Post on 11-Jul-2020
Specializing in Pedagogy And Content for Education in Secondary Schools
S.P. A.C.E.S. District Learning Day September 16, 2016
12:00 – 3:00
Geometry & Advanced Math
Components of Effective Mathematics
Instruction
Jennifer Campbell – Instructional Curriculum Coach
iZone High School Team
Be Present Contribute Respect each Others Time Student Centered Ideas Positive Interactions
We are ONE, the iZONE!!!
Components of Effective Mathematics Instruction
Meeting Norms
The iZone High School Instructional Support Team's VISION is to be a highly valued team that provides effective content and pedagogical support for teachers to increase student achievement that leads to college and career readiness,
lifelong learning, and productive citizenship.
Our MISSION is to provide data-driven instructional support through content coaching and professional development that increases teacher capacity. Building positive relationships,
communicating effectively, embracing diversity, and engaging in on-going reflective practices are the
cornerstones of this work.
HS Vision & Mission
Components of Effective Mathematics Instruction
We must move our schools from the bottom 5% to the top 25%!
To accomplish this, we must ensure that effective instruction takes place
EVERYDAY and in EVERY school.
Components of Effective Mathematics Instruction
Goal of the iZone
Session Goals
Know • The components of effective mathematics instruction
Understand • How the 8 Mathematical Teaching Practices are
essential for effective mathematics instruction
Do • Plan a task using the components of effective
mathematics instruction
Components of Effective Mathematics Instruction
How does an effective mathematics lesson look and sound?
Components of Effective Mathematics Instruction
Take a few minutes to write down and discuss some elements that should be present in every math
lesson.
Effective teaching requires being able to support students as they work on challenging tasks without
taking over the process of thinking for them (NCTM, 2000).
Components of Effective Mathematics Instruction
Rationale
• Building a practice of engaging students in academically rigorous tasks supported by meaningful
discourse facilitates effective teaching.
Components of Effective Mathematics Instruction
Rationale, Cont.
• Students develop an understanding of mathematical ideas, strategies, and representations and teachers gain insights into what students know and what they
can do. • These insights prepare teachers to consider ways that
advance student understanding of mathematical ideas, strategies, or connections to representations.
Mathematical Teaching Practices
• Building a practice of engaging students in academically rigorous tasks supported by meaningful
discourse facilitates effective teaching.
Components of Effective Mathematics Instruction
Structures and Routines of a Lesson
• Students develop an understanding of mathematical ideas, strategies, and representations and teachers gain insights into what students know and what they
can do. • These insights prepare teachers to consider ways that
advance student understanding of mathematical ideas, strategies, or connections to representations.
What are the mathematical goals for the lesson (i.e., what is it that you want students to know and understand about mathematics as a result of this lesson)?
What questions will you ask to help
students access their prior knowledge?
What are all the ways the task can be solved?
What misconceptions might students
have? Errors?
What are the expectations for students as they work on and complete this
task?
How will you introduce students to the activity so as not to reduce the
demands of the task and provide access to all students?
What will you hear that lets you know
students understand the task?
Components of Effective Mathematics Instruction
Planning for the Task
Components of Effective Mathematics Instruction
Set-up Phase
• Brief, between 1-2 minutes, no more than 5 minutes
• Introduces the task without taking over the student’s thinking
• Make sure students understand the context of the problem and what the task is asking them to solve
• Should not be used to teach students how to complete the task
Components of Effective Mathematics Instruction
Explore Phase
• Private Work time • Small Group Problem Solving • Students make sense of and discuss the
mathematics in the task • Monitor Student Engagement • Ask assessing and advancing questions
Components of Effective Mathematics Instruction
Think About It!!! What will you do or say if no progress has been made on the task?
What will you see or hear that lets you know how students are thinking
about the mathematical ideas?
What questions will you ask to assess students’ understanding of key mathematical ideas, problem solving strategies, or the
representations?
What questions will you ask to advance students’ understanding of the mathematical ideas?
What questions will you ask to encourage all students to share their thinking with others or to assess their understanding of their peer’s
ideas?
How will you ensure that students remain engaged in the task?
