Mathematics Information for Parents

April 27, 2016


As promised, here are the notes from Professor Sharma's parent night from April 13th and the outline of next steps for the Middle School as we move forward with our math curriculum shifts.


Math Summary and Next Steps

Cape Elizabeth Schools

Professor Mahesh Sharma founder and President of the Center for Teaching/Learning of Mathematics in Framingham, Massachusetts has been working with the Cape Elizabeth Schools to conduct a review of the mathematics program, to provide ongoing professional development, and to make recommendations for next steps.

Professor Sharma has come for three sessions thus far to work with teachers and administrators, has spent a day observing middle school mathematics classes, and conducted an initial parent/guardian informational session Wednesday, April 13th. He will have joined us for a fourth day (on the 26th) at the time of this publication.

The work around the mathematics program has centered on realigning the curriculum to the Common Core State Standards for Mathematics, examining existing curricula, reviewing the course offerings and sequence of courses K-12, and providing ongoing professional development to support teaching pedagogy to build mathematical thinking and concept mastery.

We want to acknowledge that it was our intent to have Professor Sharma provide a theoretical foundation for developing mathematical literacy at the parent information session, but we had also intended to provide many more specifics about next steps in Cape Elizabeth.  We know many were frustrated and were hoping to hear much more about what can be expected moving forward.  We apologize that the evening did not meet those expectations.


This document serves as a summary of the informational session held April 13th, provides an overview of the platform for concept mastery at key intervals, and outlines the adjustment of courses being put into place at the middle school.

Summary of April 13th Parent Guardian Session

Some key points made by Professor Sharma:

Numeracy skills are the drivers of successful math students.

If students have a mastery of numeracy by fourth grade, they can then use those numeracy skills to learn anything in mathematics.

Professor Sharma recommends a pedagogical approach that utilizes:

  • 25% of class time--whole class tool building
  • 50% of class time--whole class main concept
  • 25% of time--differentiated practice, small group, individual as needed.

Intervention is in addition to this, not in place of this.

At each grade level certain skills must be mastered so students can perform the operations correctly, consistently, and fluently with understanding in the standard form without a calculator: 

Grades K-2-Mastery of Additive Reasoning

K-Number sense



Grades 3 & 4-Mastery of Multiplicative Reasoning

                  3-Multiplication facts

                  4-Division facts 

Grades 5 & 6-Mastery of Proportional Reasoning

                  5-Multiplication tables, divisibility rules, prime factorization,

                      short division  

6-Integers and fractions

Grades 7 and 8-Mastery of Algebraic thinking

Algebra is generalized arithmetic.  Children who have not mastered the principles of arithmetic may be able to do the procedures but may not make the conceptual connections, comprehending the relationships between ideas and their applications.

Every math concept has three components:

1.    linguistic

2.    conceptual

3.    procedural

Common Core Math Standards are founded on three legs:

1.    Non-negotiable skills

2.    Rigor

3.    Coherence 

Professor Sharma explained how pre-Algebra and pre-Calculus are American constructs.

He also discussed possible sequence of courses through high school and paths to reach the apex course of Calculus. Discrete Mathematics and AP Statistics were also discussed as apex course options, depending upon a student’s career trajectory and interests.



The district leadership--the three building principals and the Director of Instruction--together have agreed to continue our work with Professor Sharma throughout the summer and the upcoming school year and are currently working with him on the schedule and contract for those dates. The gaps identified in our work over the past two years have existed over a long period of time, and though they are highlighted by the recent changes at the middle school, they preceded those changes. Instructional shifts are being made at all math levels. Our work over the next 12-18 months is to re-evaluate our course sequence K-12 for scope and content and to provide our teachers with additional tools to meet the instructional needs of their students regardless of the course in which they are placed.  The focus will be on making sure that students have the additive, multiplicative, and proportional reasoning skills they need to be successful in higher mathematics.





