Podcast
Questions and Answers
What are the three key instructional shifts in the CA CCSSM?
What are the three key instructional shifts in the CA CCSSM?
Focus, coherence, and rigor
Which of the following is NOT one of the aspects of rigor required by the CA CCSSM?
Which of the following is NOT one of the aspects of rigor required by the CA CCSSM?
The CA CCSSM require the application of mathematical concepts and procedures throughout all grade levels. Students are expected to use mathematics and choose the appropriate concepts for __________ even when they are not prompted to do so.
The CA CCSSM require the application of mathematical concepts and procedures throughout all grade levels. Students are expected to use mathematics and choose the appropriate concepts for __________ even when they are not prompted to do so.
application
The teaching of mathematics should proceed in a strictly linear order according to the CA CCSSM.
The teaching of mathematics should proceed in a strictly linear order according to the CA CCSSM.
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How do teachers ensure coherence in mathematics instruction?
How do teachers ensure coherence in mathematics instruction?
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Which of the following practices is included in the Standards for Mathematical Practice?
Which of the following practices is included in the Standards for Mathematical Practice?
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What is the primary focus for instruction in grade five according to the framework?
What is the primary focus for instruction in grade five according to the framework?
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What is the first principle of instructional design for students to achieve learning with understanding?
What is the first principle of instructional design for students to achieve learning with understanding?
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Which instructional model emphasizes self-discovery?
Which instructional model emphasizes self-discovery?
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What are the five cognitive stages in the 5E model?
What are the five cognitive stages in the 5E model?
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The ______ phase in the three-phase model allows students to work independently.
The ______ phase in the three-phase model allows students to work independently.
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Singapore Math focuses on developing students' problem-solving abilities.
Singapore Math focuses on developing students' problem-solving abilities.
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What is a key component of cooperative learning in mathematics instruction?
What is a key component of cooperative learning in mathematics instruction?
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What does cognitively guided instruction emphasize?
What does cognitively guided instruction emphasize?
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How does problem-based learning engage students?
How does problem-based learning engage students?
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The five practices for orchestrating productive mathematics discussions include anticipating, monitoring, selecting, ________, and connecting.
The five practices for orchestrating productive mathematics discussions include anticipating, monitoring, selecting, ________, and connecting.
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Match the following instructional strategies with their descriptions:
Match the following instructional strategies with their descriptions:
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How much money does Marissa have?
How much money does Marissa have?
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What story problem can be written about how Marissa spends her money?
What story problem can be written about how Marissa spends her money?
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What tools can students use to understand perimeter?
What tools can students use to understand perimeter?
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What is the area that students should find rectangles for?
What is the area that students should find rectangles for?
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What should students compile based on their findings?
What should students compile based on their findings?
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What two payment options does Leonard suggest to his mother?
What two payment options does Leonard suggest to his mother?
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What should students calculate for Ms. Olsen's sidewalk?
What should students calculate for Ms. Olsen's sidewalk?
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What must students avoid when calculating the area of Ms. Olsen's sidewalk?
What must students avoid when calculating the area of Ms. Olsen's sidewalk?
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How can students determine how many jerseys to order for Bill's baseball team?
How can students determine how many jerseys to order for Bill's baseball team?
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The cost for Print It per jersey is ____.
The cost for Print It per jersey is ____.
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What does the task of estimating areas of countries involve?
What does the task of estimating areas of countries involve?
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What estimation methods were used based on the world map?
What estimation methods were used based on the world map?
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What is the role of students during the Charades activity?
What is the role of students during the Charades activity?
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What is the purpose of the Clues (Barrier Games) strategy?
What is the purpose of the Clues (Barrier Games) strategy?
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In the Coming to Consensus strategy, what do group members do?
In the Coming to Consensus strategy, what do group members do?
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What do explorers and settlers do in this instructional strategy?
What do explorers and settlers do in this instructional strategy?
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What activity do students engage in during the Find My Rule strategy?
What activity do students engage in during the Find My Rule strategy?
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What do students do in the Four Corners activity?
What do students do in the Four Corners activity?
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In the Give One, Get One strategy, what do students exchange?
In the Give One, Get One strategy, what do students exchange?
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During the Inside/Outside Circle activity, what do students do?
During the Inside/Outside Circle activity, what do students do?
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What is the goal of the Jigsaw strategy?
What is the goal of the Jigsaw strategy?
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What is the purpose of using KWL as a diagnostic tool?
What is the purpose of using KWL as a diagnostic tool?
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What do students do during the Line Up activity?
