No. 1 thing that is in Knowing what math is used for!!
Slide 5
Make sense of problems and persevere in solving them Whats
InWhats Out Teachers facilitate discussion in problem solving.
Students are involved in classroom discourse with one another,
making conjectures and planning solutions. Students are actively
engaged and are visibly thinking students are DOING math. Teachers
are allowing time for productive struggle. Teacher
lecturing/demonstrating for an extended period of time Students
passively taking notes Students are following PROCEDURES Quiet
classrooms
Slide 6
Reason abstractly and quantitatively Whats In Whats Out
Students are encouraged to provide a range of representations and
solutions of math problem situations. Opportunities for students to
make sense of quantities and their relationships in problem
situations. Engaged in problems that require flexible use of
properties of operations and objects. Students are expected to do
certain problems using a certain method Formulaic problems that
require little critical thinking. Students attending only to the
memorization of rules/procedures.
Slide 7
Constructing viable arguments and critiquing the reasoning of
others. Whats InWhats Out Students are given opportunities to make
conjectures inquiry. Students are given opportunities to construct
arguments and critique arguments of others in writing and through
dialogue. Students are encouraged to justify their conclusions and
communicate them to others. Students work independently in silence.
Assignments are based strictly on procedures and following
algorithms. Teacher telling students how to solve problems.
Slide 8
Model with Mathematics Whats InWhats Out Opportunities to apply
the mathematics they know to everyday life, society and the
workplace. Rich tasks that focus on conceptual understanding and
relationships. Students analyze relationships and draw conclusions
based on assumptions. Manufactured real- life problems that only
require knowing a formula. Problems focused only on procedures and
concepts
Slide 9
Use appropriate tools strategically Whats InWhats Out Problem
solving tasks that require students to consider a variety of tools
for solving (tools might include pencil/paper, concrete models,
ruler, protractor, scientific or graphing calculator, spreadsheet,
various software programs, etc.) The use of technology tools to
explore and deepen the understanding of concepts. The use of
calculators is never allowed. Limited access to mathematical tools
in the classroom. The use of technology is not an integral part of
the learning environment.
Slide 10
From Whats Out to Whats In Making the shift
Slide 11
Make sense of problems and persevere in solving them What We
Want to See Examples Teachers facilitate discussions in problem
solving. Students are involved in classroom discourse with one
another, making conjectures and planning solutions. Students are
actively engaged in solving problems and thinking is visible.
Teachers are allowing time for problem solving and practice.
Open-minded problem with no solution pathway evident; may have more
than one right answer. Collaborative work environment in which
students are discussing and sharing ideas. Teacher asks probing
questions to facilitate discussion. Teacher gives students help
grappling with problems.
Slide 12
Reason abstractly and quantitatively What We Want to See
Examples Students are encourages to provide a range of
representations and solutions of math problem situations.
Opportunities for student to make sense of quantities and their
relationships in problem situations. Engaged in problems that
require flexible use of properties of operations and objects. Tasks
that allow for pausing during the manipulation process; students
show understanding of what symbols represent. Provide rich tasks
that require the use of symbols. Students regularly consider units
involved in problem situations.
Slide 13
Constructing viable arguments and critiquing the reasoning of
others What We Want to See Examples Students are given
opportunities to make conjectures and explore the truth of their
conjectures. Students are given opportunities to construct
arguments and critique arguments of others in writing and through
dialogue. Students are encouraged to justify their conclusions and
communicate them to others. Tasks that allow students to analyze
situations by breaking them into cases. Tasks that require students
to justify, defend/refute and communicate examples and
counterexamples. Classroom environment encourages the exchanged of
ideas between students with facilitation from teacher.
Slide 14
Model with mathematics What We Want to See Examples
Opportunities to apply the mathematics they know to everyday life,
society and the workplace. Rich tasks that focus on conceptual
understanding and relationships. Students analyze relationships and
draw conclusions based on assumptions. Problem solving situations
that require students to develop essential questions. Problem
solving situations that require students to use a variety of
mathematical concepts.
Slide 15
Use appropriately tools strategically What We Want to See
Examples Problem solving tasks that require students to consider a
variety of tools for solving (tools might include pencil/paper,
concrete models, ruler, protractor, scientific or graphing
calculator, spreadsheet, various software programs, etc). Students
are familiar with appropriate tools and make sound decisions about
when each tool might be helpful. The use of technological tools to
explore and deepen the understanding of concepts. Problems solving
situations that require students to use technology. Problem solving
situations that involve concrete models. Technology is used to
enhance solutions, not distract from. Students are encouraged to
share their own ideas about using technology to solve
problems.
Slide 16
Attend to precision What We Want to See Examples Opportunities
for students to explain and/or write their reasoning to others.
Students use and clarify mathematical definitions in discussions
and in writing. Students calculate accurately and efficiently,
understand and state the meaning of symbols, and express numerical
answers with a degree of precision. Performance tasks with rubrics.
Students work collaboratively using correct academic language.
Students examine claims and make explicit use of definitions.
Slide 17
Look for and make use of structure What We Want to See Examples
Opportunities and time for students to explore patterns and
relationships to solve problems. Teacher facilitates conceptual
understanding through problem solving. Problems that encourage the
use of patterns. Students are given time to investigate and use
intuition.
Slide 18
Look for and express regularity in repeated reasoning What We
Want to See Examples Problem situations that allow students to
explore regularity and repeated reasoning. Through the use of
regularity, students are led to generalizations which may include
formulas. Students notice if calculations are repeated, and look
both for general methods and for shortcuts. Problems that encourage
multiple methods. Problems that require multiple steps/sub-
problems to work through.
Slide 19
Slide 20
Possibilities The Common Core State Standards offer the
possibility and potential for all students to access math
curriculumit is up to us to do our part to ensure that
happens.