Conceptua Math Professional Development to Enact Best Practice

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What is Conceptua Math? Online Solution with Best Practice Built- in – Interactive Visual Models Learning moves from models to procedures – Rich Classroom Discussions Standards for Mathematical Practice Productive Talk Moves – Adaptive Teaching Teachers chose instructional path Formative Assessments Differentiation built in Data and reporting

What is Conceptua Math? Conceptua Math Structure – Lesson Sequence Opener Guided Lesson Closer – Assessment and Differentiation – Extensions Productive Talk Moves Preparing to Teach

A key factor, which distinguishes ‘expert’ learners from ‘novices’, is the ability to organize or chunk thinking around big ideas. Organizing information into a conceptual framework around big ideas facilitates greater retention, recall and transfer of learning. -National Research Council, 2000, Miller, G CONCEPTUA MATH STRUCTURE

Structure Class Dashboard allows the teacher to teach – Student progress monitored and reports printed – Assign Lessons or Topics – View Lesson Openers, Guided Lesson, Closers – Access to Investigations and Tools

Structure Curriculum Library content is organized into Units around Big Ideas Curriculum Library View by: – Domain: Big Ideas – Grade Level: Units

Structure Tool Library allows the teacher to create problems using any of the tools.

Structure PD on Demand is a series of support videos and documents just in case…

Structure Class Management allows the teacher modify enrollment in an existing class or create additional classes

Units Each unit contains: Approximately four topics, each containing a week of daily skill building lessons Weekly tool investigations A Real World Investigation

Models to Procedures Grade 4: Equivalent fractions name the same amount by using different-sized fractional parts. Grade 3 Fractions can be modeled in multiple ways. Grade 5: Multiplication is used to find the product of groups of items and is the same as repeated addition. The groups of items are parts of a whole.

Research has demonstrated that highly effective teachers deliver well-structured lessons that accommodate diverse learners. -Lloyd, Kameenui and Chard 1997 THE LESSON SEQUENCE

Confidential and Proprietary 14 Opener Guided Lesson CloserExtension Daily Lesson Sequence

The Opener Opener Guided Lesson Closer Extensions Introducing students to content facilitates students’ learning by communicating the purpose of the lesson, connecting new learning to prior knowledge and cueing students to the responses required in guided practice. -Brophy 1998, Good and Brophy 2000

Purpose of a Lesson Opener is to... Hook: Gain the students’ attention Link: Activate prior knowledge and linking that knowledge to new learning Facilitate Discourse: Elicit specific strategies and highlight relationships State learning outcomes: Students are more efficient learners if they know what they are supposed to learn

Teacher Facilitated during Openers and Closers PRODUCTIVE TALK MOVES

Productive Talk Moves 1.Revoicing: Teacher repeats some or all of what the student has said. Students verify. 2.Repeating: Asking students to restate someone else’s reasoning 3.Reasoning: Asking students to apply their own reasoning to someone else’s reasoning 4.Adding on: Prompting students for further participation 5.Waiting: Using wait time Chapin, O’Connor, Anderson. Classroom Discussions: Using Math Talk to Help Students Learn. 2009

Revoicing Enables the teacher to deal with the lack of clarity of many student contributions. – “So you’re saying … Is that right?” – “Let me see if I understand….”

Restating Restating ensures that students will listen when others provide explanations and helps students formulate/deepen their own understanding. – “John, can you repeat in your own words what Maria just said?” – “So Mark, you are saying…” – “Juli, can you use the models and repeat what Larry just said?”

Reasoning Focuses students on reasoning about another’s claim. Requires students to listen, compare their understanding to that of the claim. – “Do you agree or disagree with Carlos? Why or why not?” – “Explain how your answer is the same or different than ___?” – “How does “student A’s” strategies connect to “student B’s” strategies?” – “What do you think about that?”

Add on Used to bring more students into the discussion. It reinforces the idea that everyone’s contribution is valued. It allows a deeper discussion. – “Does someone have another answer?” – “Does anyone want to add to that?”

Student Communication Students need clear models for what explanations sound like. – “I agree with ____ because of ______.” – “I do not understand _____. Can you explain it again?” – “I disagree with ___________ because ________.” – “How did you decide to____________?”

Observe an Opener Opener at Crescent Elementary School, Georgia Web access necessary

Your Turn for an Opener Grade Fractions Grade Multiplication Grade Fractions

The Guided Lesson Opener Guided Lesson Closer Extensions The “soul of the lesson” is the guided practice, which “must occur under the observant eye of the teacher, who in turn must look to see if the class as a whole is succeeding on each successive step” by checking for understanding or formative assessment. -Schmoker Published Online at Education Week: June 4, 2013

The Guided Lesson Role of the Teacher – Monitor – Questioning – Clarifying – Redirecting – Provide feedback How to Manage – Signals – Menus – Journaling

Remember that you can use the short-cut keys to preview any lesson Windows: Hold Control & Shift keys and Press Mac: Hold Command & Shift keys and Press Your Turn for the Guided Practice Preview a Guided Lesson Grade Fractions Grade Multiplication Grade Fractions Stop Here-- 

Share examples of best practice built into the lessons that you previewed. GUIDED PRACTICE

The Formative Assessment Opener Guided Lesson – Formative Assessment Closer Extensions “Formative assessment is a crucial tool for simultaneously improved classroom practice and students’ performance.” -Petit & Zawojewski, 2011

Purpose of Formative Assessment Adaptive Teaching – Process of conducting individual conferences/interviews to: Determine the reasoning behind errors Re-teaching to address misconceptions Requiring students to justify answers and explain their thinking The Role of the Teacher – Differentiate instruction – Address misconceptions – Check for understanding – Create a positive learning environment

Your Turn to Practice a Formative Assessment Work in pairs, to complete and fail the formative assessment partner A select the R lesson partner B select the P lesson

The Closer Opener Guided Lesson Closer Extensions At the end of a lesson, a short concentrated time period of five to eight minutes should be set aside to provide students with the opportunity to evaluate lesson content and to reinforce skills taught. “This is the time in the lesson when student reflection is necessary for internalization of the skills covered.” -Supon, 1994

The Purpose of the Closer is to… Bring the lesson to a logical conclusion – Clarification of concepts – Check for understanding Engage students in summarizing – Students summarize and justify thinking – Students actively participate – Summarizing supports lesson objective and key concept

Journal Prompts

Your Turn for the Unit Exploration Remember that you can use the short-cut keys to preview any lesson Windows: Hold Control & Shift keys and Press Mac: Hold Command & Shift keys and Press Preview a Unit Grade Fractions Grade Multiplication Grade Fractions

Share your thoughts on the unit and any questions about the lesson sequence UNIT EXPLORATION AND LESSON SEQUENCE

Extensions Opener Guided Lesson Closer Extensions – Tool Investigations – Real World Investigations – Student Tools “Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.” -Standards for Mathematical Practice MP4