### What is Deep and Enduring Understanding?

As the physicist Albert Einstein once said, “You do not truly understand something unless you can explain it to your grandmother.”

One of the clearest definitions for what understanding is comes from the founder of the home school
movement. It has been recently been brought to light by Keith Leithwood in a book he co-authored,* Teaching for Deep Understanding* (ETFO/OISE and Corwin Press, 2004).

Students deeply understand a concept, principle, truth, expertise, and/or
insight when they are able to:

• state it in their own words;

• give examples of it [and also give non-examples of it];

• recognize it in various guises and circumstances;

• see connections between it and other facts
or ideas;

• make use of it in various ways;

• foresee some of its consequences; and

• state its opposite or converse.

(Holt’s seven-point list, Holt, 1964, pp36-37; Leithwood, K., et. al., 2004, *Teaching
for Deep Understanding: Towards the Ontario Curriculum That We Need*, p23).

How Children Learn Performance
Tasks Inquiry Learning Planning Resources

### Techniques to promote Thinking, Understanding, and Learning

In her article,* Tools to Enhance Young Children's Thinking* (Young Children, National Association
for the Education of Young Children, September 2010), Angela K. Salmon urges teachers to instruct children how to think using Thinking
Routines.

According to Salmon, it is important for teachers to use thinking routines on a regular basis, not only to give children a sense of security and confidence, but also to create habits of mind as they develop a culture of thinking. When thinking routines become part of the classroom culture through repeated practice, they create patterns of thinking and learning that become part of the child’s intellectual character (Ritchhart 2002).

Salmon also emphasizes that thinking routines and documentation of learning are tools that enhance children’s cognitive development by helping them become aware of their own creative thinking and problem-solving skills. According to her, they not only activate children’s prior knowledge but also expand their thinking and understanding.

Salmon writes that there are no obstacles to teaching thinking routines. First, thinking routines are easy to teach and developmentally age-appropriate. Second, research has shown that critical thinking can be explicitly taught (Tishman, Perkins, & Jay 1995; Ritchhart & Perkins 2005, 2008; Barahal 2008; Salmon 2010).

Salmon has outlined seven critical thinking routines to be taught, most of which can be found on the visible thinking website. They are:

**This routine . . .
. . . encourages this type of thinking **

What Makes You Say That? interpretation with justification

Think/Puzzle/Explore setting the stage for deeper inquiry

Think/Pair/Share active reasoning and explanation

Circle of Viewpoints exploring diverse perspectives

I Used to Think . . . Now I Think . . . reflecting on how/why our thinking has changed

See/Think/Wonder exploring works of art/other interesting things

Color, Shapes, Lines exploring the formal qualities of art

If you would like to learn more about The Visible Thinking Project, created by Patricia Palmer, David Perkins, Ron Ritchhart, Shari Tishman, please click here: http://www.simplesite.com/builder/pages/editpagecontent.aspx?pageid=421504410

### Techniques to Check for Understanding

A large number and wide variety of engaging strategies can be used by teachers in the classroom to check for understanding. Most of these methods are enjoyable or even fun. Many of them are relatively new techniques -- adopted since 2000.

3‐2‐1/
Fist to Five/ Thumbs Up, Thumbs Down/

Students communicate their level of understanding to teacher using their fingers.

4‐3‐2‐1 Scoring Scale

A posted scale that can be used either as a quick check with hand or a numerical value
for students to self‐assess on a written assignment.

ABCD Whisper

Students should get in groups of four where one student is A, the next is B, etc. Each student will be asked to reflect on a concept and draw a visual of his/her interpretation.
Then they will share their answer with each other in a zigzag pattern within their group.

Capacity Matrix

The capacity matrix is a charting technique used to break down topic areas into steps for achieving a specific result. It identifies
tasks, knowledge levels, and understanding of the topic area.

Circle, Triangle, Square

(Circle) Something that is still going around in your head (Triangle) Something pointed that stood out in your mind (Square) Something that “Squared”
or agreed with your thinking.

Clickers Electronic surveying devices that give instant feedback and data.

Decisions, Decisions

(Philosophical Chairs)

Given a prompt, class goes to the side that corresponds to their opinion on the topic,
side share out reasoning, and students are allowed to change sides after discussion.

Entrance/Exit ticket

Each student will be given a ticket to complete before leaving the room answering: What is the most important thing I learned today?
What questions do I still have? These tickets can be given to the teacher when exiting the room or upon entering the next day. The teacher uses this information to guide the instruction.

Every Pupil Response

Each student receives
a pink and yellow card. Each color represents a specific response. Students raise the card to provide the correct response to a teacher directed question.

Example/Non‐Example

Given a concept, students sort or write various examples/non‐examples.

Example/Non‐Example

Given examples/non‐examples, students determine concept.

Fill In Your Thoughts

Written check for understanding strategy where students fill the blank. (Another term for rate of change is ____ or ____.)

Flag
It

Students use this strategy to help them remember information that is important to them. They will “flag” their ideas on a sticky note or flag die cut.

Function Aerobics

Students demonstrate their knowledge of transformations
of functions by physically moving their arms and body.

Give One, Get One

Cooperative activity where the students write response to a prompt, meet up with another student and share ideas so that each leaves with something to add to
their list.

Handprint (5 things you learned today): Draw your handprint. In each finger, write one thing you learned today.

Human Graph

A kinesthetic activity where students in the class physically move to create a histogram, where
each student represents a data point rating their view Interlocking Paper Plates. Two color plates used for students to provide feedback to teacher by sliding the two color sections to show level of understanding.

Onion Ring

Students
form an inner and outer circle facing a partner. The teacher asks a question and the students are given time to respond to their partner. Next, the inner circle rotates one person to the left. The teacher asks another question and the cycle
repeats itself.

Pop It (Bubble Wrap)

Students write what they want to know about a topic on a dot sticker. Place each sticker on the bubble wrap. When a topic is covered, the student pops the bubble.

Project Study Group

Analyzing incorrect
responses in multiple choice questions.

Quick Writes

A timed writing in response to a question or prompt (can be used before, during, or after instruction).

Rubric

A scoring guide using subjective assessments that is generally
composed of dimensions for judging student performance.

Say Something

Students take turns leading discussions in a cooperative group on sections of a reading or video.

Slap It

Students are divided into two teams to identify
correct answers to questions given by the teacher. Students use a fly swatter to slap the correct response posted on the wall.

Student Data Notebooks

A tool for students to track their learning: Where am I going? Where am I now? How
will I get there?

Take and Pass

Cooperative group activity used to share or collect information from each member of the group; students write a response, then pass to the right, add their response to next paper, continue until they get
their paper back, then group debriefs.

Timed Pair Share

Given a prompt, students pair up and share their perspective for a given amount of time, taking turns (A talks, B listens, then B talks, A listens).

Triangular Prism (Red, Yellow,
Green)

Students give feedback to teacher by displaying the color that corresponds to their level of understanding.

Word Sort

Given a set of vocabulary terms, students sort in to given categories or create their own categories for
sorting.

Whip Around

Teacher poses a question and students list three items. All students stand. Teacher randomly calls students to share, if their topic is called they sit. Teacher continues til all students are sitting.