A Concept-Driven, Diverse Learning Environment to Address theCommon Core Standards J. Bryson .. S. Pasadena R. Neufeld .. Neufeld Learning Systems Inc. ASCD Los Angeles … March 15, 2014
Team Leaders/Administrators • Convince teachers to teach for understanding. • Prepare parents that teachers may not provide all of the answers. • Prepare parents that students will be grappling with challenging material. • Note answers are important but not sufficient.
The standards were • drafted by experts and teachers from across the country • and are • designed to ensure students are prepared for today’s entry-level careers, freshman-level college courses, and workforce training programs. • The Common Core focuses on • developing the critical-thinking, problem-solving, and analytical skills students will need to be successful. http://www.corestandards.org/what-parents-should-know/
Mathematically capable students: CCSS for Math Practice
Instructional Paradigm Shift To Developing deep student understanding and procedural fluency
Instructional Paradigm Shift: Teachers Talk Less. Listen More!
Instructional Paradigm Shift: Students Watch Less. Do More!
“Active learning practices have a more significant impact on student performance than any other variable, including student background and prior achievement.” Dr. Brigid Barron and Dr. Linda Darling-Hammond, Stanford University Teaching for Meaningful Learning: A Review of Research on Inquiry-Based and Cooperative Learning
Instructional Model: Percent Sense From Calculate the following percents. 55% of 40 120% of 60 40% of 8 30% of 12 10% of 184
To Choose one: <, =, or >. A: Predict which of >, =, or < would make the statement true and explain why you think so– without calculations. B. Verify the accuracy of your partner’s prediction by doing the calculation. • 55% of 40 _______ 55% of 60 • 120% of 60 _______ 60 • 40% of 8 ________ 30 % of 8 • 30% of 12 _______ 10% of 184 What generalizations might be true about percents?
Assessment Paradigm Shift From Testing content knowledge and skill mastery
Assessment Paradigm Shift To Assessing mathematical practice competency and procedural fluency
Use the … tool to create a linear model. What is the equation?
Interpret the slope… in context. Based on the equation … predict.
Explain whether [it’s]… reasonable in context. Would these…change the model?
draw it build it write it talk it OWN IT!! Create an individual-centered approach but within a multiple approach opportunity.
The Curriculum: • Envisions a higher level of rigor based on a deeper understanding of a pared down number of curricular objectives. • Poses a challenge for teachers who must not only be fluent in content but also attain the particular pedagogy to be able to convey it to their students.
The Emphasis is on: • Students doing mathematics. • Students demonstrating thinking and learning. • Students grappling with challenging tasks in a learning environment that will support equity in schools.
Students: • Engage in Discourse. • articulate their own ideas • Critique the reasoning of their peers… • …respectfully. • consider their peers’ perspectives • Dialog to construct mathematical understandings.
Teachers & Students Use: • Probing Questions • Show me another way … • How are these the same / different … • What would you do if … • Why did you … • What else could you have done … • Productive Talk Moves • Revoicing - Repeating and asking for clarification • Repeating - Students restate someone else’s reasoning • Reasoning - Apply their reasoning to another’s reasoning • Adding on - Prompting for further participation • Waiting - “Take your time. We will wait.”
MODEL THE PROCESS 30th picture? 30th number? 3 5 7 … Show me another way Pictures – Words - Numbers
Build it - Draw it - Write it – Talk it – Then OWN IT!! M Hilliard PS.. Toronto
Reflect and Connect: Surface Area & Volume Now check .. Reflect and Connect .. on framework .. See Support sheet handed out.
Challenges for Teachers • Broad range of abilities • Mathematics • Literacy • Learning styles • Teachers are being asked to teach in ways that they were never taught. • Teach conceptual understanding • “Go deep” • Make connections
A mathematics teacher should be able to: • Unpack familiar math concepts to lead to clear understanding. • Require knowledge of an explanation of a concept. • Understand methods and solutions different from his or her own.
Concepts, Skills, & Procedures • “Go Deep! Show me your understanding” Assessment .. .. enables instruction to be adjusted 1 • Expressing Math Reasoning 2 • Modeling/Applications 3
MODEL THE PROCESS • Access to Resources: • UMath X: Concepts - Assessments - Tracking • Resources: Frameworks for Learning • Get Started • Work at It • Reflect and Connect
Frameworks Frameworks are 3 part lessons to model implementation.
Build it. See instructions below to navigate some specific fraction sections.
The Online Resource • UMath X is a concept-driven learning platform to support the diversity of teachers, students and parents in their construction of math knowledge. • Reach every student and teacher … • anytime and anywhere. • UMath X is aligned to the Common Core and modelled on the 3 part lesson to involve activities from concrete to abstract, integrating multiple approaches, entry points and representations.
Lessons for You & Your Class • Login to UMath X .. www.neufeldlearning.com • Strands – Sections – Lessons –SubLessons • 5.NBT.02.07 • – Fractions – Add Decimals – Right to Left – With Grids • 6.RP.01.03a • – Fractions – Ratio & Proportion – Ratio Table • 8.F.01.01 • -Algebra – Algebraic Thinking – Function Machine • 5.NF.02.06 – Multiplying Fractions – Problem with Pictures -Boris • THE TEST – enables instruction to be adapted
Wrap It Up . . . Reflect and Connect. • Manipulatives, Paper, Computer, Partner, Teacher, Frameworks • “How did you learn best ?” • For which of these do you need support? • Instructional Practices, Pedagogy, Content Knowledge • Which modeled strategies helped you “go deep?” • Where are your strengths? • For which do you need additional training?
Wrap It Up . . . A Professional Learning Plan A System for Engaging All Students with High Quality Tasks www.neufeldlearning.com/TrainingDocuments • ACCESS: • www.neufeldlearning.com/frameworks • www.neufeldlearning.com/preview • Login … first name.student • Password … last name • Visit Booth 312 or email me for access. R. Neufeld … email@example.com