Teaching for Understanding

Page 1©2016 Jay McTighe

Teaching for Understanding

Understanding must be earned!

Understanding requires active meaning-making by the learner.

Teaching for Understanding

Page 2©2016 Jay McTighe

Teaching and Learning for Understanding

Acquire important

knowledge and skills

Make Meaning of “big ideas”

Transfer Learning to

new situations

What is fair?

How can math help us think

about fairness?

© 2015 Jay McTighe 4

Stage 3 – Teaching for Understanding

What is Fair?Who won this year’s 7th grade race around the campus?

Every year at Birdsong Middle School, there is an all-class race. Below are the results for the 7th grade (which is made up of four different classes). But there is a problem: no one agrees on who won! One person thinks Class C should win the trophy because they had the 1st runner overall in the race. Another person thinks Class D should win because they had 3 runners come in under 10th place. A third person says: just find the average. But a 4th person said: wait a minute – Class C had more students in their class than Class D. Averages won’t be fair! A 5th person says: use the scoring system in Cross Country – just add up the place of finish of the top 5 finishers in each class and the lowest total wins. A 6th person says – unfair! Some classes did well in the first few runners but poorly in the middle! Why should they win? Now, everyone is confused and arguing.

What is the fairest way to determine the winner? Which class should win the trophy? Your group, well-known in the school as a group of expert mathematicians (and respected for your sense of fairness) is being consulted as to who should win the trophy. What will you recommend and why?

Class rank Class A Class B Class C Class D 1 4 6 1 2 2 9 7 3 5 3 11 10 14 8 4 12 13 18 15 5 20 16 19 17 6 21 22 23 31 7 25 24 28 33 8 26 27 30 36 9 29 34 32 37 10 35 39 41 38 11 43 40 44 46 12 45 42 47 51 13 49 48 50 55 14 54 52 56 57 15 61 53 60 58 16 65 62 63 59 17 69 66 64 67 18 70 72 68 19 71 73 20 74

Notes on the chart:

• The numbers in the chart, from 1 to 74 represent the place of finish of that runner. So, the overall race winner was from Class C, the number two runner overall was in Class D, etc.• Class rank refers to the rank of finish place in that class, not the overall race. So, the first runner in class A was 4th overall in the race, the 2nd best runner in class A came in 9th overall, etc.• The blanks reflect the fact that each of the 4 classes has a different number of students.

Individual ranking of runners for all 7th-grade classes:

Teaching for Understanding

Page 3©2016 Jay McTighe

EQ – How can mathematics help us judge fairness?

Other meaning-making questions and activities: ●  What do we mean when we say that the rules of a game

of chance are “not fair”? What role does mathematics play in our judgment?

●  Why is it fair to have one person cut the cake and the

other person to choose the piece? ●  When is straight majority voting “fair” and when is it “not fair”?

●  When is it “fair” to consider an “average” in ranking performance (e.g. salaries, home prices, batting average) and when is it “unfair”?

NOTE: The content* is learned as a means to answer questions and

help solve problems!

*Measures of central tendency: ◆  Mean

◆  Median

◆  Mode

◆  Standard Deviation (range/variance)

Meaning Making & Transfer Activity

Based on our study in this unit of various measures of central tendency, and the pros and cons of using “averages” (and other such measures) in various situations, propose and defend a “fair” grading system for use in this school.

How should students’ grades be calculated? Explain why your proposed grading system would be better than the current system?

Teaching for Understanding

Page 4©2016 Jay McTighe

Performance Task: Making the Grade

Your math teacher will allow you to select the measure of central tendency (i.e., mean, median or mode) by which your quarterly grade will be calculated. Review your grades for quizzes, tests, and homework to decide which measure of central tendency will be best for your situation. Write a note to your teacher explaining why you selected that method.

