Critical Tasks in FIU Mathematics Education Programs to...

Updated 6/4/10

Critical Tasks in FIU Mathematics Education Programs to Assess Florida Educator Accomplished Practices (FEAPs)

Course FEAPs Assessed Assessment Title Assessment Description

MAE 4393

FEAPs 4, 8, 9, 12

Scientific/Math Inquiry Project

Authentic math/science instruction engages students in inquiries which generate questions, establish appropriate methods for researching those questions, collect and analyze data to address the questions and report the results in appropriate ways. Inquiry projects such as these can be found in the science fair or in whole class projects which engage students in investigating and improving their local environment. You will engage in an out-of-class, mathematical or scientific inquiry.

MAE 4394

FEAPs 3, 5, 7, 8, 10

Multicultural Math/Science Lesson & Reflection

Develop a multicultural mathematics lesson that brings together the teaching of mathematics or science through a cultural context. The lesson will be aligned with recent theories of learning and will demonstrate ways of addressing diverse student needs for learning the intended mathematics and/or science content and processes.

RED 4325

FEAPs 1-12

Lesson Plan 3 and

Refection

Semantic Mapping and Concept of Definition Map Lesson Plan to Assess and Scaffold Student’s Vocabulary. Purpose: The purpose of Lesson Plan 3 and Reflection is to create a Semantic Mapping and Concept of Definition lesson plan to assess, scaffold, and increase student(s)’ vocabulary and conceptual growth in accordance with their cognitive, social, linguistic, cultural, emotional, and physical needs.

Process: Using the results of Lesson 1 and 2, identify student’s morphological and semantic vocabulary skills taking into consideration their cognitive, social, linguistic, cultural, emotional, and physical needs. Create a lesson plan that will scaffold student(s)’ needs using a different text about the same topic from Lesson 1 and 2. Conduct the lesson. Write a reflection.

1. Lesson Plan 3 2. Rubric 3. Reflection (4 parts)

a. What did you learn about writing a content lesson plan which included identifying and scaffolding students’ vocabulary skills? b. What did you learn about examining and assessing students’

vocabulary skills in a content area lesson? c. How does what you learned impact the decisions you make regarding

your students’ learning needs in accordance with their cognitive, social, linguistic, cultural, emotional, and physical needs? (Think about FEAPs.)

d. How does learning about vocabulary in texts that will be read in content area lessons help inform you as a reading professional?

All Critical Tasks are evaluated on a 3-Point Rubric: (3) Target , (2) Satisfactory , (1) Unsatisfactory

Updated 6/4/10

Critical Tasks (con’t)

Course FEAPs Assessed Assessment Title Assessment Description

TSL 4324

FEAPs 1,4,5,7,10

Field Assignment-

Case Study Learner

The field assignment in this class will be a case study in which individual students will meet with and tutor an English Language Learners from a field school or from the English Language Institute at FIU. Students will be required to meet with the learner a minimum of six times, plan a course of study for the learner that addresses specific language learning issues as identified by the learner, student and mentor teacher, and work on those issues in ways that correlate with the ESOL methods, theories and techniques taught in this course.

MAE 3651

FEAPs 2, 4, 7, 8, 12

Reasoning with GSP – Power Investigation

A GSP “Power” Investigation is a GSP multi-sketch mathematical investigation that you create for a specific instructional purpose. The multi-sketch investigation should have a certain degree of sophistication to show how powerful the dynamic geometry software is. The multi-sketch investigation will consist of the following: sketches that can be used to explore changes in parameters and reason about observed patterns in the construction of mathematical relationships or concepts, multiple pages linked through page tabs and link buttons, at least one custom tool, varied custom buttons, and questions directing the investigation. A

MAE 4330

FEAPs 1 - 12

Microteaching Group Project with Research Lesson & Report.