Grade 5

·  Grade 5 Mathematics

Grade 6

·  Grade 6 Common Core Standards

·  Pre-Algebra

Grade 7

·  Grade 7 Common Core Standards

·  Pre-Algebra

·  Algebra I

Grade 8

·  Grade 8 Common Core Standards

·  Algebra I

·  Geometry

These courses and the concepts that follow have come from our ongoing professional development with Professor Mahesh Sharma and have been reviewed by the Middle School Math Teachers and are agreed to be best next steps for our students. 

Our mathematics instruction continues to focus on implementing the Common Core with consistency, coherence, and to achieve mastery. Mastery means students can demonstrate three components: understanding, fluency, and applicability.


We examine teaching pedagogy at the same time that we talk about achieving mastery of standards.  With this in mind, our pedagogical approach at the middle school will be moving toward including:

·   25% of class time on whole class tool building

·   50% of class time on whole class instruction exploring the main concept

·   25% of time on differentiated practice that includes small group and individual instruction as needed

Any required intervention and remediation would be provided in addition to classroom instruction and not in place of it. 

Every math concept has a linguistic, conceptual, and procedural component.  When assessing to determine movement on to the next skill and or next level, we must assess understanding of the language, the concept, and the procedure. Re-evaluation of our use of local and standardized assessments will include this analysis.


Middle School Teachers have been working during their weekly common planning time and during sessions with Professor Sharma to complete the following:

1.  Identify the math courses and the number of levels of each class

2.  Identify the Common Core Non-Negotiable Skills at each grade

     level and within each course

3.  Establish the placement/readiness criteria for each course

4.  Administer placement measures

5.  Recommend students for each course at each level

6.  Design an appeals process


Throughout our process, we have remained grounded in Professor Sharma’s reminder that our loyalty must be to children and to mathematics.






List of Games 2015

Link to PDF

Handout from Professor Sharma's April 13, 2016 Parent Night talk on mathematics.
Professional Development Opportunities:  Click here for changing resources available for recertification and continuing professional learning.

UbD Backwards Design Curriculum Unit Planning Document--Marshall/McTighe  

Understanding By Design Template 1.0 (Google Spreadsheet Version)

(Source: Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005) (Word Version and other downloads available as resources)


Graduation Standards

CapeElizabeth School Department 2014-15 NCLB Report Card  Please note that the data does not include 2014-15 testing as 

this was a benchmarking year for the new assessment (SmarterBalanced). 

Cathy Stankard
Interim Director of Instruction

No Child Left Behind school and district report cards

Curriculum, Instruction and Assessment Planning Committee

In 2005, while a candidate for the superintendency and into the beginning year as the Superintendent of Cape Elizabeth Schools, a consistent message from staff was the need to move from Local Assessment System (LAS) planning to actual curriculum development. Based on the direction set by the Department of Education and on the needs addressed by the staff, Sarah Simmonds, the Cape Elizabeth Curriculum Director, was asked to spend the fall of 2005 with the assessment team to review what they were doing and to help develop a plan to move from formulating assessments to actual curriculum development. In January of 2006 the transition was made from the LAS to the Curriculum, Instruction and Assessment (CIA). The new committee was composed of some former LAS Committee members, some new members and included the superintendent, the three principals, the two assistant principals, the Instructional Support Director, and two School Board members. 

During the next few months, work progressed well. As a result of the accreditation development at Cape Elizabeth High School, the curriculum work became much more focused under Jeff Shedd's leadership. During the summer of 2006, many staff participated in professional development focused on curriculum planning and design. During the 2006-2007 academic year, research, group meetings, and discussions led to more clearly defining curriculum templates, developing programs, and working on management issues. Continued staff development during the summer of 2007 was completed.

The development of the Curriculum Management Plan (see below) was accomplished in 2008. Due to serious budget constraints, the position of curriculum director was eliminated in 2008 and the the entire administrative team became leaders in the CIA development process. During the 2008-2009 and then the 2009-2010 academic years and summers, much work was completed in all subject areas. With the development of the Teaching and Learning Committee of the School Board in 2009, summative reports in the areas of Science, English Language Arts (ELA), World Language, Guidance and Mathematics will be reviewed during 2009-2010. During 2010-2011 summative reports in Social Studies, Art, Music, Drama, and Technology will be presented to the School Board.

