Executive Summary for Mathematics

Purpose Statement

The K-12 Mathematics Curriculum is Easton, Redding, and Region 9’s (ER9) plan for instruction.  It provides the framework for what students need to know and be able to do in order to apply mathematics in a real world environment.

Guiding Principles

A set of guiding principles frames the mathematics curriculum to ensure that students will:

• Learn to value mathematics

• Be confident in their ability to do mathematics

• Communicate mathematically

• Reason mathematically

• Make connections between mathematics and other areas

Standards

The ER9 K-12 Mathematics Curriculum is based on a combination of standards developed by the National Council of Teachers of Mathematics (NCTM) in conjunction with the Connecticut Framework (Scroll down to Mathematics) for mathematics.  The primary expectations for students learning the content of mathematics in ER9 are that students will demonstrate mastery in a range of numerical, algebraic, geometric and statistical concepts.  In addition, students will demonstrate mastery in applying skills to formulate, analyze and solve real world problems in order to facilitate inquiry and the exploration of real-world phenomena.  These experiences will support students in the continued development and appreciation of mathematics as a discipline.

In association with these mathematics expectations, students will develop mastery in basic mathematical skills including the ability to:

• Apply number sense

• Add, subtract, multiply, and divide whole numbers, fractions, decimals, and integers

• Estimate results for a reasonable answer

• Understand and use ratios, proportions, and percents

• Make and use measurements in a variety of spatial representations

• Organize and interpret data that are presented in charts and graphs

• Apply basic algebraic and geometric concepts

The ER9 Mathematics Committee has laid out the NCTM standards at the various grade levels and categorized them according to three broad conceptual areas:

• Standards based on data and logic (classification, patterns, probability and statistics, graphs, and algebraic properties and functions)

• Standards based on spatial relationships (geometrical relationships, measurement, and time)

• Standards based on numerical relationships (place value and number concepts, counting, and comparing, addition and subtraction, multiplication and division, fractions, decimals, percents, and money)

These detailed standards listed for each grade level are closely aligned with the content standards found in Connecticut’s Framework for Mathematics.  The curriculum is presented at each grade level with the content and skills developmentally appropriate.  These are laid out in the Math Competency Grid (K-8) and the Math Competency Grid (9-12) developed by the teachers for each grade level.

The Curriculum

The Mathematics Committee designed the curriculum around the concept of a Learning Spiral.  Within the framework of the K-12 structure, mathematics concepts and skills are introduced and reinforced at specific grade levels.  Students have many opportunities to demonstrate mastery of these concepts of skills within increasingly complex learning environments.

The K-12 curriculum is designed to use grades K-3 as the developmental phase of learning where a number of mathematical concepts and skills are introduced, reinforced, and mastered.   As students move through grades 4 and 5, they continue to demonstrate mastery of developmentally appropriate concepts and skills.  In this K-5 phase, students complete common locally developed assessments aligned closely to mathematics standards designated for these initial years.  Students take the first Connecticut Mastery Test (CMT) in the fall of grade four.

Concepts and skills move from concrete to more abstract understandings as the student matures.  Instruction in grades 6-8 is designed to have students demonstrate mastery in mathematics concepts and skills through specific common assessments aligned closely with an agreed to set of mathematical standards for the middle grades.  In addition to the common assessments, students take the CMT’s in mathematics in the fall of grade six and eight.  Students who demonstrate mastery in basic math concepts and skills may qualify to take Algebra I in grade eight. 

When students enter the high school, they have available to them a challenging and varied assortment of courses based on their demonstrated mastery of basic math concepts and skills.  Students who have completed Algebra 1 at a high level of mastery can take Honors or Advanced Geometry.  The remaining students who have met mastery of basic concepts and skills can take Algebra at the Integrated Algebra 1 or Advanced Algebra 1 levels.  Students who need further assistance with mastering basic concepts and skills can take Pre-Algebra or General Math.  Students then follow a sequenced continuum of courses such as Geometry, Algebra 2, Analysis and Calculus or AP Statistics at various levels of sophistication.  There is also a sequence of practical/applied courses.  Even though there are levels of courses, students are placed in levels that are appropriate to their abilities and movement between the levels is common.  The Connecticut Academic Performance Test (CAPT) assesses all students in grade 10 and students who fail to meet the state goal can retake the assessment in grade 11 and grade 12.

