Focusing on Challenging Mathematical Tasks:

A Strategy for Improving Teaching and Learning

Focusing on Challenging Mathematical Tasks:

A Strategy for Improving Teaching and Learning

An online professional development

community through practice:

Using real life examples versus being told what is best. Teachers need to see connection to classroom in workshops.

An online professional development

community through practice:

Using real life examples versus being told what is best. Teachers need to see connection to classroom in workshops.

Our goal in this Online PDOur goal in this Online PD

To use the tools in this lesson in your classroomand come discuss your experiences of what “works” this with an online math ed community.To be able to compare results (understanding) and have evidence for better way with other math ed professionals.

To use the tools in this lesson in your classroomand come discuss your experiences of what “works” this with an online math ed community.To be able to compare results (understanding) and have evidence for better way with other math ed professionals.

OverviewOverview

Discuss the components of the task-based model for Professional Development

Discuss the role of tools in the model

Discuss the components of the task-based model for Professional Development

Discuss the role of tools in the model

Task-Focused ActivitiesTask-Focused ActivitiesDistinguishing between high- and low-level mathematics tasks

Solving high-level mathematical tasks

Analyzing high-level mathematics tasks and work produced by students on these tasks

Maintaining the cognitive demands of high-level tasks during instruction

Distinguishing between high- and low-level mathematics tasks

Solving high-level mathematical tasks

Analyzing high-level mathematics tasks and work produced by students on these tasks

Maintaining the cognitive demands of high-level tasks during instruction

Task-Focused ActivitiesTask-Focused ActivitiesDistinguishing between high- and low-level tasks

Develop teachers’ capacity to determine the kind and level of thinking required to solve a particular mathematics task

Comparing pairs of tasks that focus on the same mathematics content but different with respect to the thinking demands Analyzing a set of tasks that differ with respect to their cognitive demands and task features (e.g., require an explanation, utilize a diagram, provide tools such as calculators)

Distinguishing between high- and low-level tasks

Develop teachers’ capacity to determine the kind and level of thinking required to solve a particular mathematics task

Comparing pairs of tasks that focus on the same mathematics content but different with respect to the thinking demands Analyzing a set of tasks that differ with respect to their cognitive demands and task features (e.g., require an explanation, utilize a diagram, provide tools such as calculators)

DistinguishingDistinguishing

Martha’s Carpeting Task

The Fencing Task

Martha’s Carpeting Task

The Fencing Task

Martha’s Carpeting TaskMartha’s Carpeting Task

Martha was recarpeting her bedroom which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?

Stein, Smith, Henningsen, & Silver, 2000, p. 1

Martha was recarpeting her bedroom which was 15 feet long and 10 feet wide. How many square feet of carpeting will she need to purchase?

Stein, Smith, Henningsen, & Silver, 2000, p. 1

The Fencing TaskThe Fencing Task

1. If Ms. Brown's students want their rabbits to have as much room as possible, how long would each of the sides of the pen be?

2. How long would each of the sides of the pen be if they had only 16 feet of fencing?

3. How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

Stein, Smith, Henningsen, & Silver, 2000, p. 2

1. If Ms. Brown's students want their rabbits to have as much room as possible, how long would each of the sides of the pen be?

2. How long would each of the sides of the pen be if they had only 16 feet of fencing?

3. How would you go about determining the pen with the most room for any amount of fencing? Organize your work so that someone else who reads it will understand it.

Stein, Smith, Henningsen, & Silver, 2000, p. 2

Ms. Brown’s class will raise rabbits for their spring science fair. They have 24 feet of fencing with which to build a rectangular rabbit pen in which to keep the rabbits.

Comparing Two TasksComparing Two Tasks

Both require prior knowledge of areaArea problems

Both require prior knowledge of areaArea problems

Way in which the area formula is used The need to generalizeThe amount of thinking and reasoning required The number of ways the problem can be solvedThe range of ways to enter the problem

Way in which the area formula is used The need to generalizeThe amount of thinking and reasoning required The number of ways the problem can be solvedThe range of ways to enter the problem