The CIA work has been challenging, rewarding, informative, reflective, and, most of all, has resulted in plans that will lead Cape Elizabeth student learning in the 21st century. My very special thanks to the staff, administrators, School Board members, and consultants who have and will continue to provide guidance as this work progresses.

Those who have participated in the CIA work over the past three years have been Linda Alfiero, Janet Amberger, Tom Eismeier, and Marianne Harrington from Pond Cove; Joanne Bearor, John Casey, Steve Connolly, Jamie Michaud, and Steve Price from the Middle School; Carrie Apanovitch, Troy Henninger, Gretchen McNulty, Angela Schipani, Jeff Shedd, and Joel Shroder from the High School; Domnic DePatsy, Alan Hawkins, Shari Robinson, and Sarah Simmonds from the school district; and Trish Brigham, Karen Burke, and Rebecca Millett from the School Board. 

                   Alan H. Hawkins, Superintendent of Schools

The Teaching and Learning Committee of the Cape Elizabeth School Board

The Mission of the Teaching and Learning Committee is to:

  • Work with the Curriculum Instruction Assessment Committee in guiding the development and review of our curricular goals as outlined in the District’s CMP.

  • Inform and direct the Board’s Annual Approval of Learning Goals, in support of our educational mission

  • To guide the Board in periodic Assessment of progress

  • To assure work is being communicated to the greater community

  • To assure a budget process driven by these goals

Teaching and Learning Curriculum Workshops

It is our objective that these workshops will provide a clearly delineated explanation of program and associated costs and value. This information should:

  • Help the board make sound budgetary decisions that support learning goals

  • Inform the board so we may effectively fulfill our responsibility to approve curriculum

  • Inform the board so that we can explain to the community the costs associated with their educational dollars.

Curriculum Management Plan (CMP)

Rationale for Curriculum Management Plan In keeping with the goals and objectives of Cape Elizabeth’s Future Directions Plan, we will create, use, and maintain a plan for curriculum development and review. As stated in the Maine Department of Education’s Guidelines for The Curriculum Development and Review Plan: 

The purpose of the Curriculum Development and Review Plan is to establish a process through which curriculum is developed, implemented, reviewed, evaluated, and revised on a regular cycle. This process should ensure that: 

• the curriculum helps the district realize its vision for educating its young people; 
• there is a method to achieve K –12 alignment of curriculum, instruction and assessment to the Maine’s Learning Results [in addition to national and local standards]; and 
• all students have meaningful and reasonable opportunities to learn, achieve and demonstrate the body of knowledge and skills represented in Maine’s Learning Results [in addition to national and local standards]

Cape Elizabeth Curriculum Management Plan 2008 - 1.5 MB PDF Document

English Language Arts (ELA)

As the administrative leader of the ELA K-12 Coordinating Committee, I am pleased to present the following report to the School Board analyzing the State of English Language Arts K-12 in Cape Elizabeth. Committee members were Linda Alfiero from Pond Cove, Jamie Michaud from the Middle School, Joel Shroder from the High School, Angela Schipani, Literacy Teacher at the High School, and Ginger Raspiller, Achievement Center Coordinator at the High School. In preparing this report, the committee members learned a lot. We have identifed what we perceive as strengths, weaknesses and future directions for our program based on student results and current curriculum. We have already begun following on the report recommendations at all levels, most notably with a visit to the Wayland, Massachusetts schools to examine how they organize for literacy instruction K-6 and the system of assessments they use to guide their own understanding of how their students are doing. We hope this is report is helpful to the Board and to the public in understanding where we are and where we believe we need to go.

Jeff Shedd

 Cape Elizabeth ELA Plan

Literacy Task Force Final Report (November 30, 2010)

Presentation to the School Board (video 11/30/10)

World Language (WL)

As the leader of the Modern Languages K-12 Coordinating Committee, I am pleased to present the following report to the School Board analyzing the state of Modern Languages K-12 in Cape Elizabeth. This report was truly a group effort as every member of the department contributed to its creation. Preparing this document gave the department the opportunity to reflect deeply on the strengths and weaknesses of our program. Through the process we have also identified a future direction for the program that is based on student results and a newly redefined curriculum. Currently, the department is moving forward along the path outlined in the district curriculum management plan. Teachers in grades 3-8 are working on completing course templates, and high school teachers are working on aligning assessments with the recently approved priority and secondary goals. We hope this report is helpful to the Board and to the public in understanding where we are and where we believe we need to be.

