Support Candidates for edTPA through

Curriculum Alignment and Embedded Assignments

Mihaela Munday Ph. D. Savannah State University

School of Teacher EducationMacon, October 22, 2015

Curriculum Mapping – How does the edTPA align with our programs?

1.To what extent does it reflect program values?2. Where do you predict that students would dowell? Where might they struggle?3. What core values and program emphases are notcaptured in the TPA?4. What kinds of assessments do you currently use(or might you need) to get at these? Andrea Whittaker UW Whitewater Presentation January 15, 2013

Integrating the five components of the edTPA portfolio:Planning InstructionAssessmentAnalysis of TeachingAcademic Language

Element edTPA Rubric # and Level of Support

2a Use problem solving to develop conceptual understanding, make sense of a wide variety of problems and persevere in solving them, apply and adapt a variety of strategies in solving problems confronted within the field of mathematics and other contexts, and formulate and test conjectures in order to frame generalizations.

8 – Limited

2b Reason abstractly, reflectively, and quantitatively with attention to units, constructing viable arguments and proofs, and critiquing the reasoning of others; represent and model generalizations using mathematics; recognize structure and express regularity in patterns of mathematical reasoning; use multiple representations to model and describe mathematics; and utilize appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others.

9 – Limited

3b Analyze and consider research in planning for and leading students in rich mathematical learning experiences.

3 – Moderate

3c Plan lessons and units that incorporate a variety of strategies, differentiated instruction for diverse populations, and mathematics-specific and instructional technologies in building all students’ conceptual understanding and procedural proficiency.

3 – Moderate

3d Provide students with opportunities to communicate about mathematics and make connections among mathematics, other content areas, everyday life, and the workplace.

8 – Moderate

3e Implement techniques related to student engagement and communication including selecting high quality tasks, guiding mathematical discussions, identifying key mathematical ideas, identifying and addressing student misconceptions, and employing a range of questioning strategies.

7 – Moderate; 8 – Limited

3f Plan, select, implement, interpret, and use formative and summative assessments to inform instruction by reflecting on mathematical proficiencies essential for all students.

5 – Strong; 10 – Limited; 11 – Limited; 13 – Limited;

15 – Limited

3g Monitor students’ progress, make instructional decisions, and measure students’ mathematical understanding and ability using formative and summative assessments.

11 – Limited; 13 – Limited; 15 – Moderate

4b Plan and create developmentally appropriate, sequential, and challenging learning opportunities grounded in mathematics education research in which students are actively engaged in building new knowledge from prior knowledge and experiences.

1 – Limited; 3 – Moderate; 7 – Limited

4c 2 – Limited; 4 – Limited

Alignment of NCTM CAEP Standards (2012) for

Secondary to edTPA Rubrics

Curriculum Alignment (sample)

NCTM Standards (2012) – Secondary (Initial Preparation)

Rule 505-3-01, REQUIREMENTS AND STANDARDS FOR APPROVING EDUCATOR

PREPARATION PROVIDERS AND EDUCATOR PREPARATION PROGRAMS.

Georgia Intern Keys Effectives

SystemCandidate

Assessment of Performance

Standards

edPTATasks and Rubrics

Courses Description of the assessment system used to provide evidence and data and

to inform continuous improvement.

1.Content Knowledge Candidates of secondary mathematics demonstrate conceptual understanding and apply knowledge of major mathematics concepts, algorithms, procedures, connections, and applications within and among mathematical content domains.

1a. Candidates demonstrate conceptual understanding and apply knowledge of major mathematics concepts, algorithms, procedures, applications in varied contexts, and connectionswithin and among mathematical domains including Number, Algebra, Geometry, Trigonometry, Statistics, Probability, Calculus, and Discrete Mathematics as outlined in the 2012 NCTM NCATEMathematics Content for Secondary.