Importance of DistinguishingImportance of DistinguishingLow-Level Tasks

High-Level Tasks

Low-Level Tasks

High-Level Tasks

Importance of DistinguishingImportance of DistinguishingLow-Level Tasks

memorizationprocedures without connections

High-Level Tasksprocedures with connectionsdoing mathematics

Low-Level Tasksmemorizationprocedures without connections

High-Level Tasksprocedures with connectionsdoing mathematics

Importance of DistinguishingImportance of DistinguishingLow-Level Tasks

memorizationprocedures without connections (e.g., Martha’s Carpeting Task)

High-Level Tasksprocedures with connectionsdoing mathematics (e.g., The Fencing Task)

Low-Level Tasksmemorizationprocedures without connections (e.g., Martha’s Carpeting Task)

High-Level Tasksprocedures with connectionsdoing mathematics (e.g., The Fencing Task)

Consider and DiscussConsider and Discuss

How do you plan to implement the ideas that emerge in professional development sessions in your own classrooms?

How do you plan to implement the ideas that emerge in professional development sessions in your own classrooms?

Task-Focused ActivitiesTask-Focused Activities

UsingMaintaining

Analyzing

Distinguishing

Solving

TOOLSTOOLS

Practice-based Professional Development Classroom Teaching

TASKS as they appear in curricular/ instructional materials

TASKS as set up by the teachers

TASKS as implemented by students

Student Learning

Stein, Smith, Henningsen, & Silver, 2000, p. 4

The Mathematics Task Framework

The Mathematics Task Framework

TASKS as they appear in curricular/ instructional materials

TASKS as set up by the teachers

TASKS as implemented by students

Student Learning

Stein, Smith, Henningsen, & Silver, 2000, p. 4

The Mathematics Task Framework

The Mathematics Task Framework

TASKS as they appear in curricular/ instructional materials

TASKS as set up by the teachers

TASKS as implemented by students

Student Learning

Stein, Smith, Henningsen, & Silver, 2000, p. 4

The Mathematics Task Framework

The Mathematics Task Framework

TASKS as they appear in curricular/ instructional materials

TASKS as set up by the teachers

TASKS as implemented by students

Student Learning

Stein, Smith, Henningsen, & Silver, 2000, p. 4

The Mathematics Task Framework

The Mathematics Task Framework

TASKS as they appear in curricular/ instructional materials

TASKS as set up by the teachers

TASKS as implemented by students

Student Learning

Stein, Smith, Henningsen, & Silver, 2000, p. 4

The Mathematics Task Framework

The Mathematics Task Framework

Pulling it All TogetherPulling it All Together

Is there any evidence that suggests that a task- focused approach to professional development

has an impact on teachers’ classroom practices?

Is there any evidence that suggests that a task- focused approach to professional development

has an impact on teachers’ classroom practices?

YES

Successful PD Research: QUASAR ProjectSuccessful PD Research: QUASAR ProjectSignificant increase in teachers’ ability to distinguish between high and low level tasks following their participationThe PD in which teachers engaged appeared to have an influence on teachers' practice, particularly with respect to their ability to use and maintain high-level tasks in their own classrooms.Teachers who showed the most growth over time were those who consistently made connections between the PD and their own classroom practice.

Stein, Smith, Henningsen, & Silver, 2000

Significant increase in teachers’ ability to distinguish between high and low level tasks following their participationThe PD in which teachers engaged appeared to have an influence on teachers' practice, particularly with respect to their ability to use and maintain high-level tasks in their own classrooms.Teachers who showed the most growth over time were those who consistently made connections between the PD and their own classroom practice.

Stein, Smith, Henningsen, & Silver, 2000

Based Upon other Successful PD’s: What will we try?

Based Upon other Successful PD’s: What will we try?

Next we will work to identify high and low level math tasks from problems in our classes and come together on Blackboard to share different problems and distinguish high and low level math tasks. Please keep in mind specific ideas of what “worked” or you need more support with.Goal: To obtain feedback about high and low level math tasks.Next: Solving high level math tasks.In addition, Shalu invited us to her classroom! She will implement these ideas and share them with us. We will also be working to develop, implement and share these experiences throughout the year.

Next we will work to identify high and low level math tasks from problems in our classes and come together on Blackboard to share different problems and distinguish high and low level math tasks. Please keep in mind specific ideas of what “worked” or you need more support with.Goal: To obtain feedback about high and low level math tasks.Next: Solving high level math tasks.In addition, Shalu invited us to her classroom! She will implement these ideas and share them with us. We will also be working to develop, implement and share these experiences throughout the year.