Prospective teachers will work in small groups through several cycles of developing, teaching and videotaping, reflecting on, and revising a mathematics lesson involving process standards, mathematical reasoning and modeling for developing concepts or relationships that addresses the needs of diverse, special and ELL students. The Process Goal for project/research lesson is to develop students’ mathematical reasoning and ability to study patterns in constructing relationships or concepts through experimenting, analyzing, conjecturing, and defending or justifying mathematical ideas. (Construct-a-Concept or Discover-a-Relationship lessons)

MAE 4942

FEAPs 1 - 12

Small Group Progression Plan

Students will develop a small group instructional plan in a major content area (e.g., reading, math) for 3 – 5 students that will document each student’s progress from the beginning to the end of the student teaching experience. The plan will include a purpose statement with goals and objectives, complete lesson plans – with objectives, assessments, and specific activities. The lessons will be implemented and tracked. Individual student progress will be documented and described. The data will be analyzed after assessment of the post-test/s. Assignment Description in Student Teaching Handbook, page 23.

All Critical Tasks are evaluated on a 3-Point Rubric: (3) Target , (2) Satisfactory , (1) Unsatisfactory

Updated 6/4/10

Assessment of FEAP 1: Assessment

FEAP Indicator Course Critical Task Description of Relevant Portion of Task/Assessment

1. Assessment

Recognizes students' readiness to learn and their individual learning

needs and plans intervention strategies.

TSL 4324 Field Assignment - Case Study Learner

The case study includes a reflection that is tied to course theory.

1.1 Analyzes individuals’ learning needs and practices techniques which accommodates differences, including linguistic and cultural difference


…demonstrates that he or she has adequately used assessment to create an action plan for the case study learner and that they have been able to efficiently implement that plan according to the needs of the learner based on linguistic and academic ability.

1.11 Maintains observational and anecdotal records to monitor students’ development



1.6 Employs traditional and alternative assessment strategies in determining students’ mastery of specified outcomes.

RED 4325 Lesson Plan 3 and Reflection

Is fully able to collect and use data gathered from a variety of sources, including both traditional and alternate assessment strategies

MAE 4330 Micro-teaching Group Project

Research lesson includes appropriate strategies to assess student learning of the content of the lesson . . .

1.8 Modifies instruction based upon assessed student performance.




MLS report demonstrates effective use of [assessment] strategies as part of the lesson revision process.

1.5 Identifies students’ cognitive, social, linguistic, cultural, emotional, and physical needs in order to design individual and group instruction.


Prospective teachers will work in small groups through several cycles of developing, teaching and videotaping, reflecting on, and revising a mathematics lesson involving process standards, mathematical reasoning and modeling for developing concepts or relationships that addresses the needs of diverse, special and ELL students.

MAE 4942


Implement lessons throughout the semester, using self-reflection to make modifications and adaptations to meet the needs of all students.

1.13 Reviews assessment data and identifies students’ strengths and weaknesses.



MAE 4942 Small Group Progression Plan

Individual student progress will be documented and described.

Updated 6/4/10

Assessment of FEAP 1: Assessment (con’t)


Assessment

1.12Interprets data from various assessment procedures TSL 4324

Field Assignment - Case Study Learner


MAE 4942 Small Group Progression Plan

Select appropriate standardized and/or informal pre- and post-assessment tools and… Analyze the data

Updated 6/4/10

Assessment of FEAP 2: Communication


2. Communication 2.6 Acquires and adapts interaction routines (e.g., active listening) for individual work, cooperative learning, and whole group activities.

RED 4325

Lesson Plan 3 and Reflection

recognizes the need for effective communication in the classroom and is in the process of acquiring techniques which will be used in the classroom.

MAE 4330

Micro-teaching Group Project

MLS research lesson and report includes appropriate strategies and techniques for communicating with students and engaging students in class and/or small group discussions, promoting student action and performance.

2.5 Communicates to all students high expectations for learning

MAE 3651


The GSP “Power” Investigation poses questions and activities that convey high expectations for learning..

MAE 4942


Develop complete and specific lesson plans that include specific objectives that are age / grade / student appropriate

2.9 Provides opportunities for students to receive constructive feedback on individual work and behavior

MAE 4942


Develop a system to track student progress

2.3 Varies communication according to the nature and needs of individuals

MAE 4942



Updated 6/4/10

Assessment of FEAP 3: Continuous Improvement


3. Continuous Improvement

3.10 Evidence of reflection and improvement in teaching activities

MAE 4394

Multicultural M/S Lesson

. . . Materials and presentation demonstrate important abilities for continuous improvement including . . . reflection . . .

