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DIRECTOR OF MATHEMATICS
MARY KEMPER
THIS DOCUMENT IS DESIGNED TO PROVIDE A VISION OF THE FUTURE OF TEACHING AND LEARNING MATHEMATICS IN OUR
DISTRICT. IT SHOULD BE USED TO FOSTER CONVERSATION AND GUIDE PROFESSIONAL LEARNING PLANS FOR TEACHERS,
ADMINISTRATORS, AND CAMPUS INSTRUCTIONAL LEADERS.
1
EFFECTIVE MATHEMATICS
TEACHING PRACTICES
PAGE 3
MATHEMATICS
CLASSROOM STRUCTURE
PAGE 4
COPPELL ISD
MATHEMATICS
INQUIRY-DRIVEN
LEARNING EXPERIENCES
PAGE 6
RESPONSE TO
INTERVENTION SYSTEM
PAGE 7
EQUITY &
ACCESS TO
HIGH
QUALITY
LEARNING
EXPERIENCES
FOR ALL
STUDENTS
PHILOSOPHY AND
TRANSFER GOALS
PAGE 2
HIGH PRIORITY LEARNING
STANDARDS
PAGE 5
DIRECTOR OF MATHEMATICS
MARY KEMPER
PHILOSOPHY FOR TEACHING AND LEARNING MATHEMATICS
High quality mathematics curriculum and instruction engages
hands, minds and intellect through authentic, active learning
that supports each student to achieve personal success. These
learning experiences, assessed through a variety of methods,
bridge the concrete and abstract by applying critical thinking
skills and problem solving strategies in meaningful and relevant
situations. Through the understanding of mathematical concepts
and reasoning, every student will be prepared to communicate
effectively using the language of mathematics as a tool to meet
future challenges.
TRANSFER GOALS FOR CISD MATHEMATICS
The students will independently use their learning to…
1
Use a problem-solving model that incorporates analyzing given information, formulating a plan or
strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and
the reasonableness of the solution.
2
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and
techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
3
Communicate mathematical ideas, reasoning, and their implications using multiple representations,
including symbols, diagrams, graphs, and language as appropriate.
4
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in
written or oral communication.
2
DIRECTOR OF MATHEMATICS
MARY KEMPER
EFFECTIVE MATHEMATICS TEACHING PRACTICES (NCTM)
Establish mathematics goals to focus learning.
Effective teaching of mathematics establishes clear goals for the mathematics that students are learning,
situates goals within learning progressions, and uses the goals to guide instructional decisions.
Implement tasks that promote reasoning and problem solving.
Effective teaching of mathematics engages students in solving and discussing tasks that promote
mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.
Use and connect mathematical representations.
Effective teaching of mathematics engages students in making connections among mathematical
representations to deepen understanding of mathematics concepts and procedures and as tools for problem
solving.
Facilitate meaningful mathematical discourse.
Effective teaching of mathematics facilitates discourse among students to build shared understanding of
mathematical ideas by analyzing and comparing student approaches and arguments.
Pose purposeful questions.
Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and
sense making about important mathematical ideas and relationships.
Build procedural
fl
uency from conceptual understanding.
Effective teaching of mathematics builds
fl
uency with procedures on a foundation of conceptual
understanding so that students, over time, become skillful in using procedures
fl
exibly as they solve
contextual and mathematical problems.
Support productive struggle in learning mathematics.
Effective teaching of mathematics consistently provides students, individually and collectively, with
opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and
relationships.
Elicit and use evidence of student thinking.
Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical
understanding and to adjust instruction continually in ways that support and extend learning.
3
DIRECTOR OF MATHEMATICS
MARY KEMPER
ELEMENTARY & SECONDARY MATHEMATICS CLASSROOM STRUCTURE
As teams of educators plan learning experiences within conceptual units of study, the following structure is provided
for guidance. Based on the learning outcomes for any given day, the educators may choose to provide opportunities
for the learners to access the mathematics through three options which include inquiry tasks, whole-group & small
group experiences, or small group alone. These options provide autonomy for teams and educators to design flexibly.
