topic in math
The student's written account of his or her growth in mathematics
Responses to challenging questions and problems
A written explanation of the contents of the portfolio
A reflection on the problem i.e. what they found easy / difficult about the problem
Sample Math Portfolio Rubric Math Department Portfolio Teacher Name: IS 52 Math Teacher Student Name:
CATEGORY Mathematical Concepts
The concepts presented in the project, including math language and concepts presented from the lessons
Strategy/Procedures The strategies and procedures used to arrive at the solutions
2 Explanation shows 50-64% understanding of the mathematical concepts needed to solve the problem(s).
1 Explanation shows less than 50% understanding of the underlying concepts needed to solve the problem(s) OR is not written.
Explanation shows 85-100% understanding of the mathematical concepts used to solve the problem(s).
Explanation shows 6584%understanding of the mathematical concepts used to solve the problems.
Typically, uses an efficient, effective, and mathematically sound strategy to solve the problem(s).
Typically, uses an effective strategy to solve the problem(s). The strategies may or may not be consistent.
Sometimes uses an effective strategy to solve problems, but does not do it consistently.
Rarely uses an effective strategy to solve problems.
Explanation is detailed and clear.
Explanation is clear.
Explanation is a little difficult to understand, but includes critical components.
Explanation is difficult to understand and is missing several components OR was not included.
The steps and solutions are 90100% correct.
The steps and solutions are 85-89% correct.
The steps and solutions are 65-84% correct.
Less than 65% of the steps and solutions are correct.
Diagrams and/or sketches are clear and greatly add to the reader's understanding of the procedure(s).
Diagrams and/or sketches are clear and easy to understand.
Diagrams and/or sketches are somewhat difficult to understand.
Diagrams and/or sketches are difficult to understand or are not used.
Explanation Using words to explain how you arrived at your particular answer Mathematical Correctness The math presented in the problem is cohesive and correct mathematically. Diagrams and Sketches
All diagrams and sketches follow with the rest of the procedure introduced.
Rubrics Section The following three rubrics are adapted from the Formative Assessment System of the New Teacher Center at the University of California, Santa Cruz and The New York City Department of Education Quality Review Report: School Quality Criteria Summary
Data Rubric Use the following rubric to evaluate how you use data. CIRCLE the descriptions that best fit your current teaching practices. Please do not score yourself holistically. The multiple descriptors for each criterion should be considered independent of one another. Developing Deepening Systemic/Sustainable A. 1 Goals - Identifies learning goals for - Identifies clear and - Identifies and integrates lessons that utilize student appropriate goals based on learning goals into all learning student content standards, with activities. Predictions of student content standards. achievement are set consideration of studentsâ€™ so that they - Provides an annual prediction learning needs. - Provides an annual prediction accurately reflect of student achievement. of student achievement that is annual goals and - Provides an annual prediction based on each studentâ€™s outcomes. - Goals are communicated to of student achievement that is individual level, as well as students without revision. based on each studentâ€™s benchmarks of achievement individual level. throughout the year.
Rating (Check One): A. 2 Instruction School, class, and student data is used to plan for and provide differentiated instruction that meets the specific needs of all the students in their charge.
Rating (Check One): A. 3 Progress Monitoring The teacher provides an objective, constantly updated understanding of the performance and progress of each student & classroom. Rating (Check One):
- Goals are developed with students to support individual learning.
- Goals are established, reviewed, and revised with students on an ongoing basis.
- Recognizes student confusion and re-teaches material primarily using the same technique.
- Regularly checks for understanding from a wide variety of students to identify student needs and modify instruction.
- Embeds broad-based checking for understanding in instruction and is able to modify and redesign lessons as needed
- Uses 1 or 2 sources of information to assess student learning and monitor student progress.
- Uses several assessments to monitor student progress and develops strategies for using assessment tools to inform instruction.
- Uses a wide range of ongoing assessment tools in instructional activities to provide consistent guidance for planning and instruction.
Communication Students and their parents/caregivers are regularly provided with information about the goals set for each student, and about each studentâ€™s progress and performance, and how they can improve. In return, the parents / caregivers are invited and enabled to provide useful information on the learning needs of their children.
- Provides students and families with information about their progress through school mandated procedures.
- Provides students with information about their current progress and how to improve their work.
- Parents/caregivers are invited to provide useful information on the learning needs of their children.
-Establishes regular communication with families and support personnel. - Parents/caregivers are invited and enabled to provide useful information on the learning needs of their children.
- Engages students, families, and support personnel in regular discussions regarding student progress and improvement plans. - Comprehensive and ongoing information about studentsâ€™ progress and improvement plans is provided to students, families, and support personnel. - Parents/caregivers regularly provide useful information on the learning needs of their children.
Rating (Check One):
Classroom Environment and Management Rubric B. 1
High Expectations A positive, safe and inclusive learning environment has been created where consistently high expectations are conveyed to both the students and their parents / caregivers.
Rating (Check One): B. 2 Rituals & Routines There are effective and consistently applied rituals and routines. Rating (Check One):
Developing - A learning environment has been created where some expectations are conveyed to students.
Deepening - A positive learning environment has been created where high expectations are conveyed to students.