RED 4325


realizes that self reflection is one of the key components of the life-long learning process along with working with immediate colleagues and teammates, and meeting the goals of a personal professional development plan

3.14 Reflects on personal judgment and can articulate to colleagues, parents, and the business community

MAE 4394


Materials and presentation demonstrate important abilities for continuous improvement including . . . reflection, as well as strong ability to present to and share learning with colleagues/peers.

3.12 Works as a reflective practitioner and develops the skills to recognize problems, research solutions, and evaluate outcomes.

MAE 4330


MLS report shows evidence of critical analysis and revision of research lesson over time . . .

3.3 Uses data from own learning environment as a basis for reflecting on /experimenting with own teaching

MAE 4330


MLS report [uses] . . . data from the learning environment . . . to effectively reflect on the lesson . . .

3.5 Communicates student progress with students, families, and colleagues

MAE 4330


MLS report [provides] . . . appropriate recommendations for improvement . . .

MAE 4942



3.9 Shows evidence of reflection and improvement in performance in teaching/learning activities.

MAE 4942


Analyze the data and relate to specific strategies and activities that were implemented.

Updated 6/4/10

Assessment of FEAP 4: Critical Thinking


4. Critical Thinking 4.9 Encourages students to develop open-ended projects

MAE 4393


The student has identified a relevant inquiry project . . .

4.2 Identifies strategies, materials, and technologies which she/he will use to expand students’ thinking abilities

MAE 4330


Research lesson clearly includes strategies that engage students in mathematical reasoning and the study of patterns in constructing relationships or concepts through experimenting, analyzing, conjecturing, and defending or justifying mathematical ideas . . .

MAE 4942


Develop complete and specific lesson plans that include appropriate subject-specific procedures, reflecting knowledge of subject matter

4.3 Identifies strategies for utilizing discussions, group interactions, and writing to encourage problem solving

MAE 4330


Research lesson clearly includes . . . Strategies [that] suggest teacher facilitation of discussion of students’ ideas . . .

4.1 Provides opportunities for students to learn higher-order thinking skills.

MAE 3651


The GSP “Power” Investigation . . . effectively [supports] students’ inquiry, critical thinking, and reasoning about mathematical concepts and relationships.



MAE 4330


. . . MLS report demonstrates appropriate analysis of students’ experimenting, analysis, and justification of mathematical ideas.

MAE 4942



4.4 Poses problems, dilemmas, & questions

MAE 4393


The student has identified a relevant inquiry project and has a substantial justification of how this project will either contribute to improving the student’s local environment or exemplifies a novel science fair project. The student clearly presents the findings of the inquiry project and uses evidence consistently to support these findings.

MAE 3651


The GSP “Power” Investigation poses questions . . .

MAE 4330


Research lesson clearly includes strategies and materials that engage students in . . . experimenting . . .

Updated 6/4/10

Assessment of FEAP 4: Critical Thinking (continued)


Critical Thinking 4.5 Develop and use rules of evidence MAE

4393 Scientific/Math Inquiry Project

The student clearly describes how their findings contribute to the body of scientific knowledge or to improving the student’s local environment. The student . . . uses evidence consistently to support [their] findings.

MAE 4330


Research lesson clearly includes strategies and materials that engage students in . . . experimenting, analyzing, conjecturing, and defending or justifying mathematical ideas.

4.8 Modifies and adapts lessons with attention to learner’s thinking;

MAE 4330


Research lesson . . . Strategies suggest teacher facilitation of discussion of students’ ideas . . .

RED 4325


acquiring performance assessment techniques and strategies that measure higher order thinking skills in students…

MAE 4942



Updated 6/4/10

Assessment of FEAP 5: Diversity


5. Diversity 5.4 Recognizes students’ learning styles and cultural and linguistic diversity and provides for a range of activities

MAE 4394


. . . reflection on lesson plan [is] clearly aligned with a multicultural education perspective to learning mathematics or science and clearly [addresses] diverse student needs.



RED 4325


and creating a climate of openness, inquiry, and support by practicing strategies such as acceptance, tolerance, resolution, and mediation.