Types of Instruction

Teachers use a variety of instructional strategies to deliver and build math concepts and skills with students.   These include directed instruction with the teacher working with the whole class to introduce a concept or skill and lead the students through guided practice putting problems on the board or by use of the overhead projector.  Sometimes students will work as pairs or in small groups and practice problems or explore math applications of the concepts and skills.  Students will do independent work by completing homework or by completing performance-based tasks applying the appropriate math concepts and skills to authentic situations.  Students commonly use computer and calculator technology to discover and/or investigate mathematical concepts as well as to practice and apply the concepts and skills developed in the classroom.  Teachers have developed Professional Handbooks with sample lessons aligned to the standards.  By linking to your son or daughter’s school and the appropriate grade or courses, you can examine sample lessons or find descriptions of learning activities that are generally used by math teachers.  You can access this information by clicking on one of the hyper links below.  At the school's Web page, click on curriculum and follow the path to the appropriate grade level.  If you choose to link to a school now, remember that you can return to this page by using your browser back button.

 SSES, RES, HKMS, JRMS, JBHS

Types of Assessment Directly Aligned to the Mathematics Curriculum

 Common Assessments

Teachers in ER9 have developed common assessments for each grade level to evaluate each student's progress with respect to the specific standards listed for the grade level or in the course of study.  Although the common assessments are used at all grade levels in each district, individual teachers and grade level teams have some flexibility as to when the common assessments are administered.  These assessments can appear in a variety of formats, i.e. quizzes, exams and performance-based applications of mathematics.  If you want to view samples of performance-based assessments, please click on the link to the Learner's Pallet and click again on Math Problem Solving.  This will take you to particular assessment instruments with samples of student work and how they have been evaluated against specific math standards.  There are a variety of scoring rubrics that are used:

• Task specific assessment criteria- where the task or assessment is broken down into several elements and the students are assessed on each element.  The teachers will often weight these elements based on the particular purpose of the task and the needs of the students.

• Analytic rubrics-where student progress is measured over time against multiple criteria using a numerical evaluation system of descriptors that indicate the level of quality for each content or skill area.

• Holistic rubrics- where the students are measured against a series of descriptive statements that indicate the student’s overall improvement in mathematics.

Throughout the assessment process, students are given the opportunity to reflect on their own progress relative to a particular task in math or improvement in math over time.  These self-reflections are important in helping students to set future learning goals.

Connecticut Assessment

In addition to these common assessments, the State of Connecticut assesses students on the various math skills through the administration of the CMT test at grades 4, 6, and 8.  Students take the CAPT test in the spring of grade 10 and may repeat it in grades 11 and 12, if they choose to achieve the goal standard that is set at a high level of mastery.

Recording Student Performance

Since the curriculum activities and assessments are closely aligned to specific mathematical concepts and standards, the teachers use a variety of recording devices to track each student's progress as measured against the standards.  These devices include:

• Math Recording Devices: with student performance noted

• CMT and CAPT scores in permanent records

• Other Standardized Testing in permanent records and report cards

• Assessments of Portfolios/Folders

Summary

The ER9 Mathematics Curriculum is consistently delivered in all grade levels and at each school.  It is aligned closely to state and national standards.  Teachers have developed some common approaches to instruction that are represented in sample lessons located at the school level of the Web site.  Students are assessed using an agreed upon set of assessments directly aligned to the content and skill standards appropriate to the grade level.  Although the common assessments are used at all grade levels in each district, individual teachers and grade level teams have some flexibility as to when the common assessments are administered.  As you explore different facets of the math curriculum, you may generate questions or feed back.  Please click on the Web master name below to communicate with us.

Back to Top

Revised: September 29, 2006.