Systemic/Sustainable - A positive, inclusive learning environment has been created where consistently high expectations are conveyed to students.
- Establishes some procedures to support student learning.
- Identifies, supports, and monitors students in following routines and procedures that are appropriate and efficient for the learning activities.
- Assists all students in developing and internalizing equitable routines and procedures.
- Students are aware of the procedures.
- Students show ownership of routines and procedures.
Respect There is an environment of mutual trust and respect between staff & students to support personal and academic development.
Rating (Check One): B. 4 Aesthetics & Organization Room is attractively decorated and clearly organized. Student projects and study centers are present.
Rating (Check One): B. 5 Student Work Current student work is celebrated and displayed on bulletin boards and within the classroom. Scoring guides and specific teacher comments provide accurate feedback on the students’ progress. Rating (Check One): B. 6 Student Leadership The teacher facilitates an environment in which students take initiative socially and academically. Student leadership within and beyond the classroom is promoted and supported.
-Establishes rapport with individual students. - Has some strategies to respond to unfairness and disrespect.
-Establishes and promotes caring and respectful relationships between staff and students. - Responds to all incidents of unfairness and disrespect equitably.
-Establishes, promotes, and fosters an environment of mutual trust and respect between staff & students to support personal and academic development. - Supports students in developing skills to respond to inequity and disrespect.
- Room is decorated but is disorganized or with generic materials.
- Room is decorated with unit-specific materials and is somewhat organized.
- Room is attractively decorated with unit-specific materials and clearly organized.
- Arranges room for teacher accessibility to or visibility of students.
- Designs movement patterns and access to resources to promote individual and group engagement.
- Uses total physical environment as a resource to promote individual and group learning.
- Student work is displayed, but may be outdated, lack teacher feedback, or fail to celebrate student accomplishments.
- Room displays represent current topics of study and are used in/integral to learning activities.
- Room displays represent current topics of study.
- Encourages student responsibility for self. - Students have classroom responsibilities with specific tasks.
- Feedback is given but may be general or not support future learning.
- Uses some strategies and activities to develop students’ individual responsibility and recognition of others’ rights and needs. - Students not only have responsibilities in the classroom, but are given the opportunity to identify needs and solve problems as they arise.
- Students are able to contribute to the changing design of the environment. - Scoring guides and specific teacher comments provide specific and accurate feedback on students’ progress.
- Facilitates an environment in which students take initiative socially and academically. - The promotion and support of student leadership extends beyond the classroom.
Rating (Check One):
Planning, Engaging, Challenging, and Differentiated Lessons C.1
Aim Clear aims are
Developing -Somewhat clear aims are established for what will be learned in lessons.
Deepening -Clear aims are established for what will be learned in lessons alongside activities that
Systemic/Sustainable -Clear aims establish the skills specific to the lesson and the strategies that can be
established for what will be learned in lessons alongside activities that promote that learning. Rating (Check One): C. 2 Interdisciplinary Links There is evidence of links between other subjects so that the knowledge and skills gained in one are driving the learning in others. Rating (Check One): C. 3 Schemata The teacher is able to make substantive connections and links to prior learning and other disciplines in order to create a context for students to synthesize learning goals with what they know. Rating (Check One): C. 4 Subject Matter The teacher uses comprehensive knowledge of subject matter to support student understanding of key concepts, themes, multiple perspectives, and relationships in and among subject areas. Activities are suitable for students’ cognitive development. Rating (Check One): C. 5 Independent Thinking A variety of challenging learning experiences is used that develop students’ independent learning, collaboration, and choice.
promote that learning.
reapplied in the future, alongside activities that promote that learning.
-Focuses on core curriculum and skills and attempts to relate content to other learning.
-There is evidence of links between other subjects so that the knowledge and skills gained in one are driving the learning in others.
-Entire units have been planned with other content areas so that there are continuous links between the subjects and the knowledge and skills gained in one are continuously driving the learning in others.
- Opens lesson by connecting with prior knowledge, life experiences and/or interest.
- Asks questions that elicit students’ prior knowledge, life experiences and/or interests.
- Few connections made to goals and objectives.
- Some connections made to goals and objectives.
- Utilizes activities to elicit questions from students regarding their prior knowledge, experiences and interests.
-Has a basic knowledge of subject matter and student development.
-Communicates key concepts, skills, and themes in an accurate, clear, and coherent manner.
-Promotes an understanding of key concepts.
- Directs learning experiences through whole group work. - Teachers make choices about student work. - Provides little opportunity for students to monitor their own work and to reflect on progress and process.
- Significant connections made to goals and objectives.
-Builds on instruction with students’ cognitive and linguistic abilities in mind.
-Flexibly uses comprehensive knowledge of subject matter and student development to ensure that all students understand key concepts, themes, multiple perspectives, and relationships in and among subject areas.
- Directs learning experiences that utilize individual and various group work structures to develop autonomy and group participation skills.
- Integrates a variety of challenging learning experiences that develop students’ independent learning, collaboration, and choice.
- Students begin to make choices about and within their work.
- Supports students in making appropriate, independent choices for learning.
