They Can Do It! Creating Successful Students by Changing
Beliefs and Building Bridges
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An overview of the research- based beliefs, strategies, content
resources, teacher work habits, and assessment tools that have
contributed to student success in mathematics since reform work
began in Georgia in 2001
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Big Ideas Student Motivation and Confidence Building Classroom
Rituals and Routines Content Resources Teaching Strategies Common
Assessments
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Motivating Students Mindset: The New Psychology of Success by
Carol Dweck
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Fixed Mindsets Believe that basic qualities, like intelligence
or talent, are fixed traits. A person is either smart or dumb and
there is no way to change this. Talent alone creates success
without effort. Spend time documenting their intelligence or talent
instead of developing them. Shy away from challenges. Tell
themselves they cant. Rationalize failure.
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Growth Mindsets Believe that basic abilities can be developed
through effort and hard work - brains and talent are just the
starting point. A person can learn more or become smarter if they
work hard and persevere. Learn more and learn it more quickly. View
challenges and failures as opportunities to improve learning and
skills.
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Research We now have decades of research demonstrating that
teaching students a growth mindsetthe knowledge that ability can be
developedleads to greater student challenge- seeking, effort,
persistence, & achievement. Students who learn this mindset
show greater motivation in school and have higher grades and test
scores.
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The Perils of Promise and Praise Read the article. List three
things that surprised or impacted you most.
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Intelligence is Malleable Neuroscientists tracking students
during their teenage years, found substantial changes in
performance on verbal and non-verbal IQ tests. Using neuroimaging,
they found corresponding changes in the density of neurons in the
relevant brain areas for these students. In other words, an
increase in neuronal connections in the brain accompanied an
increase in IQ-test performance, while a decrease in neuronal
connections in the brain accompanied a decrease in IQ-test
performance. Four steps for establishing a growth mindset in your
classroom: http://blogs.edweek.org/teachers/classroom_qa_with_la
rry_ferlazzo/2012/10/response_classroom_strategies_t
o_foster_a_growth_mindset.html
http://blogs.edweek.org/teachers/classroom_qa_with_la
rry_ferlazzo/2012/10/response_classroom_strategies_t
o_foster_a_growth_mindset.html
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Strategies for Building Confidence and Promoting Engagement
Creating Experts Crediting Competence Scripting for Success
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Shaded Triangle The diagram above shows a rectangle, with a
shaded triangle inside. Create an expression for the area of the
shaded triangle.
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Shaded triangle Read the problem to yourself. Try and think of
a good starting point for the problem. Share your ideas with your
partner.
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Shaded triangle Read the problem to yourself. Try and think of
a good starting point for the problem.(1 to 2 minutes). Share your
ideas with your partner. (2 minutes). Teacher reads the problem
aloud. What is a good way to start the problem?
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Promoting Engagement: The Three Read You are a medical
assistant in a pediatricians office and one of your
responsibilities is evaluating the growth of newborns and infants.
Your first patient, a baby girl named Ivy Smith, was 21.5 inches
long at 3 months old. At 8 months, you measure her at 24 inches
long. For your medical records, all measurements must be given both
in inches and in centimeters: 1 inch = 2.54 cm
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The Three Read 1. Read the scenario silently. Be ready to
describe the situation. What is this about? 2. Read the scenario
silently again. This time, list the information you feel is
important in this situation. 3. Lets read the scenario aloud. Write
____ questions that you feel the textbook, a test writer or your
teacher might ask about this situation.
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The Metacognition of the Three Read: What does it do?
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Classroom Rituals and Routines
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Pairing of Students (TKES Standards 1, 3, 4, 7, 8) Arrange room
for student engagement and a conducive learning environment
Homogenous pairs Struggling students seated front and center of the
room Allows for differentiation (scaffolding and extension)
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Questioning (TKES Standards 3, 5, 6, 8) Limit whole-group
questioning Informally assess individual student understanding
(white boards, thumbs up or down, etc.) Use on-going formative
assessment of individual students to inform instruction Call on
students randomly (random number generator, popsicles sticks, name
cards, etc)
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Definitive Standards-Based Classroom Structure (TKES Standards
1, 2,3, 5, 6, 7, 8) Use of a timer Warm up- accesses prior
knowledge and leads into the opening Opening- learning targets made
clear and connected to prior knowledge Work Session- use
standards-based units as primary resource Closing- summary of the
days Big Ideas
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Resources and Content Unit development Plan at the unit level
Based on GaDOE Frameworks Commitment not to write but to FIND tasks
All resources from sites written or endorsed by the writers of
CCSS-M
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Unit Development The Process Examine the standards included in
the GaDOE unit. Study the intent of the standards Transformational
Geometry Untangling Functions and Equations Establish unit goals
Work through DOE tasks Accept/reject/revise DOE Tasks Find new
tasks and skills practice
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An Example: Coordinate Algebra Unit 2 CA Overview of Units 1
and 2 Unit goals Task List
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Planning and Teaching a Lesson: We are still not getting it!!!