1.Professional Knowledge1.1, 1.4

    

MAED 4416 1.State-required Licensure Test: GACE

  2.Alignment to NCTM CAEP Mathematics Content for Secondary

MATH 1113 Pre-CalculusMATH 2111 Calculus IMATH 3101 Linear AlgebraMATH 3201 Probability and Statistics IMATH 3401 Modern GeometryMATH 3211 Foundation of Higher Math

3. Individual Candidate performance data.

Task 1Rubric 1

MAED 4417EDUC 4475

4. Task 1 -Planning Commentary 

  MAED 4416 5. Course Portfolio

Secondary Mathematics EducationCurriculum Mapping

Developing new courses (BSED)

MAED 3000 Connections in Secondary School Mathematics

Using the NCTM Standards as a guideline and replacing traditional teaching of Algebra I, Geometry, Algebra II, this course blends the mathematics of algebra, geometry, trigonometry, probability, statistics, and discrete mathematics. The course bridges connections of all sorts: those between different mathematical areas; mathematics and science; mathematics and other subject areas; and mathematics and the real world of people, business and everyday life. The course integrates technology through the use of graphing calculators and computers, which students use to make conjectures; validate findings; and investigate concepts, problems, and projects in greater depth. The emphasis on writing and the use of alternative types of assessment in this course is designed to help the student teachers to adapt their teaching strategies in order to meet every student’s need.

EDUC 3130 Content Area Literacy for Diverse Classroom This course explore methods for teaching middle and high school to read, write, think, and learn in ways that allow them to master the subject matter and meaningfully apply their understanding. Candidates learn to plan lessons that teach content and nurture greater literacy. Pre-, during-, and post-reading strategies are explored, along with assessment methods that give students a continual view of their literacy progress and achievement. Classroom adaptations for culturally and linguistically diverse population in the content areas are also addressed.

Developing new courses (BSED)

MAED 3001 Qualitative and Quantitative Research Methods in Mathematics Education

This course will examine qualitative methods and quantitative methods. In qualitative research, interviewing, observations and document analysis will be the major source of the qualitative data for understanding the phenomenon under study. Observations will involve collecting qualitative information about human actions and behaviors in social activities and events in a real social environment, such as classroom teaching and learning.

MAED 3002 Planning, Managing & Assessing the 6-12 Divers Mathematics Classroom

The focus of the course is developing reflective teachers who draw upon a wide array of solutions to secondary classroom challenges when planning instruction for preadolescent and adolescent students. The class uses case studies to discuss and prepare candidates to deal with the effects of diverse characteristics and cultures of the adolescent. The course will provide candidates opportunities to apply conceptions of curriculum, instruction, classroom management and discipline, multimedia, human resources, and assessment in the context of an actual secondary classroom.

MAED 4417 Assignments

Embedded Assignments

The balance between conceptual understanding and computational proficiency is achieved when the curriculum enables and encourages students to build on the mathematics they already know.

Substantive feedback from aligned rubrics on their performancesMAED 4416 Mathematics Sequenced Unit Plans Rubric

Level 1

Level 2

Level 3

Level 4

Level 5

Planning for

Mathematical Understanding

CAEP 1.1, 1.3, 4(a)(d)(l)(n) INTASC 7a-e, i- l , n-q; 9 c NCTM 7. 2 edTPA Rubrics1,2,4,5

Candidate’s plans are incomplete. They focus solely on facts and/or procedures with no connections to concepts or mathematical reasoning and/or problem solving. Methods or strategies of instruction are not evident and/or are inappropriate for the content.

Plans slavishly follow standards with little consideration of what students are ready for, making learning with understanding difficult. Candidate’s plans support student learning of facts and procedures with vague concepts and mathematical reasoning and/or problem solving skills.

Plans for instruction demonstrate knowledge of content standards (CCGPS), use of appropriate learning materials, and commitment to learning with understanding. They are built on each other to support learning of facts and procedures with clear connections to concepts and mathematical reasoning and/or problem skills.

Plans for instructions demonstrate knowledge of the content appropriate for students, use of stimulating curricula that allows multiple approaches to content, and commitment to learning with understanding. They are built on each other to support learning of facts and procedures with clear and consistent connections to concepts and mathematical reasoning and/or problem solving skills.

Level 4 plus:

Candidate explains how she/he will use learning tasks and materials to lead students to make clear and consistent connections.