What do students do during the Line Up activity?
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How does the Numbered Heads Together strategy ensure accountability?
How does the Numbered Heads Together strategy ensure accountability?
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In the Quiz, Quiz, Trade strategy, what do students do?
In the Quiz, Quiz, Trade strategy, what do students do?
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What is the main outcome of a Socratic Seminar?
What is the main outcome of a Socratic Seminar?
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What is the Think-Pair-Share strategy used for?
What is the Think-Pair-Share strategy used for?
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How does the Think-Write-Pair-Share strategy differ from traditional Think-Pair-Share?
How does the Think-Write-Pair-Share strategy differ from traditional Think-Pair-Share?
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During the Whiparound activity, what do students do?
During the Whiparound activity, what do students do?
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What do students do in the Wraparound activity?
What do students do in the Wraparound activity?
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What kind of representations can be beneficial in math instruction?
What kind of representations can be beneficial in math instruction?
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What are concrete models used for in math instruction?
What are concrete models used for in math instruction?
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What role does interactive technology play in math instruction?
What role does interactive technology play in math instruction?
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Study Notes
Overview of Instructional Strategies
- Aimed at enhancing teachers' repertoire of instructional strategies, not prescribing specific methods.
- Effective teaching aligns strategy choice with material and student needs.
- Lessons must engage all students and enhance mastery of the California Common Core State Standards for Mathematics (CA CCSSM).
Lesson Structure
- Lessons should typically last 50-60 minutes, excluding homework.
- Regular exposure to new information is essential for building conceptual understanding and practice of skills.
- Teaching requires careful sequencing to ensure all standards are addressed without strict linearity.
Key Instructional Shifts
- Focus: Concentration on grade-level standards for deeper understanding.
- Coherence: Attention to learning progression across grades and linking major topics within grades.
- Rigor: Development of conceptual understanding, procedural skill, and application.
Rigor in Mathematics Education
- Rigor consists of three aspects:
- Conceptual Understanding: Teaching mathematical concepts in various contexts to promote meaningful learning.
- Procedural Skill and Fluency: Structuring practice for procedural mathematics, ensuring fluency is achieved through well-planned instruction.
- Application: Encouraging students to use mathematics in real-world contexts, reinforcing relevance and motivation.
Standards for Mathematical Practices
- Eight practices that promote expertise in mathematics include:
- Problem-solving perseverance.
- Reasoning abstractly and quantitatively.
- Constructing viable arguments.
- Modeling with mathematics.
- Using appropriate tools strategically.
- Attending to precision.
- Looking for and making use of structure.
- Expressing regularity in repeated reasoning.
- Instruction must integrate these practices effectively, creating a safe space for discourse.
Critical Areas of Instruction
- Critical Areas guide instruction at each grade level, with a focus on:
- Developing fluency and understanding of fractions.
- Integrating decimal operations into the place-value system.
- Understanding volume measurements.
- Each grade-level chapter includes a reference for planning instruction, illustrating focus, coherence, and rigor.
General Instructional Models
- Various instructional models help align teaching with CA CCSSM and the critical instructional features.
- Effective instruction should be organized around problematic tasks, provide meaningful learning scaffolds, offer ongoing assessment, and promote collaboration.
- A combination of instructional models is necessary to cater to diverse student populations in California classrooms.### Instructional Models
- Instructional models vary from explicit to implicit instruction, affecting teacher roles and student learning.
- Explicit Instruction: Teacher-centered approach, focuses on direct assistance and skills mastery.
- Interactive Instruction: Combines explicit and implicit methods, balancing teacher and student regulation of learning.
- Implicit Instruction: Student-centered, emphasizes self-discovery and personal meaning construction.
5E Model
- Comprises five stages: engage, explore, explain, elaborate, and evaluate.
- Teachers serve as facilitators, guides, and models to encourage inquiry and creative thinking.
- Focuses on interaction, problem-solving, and effective communication among students.
Three-Phase Model
- A structured strategy for direct instruction involving three phases:
- Phase 1: Introduction and explanation of new concepts.
- Phase 2: Guided practice leading to independent application.
- Phase 3: Independent work and assessment of understanding.
Singapore Math
- Emphasizes number sense, mental math skills, and conceptual understanding through a concrete-to-pictorial-to-abstract progression.
- Prioritizes mastery before revisiting concepts, focusing on model drawing for problem-solving.
Concept Attainment Model
- An inductive approach where students categorize ideas/objects based on given examples and non-examples.
