TEACHER SKILLS FORUM: REVOLUTIONISING EDUCATION

DECEMBER 2014Raising the Level of Cognitive Demand

in Math and Science Classes

Sub-Plenary

Professor Katherine K. Merseth

Harvard University

Agenda

• Discussion about the Culture of Teaching• Exploration of the Instructional Core• Presentation of Model for Observation called Instructional Rounds

• Deepening the level of Cognitive Demand

The Complexity of Teaching

“After 30 years of doing such work, I have concluded that classroom teaching…is perhaps the most complex, most challenging, and most demanding, subtle, nuanced, and frightening activity that our species has ever invented…The only time a physician could possibly encounter a situation of comparable complexity would be in the emergency room of a hospital during or after a natural disaster”

Lee Shulman, Stanford Professor, The Wisdom of Practice

School improvement: The next level of work:

Importance of Values/Perspectives

• Deficit model in Academics vs. Growth Mindset in Academics

• Reality of Accountability Environment• 21st Century Skills vs 20th Century Skills• Accountability Trade for Autonomy

THE WORK OF IMPROVEMENT:FROM TECHNICAL TO CULTURAL

Schedules Structures Roles Types of professional

development, when Protocols, rubrics Assessments Accountability systems

Beliefs about student learning

Pedagogical content knowledge

Norms for group work Discourse about practice Mutual accountability Distributed leadership

TECHNICAL CULTURAL

© Richard F. Elmore with Permission

What Elements will support Improving Instructional Practice?

• Setting a culture for learning• Shared accountability• Trust• Clarity of Purpose• Expertise• Collaboration• Safety

• What other characteristics or elements can you name?

Comfortable High Performance

Apathy Anxiety

Accountability

highlow

Psycho

logica

l Sa

fety

high

low

Elements for Improving Instruction

Practitioners engage in face-to-face interaction around the practice of teaching and learning

The work occurs in social interactions among colleagues

Engagement comes from colleagues working together on a problem of practice

The work is embedded in a positive culture based on TRUST

The commitment is to continuous improvement. Everyone getting better

What Process will help Improve Instructional Practice?

• Establish a Process for Improvement• Observation Protocol• Schedule for observations• Peer observations• Time for feedback and reflection

• Instructional Rounds—Questions to ask• What are the children doing and saying?• What is the teacher doing and saying?• What is the instructional task?• What would the children be able to do and what would they know if

they did everything the teacher asked?

One helpful tool is to FOCUS on the Instructional Core

TEACHER STUDENT

CONTENT

WHAT IS THE INSTRUCTIONAL CORE?

Instructional Rounds by Elmore, City, et al.

Task

Instructional Tasks• Tasks form the basic unit of instruction in classrooms.

• “Tasks influence learners by directing their attention to

particular aspects of content and by specifying ways of processing information”

• Students work in school is defined by the academic tasks they encounter – tasks regulate information and processing. IT IS WHAT WE ASK OF THEM!

• It is in our control!

Doyle, Walter. 1983. "Academic work." Review of Educational Research.Summer 1983 vol. 53 no. 2 159-199

Bloom’s Taxonomy

is a hierarchical system of ordering thinking skills. The levels go from lower to higher, with the higher levels inclusive of the cognitive skills from the lower levels.

New Version of Bloom’s Taxonomy (1990s)

Lower Cognitive Demand

Higher Cognitive Demand

Why was the second exercise harder than the first?

Students, by and large, in good high schools are being taught procedures

and more generally are not being asked to think, to puzzle, to take risks, or to conjecture. The emphasis is on

getting the right answer, not about thinking.

The tasks they are asked to complete are routinely low level

Productive Struggle Modeled in Classrooms

• Problems that are not obvious• Problems that benefit from discussion, making learners aware of multiple approaches to understanding

• Reward not for the correct answer but rather for the reasoning-- the thinking exhibited

• But struggle must be modeled and talked about in classroom with students. A new way of thinking

How do you develop this in your students?

• It has to do with curriculum, yes, but MORE IMPORTANTLY it has to do with HOW the classes are taught.

