1. “Understand Why” rather than “Remember How”
Build it, Draw it, Talk it, Write it
… then OWN Fractions
“Understand Why” rather than “Remember How”
R. Neufeld, November 2014
November Rudy Neufeld, Neufeld Learning Systems Inc.
I have adapted this powerpoint to set the tone in a 1.5 hour presentation to a 3 hour or full day professional learning session.
UMath X and corresponding frameworks for learning are used to create a diverse learning environment for grades 2 to 6.

2. “Understand Why” rather than “Remember How”
Engage, Build,
Reflect, Apply
… then OWN Fractions
“Understand Why” rather than “Remember How”
November, 2014

3. GO DEEP!
Promote a Concept-Driven, Diverse Learning Environment to Address the Curriculum

4. The objective of this powerpoint is:
.. to set the tone for a 1.5 hour to full day professional learning session to use UMath X and corresponding 3 part lessons (frameworks for learning) in order to create diverse learning environments for grades 2 to 5.

5. Change the mindset
from
“remembering how” to
“understanding why”

6. Instructional Paradigm Shift: Teachers
Talk Less.
Listen More!

7. Instructional Paradigm Shift: Students
Watch Less.
Do More!

8. “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 8

9. Good Mathematics is: We must encourage “GRAPPLING”
-not about how many answers you know.
-but about what you do when you don’t know answers.
We must encourage
“GRAPPLING”

10. Too often people feel that if they can’t get the “answer” immediately that they could never get it!

11. Team Leaders/Administrators
convince teachers to teach for understanding.
prepare parents for the fact that teachers may not be providing all of the answers.
prepare parents that students will be grappling with challenging material.
note answers are important but not sufficient.

12. OWN IT!! draw it build it write it talk it
Create a self-paced approach but within a multiple approach opportunity.

13. 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.

14. The Emphasis is on: students doing mathematics.
students demonstrating thinking and learning.
students grapple with challenging tasks in a learning environment that will support equity in schools.

15. Students:
Engage in Discourse. Students articulate their own ideas and seriously consider their peers’ perspectives as a way to construct mathematical understandings.
Encourage students
to listen carefully to one another’s ideas
to disagree and question with respect … “ I beg to differ!”
… “ Excuse me. Can we talk about that?”

16. Teach students to : Use Effective Questions Use Productive Talk Moves
Show me another way …
How are these the same / different …
What would you do if …
Why did you …
What else could you have done …
Use 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.”

17. Challenges for Teachers
Broad ability ranges within a class
Need for differentiated instruction - RTI
Wide range of literacy skills
Diverse learning styles
Teachers are being asked to teach in ways that they were never taught.
Need to “go deep” and teach with understanding.

18. Teachers must be able to…
Unpack familiar math concepts to lead to understanding.
Require knowledge of an explanation of a concept.
Understand methods and solutions different from their own.

19. Our Vision 20 years ago was to …
Design a concept-driven learning platform to support the diversity of teachers, students and parents in their construction of math knowledge.
Design a platform to reach every student and teacher … anytime and anywhere.
Design a platform aligned to the curriculum and modeled on a 3 part lesson to involve activities from concrete to abstract, integrating multiple approaches, entry points and representations.

20. The Result in 2014
UMath X, the 10th version of Understanding Math, is a computer assisted learning system that includes browser based software and related resources to offer 100% coverage of curriculum.
Concepts - Assessments - Tracking
Frameworks for Learning are 3 part content-driven lessons to model the implementation of UMath X to create diverse learning environments.
Get Started
Work at It
Reflect and Connect

21. UMath X is a learning environment that:
supports constructivist thinking.  
People build their own understandings and knowledge of the world through personal and collaborative experiences that encourage reflection.
demonstrates differentiated instruction through an interactive multi-sensory approach.
uses multiple entry points and seamless integration to support both content and instruction.

22. Frameworks.. 3 part lessons model UMath X Implementation

23. Build it.
See instructions below to navigate some specific fraction sections.

24. Build it, Draw it, Talk it, Write it … OWN IT!!

25. MODEL the Process: .. whole group
..differentiated instruction one on one
Login to UMath X learning environment ..
Find concept to be taught in UMath X menu or in Curriculum Menu
Find a framework or design your own.
** CCSS Menu UMath X Menu
3.NF Fractions – Meaning of Fraction – Intro .. Think, Write, Say 4.NF Fractions – Equivalent Fractions – Pattern Blocks etc
5.NF Fractions – Adding Fractions – Word Problems – Eating Candy
5.NF Fractions – Mult Fractions – Real World Problem– Boris’ Money
5.NBT Fractions–Add & Subt of Decimals–Add Decimals–Method 3– Right to Left–Ex 1–With Grids
6.NS Fractions – Dividing Fractions – Modeling Ex – Model 1 to 6
** or use Texas TEKS, VA SOLs, Ontario Expectations or Florida 2014 standards