5.6 Selects appropriate culturally and linguistically sensitive materials for use in the learning process

MAE 4394


Instructional activities . . . are clearly aligned with a multicultural education perspective to learning mathematics or science . . .

5.3 Recognizes the cultural and linguistic diversity and experiences of individual

students to enrich instruction for the whole groups.



5.2 Fosters a learning environment in which all students are treated equitably

MAE 4330


Research lesson includes strategies and materials that support the equitable treatment of all students and support the involvement of all students . . .

5.5 Has a repertoire of teaching techniques and strategies to effectively instruct all students.

MAE 4394


Instructional activities . . . clearly address diverse student needs.

MAE 4330


Research lesson . . . includes appropriate accommodations for diverse learners (e.g., ELL, ESE). MLS report reveals appropriate consideration of diverse student learning.

MAE 4942


Develop complete and specific lesson plans that include activities that reflect the Multiple Intelligences / Differentiated Instruction

5.9 Selects and introduces materials and resource that are multicultural

MAE 4394


Instructional activities . . . are clearly aligned with a multiculatural education perspective . . .

MAE 4942


Develop complete and specific lesson plans that include appropriate materials

Updated 6/4/10

Assessment of FEAP 5: Diversity (con’t)


Diversity 5.1 Accepting and valuing students from diverse cultures and linguistic backgrounds

RED 4325


Is competently establishing a comfortable environment which accepts and fosters diversity demonstrating knowledge and awareness of varied cultures and linguistic backgrounds



MAE 4942


Select a small group of 3 – 5 students and develop an instructional plan for one subject area, specific to the cognitive, linguistic, cultural, behavioral, and/or physical needs of each student

Updated 6/4/10

Assessment of FEAP 6: Ethics


6. Ethics 6.1 Makes reasonable effort to protect students from conditions harmful to learning and/or to the student's mental and/or physical health and/or safety

MAE 4330


MLS report demonstrates . . . ethical behavior in work with students . . .

MAE 4942


Develop complete and specific lesson plans that include specific objectives that are age / grade / student appropriate and [include] appropriate subject-specific procedures.

6.7 Maintains honesty in all professional dealings

MAE 4330


MLS report demonstrates honesty . . . in work with students, MLS partners, and in use and analysis of classroom data.

MAE 4942

Small Group Progression Plan Syllabus, page 2

While collecting, analyzing, and reporting data, interns are expected to comply with ethical standards of behavior for teachers as outlined in the Code of Ethics

Code of Ethics RED 4325


Competently adheres to the Code of Ethics and Principles of Professional Conduct of the Education Profession of Florida.

Updated 6/4/10

Assessment of FEAP 7: Human Development & Learning


7. Human Development & Learning

7.3 Builds a portfolio of

activities used successfully to engage and motivate students at appropriate developmental levels.



7.6 Recognizes learning theories, subject matter structure, curriculum development, student development, and first and second language acquisition processes.

MAE 4394


All instructional strategies and activities are well organized and clearly aligned with recent learning theories . . .

MAE 3651


Reasoning essay effectively uses theories of learning (e.g., van Heile’s levels of geometric thinking) in response to the given questions. . .

MAE 4330


Research lesson includes strategies and classroom practices that . . . are aligned with theories of learning that support recent reforms . . .

7.1 Recognizes developmental levels of students and identifies differences.

MAE 4394


. . . Lesson includes appropriate accommodations for diverse student learning.

MAE 4942


. Individual student progress will be documented and described.

7.5 Varies activities to accommodate different learning needs, developmental levels, experiential backgrounds, linguistic development, and cultural heritage

MAE 4330


Research lesson includes strategies and classroom practices that . . . accommodate different learning needs (e.g., ESE, ELL, etc.) and developmental levels . . .

MAE 4942


Develop complete and specific lesson plans that include specific objectives that are age / grade / student appropriate, appropriate materials (e.g., multi-sensory), ESE and ESOL strategies, appropriate subject-specific procedures, reflecting knowledge of subject matter, assessment that matches objective, and activities that reflect the Multiple Intelligences / Differentiated Instruction

7.7 Uses alternative instructional strategies to develop concepts and principles and is aware of the rationale for choosing different methods

MAE 3651


. . . The GSP “Power” Investigation incorporates strategies that are clearly aligned with recent learning theories, research, and documented best practice (e.g., NCTM standards).

