Which of the following items must you consider when planning instruction in your class?

Place a dot next to each item. UbD IFL/POL IEP/504/UDL ESL/SIOP PLCs PEP LFL and Research-based Strategies NCEES

Transformational Teaching

Teach like an

MVP

Beth NeillMary Rogers

Session GoalHow can a sequenced, task-based curriculum engage students in rigorous problem solving activities, but also support skill and procedural fluency development while meeting all of the many instructional demands placed on teachers?

Math Teaching Practice:Implement Tasks that Promote Reasoning and Problem Solving

• “Tasks may begin as high-level tasks for students who are initially learning about the underlying mathematics.

• Eventually, as students solidify their understanding of the underlying mathematics, these tasks may become more routine experiences for them.

• Students then need tasks that further extend these mathematical ideas in ways that continue to deepen understanding and strengthen mathematical reasoning and problem solving.” (p. 22)

“Over time, the cumulative effect of the use of mathematics tasks is students’ implicit development of ideas about the nature of mathematics… “ (p. 20)

5.1

5.25.3

How does the mathematical understanding change from the beginning to the end of the learning cycle?

Through the teachers’ lens

The Learning Cycle

Develop Understanding

Surface student thinking

Solidify Understanding

Examine and extend

Practice Understanding

Build Fluency

The Learning Cycle

Develop Understanding

Surface student thinking

Solidify UnderstandingExamine and extend

Practice Understanding

Build Fluency

CCSSM Function Progression from a Learning Cycle Perspective

8.F.5 Sketch a graph that exhibits the qualitative features of a function that has been described verbally.8.F.1 Understand that a function is a rule that assigns to each input exactly one output.

8.F.2 Compare properties of two functions each represented in a different way.8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear).

F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

Develop Understanding

Surface student thinking

Solidify UnderstandingExamine and extend

Practice Understanding

Build Fluency

Connecting the Learning Cycle to the Math Practice Standards

Make sense of problems and persevere in solving them.

Use appropriate tools strategically

Look for and make use of structure

Construct viable arguments and critique the reasoning of others

Look for and express regularity in

repeated reasoning

Model with mathematics

Reason abstractly and quantitativelyAttend to precision

Dev

elop

Solid

ify

Prac

tice

Ideas

Strategies

Representations

Concepts

Algorithms

Tools

Definitions &Properties

Procedures

Models

Mathematical Understanding Continuum

Emerging mental images: ideas, strategies, and representations are fragile as they are surfaced during students’ initial experiences with tasks designed to elicit those images (Develop Understanding) They need to be examined for accuracy and completeness, as well as extended and connected through multiple exposures and experiences until they become more tangible, solid and useful: concepts, algorithms, tools (Solidify Understanding). Although understanding has been developed and solidified, it needs further refinement to become fluent: definitions or properties, procedures, models (Practice Understanding). These definitions and properties, procedures, and models must be consistent with the broader mathematical “community of practice”.

The Teaching CycleConnecting to the 5 Practices of Orchestrating a Productive Mathematical Discussion

Anticipating

Monitoring

Selecting

Sequencing

Connecting

How do the learning and teaching cycles address individual student needs?

• Multiple representations• Formative assessment• Writing• Summarizing• Low threshold• High ceiling• Multiple entry points• Varied solution paths• Coherent and cohesive• Procedural fluency through

conceptual understanding• Assessing and advancing questions• Collaboration• Scaffolding• Challenge• Higher order thinking• Discourse• Engagement

Multiple representationsFormative assessmentWritingSummarizingLow thresholdHigh ceilingMultiple entry pointsVaried solution pathsCoherent and cohesiveProcedural fluency through conceptual understandingAssessing and advancing questionsCollaborationScaffoldingChallengeHigher order thinkingDiscourseEngagement

Understanding by Design (UbD)

Multiple representationsFormative assessmentWritingSummarizingLow thresholdHigh ceilingMultiple entry pointsVaried solution pathsCoherent and cohesiveProcedural fluency through conceptual understandingAssessing and advancing questionsCollaborationScaffoldingChallengeHigher order thinkingDiscourseEngagement

Institute for Learning: Principles of Learning

Multiple representationsFormative assessmentWritingSummarizingLow thresholdHigh ceilingMultiple entry pointsVaried solution pathsCoherent and cohesiveProcedural fluency through conceptual understandingAssessing and advancing questionsCollaborationScaffoldingChallengeHigher order thinkingDiscourseEngagement

Individualized Education Plan (IEP)Section 504

Universal Design for Learning (UDL)

Multiple representationsFormative assessmentWritingSummarizingLow thresholdHigh ceilingMultiple entry pointsVaried solution pathsCoherent and cohesiveProcedural fluency through conceptual understandingAssessing and advancing questionsCollaborationScaffoldingChallengeHigher order thinkingDiscourseEngagement

English Language Learners (ELLs)Sheltered Instruction Observation Protocol (SIOP)

Multiple representationsFormative assessmentWritingSummarizingLow thresholdHigh ceilingMultiple entry pointsVaried solution pathsCoherent and cohesiveProcedural fluency through conceptual understandingAssessing and advancing questionsCollaborationScaffoldingChallengeHigher order thinkingDiscourseEngagement

Professional Learning Communities (PLCs)

Multiple representationsFormative assessmentWritingSummarizingLow thresholdHigh ceilingMultiple entry pointsVaried solution pathsCoherent and cohesiveProcedural fluency through conceptual understandingAssessing and advancing questionsCollaborationScaffoldingChallengeHigher order thinkingDiscourseEngagement

Personalized Education Plans (PEPs)

Multiple representationsFormative assessmentWritingSummarizingLow thresholdHigh ceilingMultiple entry pointsVaried solution pathsCoherent and cohesiveProcedural fluency through conceptual understandingAssessing and advancing questionsCollaborationScaffoldingChallengeHigher order thinkingDiscourseEngagement

Learning Focused Lessons (LFL)Research Based Instructional Strategies

Multiple representationsFormative assessmentWritingSummarizingLow thresholdHigh ceilingMultiple entry pointsVaried solution pathsCoherent and cohesiveProcedural fluency through conceptual understandingAssessing and advancing questionsCollaborationScaffoldingChallengeHigher order thinkingDiscourseEngagement

NC Educator Evaluation System (NCEES)

Other Task-based Curriculums that Support the Learning Cycle

Transformations must be cultivated.

Take it one Learning Cycle at a time.

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