1. We should offer math as a learning subject, not a performance
subject. Students see their role as answering questions correctly.
We need to give students more space to learn. 2. Classrooms should
teach multi-dimensional mathematics. One dimensional Repeat the
teachers methods. Multidimensional Students ask their own
questions, model, reason, problem solve, communicate and connect
ideas.
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3. All students should be encouraged to take their mathematics
learning to the highest possible levels. (Tracking before the 10 th
grade is a huge problem.) 4. Math classrooms should encourage more
depth and less speed. Jo Boaler: Why Students Need the Common Core
www.youcubed.org
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Mathematics Teaching Practices 1. Establish mathematical goals
to focus learning. 2. Implement tasks that promote reasoning and
problem-solving. 3. Use and connect mathematical representations.
4. Facilitate meaningful mathematical discourse.
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Mathematics Teaching Practices 5. Pose purposeful questions. 6.
Build procedural fluency from conceptual understanding. 7. Support
productive struggle in learning mathematics. 8. Elicit and use
evidence of student thinking. NCTM Principles to Actions: Ensuring
Mathematical Success for All
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Solving Systems of Linear Equations by Graphing Bellringer:
Graph these two linear equations on the same coordinate plane. 2x +
3y = 16 and x y = 3.
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Solving Systems of Linear Equations by Graphing Goals You will
be able to find exact or approximate solutions of systems of two
linear equations in two unknowns by graphing. You will understand
that graphical solutions of systems may be approximate rather than
exact.
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Solving Systems of Linear Equations by Graphing Opening:
Discussion of the warm-up. What do you notice about the graphs of
the equations? What is the significance of this point? Explain that
two or more equations can be considered a system of equations. In
this case, we have a system of two linear equations in two
unknowns. What do you think it means to find the solution of a
system of equations. How many solutions does this system have? What
is the solution? How can you be sure your solution is correct?
Worktime: 1 3,( discussion), 4 - 5 Closing: Presentations. Ask
students to discuss Problems 4 and 5. Introduce the terms
consistent, inconsistent, dependent, and independent. Why might we
need an algebraic way to solve systems of equations in addition to
a graphical method?
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Solving Systems of Linear Equations by Graphing Probing and
prompting questions: What do you notice about the graphs of the
equations? What is the significance of this point? What is the
relationship between a linear equation and its graph? (Students
have noticed graphs of the equations are the same line.) What does
this tell you about the solution set of the system? Explain. How
many points are in the solution set? Does every point in the plane
make this system true? (Students have noticed that there are no
points of intersection.) What does this tell you about the solution
set of the system? Explain. How would you describe the graphs of
these two equations? Could you have told that without graphing the
equations? Explain.
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Lesson Planning Work the task alone. Discuss solutions with
your colleagues. List the mathematics involved in the task. Decide
whether the task is aligned to the indicated standard(s). Determine
the Standards for Mathematical Practice addressed. Determine the
time required to enact the task.
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For each lesson Establish the goals of the lesson. (Goals are
different from posting or reading the standards.) Identify what
students should know and understand. Be as specific as possible.
Identify new vocabulary. Determine pre-requisite skills. Develop a
bell ringer, opening, work session, and closing. Anticipate student
responses to the work and write probing questions to address those
responses.
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An Excellent Assessment Program Ensures that assessment is an
integral part of instruction. Provides evidence of proficiency with
important mathematics content and practices. Includes a variety of
strategies and data sources. Informs feedback to students,
instructional decisions and program improvement.
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Common Unit Assessments Less Like This
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More Like This This is a rough sketch of 3 runners progress in
a 400 meter hurdle race. Imagine that you are the race commentator.
Describe whats happening as carefully as you can. You do not need
to measure anything accurately.
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Both PARCC and Smarter Balance will emphasize: Concepts and
Procedures (40%) Problem Solving (20%) Reasoning (20%) Modeling
with mathematics (20%)
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Common Unit Assessments Format 40% Selected response 40%
Constructed response 20% Extended performance task
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Goals To raise student achievement in mathematics To increase
students stamina for taking more rigorous assessments such as the
Georgia Milestones, PSAT, SAT, and ACT
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Two Different Plans Separate tests (Teacher tests and more
rigorous tests administered separately) Teacher created items
combined with more rigorous items to form one test.(These students
did better on EOCT)
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The Process Teachers meet to develop tests before they begin
the unit. (Conversation and choices of items help increase rigor
and drive instruction.) Items are chosen from resources created or
endorsed by CCSS-M writers and individuals or groups advising PARCC
and Smarter Balance All items must meet the CCSS-M Assessment Item
Quality Criteria. Assessment is evaluated for alignment to the
CCGPS using the CCSS Evaluation Tool
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The Process Tests are graded using a common rubric. Grades on
more rigorous items are scaled so as not to destroy student
averages. Unit tests are both summative and formative. Data is
aggregated and used to assess strengths and weaknesses of
individual students, to identify topics for whole class
re-engagement, and to compare and improve instructional techniques
of individual teachers.