RED 4325


draws upon well established human development/ learning theories and concepts and a variety of information about students, the preprofessional teacher plans instructional activities.

MAE 4942


Analyze the data and relate to specific strategies and activities that were implemented

Updated 6/4/10

Assessment of FEAP 8: Knowledge of Subject Matter


8. Knowledge of Subject Matter

8.1 Communicates knowledge of subject matter in a manner that enables students to learn

MAE 3651


Mathematics content in GSP “Power” Investigation is accurate and promotes a clearly coherent understanding and learning of the content through exploration and analysis. Materials include no mathematics errors.

MAE 4394


Mathematics or science content in lessons and related activities . . . promotes coherent understanding and learning of the content . . .

MAE 4330


MLS report and research lesson demonstrate . . . Instructional strategies and materials [that] are appropriate for the mathematics learning outcome(s) (i.e., goals, objectives, SSS). . .

MAE 4942



8.3 Uses the materials and technologies of the subject field in developing learning activities

MAE 4393


The student has identified research questions and methods which will allow the student to address those questions.

MAE 4394


Mathematics or science content in lessons and related activities is accurate . . .

MAE 4330


[Research Lesson has] Instructional strategies and materials [that] are appropriate for the mathematics learning outcome(s).

MAE 4942


Develop complete and specific lesson plans that include appropriate materials (e.g., multi-sensory)

8.2 Increases SMK to integrate learning activities

RED 4325


[Candidate] is beginning to understand that the subject is linked to other disciplines and can be applied to real world integrated settings.

MAE 4942


In collaboration with your cooperating teacher (CT), select a small group of 3 – 5 students and develop an instructional plan for one subject area

Updated 6/4/10

Assessment of FEAP 9: Learning Environment


9. Learning Environment

9.14 Maintains academic focus by varied motivational devices

MAE 4393


The student clearly describes how their findings contribute to the body of scientific knowledge or to improving the student’s local environment.

9.4 Recognizes cognitive, linguistic, and affective needs of individual students

RED 4325


Fully understands the importance of setting up effective learning environments and has techniques and strategies … understands that s/he will need a variety of techniques and work to increase his/her knowledge and skills.

9.7 Provides a safe place to take risks MAE

4330 Micro-teaching Group Project

MLS report discusses and research lesson involves techniques appropriate for fostering a safe environment that encourages each student to take intellectual risks. . .

9.12 Uses learning time effectively MAE

4330 Micro-teaching Group Project

Time is structured appropriately to explore sound mathematics and involves the use of techniques that foster smooth, efficient, well-paced routines.

9.1 Practices a variety of techniques for establishing smooth and efficient routines

MAE 4330


MLS report . . . is structured appropriately to explore sound mathematics and involves the use of techniques that foster smooth, efficient, well-paced routines.

MAE 4942



9.13 Provides clear directions for instructional activities and routines

MAE 4330


MLS report discusses . . . the use of techniques that foster smooth, efficient, well-paced routines.

MAE 4942



9.2 Applies the established rules and standards for behaviors consistently and equitably.

MAE 4942


Individual student progress will be documented and described.

9.9 Monitors learning activities by providing feedback and reinforcement to students

MAE 4942


Implement lessons throughout the semester, using self-reflection to make modifications and adaptations to meet the needs of all students Analyze the data and relate to specific strategies and activities that were implemented

Updated 6/4/10

Assessment of FEAP 10: Planning


10. Planning 10.1 Identifies student performance outcomes for planned lessons.

MAE 4394


Instructional goals, objectives, and NGSSS are specifically identified and clearly stated . . .

10.4 Provides comprehensible instruction based on performance standards required of students in Florida public schools.

MAE 4330


Instructional goals, objectives, and SSS are appropriate, clearly stated, and directly represent the expected learning . . .

10.13 Helps students develop concepts through a variety of methods

MAE 4330


[Goal for the]project lesson is to develop students’ mathematical reasoning and ability to study patterns in constructing relationships or concepts through experimenting, analyzing, conjecturing, and defending or justifying mathematical ideas

10.3 Plans activities to promote high standards for students through a climate which enhances and expects continuous improvement

MAE 4394


Instructional goals, objectives, and NGSSS . . . directly represent the learning expected as a result of the lesson, including intended activities.

