introduction to envisions
DESCRIPTION
Introduction to Envisions. Facilitator: Kristie Martinez. Reflect on your own mathematical learning. Which sentence(s) 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. - PowerPoint PPT PresentationTRANSCRIPT
Introduction to EnvisionsIntroduction to EnvisionsIntroduction to EnvisionsIntroduction to EnvisionsFacilitator: Kristie MartinezFacilitator: Kristie Martinez
Reflect on your own mathematical learning. Which sentence(s) best describes the message you
received during your years as a mathematical learner?
1. Arriving at the correct answer to a problem is the most important thing.
2. The methods used to solve a problem are just as important as arriving at the correct solution.
3. 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.
4. 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.
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?
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 activelyProvide appropriate hints
Provide worthwhile extensions
DURING
Class DiscussionPromote a mathematical community of learners
Listen actively without evaluationSummarize main ideas and identify future problems A
FTER
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
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
Mathematical Practices1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of
others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.
• How did you solve?• Did anyone solve it another way?
PBIL- Problem Based Interactive Learning
• This is where the math practices live
• Part 2 of the daily lesson• Focus/Engage/Pose the Problem
Four Part Daily Lesson
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 Part 2 and Part 3
1. Daily Common Core Review
This helps you reinforce the Common Core Standards.
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
2- Problem Based Interactive Learning
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.
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
Lesson Format• Set the Purpose• Connect• Go over vocabulary• Pose the problem- seats• Share solutions-carpet• Model/Demonstrate• Video• Guided Practice• Independent Practice- seats• Share- carpet