1. Introduction to Envisions
June 24th, 2013

2. Reflect on your own mathematical learning
Reflect on your own mathematical learning. Which sentence best describes the message you received during your years as a mathematical learner?
Arriving at the correct answer to a problem is the most important thing.
The methods used to solve a problem are just as important as arriving at the correct solution.
There is only one way to solve a problem and it is the teacher’s way. The teacher is responsible for telling students that one way.
There are many ways a problem can be solved that will ultimately lead to the correct solution. It is the responsibility of students to pursue a variety of ways and justify their reasoning.

3. Pose the Problem If you add 7 to itself you get 14. If
you make the first number one more
and the second number one less you get
the same sum.
Is this true for all counting numbers?

4. A Three-Part Format for Problem-Based Instruction
Getting Ready
Activate prior knowledge
Be sure the problem is understood
Establish clear expectations
BEFORE
Students Work
Let go!
Listen actively
Provide appropriate hints
Provide worthwhile extensions
DURING
Class Discussion
Promote a mathematical community of learners
Listen actively without evaluation
Summarize main ideas and identify future problems
AFTER

5. Benefits evaluate math knowledge
students begin to critique each other’s work
make connections before moving on
make math explicit
the person who talks the most, learns the most
students prove answers
push for understanding

6. A problem can be defined as an activity or task that encourages mathematics by…
beginning where the students are
highlighting the math that students are to learn in a problematic or engaging way
requiring justifications and explanations for answers and methods

7. Mathematical Practices
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Use appropriate tools strategically.
Attend to precision.
Look for and make use of structure.
Look for and express regularity in repeated reasoning.
How did you solve?
Did anyone solve it another way?

9. PBIL- Problem Based Interactive Learning
This is where the math practices live
Part 2 of the daily lesson
Focus/Engage/Pose the Problem

10. Four Part Daily Lesson

11. Core vs. More 1- Daily Common Core Review- (More)
2- Problem-Based Interactive Learning (Core)
3- Develop the Concept: Visual (Core)
4- Close/Assess and Differentiate (Core-some)
Part 2, Part 3 and some of Part 4- Core
Program suggests 60 mins for “Core” instruction

12. 1. Daily Common Core Review
This helps you reinforce the Common Core Standards.

13. 2- Problem Based Interactive Learning
This part allows teaching and learning of the Mathematical Practices
Engages students
Students solve and discuss a problem
Makes the important math explicit
Deepens understanding

14. 2- Problem Based Interactive Learning

15. 3- Develop the Concept: Visual
Step by step visual instruction that makes the math explicit
Visual concept development- students are able to see ideas developed in visual displays
Visual Learning Bridge- pictorial, step-by-step bridge between the PBIL activity and the lesson. This helps students focus on one idea at a time as well as see connections within a sequence of ideas.
Guiding questions are provided in blue print
Pictures with a purpose- representations of math concepts
Visual Learning Animations can be used to present the Visual Learning Bridge digitally with animation.

16. 4- Close/ Assess and Differentiate
Close the lesson- Essential Understanding
Daily Quick Check assesses student understanding and allows for differentiation
Differentiated Instruction- Center activities that provide appropriate level of Intervention, Practice or Enrichment

17. Lesson Format Pose the Problem on board- carpet Go over vocabulary
Set the Purpose
Connect
Have students work on pose the problem-seats
Share solutions-carpet
Model/Demonstrate
Video
Guided Practice
Independent Practice- seats
Share- carpet