RED 4325


Fully recognizes the importance of setting high expectations for all students, works with other professionals to design learning experiences that meet students’ needs … seeks advice/information from appropriate resources (including feedback), interprets the information, and modifies her/his plans appropriately

MAE 4330


. . . Research lesson includes materials and procedures appropriate for the goals, objectives and SSS. . .

10.2 Plans and conducts lessons with identified student performance and learning outcomes



MAE 4330


. . . Research lesson . . . clearly [specifies] teachers’ actions and communications with students, and students’ actions and possible expected communications. . .

MAE 4942


Select appropriate standardized and/or informal pre- and post-assessment tools and administer to each student at the beginning and end of the semester. Implement lessons throughout the semester, using self-reflection to make modifications and adaptations to meet the needs of all students

Updated 6/4/10

Assessment of FEAP 10: Planning (con’t)


Planning 10.10 Plans activities that engage students in learning activities and employs strategies to re-engage students who are off task

MAE 4942


Analyze the data and relate to specific strategies and activities that were implemented

10.11 Demonstrates instructional flexibility and an awareness of the teachable moment

MAE 4942



Updated 6/4/10

Assessment of FEAP 11: Role of the Teacher


11. Role of the Teacher

11.4 Uses the community to provide students with a variety of experiences

RED 4325

Lesson Plan 3 and Refelction

Competently communicates and works cooperatively with families and colleagues to improve the educational experiences at the school

11.8 Works with colleagues to identify students educational, social, linguistic, cultural, and emotional needs

MAE 4330


MLS report is well-organized and professionally presented. It demonstrates effective collaboration in the planning, reflection and revision process.

MAE 4942


In collaboration with your cooperating teacher (CT), select a small group of 3 – 5 students and develop an instructional plan for one subject area, specific to the cognitive, linguistic, cultural, behavioral, and/or physical needs of each student.

11.3 Proposes ways in which families can support and reinforce classroom goals, objectives, and standards

MAE 4942


Reflect on the data and discuss strengths and challenges of your plan

11.6 Can describe overt signs of child abuse and severe emotional distress and knows to whom such observations should be reported

MAE 4942

Small Group Progression Plan Syllabus p. 2

Interns suspecting child abuse and/or severe emotional distress should report immediately to the appropriate school personnel.

Updated 6/4/10

Assessment of FEAP 12: Technology


12. Technology 12.3 Can identify and use standard references in electronic form

MAE 4393


The student has identified a relevant inquiry project and has a substantial justification of how this project will either contribute to improving the student’s local environment or exemplifies a novel science fair project The student makes a clear presentation of their poster, and can eloquently describe all elements of the project.

12.5 Teaches students to use available computers and other forms of technology.

MAE 3651


GSP “Power” Investigation . . . includes all GSP requirements for the multi-sketch investigation in effective ways.

MAE 4942


Develop complete and specific lesson plans that include appropriate subject-specific procedures, reflecting knowledge of subject matter.

12.7 Uses technology to assist with instructional and classroom management

MAE 4393


The student makes a clear presentation of their poster…

RED 4325


provides students with opportunities to actively use technology and facilities access to the use of electronic resources; uses technology to manage, evaluate, and improve instruction

MAE 4330


MLS report demonstrates appropriate use of technology for . . . delivering instructions . . .

MAE 4942


Develop complete and specific lesson plans that include appropriate materials (e.g., multi-sensory), and appropriate subject-specific procedures, reflecting knowledge of subject matter

12.6 Uses technology in lesson and material preparation

MAE 3651


GSP “Power” Investigation demonstrates a sophisticated knowledge of GSP for supporting diverse students’ learning of mathematics through exploration. It includes all GSP requirements for the multi-sketch investigation in effective ways.

MAE 4393


The student makes a clear presentation of their poster…

MAE 4330


MLS report demonstrates appropriate use of technology for developing instructional materials . . .

MAE 4942


Develop a system to track student progress (e.g., graph)

Critical Tasks in FIU Mathematics Education Programs to...

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