 Angela Schipani


As the administrative leader of the Guidance K-12 Coordinating Committee, I am pleased to present the following report to the School Board analyzing the State of Guidance in Cape Elizabeth. Committee members were Belinda Snell, Sharon Merrill, and Brandy Lapointe from the High School, Kim Sturgeon and Gretchen McCloy from the Middle School, and Cindy Perkins and Bobbie Sheckart from Pond Cove. In preparing this report, the committee members learned a great deal about guidance from a K-12 perspective. We have identifed what we perceive as strengths, weaknesses and future directions for the guidance programs based on student needs and current perspectives. As we have examined how we organize for guidance services including direct instruction, the counselors have already begun working on some of the report recommendations at all levels. We hope this report is helpful to the Board and to the public in understanding where we are and where we need to go.

Alan H. Hawkins

K-12 Comprehensive and Developmental Guidance Report

C.E. Guidance Curriculum Goals Aligned to ASCA Nat'l Standards

ASCA (American School Counselor Assn) K-12 Guidance Goals

Implementing a Comprehensive School Counseling Program (presentation slides, from March 23, 2010)

Teaching & Learning Committee - Q & A 


The Cape Elizabeth Science Committee has constructed a State of the Schools Science Report to inform the community about the creation of an articulated K-12 curriculum.  This curriculum provides continuity and coherence among all grades and closely follows state and national standards.  Teachers are in the process of revising and creating local common assessments, as well as utilizing state, national and international data to inform teaching and learning.  The document demonstrates our commitment to providing Cape Elizabeth students with substantive experiential learning integrating science, technology, engineering, and mathematics.  

The science committee looks forward to an opportunity to dialogue with the community about the science in our schools, as we welcome feedback.  We willingly share our strengths and needs as a district and have charted a course to guide our future professional development, as always, with improved student learning as the target.

Steve Connolly

Science Goals

State of the Schools Science Report

Presentation to the School Board (video/October 26, 2010)


The Cape Elizabeth math committee is pleased to present the following state of the schools K-12 district mathematics report. All teachers at all three levels were involved in the compilation of this report. We are confident that this report is both comprehensive and informative and that it confirms the fact that Cape Elizabeth has a very strong mathematics program. Since our teaching culture has long been one based on continuing, on-going improvement we welcome your questions, comments and suggestions. Our conversations and future professional development work on mathematics curriculum, instruction and assessment can only benefit further when championed by the broadest possible range of input, knowledge and perspective.

John Casey


Follow this link for more information on the district's Technology Plan.

Gary Lanoie

Presentation to the School Board (video/January 25, 2011)

Social Studies

As we move toward a collaborative and aligned curriculum in our schools, there has been much research and discussion about the complexities involved in articulating a Social Studies Curriculum. At the national, state and local level it has become painfully apparent that the number of areas covered and the time span encompassed by the Social Studies --- politics, history, economics, sociology, geography etc., not to mention the important skills and abilities cultivated by the discipline --- run broad and deep. The inability of even the best and brightest to come to consensus about what is most important to teach is reflected in the lack of any excellent national external assessment. 
This report reflects intense deliberations and research about what is most important for our graduates to know and be able to do, as well as the scaffolding that must take place in order to get them there. It endeavors to support critical thinking, articulate communication and global mindedness.

Troy Henninger

Social Studies Report Intro
Cape Elizabeth Social Studies Report  (May 2011)
Social Studies Priority Learning Goals 
(May 2011)

Presentation to the School Board (June 2, 2011)

Visual and Performing Arts

K-12 Music Report (April 24, 2012)
K-12 Arts Report (April 24, 2012)

Health and Physical Education

K-12 Health and P.E. Report (May 22, 2012)
School Health Ed Guide (May 22, 2012)

Maine Learning Results for K-12 Health & Physical Education