P la n n in g to S u p p o rt V a r ied

S tu d en t L ea rn in g N eed s

C A E P 1 .2 , 1 .4 , 6 c ,6 d IN T A S C 2 a ;2 c ;2 d ;2 f;2 g ;2 h ;2 j;2 k ;2 m ;8 p ;9 d N C T M 7 .3 e d T P A R u b ric 2

There is little or no evidence of planned supports. OR Candidate does not attend to requirements in IEPs and 504 plans.

Planned supports are loosely tied to learning objectives or the central focus of the learning segment. AND Candidate attends to requirements in IEPs and 504 plans.

Planned supports are tied to learning objectives and the central focus with attention to the class as a whole. AND Candidate attends to requirements in IEPs and 504 plans.

Planned supports are tied to learning objectives or the central focus. Supports address the needs of specific individuals or groups with similar needs. AND

Candidate attends to requirements in IEPs and 504 plans.

Level 4 plus:

Supports include specific strategies to identify and respond to preconceptions, common errors, and misunderstanding.

Substantive feedback from aligned rubrics on their performancesMAED 4416 Mathematics Sequenced Unit Plans Rubric

A ssessm en t CAEP 4(f) INTASC6a,b, d, e ,6j, g, m, q -u NCTM 7.5 e d T P A R u b ric 5

The assessments only provide evidence of students’ procedural skills and/or factual knowledge. Assessments are not aligned with the central focus and standards/objectives for the learning segment

Either formal or informal assessment strategies or instruments are mentioned but there are no concrete examples. The assessments provide limited evidence to monitor students’ conceptual understanding, procedural fluency, and mathematical reasoning and/or problem solving skills during the learning segment.

Provides concrete examples of at least one question for each type of student, and describes at least one other informal way to gather information about student progress. When appropriate, uses formal assessment to measure student learning. The assessments provide evidence to monitor students’ conceptual understanding, procedural fluency, and mathematical reasoning and/or problem solving skills during the learning segment.

Provides examples of a variety of questions to be asked when students seem to be progressing well or when they are struggling. Describes at least one other method of gathering knowledge of student progress. When appropriate, uses formal assessment to measure student learning. The assessment provide multiple forms of evidence to monitor students’ conceptual understanding, procedural fluency, and mathematical reasoning and/or problem solving skills throughout the learning segment.

Level 4 plus:

The assessments are strategically designed to allow individuals or groups with specific needs to demonstrate their learning.

A ssimilation o f K nowledge

INTASC 2c,l,n

NCT M 8 .7 edTPA Rubrics

1,2,5,6,7,8

Connections between prior knowledge and new learning experiences are not evident.

Attempts to build on prior knowledge, but is not able to help students develop the new concept.

Uses learning activities that build on prior knowledge, but students may not see how the learning experiences develop a new concept.

Uses a variety of learning activities that build on prior knowledge and help students articulate how the learning experiences develop a new concept.

Level 4 plus:

Values knowledge outside his/her own content area and how such knowledge enhances learner exploration, discovery and expression across content areas.

Academic Language for Secondary MathematicsLevel 1 (5 pts) Level 2 (20 pts) Level 3 (40 pts) Level 4 (50 pts)

Understand Language Demands and ResourcesINTASC-2013.2.i INTASC-2013.4.h

Candidate's description of students' academic language proficiency at lower levels is limited to what they cannot do.

Language genre(s) discussed are only tangentially related to the academic purposes of the learning segment.

Candidate identifies unfamiliar vocabulary without considering other linguistic features.

OR

Candidate did not identify any language demands of the learning and assessment task.

Candidate describes academic language strengths and needs of students at different levels of academic language proficiency.

The language genre(s) discussed are clearly related to the academic purposes of the learning and language demands are identified.

Candidates identifies vocabulary that may be problematic for students.

Candidate describes academic language strengths and needs of students at different levels of academic language proficiency.

The language genre(s) discussed are clearly related to the academic purpose of the learning segment and language demands are identified. One or more linguistic features and/or textual resources of the genre are explicit identified.Candidate identifies essential vocabulary for students to actively engage in specific language tasks.

Candidate describes academic language strengths and needs of students at the full range of academic language proficiency.