Within this structure, each day includes a number sense routine for elementary and an algebraic thinking routine for
secondary. With this focus on our High Priority Learning Standards and certain instructional routines, all students are
granted access to our guaranteed and viable curriculum. Each day also includes an opportunity for the learners to
reflect on their learning in relation to their goals while time for practice and connect is the fi nal component to the
classroom structure.
4
NUMBER SENSE ROUTINE
(ELEMENTARY) / ALGEBRAIC
THINKING ROUTINE (SECONDARY)
REFLECTION
PRACTICE & CONNECT
INQUIRY TASK
NUMBER SENSE ROUTINE
(ELEMENTARY) / ALGEBRAIC
THINKING ROUTINE (SECONDARY)
WHOLE GROUP MINI LESSON
SMALL GROUP MATHEMATICS
REFLECTION
PRACTICE & CONNECT
NUMBER SENSE ROUTINE
(ELEMENTARY) / ALGEBRAIC
THINKING ROUTINE (SECONDARY)
REFLECTION
PRACTICE & CONNECT
SMALL GROUP MATHEMATICS
Option 2
Option 3
INQUIRY TASK
WHOLE GROUP
MINI LESSON
SMALL GROUP
MATHEMATICS
PRACTICE &
CONNECT
NUMBER SENSE /
ALGEBRAIC THINKING
ROUTINE
REFLECTION
Option 1
DIRECTOR OF MATHEMATICS
MARY KEMPER
HIGH PRIORITY LEARNING STANDARDS
Topics for Kindergarten - Grade 5 Mathematics
Counting and Recognizing Whole Numbers
Comparing and Ordering Numbers
Composing and Decomposing Numbers (Place Value)
Operations with Whole Numbers and Decimals
Operations with Fractions
Data Analysis
Topics for Grade 6 - Grade 8 Mathematics
Number and Operations
Equations
Proportionality
Geometry
Multiple Representations (Linear)
Topics for Algebra I*
Attributes of Functions
Polynomial Operations
Solving Equations
Writing Equations for Functions
*HPLS for courses beyond Algebra I to be fi nalized
5
DIRECTOR OF MATHEMATICS
MARY KEMPER
INQUIRY-DRIVEN LEARNING EXPERIENCES
Purpose
Learning experiences are designed to promote inquiry on the part of the students as they question, estimate, consider,
solve, and reflect on the mathematical tasks in pursuit of understanding the concept within the learning goal. In
addition, inquiry is utilized by the educator while he/she seeks to understand the students’ thinking and processes
used to solve problems.
Structure
Inquiry-driven learning experiences may include rich tasks, computational thinking/coding experiences or may be
structured in the form of a 3-Act Mathematical Task:
•
Act One:
The central conflict of the story or task is introduced through images, videos, or experiences while limiting
the text-dependence as much as possible. At this point, a question is developed and an estimate is considered.
•
Act Two:
The student seeks out or develops necessary resources or tools and utilizes these to solve the problem.
•
Act Three:
The story or task conflict is resolved and the student reflects on the solution in comparison to his/her
own work.
Accessibility
Attention should be paid to the mathematical tasks assigned so that all students may access the content. Low floor/
high ceiling tasks are those that allow for all students to engage in the mathematics (low threshold) and work without
limitation (high threshold).
6
DIRECTOR OF MATHEMATICS
MARY KEMPER
RESPONSE TO INTERVENTION SYSTEM FOR K-5 MATHEMATICS
Scope & Sequence
Teams of educators access the Scope & Sequence document in order to design learning experiences aligned to the
standards articulated within each unit of study.
High Priority Learning Standards
Coppell ISD High Priority Learning Standards are the identifi ed standards we guarantee all students will learn.
Therefore, educators will design and deliver intentional learning experiences, continual assessments, and targeted
interventions and extensions.
Universal Screening
7
