components of effective mathematics instruction · discourse facilitates effective teaching....

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


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.


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


How does an effective mathematics lesson look and sound?


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).


Rationale

•  Building a practice of engaging students in academically rigorous tasks supported by meaningful

discourse facilitates effective teaching.


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.


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?


Planning for the Task


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


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


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?


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


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?


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.


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!


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?


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.


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?


What supported your learning?

Reflection


What will you implement in your next lesson?

Commitment

Contact

Jennifer Campbell (504) 266-1612

[email protected]

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

components of effective mathematics instruction · discourse facilitates effective teaching....

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