The language genre(s) discussed are clearly related to the academic purpose of the learning segment and language demands are identified. One or more genre-related linguistic features or textual resources of the specific tasks/materials are explicitly identified and related to students' varied levels of academic language proficiency.

Candidate identifies for instruction related clusters of vocabulary.

Developing Students' Academic Language RepertoireINTASC-2013.2.e INTASC-2013.2.i INTASC-2013.5.h NCTM-K-12.8.1

The candidates gives little or sporadic support to students to meet the language demands of the learning tasks.

ORLanguage and/or content is oversimplified to the point of limiting student access to the core content of the curriculum.

The candidate uses the scaffolding or other support to address identified gaps between students' current language abilities and the language demands of the learning tasks and assessments, including selected genres and key linguistic features.

The candidate's uses of scaffolding or other support provides access to core content while also providing explicit models, opportunities for practice, and feedback for students to develop further language proficiency for selected genres and key linguistic features.

Candidate articulates why the instructional strategies chosen are likely to support specific aspects of students' language development for different levels of language proficiency.

The candidate's use of scaffolding or other support provides access to core content while also providing explicit models, opportunities for practice, and feedback for students to develop further language proficiency for selected genres and key linguistic features.

Candidate articulates why the instructional strategies chosen are likely to support specific aspects of students' language development for the full range of language proficiency and projects ways in which the scaffolds can be removed as proficiency increases.

Language Acquisition in Mathematics Assignments

Graphing Organizers-Verbal and Visual Word Association(VVWA) described in The teaching of Reading in Mathematics by M.Barton and C.Heidema(2002), places a vocabulary word into one section of a four-by-four graphic. The remaining three sections are filled with a visual representation of the word, a definition and/or an equation, and finally, a personal association.-Use of compare and contrast activities. -Tables-Charts-Diagrams

VVWA(Verbal and visual word association) for the Slope of a line

Compare and contrast activity for exponential, linear and quadratic functions

Geometry of a Circle-Semantic Map Meaning

Semantic

Concepts Representation Tool

 

History

Definitions:

-Circle symbolizes the expansiveness of the cycles in time, life and nature itself. A mirroring of perception.

-Literature circles are small, temporary discussion groups.

-Mathematical circle is a plane shape, in which all sets of points on a plane are a fixed distance from a center.

 

Keywords

-Inclusion

-Wholeness

-Focus

-Unity

-Nurturing

-Cycles

-Initiation

-Everything

-Perfection

-Womb

-Centering

-Revolution

-Infinity

-Mobility

Completion

Unit Circle

Circle Equations

Polar and Parametric Equations

 

 

Chemistry

 

 

 

 

Biology

 

 

 

 

 

 

Astronomy

 

The study of the circle goes back beyond the recorded history. The invention of the wheel is a fundamental discovery of properties of a circle. The Greeks considered the Egyptians as the inventors of geometry. Ahmes, who is a scribe and the author of the Rhind papyrus, gives a rule for determining the area of a circle that corresponds to 256/81 or approximately 3.16. Thales found the first theorems relating to circles around 650 BC. The Euclid's Book III, Euclid's Elements set to work properties of circles and problems of inscribing polygons. One of the problems of Greek mathematics was the problem of finding a square with the same area as given circle. Several of the 'famous curves' were first attempted to solve this problem. Anaxagoras in 450 BC is the first recorded mathematician to study this problem.

 

Circle

Challenging for students- Task 3

Possible reasons for low scores on Task 3:-Fatigue by the end of this process-Weak background in assessing student work, developing rubrics, aligning assessments to objectives and rubrics

Rubric 3

While preassessing students is not required by edTPA, doing so may help candidates who are new to their placement quickly identify student learning needs and strengths.

Rubric 5

Examples of assessments: Think pair share, KWL informal assessments, Oral, written, diagrams, mapping

IEP/504 accommodations are met (longer time, scribe); if no IEPs/504s than not applicable

Level 4: multiple assessments in multiple ways throughout start out with KWL, then do think-pair-share, then do group work where they create multimedia, then give formative assessment assessment is throughout.

Rubric 11

• Talking about whole class and supporting it with evidence • Assessment and results of assessment • Rubric results, pie chart, table of scores, etc.