- Encourages hypothesis testing, critical thinking, and active participation in discussions.
Cooperative Learning Model
- Promotes teamwork in problem-solving, allowing students to share reasoning and critique others' arguments.
- Supports diverse learners by providing structured group tasks while teachers monitor and assist.
Cognitively Guided Instruction
- Students explore various problem-solving strategies, justify their reasoning, and explain their thought processes.
- Encourages ownership of learning, fostering a positive disposition toward mathematics.
Problem-Based Learning
- Engages students in real-world problem-solving using guided or unguided inquiry.
- Promotes perseverance, reasoning, and intellectual independence through collaborative learning.
Student Engagement Strategies
- Vital for maintaining focus and enhancing learning environments.
- Examples include Number Talks (mental math discussions) and Five Practices for Mathematics Discussions (anticipate, monitor, select, sequence, connect).
Student Engagement Techniques
- Appointment Clock: Students schedule discussions using a clock format.
- Carousel-Museum Walk: Groups present work on poster boards while others evaluate.
- Charades: Students act out math problems for peers to solve.
- Clues (Barrier Games): Pairs communicate problem-solving information using barriers to enhance understanding.
- Coming to Consensus: Groups collaboratively find solutions and present them to the class.
- Explorers and Settlers: Engages students in exchanging definitions and solving problems in designated roles.
Importance of Communication
- Mathematical discourse enriches understanding and connects everyday language with mathematical concepts.
- Writing enhances thinking and serves as an assessment tool, revealing students’ thought processes.### Classroom Engagement Strategies
- Find Your Partner: Students receive cards with rules and examples, matching them through circulation. Promotes inductive/deductive reasoning and problem-solving skills.
- Four Corners: Students gather in designated corners based on topic interest, then respond to problems related to the categories, providing an interactive grouping experience.
- Give One, Get One: Students brainstorm solutions to a problem, sharing and receiving steps with partners, encouraging collaboration and collective knowledge-building.
- Inside/Outside Circle: Concentric circles facilitate peer dialogue, where students ask and answer questions, enhancing communication and mathematical reasoning.
- Jigsaw: Students become experts on specific concepts and teach others, promoting collaborative learning and peer instruction.
- KWL Chart: Used for assessing what students know, want to know, and need to learn, helping tailor instruction to student readiness.
- Line Up: Students line up by criteria (e.g., smallest to largest), explaining their reasoning, fostering quick thinking and communication.
- Making a List: Pairs of students create lists of steps needed to solve complex problems, aiding in logical reasoning skills.
Cooperative Learning Strategies
- Numbered Heads Together: Each student contributes to group problem-solving, ensuring accountability and collective understanding.
- Quiz, Quiz, Trade: Students quiz each other with prepared cards, reviewing material while fostering cooperative learning.
- Socratic Seminar: In-depth discussions on complex ideas or scenarios, encouraging deeper understanding through critical thinking and defense of viewpoints.
- Team Share: Teams collaborate on problems and present their solutions, encouraging group participation and articulation of mathematical reasoning.
- Think–Pair–Share: Students think, then pair-share their responses, enhancing their ideas through discussion and refining understanding through collaboration.
- Think–Write–Pair–Share: Variations allowing students to write and then share their ideas, promoting clarity and structured responses.
Tools for Mathematics Instruction
- Visual Representations: Diagrams, graphic organizers, and flowcharts help illustrate relationships in mathematical concepts, enhancing student comprehension.
- Concrete Models: Manipulatives provide hands-on learning opportunities, aiding students in understanding both basic and complex concepts like the Pythagorean Theorem.
- Interactive Technology: Engaging software and applications can enhance learning if they align with educational standards and goals.
Example Mathematical Tasks
- Marissa's Savings: A multi-step problem involving monetary amounts that teaches practical application of arithmetic and problem-solving.
- Understanding Perimeter: Hands-on activities with rubber bands and geoboards help students grasp the concept of perimeter through exploration and pattern recognition.
- After-School Job: A problem encouraging students to analyze two payment options and use of numerical patterns to solve real-world scenarios, integrating concepts of exponential growth and decision-making.
Overall Objective
- Strategies are designed to promote engagement, accountability, and collaboration among students while providing effective tools and tasks that resonate with real-world applications, ensuring comprehensive understanding of mathematical concepts.
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Description
Explore the instructional strategies outlined in the Mathematics Framework for California Public Schools. This chapter aims to enhance teachers' approaches to teaching mathematics from Kindergarten through Grade Twelve, providing a variety of strategies to support diverse learning needs.