Other Evidence: Measures of Central Tendency

☛  quizzes on specific skills (e.g., calculating mean, identifying median)

☛  finding and explaining “real

world” examples of each measure (e.g., scoring in diving competitions)

Teaching and Learning for Understanding

Acquire important

knowledge and skills

Make Meaning of “big ideas”

Transfer Learning to

new situations

Teaching for Understanding

Page 5©2016 Jay McTighe

You Can Use A.M.T. to…

❏  Develop assessments and lessons

❏  Code learning events (Stage 3)

❏  Code assessments (Stage 2)

❏  Observe and give feedback

❏  Reflect on lessons & units

✔

✔

✔

✔

✔

© 2015 Jay M

cTighe 6

Sta

ge 3

– T

eachin

g fo

r U

ndersta

ndin

g

ACQUIRE MAKE MEANING TRANSFER

This goal seeks to help learners acquire factual information and basic skills.

This goal seeks to help students construct meaning (i.e., come to an

understanding) of important ideas and processes.

This goal seeks to support the learner’s ability to transfer their learning autonomously and effect-ively in new situations.

Three InterrelatedLearning Goals �

Teacher Role/Instructional Strat-

egies

Note: Like the above

learning goals, these

three teaching roles

(and their associated

methods) work togeth-

er in pursuit of identi-

fied learning results.

Direct Instruction In this role, the teacher’s primary role is to inform the learners through explicit instruc-tion in targeted knowledge and skills; differentiating as needed. Strategies include: m diagnostic assessment m lecture m advanced organizers m graphic organizers m questioning (convergent) m demonstration/modeling m process guides m guided practice m feedback, corrections, m differentiation

Facilitative Teaching Teachers in this role engage the learners in actively processing information and guide their inquiry into complex problems, texts, projects, cases, or simulations; differentiating as needed. Strategies include: m diagnostic assessment m using analogies m graphic organizers m questioning (divergent) & probing m concept attainment m inquiry-oriented approaches m Problem-Based Learning m Socratic Seminar m Reciprocal Teaching m formative (on-going) assessments m understanding notebook m feedback/ corrections m rethinking and reflection prompts m differentiated instruction

Coaching In a coaching role, teachers establish clear performance goals, supervise on-going op-portunities to perform (indepen-dent practice) in increasingly complex situations, provide models and give on-going feed-back (as personalized as pos-sible). They also provide “just in time teaching” (direct instruc-tion) when needed. Strategies include: m on-going assessment, m providing specific feedback in the context of authentic application m conferencing m prompting self assess- ment and reflection

Learning Goals and Teaching Roles

Best Learning exercise - Part 1

What was the best learning experience you have ever encountered? Focus on the design (the tasks, goals, methods, sequence, resources used, assessments, etc.) – not your interests or the talents of the teacher.

“Best” = the design resulted in highly engaged and effective learning.

Teaching for Understanding

Page 6©2016 Jay McTighe

Design Exercise - Process

Part I ●  Individual reflection & writing (3 min.) ●  Share examples w/ group (8 min.) ●  Listen for common elements

Part II

●  Generalize with your group (5 min.) “The best designs…”

Suggestion: select a recorder to summarize

The Best Designs - responses... ACSI Conference 10/23/16

•

Anticipating Concerns

“Yes, but…”

Won’t UbD ta

ke away

my academic freedom?

How can I plan UbD units

for eve

rything I teach?.

Teaching for Understanding

Page 7©2016 Jay McTighe

Freedom Within Structure Stage 1 – Desired Results

Stage 2 – Assessment Evidence

Stage 3 – Learning Plan

•  School Mission •  Program Goals

•  Content Standards

•  Cornerstone Assessments

•  Common Rubrics & Performance Standards

•  Instruction (lesson plans, instructional

strategies, sequence, grouping, resources)

Agree to agree.

This is our job!

Agree on some common evidence.

Academic freedom & teacher autonomy

Ideas for Action

E  Think big.

E  Start small.

E  Go for an “early win.”

!  too demanding for “everyday meals”

therefore, !  work smart:

create one, share many

“Gourmet” Unit Design