They Can Do It! Creating
Successful Students by Changing
Beliefs and Building Bridges
An overview of the researchbased 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
Big Ideas
Student Motivation and Confidence
Building
 Classroom Rituals and Routines
 Content Resources
 Teaching Strategies
 Common Assessments

Motivating Students
Mindset:The New Psychology
of Success by Carol Dweck
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 can’t.
 Rationalize failure.
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.
Research
“We now have decades of research
demonstrating that teaching students a growth
mindset–the knowledge that ability can be
developed–leads to greater student challengeseeking, effort, persistence, & achievement.”
Students who learn this mindset show greater
motivation in school and have higher grades
and test scores.
The Perils of Promise and Praise

Read the article.

List three things that surprised or
impacted you most.
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
Strategies for Building Confidence
and Promoting Engagement

Creating Experts

Crediting Competence

Scripting for Success
Shaded Triangle
The diagram above shows a rectangle, with
a shaded triangle inside.
Create an expression for the area of the
shaded triangle.
Shaded triangle

“Read the problem to yourself. Try and
think of a good starting point for the
problem.

Share your ideas with your partner.
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?”

Promoting Engagement:
The Three Read
You are a medical assistant in a
pediatrician’s 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
The Three Read
1.
2.
3.
Read the scenario silently. Be ready to
describe the situation. What is this
about?
Read the scenario silently again. This
time, list the information you feel is
important in this situation.
Let’s read the scenario aloud. Write
____ questions that you feel the
textbook, a test writer or your teacher
might ask about this situation.
The Metacognition of the Three
Read: What does it do?
Classroom Rituals and
Routines
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)
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)
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 day’s Big Ideas
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
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
An Example: Coordinate Algebra
Unit 2
CA Overview of Units 1 and 2
 Unit goals
 Task List

Planning and Teaching a Lesson: We
are still not getting it!!!
1.
2.
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.
Classrooms should teach multi-dimensional
mathematics.
One dimensional – Repeat the teacher’s
methods.
Multidimensional – Students ask their own
questions, model, reason, problem solve,
communicate and connect ideas.
3.
4.
All students should be encouraged to
take their mathematics learning to the
highest possible levels. (Tracking before
the 10th grade is a huge problem.)
Math classrooms should encourage
more depth and less speed.
Jo Boaler: Why Students Need the Common
Core www.youcubed.org
Mathematics Teaching Practices
1.
2.
3.
4.
Establish mathematical goals to
focus learning.
Implement tasks that promote
reasoning and problem-solving.
Use and connect mathematical
representations.
Facilitate meaningful mathematical
discourse.
Mathematics Teaching Practices
5.
6.
7.
8.
Pose purposeful questions.
Build procedural fluency from
conceptual understanding.
Support productive struggle in learning
mathematics.
Elicit and use evidence of student
thinking.
NCTM Principles to Actions: Ensuring Mathematical Success for All
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.
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.
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?
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.
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.

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.

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.

Common Unit Assessments
Less Like This
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 what’s happening
as carefully as you can. You do not need to measure anything accurately.
Both PARCC and Smarter Balance
will emphasize:
 Concepts
and Procedures (40%)
 Problem Solving (20%)
 Reasoning (20%)
 Modeling with mathematics (20%)
Common Unit Assessments
Format
 40% Selected response
 40% Constructed response
 20% Extended performance task
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
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)
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
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.
