Nurturing ‘Growth Mindsets’ and ‘Built-In Differentiation’ (a UMathX Initiative) For K to Alg1 Subtopic at Sessions: Deepen Algebraic & Fractional Thinking within a Blended ‘Learning Pit’ (smarter not harder) R. Neufeld Common Core Standards Conference Sessions at: MCTM.. Maryland OCTM .. Ohio NCTM .. Philadelphia DACTM .. Detroit CMC .. Palm Springs, CA AMTNYS .. Rye, NY Al CCLC UMathX Initiative www.umathx.com

WERE YOU “TAUGHT” OR WERE YOU “TOLD”? WHAT IS THE DIFFERENCE?   DO YOU “TEACH” DO YOU “TELL”?

Nurturing a “Growth Mindset” Environment Preliminary to a UMathX Initiative The Influence of Papert, Robots, and Logo Seymour Papert (1928 – 2016) was a South African-born American mathematician, computer scientist, and educator, who spent most of his career teaching and researching at MIT. He was a pioneer of artificial intelligence, and of the constructivist movement in education.  I met him at “Learning and Common Sense Society of Minds” Symposium in 1988 at MIT. CONSTRUCTIVIST LEARNING is based on the belief that learning occurs as learners are actively involved in a process of meaning and knowledge construction as opposed to passively receiving information. Learners are the makers of meaning and knowledge. (Aha … “Teaching” vs “Telling”?)

Nurturing a “Growth Mindset” Environment Preliminary to a UMathX Initiative These resources supported the following:

Nurturing a “Growth Mindset” Environment Preliminary to a UMathX Initiative Teach the Robot Learn by Teaching Predict Many Solutions Learn from Mistakes Working with Hearing Impaired Students at Summer Camp “Talk” about it

Nurturing a “Growth Mindset” Environment Preliminary to a UMathX Initiative

Nurturing a “Growth Mindset” Environment Preliminary to a UMathX Initiative Papert developed the LOGO programming language while at MIT. LOGO is a tool to improve the way we think and solve problems. A small mobile robot called the "LOGO Turtle" was developed.

Nurturing a “Growth Mindset” Environment A UMathX Initiative The UMathX Initiative had it’s beginnings in the late 1980s. ”The Objective of a UMathX Initiative is to have it all – a full service K to Algebra 1 learning environment, supporting a ‘growth mindset’ within a “learning pit” encouraging students and teachers to ‘grapple’ with concepts.”(Global Education Conference)

Nurturing a “Growth Mindset” Environment A UMathX Initiative See the video http://www.jamesnottingham.co.uk/learning-pit/

OBJECTIVES OF The UMathX Initiative SPARK deeper understanding TRANSFORM a “valley of despair” to productive struggling in a “learning pit” MODEL a diverse learning environment with built-in differentiation Detailed Objectives… To implement an initiative based on a browser-based, computer-assisted learning environment, UMathX, the 10th version of Understanding Math, that blends a wide variety of approaches to help students develop deeper understanding of mathematics concepts from K to Algebra 1.   To support a ‘growth mindset’ leading to academic success by understanding the functionality of: 1. productive struggling – “teach” not “tell” 2. assessments 3. diagnostics 4. data analysis   To embrace failure as an opportunity to develop new strategies to learning concepts. To model Implementation of UMathX through 3 part lessons, “Frameworks for Learning” which lead students to “build it”, “draw it”, “talk it”, “write it” and then “OWN IT”.   Part 1 - Getting Started Part 2 - Working at It Part 3 - Reflect and Connect To model whole-class learning with built-in differentiation for all through multiple entry points and a single exit point through specific examples within curriculum.  

The UMathX Learning Environment UMathX, the 10th version of Understanding Math, is a browser-based, computer-assisted learning system that blends a wide variety of approaches to help students develop deeper understanding of mathematics concepts from K to Algebra1.   In UMathX, a mistake is seen as an opportunity to learn.   UMath X creates opportunities for productive struggling, for grappling, for meaningful discourse yet gives hints towards an answer. Students “built it”, “draw it”, “talk it”, “write it” and then they “OWN IT!” STEP 1: Visit www.umathx.com and select each of the following 6 short VIDEOS: UMathX – What is it? … “The Learning Pit” UMathX – Frameworks for Learning UMathX – Walk Through UMathX - Assessments UMathX – Navigation UMathX – Data Analysis  

Built-In “Differentiated instruction”, now STEP 2: A GLIMPSE of the Learning Environment. Option 1: You are not a member of this Initiative: Use any browser and key in the URL … www.umathx.com Select Preview and Register or Login if you have already registered. If you wish to use it, I have already registered you as: Login:________ Password ________ Choose to access as a Student or Teacher or School Lead or District Lead Option 2: If you are a member of an Initiative, you have been given a secure login and password. Use www.umathx.com/______ (all lower case) For a GLIMPSE of “Growth Mindsets” and Built-In “Differentiated instruction”, now LOG into UMathX (If you have any questions, email me at … rneufeld@umathx.com)

