1. 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

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

3. 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”?)

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

5. 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

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

7. 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.

8. 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)

9. Nurturing a “Growth Mindset” Environment A UMathX Initiative
See the video

10. 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.

11. 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 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

12. 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 …
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 (all lower case)
For a GLIMPSE of
“Growth Mindsets” and
Built-In “Differentiated instruction”, now
LOG into UMathX
(If you have any questions, me at …

13. 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 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 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 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 & in CCSS curriculum menu.

14. CLICK

17. Accommodate Blended Learning) Model RtI with Tiered Frameworks(

18. Frameworks (3 Part Lessons for Blended Learning – TIER 1

19. Frameworks (3 Part Lessons for Blended Learning – TIER 2

20. Frameworks (3 Part Lessons for Blended Learning – TIER 3

21. The UMath X Menu
is converted into
the CCSS Menu.

22. The Common Core
selection
offers 2 options.

23. The Common Core
selection
offers 2 options.

30. The UMath X Menu
is converted into
the CCSS Menu.

32. Frameworks (3 Part Lessons to Model Blended Learning)

34. 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.

35. Frameworks (3 Part Lessons for Blended Learning)

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

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

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

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

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

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

47. The UMath X Menu
is converted into
the CCSS Menu.

52. Frameworks (3 Part Lessons to Model Blended Learning)

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

57. 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.

58. 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.

59. ASSESSMENTS, DATA ANALYSIS
SHOW GROWTH
ASSESSMENTS, DATA ANALYSIS

60. 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
toll free
cell