S.P. A.C.E.S. District Learning Day
September 16, 2016
12:15 – 3:15
Algebra I & Algebra II
Components of
Effective Mathematics
Instruction
Structures and Routines of a lesson
William Kinard III, Ed.D. – Instructional Math Coach
Specializing in Pedagogy And Content for Education
in Secondary Schools
iZone High School Team
Meeting Norms
Be Present
Contribute
Respect each others’ time & ideas
Positive Interactions
We are ONE, the iZONE!!!
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.
Vision & Mission
iZone Goal
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.
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 lesson using the components of effective
mathematics instruction
What 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.
Stop and Jot
Rationale
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.
• 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.
8 Mathematical Teaching
Practices (MTPs)
Structures & Routines of a Lesson
Planning Questions for
the Task
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?
Set-Up Phase
Involves introducing students to the activity without taking
over students’ thinking
Ensure that students understand the concept of the
problem and what the task is asking them to solve
Brief (between 1-2 minutes, but no more than 5 minutes)
The Set-up Phase should not be used to teach
students how to complete the task!!!
Explore Phase
Provides opportunity for students to work individually
(private work time) and in small groups
Students make sense of and discuss the mathematics in
the task
Monitor student engagement during private work time and
small group discussion
Ask assessing and advancing questions
Explore Phase
(Questions) 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
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?
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?
How will you ensure that, over time, all students will have the opportunity to participate and be recognized as
competent?
Expectations for Group Discussion
• Share solution paths.
• 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.
Dream Job Task
The Situation: You are offered a 30-day trial period at your dream job.
However, the owner of the company is a little unusual so the pay options are
non-traditional. They offer you three different pay options for the 30 days as
listed below:
• Option 1: $60,000 a day
• Option 2: You make one penny the first day, two pennies the second day,
four pennies the third day, eight pennies the fourth day, etc.
• Option 3: On your first day of work, you get a $1. On your second day of
work, you get $4. On your third day of work, you get $9. On your fourth day
of work, you get $16. It continues this way for 30 days. Once you've
completed the 30 days, you will receive a completion bonus of $500,000.
My Questions about the Task
• Also discuss the MTPs and how the unfold
in the task. Ex: MTP 3 goes into the
different representations.
Your Turn!!!
Using the task, go through the phases of structures and routines of a
lesson.
Set-up Phase
How will you introduce students to the activity so as 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?
Reflection
What supported your learning?
Commitment
What will you implement in your
next lesson?
Questions???
If you have any questions, here is my contact
information:
William Kinard III, Ed.D.
(601) 613-7478
Survey
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