alabama college- and career-ready standards for mathematics quarterly meeting #3 thinking through a...
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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