Slides which follow give more details for lessons below. Step 3: Specific Lessons at your Grade Level Slides which follow give more details for lessons below. LESSONS: within UMathX Menu within CCSS/College & Career Ready Standards Operations – Demonstrate Addition Facts – Making 5 - A K.OA.01.03 Place Value 2. Model Numbers Grouped in Packs–C–1)Ones & Groups of Ten K.NBT.01.01 Operations 12) Add 3 or 4 # – A – Add 3 # Vertically 1.OA.03.06 Fractions –The Meaning of Fractions – Think, Write, Say – tier 1, tier 2, tier 3 3.NF.01.01 Operations – 27) Introduce Mult Facts - 2, 3, 4, 5 - Mult: Groups of 4 3.OA.01.01 Decimals to tenths, hundredths, thousandths 4.NF.03.06; 5.NBT.01.03a Multiply 2 Digit Numbers – Partial Products – Ex. 1 - tier 1, tier 2, tier 3 4.NBT.02.05 Add Fractions – Pattern Blocks & Word Prob – Eat Candy - tier 1, tier 2, tier 3 5.NF.01.01 Multiply Fractions – Developing the Rule - tier 1, tier 2, tier 3 - word problems 5.NF.02.04a Fractions – Ratios and Proportions – Ratio Table - tier 1, tier 2, tier 3 7.RP.01.02c Dividing Fractions– Modeling Examples – 1,2,3,4,5,6 – tier 1, tier 2, tier 3 6.NS.01.01 Measurement – Per&Area Polygons – Area Polygons – tier 1, tier 2, tier 3 7.G.02.06 Graphing without a Scale – tier 1, tier 2, tier 3 8.F.02.05 Graphing – Linear Relations – Elastic – Table, Equation, Graph - tiers 1, 2, 3 8.F.02.04 Slope & Line – Walk in Real World - tier 1, tier 2, tier 3 8.EE.02.06 Graphing – Relations, Equations, Functions – Relations – Ex2: tiles, Part 1 A.CED.01.02 Graphing–Quadratic Functions–Maximize Cage Area–- tier 1, tier 2, tier 3 A.CED.01.02 Algebra – Factoring Expressions – Factoring Trinomials – With Tiles A.SSE.01.02 Frameworks for Learning .. are available at www.umathx.com/frameworks & in CCSS curriculum menu.

CLICK

Accommodate Blended Learning) Model RtI with Tiered Frameworks (http://www.umathx.com/frameworks/)

Frameworks (3 Part Lessons for Blended Learning – TIER 1

Frameworks (3 Part Lessons for Blended Learning – TIER 2

Frameworks (3 Part Lessons for Blended Learning – TIER 3

The UMath X Menu is converted into the CCSS Menu.

The Common Core selection offers 2 options.

The Common Core selection offers 2 options.

The UMath X Menu is converted into the CCSS Menu.

Frameworks (3 Part Lessons to Model Blended Learning)

The UMath X menu is based on a CONCEPTUAL FOCUS. is converted into the CCSS Menu. The UMath X menu is based on a CONCEPTUAL FOCUS. It allows student and teacher to follow a CONCEPTUAL PATH rather than an often disjointed grade focus. It is flexible in that one can focus on concepts in a certain grade and conceptual scaffolding over a number of grade levels.

Frameworks (3 Part Lessons for Blended Learning)

Generic URL .. www.neufeldlearning.com/preview Generic Login .. student Generic Password .. studentpwd

Instructional Scaffolding The UMath X Menu is converted into the CCSS Menu.

Frameworks(on paper) & Lessons (on computer) .. 3 part outlines on 2 pages

Tiered Frameworks… online” NOTE: All 3 tiers FUNNEL learning to the same “big picture” of the concept.

NOTE: All 3 tiers FUNNEL learning to the same “big picture” of the concept.

NOTE: All 3 tiers FUNNEL learning to the same “big picture” of the concept.

The UMath X Menu is converted into the CCSS Menu.

Frameworks (3 Part Lessons to Model Blended Learning)

Pictures – Words - Numbers 30th number? Pictures – Words - Numbers

It is OK to GRAPPLE!! more than “persevering” more than “engaging” “productive” struggling Too many feel that if we do not “get it” in the first few seconds that we will NEVER get it! We need to be able to “grapple”. “Grappling” is much more than “persevering” and “engaging” In “grappling” one is in competition with him/her self. They are in competition with themselves.

Productive Math Talk Moves Say it another way. Show me another way... ? Repeat it How are these same/different? Reason through What would you do if...…? Add On What else could you have done? Why did you...…? Effective Questions Students articulate their own ideas and consider peer perspectives as a way to construct understandings.

ASSESSMENTS, DATA ANALYSIS SHOW GROWTH ASSESSMENTS, DATA ANALYSIS

IN PREPARATION for taking part in a UMathX Initiative: First – check the 6 videos Then – use the “preview” for 1 to 30 days. THEN contact us for a skype Then we Invite you to The UMathX Initiative (full access for 1 class & yourself) We look forward to having you part of the UMathX Initiative. R. Neufeld rneufeld@umathx.com 866 429 6284 toll free 407 952 2551 cell