Components of Effective Mathematics Instruction
Share, Discuss, Analyze Phase
• Selecting and Sequencing
• Students engage in mathematical discussion
• Teacher facilitates mathematical discussion
• Questions are used to press and elicit from students their understanding of
the mathematical ideas of the lesson
• Questions focus on understanding the meaning of the mathematical ideas
as they appear in different representations and different solution paths, and
as they appear in relationship to other operations or concepts
Components of Effective Mathematics Instruction
Think on These!!!
How will you orchestrate the class discussion so that you accomplish your mathematical goals? Specifically: Which solution paths do you want to have shared during the class discussion? In what order will the solutions be presented? Why? In what ways will the order in which solutions are presented help develop students’ understanding of the mathematical ideas that are the focus of your lesson? How will you ensure that, over time, all students will have the opportunity to participate and be recognized as competent?
What specific questions will you ask so that students will: -make sense of the mathematical ideas that you want them to learn? -expand on, debate, and question the solutions being shared? -make connections between the different strategies that are presented? -look for patterns? -begin to form generalizations? What relationships can be discovered between the solution paths? How can one solution help you think about another?
Components of Effective Mathematics Instruction
Expectations for Group Discussion
• Share solution paths.
• Use Accountable Talk.
• Listen with the goals of: putting the ideas into your own words; adding on to the ideas of others; making connections between solution paths; and asking questions about the ideas shared.
• The goal is to understand the mathematics and to make connections among the various solution paths.
Components of Effective Mathematics Instruction
Engage in a Task
“Is There an Easier Way?”
You have learned that corresponding parts of congruent polygons are congruent, and you have learned that rigid motions maintain
congruence. In order to determine if two triangles are congruent, will you need to verify that all sides and all angles are congruent? Use a ruler,
compass, and protractor to draw triangles with the given dimensions and see what you can discover!
Components of Effective Mathematics Instruction
Questions
Explore Phase Questions Assessing -Show me what you’ve tried. -Show me how you used the tools to draw your triangles. Advancing -How can you draw a rough sketch of each triangle showing all of the given information? Now, how can you use a ruler, protractor, or compass to draw the triangle with the given measurements? -Fix any errors you see. Try to be as precise as the tools let you be. If you are stumped, see if a group mate can help. -What did you notice as you drew each triangle? Do you think you can draw a triangle with the same measurements that is not congruent with the one you have already drawn? Why or why not?
Components of Effective Mathematics Instruction
Questions
Share, Discuss, Analyze Phase Questions -I’d like to have volunteers to come to the front to show us how you drew the three triangles with the given dimensions. Explain your method. -How did you use the compass and ruler to draw sides of a given length? How did you use the protractor to draw angles of a given measure? -What did you discover when you compared your triangles from question #1? -Why do you think these criteria produced congruent triangles? -What did you discover when you tried to draw each other’s triangles? -When you drew the triangles with a given conditions, you found that if you knew the lengths of three sides, the lengths of two sides and the size of the included angle, or the measure of two angles and the length of the included side, there was only one possible triangle that you can draw. So I think that you are all convinced that these criteria will guarantee that triangles will be congruent.
Components of Effective Mathematics Instruction
Your Turn!!
Using a task, go through the phases of structures and routines of a lesson.
Set-up Phase How will you introduce students to the activity, so not to reduce the
demands of the task and provide access to all students? Explore Phase
What assessing and advancing questions might you ask? Share, Discuss, and Analyze Phase
What questions will you ask to engage students in a class discussion about the mathematics in the task, aligned to the
standard?
Components of Effective Mathematics Instruction
What supported your learning?
Reflection
Components of Effective Mathematics Instruction
What will you implement in your next lesson?
Commitment
Contact
Jennifer Campbell (504) 266-1612
campbellj3@scsk12.org
www.izonehighschoolteam.weebly.com
Survey
Please use the link or QR Code to complete the survey. Please complete the survey before exiting the session.
https://www.surveymonkey.com/r/Preview/?sm=2sq4HHQYLCXuNOALTZR4_2BX98_2BOzuZl5wIbQcGgLyDZc_3D