Alabama College- and Career-

Ready Standards for

Mathematics

Quarterly Meeting

#3

Thinking Through A Lesson

Thinking Through a Lesson: Successfully Implementing High-Level Tasks Session I:

Outcomes:

• Discuss and examine the thought process of developing a lesson/unit that is standards-based.

• Select rich tasks that match student friendly outcomes and provide evidence of student learning.

Why Lesson Planning?

The effectiveness of a lesson

depends significantly on the

care with which the lesson plan

is prepared.

(Brahier, 2000)

Why Lesson Planning?

Good planning “shoulders much of the burden” of teaching by replacing “on the fly" decision making” during a lesson with careful investigation into the what and how of instruction before the lesson is taught.

(Stigler & Hiebert, 1999, p.156)

During the planning phase, teachers make

decisions that affect instruction dramatically.

They decide what to teach, how they are

going to teach, how to organize the

classroom, what routines to use, and how to

adapt instruction for individuals.

(Fennema & Franke, 1992, p. 156)

Why Lesson Planning?

An effective mathematical task is needed to

challenge and engage students intellectually.

Read an

excerpt from

the article:

What causes high-level cognitive demand tasks to decline?

Comparing Two Mathematical Tasks

Solve Two Tasks:

•Martha’s Carpeting Task

• The Fencing Task

How are Martha’s Carpeting Task and the Fencing Task the same and how are they different?

Comparing Two Mathematical Tasks

Do the differences between the Fencing Task and Martha’s Carpeting Task matter?

Why or Why not?

Comparing Two Mathematical Tasks

Similarities and Differences

Similarities

• Both are “area” problems

• Both require prior knowledge of area

Differences

• The amount of thinking and reasoning required

• The number of ways the problem can be solved

• Way in which the area formula is used

• The need to generalize

• The range of ways to enter the problem

Does Maintaining Cognitive Demand Matter?

YES

Linking to Literature/ Research:

The QUASAR ProjectThe Mathematical Tasks Framework

TASKS

as they appear in curricular/ instruction

al materials

TASKS

as set up by the

teachers

TASKS

as implemented

by students Studen

t Learning

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

Stein & Lane, 2012

A.

B.

C.

High High

Low Low

High LowModerate

High

Low

Task Set Up

Task Implementation

Student Learning

Patterns of Set up, Implementation, and Student

Learning

Factors Associated with the Maintenance and Decline of High-Level Cognitive

Demands• Routinizing problematic aspects of the task

• Shifting the emphasis from meaning, concepts, or understanding to the correctness or completeness of the answer

• Providing insufficient time to wrestle with the demanding aspects of the task or so much time that students drift into off-task behavior

• Engaging in high-level cognitive activities is prevented due to classroom management problems

• Selecting a task that is inappropriate for a given group of students

• Failing to hold students accountable for high-level products or processes

(Stein, Grover & Henningsen, 2012)

• Scaffolding of student thinking and reasoning

• Providing a means by which students can monitor their own progress

• Modeling of high-level performance by teacher or capable students

• Pressing for justifications, explanations, and/or meaning through questioning, comments, and/or feedback

• Selecting tasks that build on students’ prior knowledge

• Drawing frequent conceptual connections

• Providing sufficient time to explore

(Stein, Grover & Henningsen, 2012)

Factors Associated with the Maintenance and Decline of High-Level Cognitive

Demands

Decline•Routinizing problematic aspects of the task

•Shifting the emphasis from meaning, concepts, or understanding to the correctness or completeness of the answer

•Providing insufficient time to wrestle with the demanding aspects of the task or so much time that students drift into off-task behavior

•Engaging in high-level cognitive activities is prevented due to classroom management problems

•Selecting a task that is inappropriate for a given group of students

•Failing to hold students accountable for high-level products or processes

Maintenance•Scaffolding of student thinking and reasoning

•Providing a means by which students can monitor their own progress

•Modeling of high-level performance by teacher or capable students

•Pressing for justifications, explanations, and/or meaning through questioning, comments, and/or feedback

•Selecting tasks that build on students’ prior knowledge

•Drawing frequent conceptual connections

•Providing sufficient time to explore

Factors Associated with the Maintenance and Decline of High-Level Cognitive

Demands

“Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking.”

(Stein, Smith, Henningsen, & Silver, 2011)

“The level and kind of thinking in which students engage determines what whey will learn.”

(Hiebert et al., 2011)

[Common Core State Standards for Mathematics] represent a significant departure from what mathematics is currently taught in most classrooms and how it is taught. Developing teachers’ capacity to enact these new standards in ways that support the intended student learning outcomes will require considerable changes in mathematics instruction in our nation’s classrooms. Such changes are likely to occur only through sustained and focused professional development opportunities for those who teach mathematics.

Sztajn, Marrongelle, & Smith, 2011

3. How can we help teachers

improve their capacity to plan

(and enact) lessons that

support students’ learning?

4. How would you conduct

professional development with

teachers to see how lesson

planning addresses content

rigor, task selection, student

engagement and math

practices, formative assessment, generating

student work samples for

assessment, and assisting

struggling students?