- Students have opportunities to reflect on and discuss progress and process.
- Students reflect on progress/process as a regular part of learning experiences.
Rating (Check One): C. 6 Modifications The teacher makes appropriate modifications for students during lessons and supports students in monitoring and communicating their own understanding. Rating (Check One): C. 7 Higher Order Thinking Questioning techniques and assignments push the students to think critically and analytically. Rating (Check One): C. 8 Engagement The lesson is well executed with excellent pacing and focus. Instruction is interesting and compelling.
- Few instructional strategies used; low student participation.
- Uses a variety of instructional strategies to elicit student participation.
- Uses some available resources and materials but not in consideration of academic and linguistic needs of the students.
- Selects strategies, resources and visuals with some consideration of academic and linguistic needs, using available resources and materials.
- Focuses questions on fact and key concepts to support learning subject matter.
- Engages students through activities and questioning strategies that support and develop skills in identification and understanding of key concepts and issues.
- Directs learning experiences and monitors student progress within a specific lesson.
-Lessons are somewhat well executed with good pacing and focus, but instructional time is not maximized. -Instruction is somewhat interesting and compelling but many students are not fully engaged (behaviorally, emotionally, and cognitively). -Students’ levels of engagement are intermittently monitored.
Rating (Check One): C. 9 Lesson Extension Homework is a meaningful extension of the lesson and reinforces its skills and concepts.
Rating (Check One): C. 10 Assessment
- Differentiates instruction to accommodate students’ diverse learning styles and to ensure all students participate. - Uses an extensive repertoire of strategies, resources and visuals that matches students’ academic and linguistic needs, using available resources and materials. - Engages students in analysis of key concepts and facts through activities and questions that consider multiple perspectives.
- Supports students in developing skills needed to monitor their own learning.
- Structures learning activities that enable students to set goals and develop strategies for demonstrating and monitoring their own learning.
-Lessons are somewhat well executed with good pacing and focus.
-Lessons are well executed with excellent pacing and focus.
-Instruction is somewhat interesting and compelling and many students are fully engaged (behaviorally, emotionally, and cognitively).
-Instruction is interesting and compelling and all students are fully engaged (behaviorally, emotionally, and cognitively).
-Students’ levels of engagement are occasionally monitored and preventive action is attempted if it is low.
-Students’ levels of engagement are constantly monitored and preventive action is taken if it is low.
- Homework is provided on a daily basis.
- Daily homework is an extension of the lesson that provides additional practice.
- Daily homework is a meaningful extension of the lesson and reinforces its skills and concepts.
- Formative or summative assessments are used to check
- Formative and/or summative assessments are used to check
- Both formative and summative assessments are
Both formative and summative assessments are used to check for learning and understanding during and at the completion of the lesson.
for learning and understanding during or at the completion of a lesson.
for learning and understanding during and at the completion of a lesson to inform future planning and lessons.
used to check for learning and understanding during and at the completion of a lesson to immediately influence planning and redirect current lessons.
Rating (Check One):
Areas of Strength:
Areas for Improvement:
DEVELOPING AS A PROFESSIONAL EDUCATOR RUBRIC
Use the following rubric to evaluate your development as a professional educator. CIRCLE the descriptions that best fit your current teaching practices. Please do not score yourself holistically. The multiple descriptors for each criterion should be considered independent of one another. Reflecting on teaching practice
Establishing professional goals and pursuing opportunities to grow professionally
Developing - Reflects on elements of teaching (e.g., pacing, procedures, discipline, movement, materials, etc.).
Deepening - Reflects on the relationship of teaching practice and student learning.
Systemic/Sustainable - Regularly integrates analysis and reflection into daily practice based on a wide variety of evidence in relationship to professional growth and student learning.
- Attends required in-service trainings.
- Actively engages in and contributes to various professional development opportunities.
- Contributes to or leads professional organizations, literature, and development opportunities to extend own teaching practice and that of colleagues.
- Expands knowledge and skills through available professional development. - Develops goals through required processes.
- Seeks out opportunities to realize professional goals. -Sets short-term professional goals based on self-assessment of effectiveness, student learning, and feedback.
-Creates opportunities to realize personal professional goals and share expertise -Sets and modifies short-and long-term goals considering self assessment and feedback from a variety of sources.
Working with colleagues to improve professional practice
- Establishes a positive working relationship with a few colleagues.
- Expands positive working relationships with colleagues and support staff.
- Seeks out trusted colleagues to consider solutions to problems with students and to gather resources.
- Works collaboratively and constructively with colleagues to plan curriculum, coordinate resources, improve student learning, reflect on practice, and solve problems.
Balancing professional responsibilities and maintaining motivation
- Maintains a professional attitude.
- Maintains a professional and positive attitude throughout the year
- Maintains motivation and commitment to all students and the professional community
-Demonstrates professional integrity, and balances professional responsibility with personal needs.
-Demonstrates and models professional integrity, and challenges self intellectually and creatively throughout career.
- Acknowledges and understands professional responsibilities.
- Engages staff in dialogue and reflection to support student learning and teacher growth in responsive and appropriate ways. - Provides leadership for and contributes to the learning of other educators.