Building Understanding in Math
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BUILDING UNDERSTANDING IN MATH Through Backwards Design and Differentiation
description
Building Understanding in Math. Through Backwards Design and Differentiation. Objective. Use a backwards design process to create a math unit that Contains goals for transfer, meaning and acquisition Purposefully addresses a 21 st century skill Includes a performance assessment task - PowerPoint PPT Presentation
Transcript of Building Understanding in Math
BUILDING UNDERSTANDING IN MATHThrough Backwards Design and Differentiation
Objective
Use a backwards design process to create a math unit that Contains goals for transfer, meaning and
acquisition Purposefully addresses a 21st century skill Includes a performance assessment task Offers a differentiation plan
Process September 6:
Stage 1 (Learning Goals) Stage 2 (Evidence –Performance Task)
On your own –for ½ credit (Sign up on SPOT) Complete Stage 2 – Other Evidence (Assessments)
October 7: Stage 3: The Learning Plan Formative Assessments Differentiation Plan
On your own – Continued Complete Unit Assure alignment between Goals, Evidence, and Learning Plan Spring Semester – Teach the Unit
What is Understanding? It’s Probably Understanding if it…
From Grant Wiggins & Jay McTighe Understanding by Design
It’s probably understanding if it… Raises additional questions or paths of
thought within the discipline Example: There are similarities and
differences between length and time.
From Grant Wiggins & Jay McTighe Understanding by Design
It’s probably understanding if it… Can be understood on a continuum,
something that kindergarteners through graduate students could study, albeit at different levels of sophistication Example: Parts of a system are interrelated. Non-example: A system has more than one
part
From Grant Wiggins & Jay McTighe Understanding by Design
It’s probably understanding if it… Can be stated as “I want students to
understand THAT…” rather than “I want students to understand Example in math?
Standards! Standard 1 – THAT At their most basic
level, numbers are abstract symbols that represent real world qualities
From Grant Wiggins & Jay McTighe Understanding by Design
It’s probably understanding if it… Is a pithy statement that reveals a truth
about the study or practice of the discipline. Example: Math is in all things.
From Grant Wiggins & Jay McTighe Understanding by Design
It’s probably understanding if it… Involves multiple layers or multiple
meanings Example: Changing the grouping or the
order of addends or factors does not change a sum or productNon-Example: 2 + 3 = 3 + 2
It’s probably understanding if it… Is an idea that is especially powerful in
understanding the discipline and across topics in the discipline. Number patterns are based on operations
and relationships. (Standard2, Concept 1 5th grade)
From Grant Wiggins & Jay McTighe Understanding by Design
It’s probably understanding if it… Provides a purpose for the discipline, the
reason for studying the discipline, and why the discipline is valuable. Computational fluency with fractions is
necessary for daily life.
From Grant Wiggins & Jay McTighe Understanding by Design
Enduring Understandings & Transfer
Group Work: Look at curriculum mapping work from the
A.M. Choose one to address. Write an enduring understanding and transfer
Enduring Understandings & Transfer
I want students to understand that _____________________ so that in the long run, without assistance, they can __________________________________.
15 Minutes – Then Share Out
FoothillsUBDPD.pbworks.comYour Wiki
Share • What Standard/Gap are you addressing? What is the Enduring
Understanding/Transfer?
Essential QuestionsJamie McKenzie: “Most essential questions are
interdisciplinary in nature. They cut across the lines created by schools and scholars to mark the terrain of departments and disciplines.”
“From Trivial Pursuit to Essential Questions” - http://www.fno.org/feb01/pl.html
Essential QuestionsJamie McKenzie: “Essential questions probe the deepest
issues confronting us . . . complex and baffling matters which elude simple answers: Life - Death - Marriage - Identity - Purpose - Betrayal - Honor - Integrity - Courage - Temptation - Faith - Leadership - Addiction - Invention - Inspiration.”