Job-Alike Reflection

Thinking Through a Lesson: Successfully Implementing High-Level Tasks Session 2

Outcomes:

• Develop student friendly outcomes that reflect the rigor and depth of content.

• Select rich tasks that match student friendly outcomes and provide evidence of student learning.

• Model teacher collaboration on identifying resources for implementing CCRS Math Standards.

Thinking Through a Lesson Protocol (TTLP) Planning Template

Learning Goals (Residue)What understandings will students take away from this lesson?

EvidenceWhat will students say, do, produce, etc. that will provide evidence of their understandings?  

TaskWhat is the main activity that students will be working on in this lesson?   

Instructional Support—Tools, ResourcesWhat tools or resources will students have to use in their work that will give them entry to, and help them reason through, the activity?

Task EnactmentWhat are the various ways that students might complete the activity?        

Instructional Support—TeacherWhat questions might you ask students that will support their exploration of the activity and bridge between what they did and what you want them to learn?  To be clear on what students actually did, begin by asking a set of assessing questions such as: What did you do? How did you get that? What does this mean? Once you have a clearer sense of what the student understands, move on to appropriate set of questions below.

Sharing and Discussing the TaskSelecting and Sequencing Which solutions do you want to have shared during the lesson?In what order? Why?  

 

Connecting ResponsesWhat specific questions will you ask so that students-make sense of the mathematical ideas that you want them to learn-make connections among the different strategies/solutions that are presented

Thinking Through a Lesson Protocol

Backwards Planning

What mathematical concepts will be developed

in the implementati

on of this task?

Set Up

What do you expect your students to do as they

engage in the lesson?

What will you see or hear that lets you know students are developing

understanding of the concepts?

What questions will you need to

ask to build mathematical

understanding?Explore Share, Discuss, and

Analyze

K-2 Sample Task

Dan’s older brother Sam collects car stickers

for his scrapbook. Sam decides to give Dan

some of his stickers. Sam gives Dan 7

stickers. Sam now has 12 stickers.

How many stickers did Sam have before

giving some to Dan?

K-2 Sample Task

3-5 Sample TaskUse the digits 3, 4, 5 and 6 to complete each number sentence. A digit can only be used once in each number sentence.

+ = 108

+ = 81 - = 31

+ = 99

+ = 90

- = 18

3-5 Sample Task

Grades 6 – 8 Sample Task REPRESENTING AND INTERPRETING PROPORTIONAL

RELATIONSHIPS: Computer Games

Grades 6 – 8 Sample Task Slippery Slopes: Saving Money

Grades 9 – 12 Sample Task

Grades 9 – 12 Sample Task

Refl

ectio

n

• What are some of the potential benefits of using the TTLP?

• With which components of the lesson planning protocol do you feel especially comfortable?

• Which components would you like to focus on more? How can the ideas and tools from this activity support you with that?

Conclusion Not all tasks are created equal -- they should

provide a variety of opportunities for students to learn mathematics.

• High level tasks are the most difficult to carry out in a consistent manner.

• Engagement in cognitively challenging mathematical tasks leads to the greatest learning gains for students.

• Professional development is needed to help teachers build the capacity to enact high level tasks in ways that maintain the rigor of the task.

Job-Alike Reflection

5. Are there any aspects of your own thinking and/or practice that our work today has caused you to consider or reconsider? Explain.

6. Are there any aspects of your students’ mathematical learning that our work today has caused you to consider or reconsider? Explain.

6a. What would you like more information about?

Resources

www.mathccc.org

Insidemathematics.org

Insidemathematics.org

map.mathshell.org.uk/materials

Mathematics Assessment Project (MAP)

• 20 ready-to-use Lesson Units for Formative Assessment for high school. cross referenced to CCSS content and practices standards. (Ultimately 20 per grade 7-12)

• Summative assessments, aimed at “College- and Career-Readiness,” presented in two forms: (1) a Task Collection with each task cross-referenced to the CCSS, and (2) a set of Prototype Test Forms showing how the tasks might be assembled into balanced assessments.

• Professional development modules

Mathematics Assessment Project (MAP)

map.mathshell.org.uk/materials

MAP Formative Assessment Lessons

• Assessment task, individual work (15 min)

• Teacher reviews work, creates questions to improve solutions

• (Whole group discussion)

• Partner or small group task to increase understanding, address misconceptions

• Debriefing discussion

• Revision of work on original assessment

The Illustrative Mathematics Project

• Hyperlinked CCSS

• Developing a complete set of tasks for each standard

• Range of difficulty

• Simple illustrations of single standards to complex tasks spanning many standards.

• Provide a process for submitting, discussing, reviewing, and publishing tasks.

• Launch Team: Phil Daro, William McCallum (chair), Jason Zimba

illustrativemathematics.org

illuminations.nctm.org/Lessons.aspx

mathedleadership.org

commoncoretools.wordpress.com

Collaborative Team Tools

Available at nctm.org