• So how do you change instructional practice? You focus on the Tasks because…

• TASK PREDICTS PERFORMANCE

A Classroom Observational Protocol• What is the teacher saying and doing?• What are the students saying and doing?• What is the task the teacher has set for the students? • If the students did everything the teacher asked them to

do, what would the students leave the classroom knowing how to do?

Massachusetts Comprehensive Assessment System 10th grade

math item

Sample Math Item: Program for International Students Assessment (PISA)

Other MCAS items: Science (8th grade)

Let’s Practice

• What do you see the teacher doing? • What do you see the children doing?• What is the Task?

TIMMS VIDEOS

Merseth © 2012

Task can also have an additional dimension in Math and Science

• A Task is the actual classroom activity students are asked to do. Tasks have two dimensions: • Cognitive demand is the degree of cognitive

functioning required by the task. It can be low level (memory) or high level (evaluation).

• Level of Content represents the number of ideas or concepts one needs to apply to address the Task. It can be one concept or multiple concepts

Cognitive Demand Dimension• Tasks can be from “low” to “high” on cognitive demand

• Knowledge, Comprehension, Low-level application• Memory (recognize or reproduce information), routine (application

of predictable/standardized formulas) • Retrieval and comprehension

• Tasks can be “high” on cognitive demand• Synthesis, Analysis, Evaluation • Understanding tasks (recognize and apply to new contexts, draw

inferences) • Analysis and knowledge utilization • “Doing mathematics”

Complexity of Content Dimension• Complexity of Content:

• How many domains of knowledge does the task require students to access? Few? Many? Are they connected?

• Tasks can be “low” in complexity of content:• One or few discrete pieces of content

• Tasks can be “high” in complexity of content:• Multiple, connected pieces of content

Task Analysis MatrixC

OG

NIT

IVE

DE

MA

ND

COMPLEXITY OF CONTENT

Low

High

Low High

Testing the Tool

Think about how you would categorize this/these task(s) that relate to place value:

• Find as many numbers as you can that have the same number of tens as 4123.

• Demonstrate how you know that you have found all of the numbers that have the same number of tens as 4123.

• What numeral is in the tens place in 4123?• Write 4123 in expanded notation.

Testing the ToolFind as many numbers

as you can that has the same number of

tens as 4123.

Demonstrate how you know that you have

found all of the numbers that have the same number of tens

as 4123.

What numeral is in the tens place in 4123?

Write 4123 in expanded notation.

CO

GN

ITIV

E D

EM

AN

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COMPLEXITY OF CONTENT

Low

High

Low High

Tool guides the development of a common language

• Teachers gather to discuss and parse out the level of common instructional tasks. The matrix represents a means to engage teachers in discussions about teaching and content in the context of the instructional core

• Ways to dig into the mathematics from a point of view of teaching

• Ways to develop a common language among a group of professionals

Use this tool to focus on the important aspects of instruction

• Looking at student work and working with teachers around instruction• Ways to deepen conversations with teachers around

student experience of and learning of mathematics in their classrooms

• Way to heighten awareness among students about mathematics

Mathematical Task Framework (Stein, et al., 2009)

• Looking at the ways in which students enact tasks

The Mathematical Tasks FrameworkTasks as

they appear in

the curricular materials

Tasks as they are set

up by teachers

Tasks as they are

enacted by students

Student learning

Take Aways• Name THREE things you learned today• Name TWO things you promise you will do as a result of

today• Name ONE person to hold you accountable to this

promise

References• Carpenter, T. & Lehrer, R. (1999). Teaching and learning

mathematics with understanding. In Fenneman, E. & Romberg, T. (eds). (1999). Mathematics Classrooms that Promote Understanding. New Jersey: Lawrence Erlbaum Associates.

• Stein, M., et al., (2009). Implementing Standards-Based Mathematics Instruction: A Casebook for Professional Development. New York: Teacher’s College Press.

• Lee Shulman, The Wisdom of Practice, Stanford University Professor,