“From Trivial Pursuit to Essential Questions” - http://www.fno.org/feb01/pl.html
INTEL TEACHING THINKING WITH TECHNOLOGYOverview: Module 3: Creating Curriculum-Framing Questions to Support Thinking Skills
Ranking Questions With your group, use the Intel Visual
Ranking Tool to rank questions according to their potential for generating deeper thinking in the classroom Open Visual Ranking:
www.intel.com/education/visualranking Log in with your team ID and password Click Ranking Questions Rank questions:
Rank questions Add comments
Login Information Teacher ID: [email protected] User Name FHE01, FHE02, FHE03,
FHE04, FHE05, FHE06, FHE07 Password: The same
Ranking Questions
Step 2: Discuss Your Ranking Discuss significant variations in rankings Discuss your ranking experience – what you
think of this tool
Asking Questions in the Classroom
Understanding Open and Closed Questions Closed questions
Test factual knowledge Contain limited range of correct responses
Open questions Build upon factual knowledge Promote higher-order thinking
Reflecting on Questions Used in Your Classroom Reflect on the questions used in a typical day in
your classroom
Curriculum-Framing Questions
Defining Curriculum-Framing Questions
Essential Questions Are overarching, foundational
“big idea” questions Can help focus several units Can be used over the course of
a year Example:
What does it take to change the world? Where can we find order and patterns?
Curriculum-Framing Questions
Unit Questions Are unit-specific, open-
ended questions Help build understanding
for the Essential Question Example:
Why leave one’s home to make a new life in a strange land?
What patterns are repeated in large and small numbers?
Curriculum-Framing Questions
Content Questions Are supporting, fact-based questions Are categorized as closed questions Help strengthen and develop
students’ understanding of larger questions
Examples: What route did the early explorer’s
take? What were the explorers looking for? Why does 1/10 = .1?
Meaning Goals Group Work Write Your Goals for Meaning-Making:
Understandings Essential Questions that will help lead to
the understandings
15 MinutesFoothillsUBDPD.pbworks.comYour Wiki
Acquisition Goals: Group Work Pick ONE 21st Century Skill that you will
focus on to model, teach, and assess Identify the math skills, identified in the
curriculum or standards, that students will demonstrate.
15 MinutesFoothillsUBDPD.pbworks.comYour Wiki
BREAK
Stand Up & Vote! If you agree with the statement, LEFT
side of room If you disagree with statement, RIGHT
side of room If you are somewhere in the middle –go
to the middle! CHALLENGE! Can you persuade middle-
of-the-room folks to join your side?
Issues in Mathematics TeachingThere needs to be a stronger emphasis on the automaticity of math in elementary school.
Issues in Mathematics TeachingOffering rewards and incentives will help motivate students to try harder at math.
Issues in Mathematics TeachingThe ultimate goal for mathematics is independent and creative problem solving.
STAGE 2: EVIDENCEHow will you know that they know it?
Performance tasks in math GRASPS method
G – Real World Goal R – Real World Role A – Real World Audience S – Real World Situation P- Real-world Products or Performances S – Standards and Criteria Indicators
From Grant Wiggins & Jay McTighe Understanding by Design
G – Real World Goal
Household budget, travel budget Building a garden – purchasing the right
amount of soil, edging, etc. What is fair?
R – Real World Role Head of household, travel agent Homeowner, landscaper Teacher
A – Real World Audience Local travel agent, parents, a younger
grade Readers of publication – blog – wiki -
newspaper School board Community
S – Real World Situation Capture their imagination! Write a clever introduction or story to
set the scene.
P – Real World Products or Performances
Travel brochure Budget spreadsheet for college student Build a real garden for the school or as a
community service project Letter to the editor
S – Standards & Criteria Indicators Model a finished product –good and not-
so-good –for the students. Allow them to critique. Consider student input in creating the
criteria from this experience
Group Work: Performance Task Brainstorm and use the GRASPS method
to determine what your performance assessment task will be.
Make sure it aligns with your Learning Goals
15 MinutesFoothillsUBDPD.pbworks.comYour Wiki
Share As teams share, check for alignment
between Learning Goals and the Performance Task Will the performance task demonstrate
understanding? Does it require transfer, meaning-making and acquisition of skills?
