Mathematics Program Guide

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Summer, 2001

 

 

Table of Contents

 

Mathematics Renewal Committee

Philosophy

 

Background Information      

Beliefs for Mathematical Thinking

Major Trends in Mathematics Education..................................................... B1 – B2

Balanced Math.............................................................................................. B-3

Important Concepts...................................................................................... B-4

 

Elementary and Middle School Outcomes

Kindergarten ................................................................................................ O-1 – O-4

Grade 1.......................................................................................................... O-5 – O-12

Grade 2.......................................................................................................... O-13 – O-20

Grade 3.......................................................................................................... O-21 – O-30

Grade 4.......................................................................................................... O-31 – O-39

Grade 5.......................................................................................................... O-40 – O-46

Grade 6.......................................................................................................... O-47 – O-57

Grade 7.......................................................................................................... O-58 – O-64

Grade 8.......................................................................................................... O-65 – O-68

 

Elementary and Middle School References

CMT Vocabulary........................................................................................... R-1 - R-3

CMT Objectives........................................................................................... R-4 - R-14

Information about Investigations.................................................................. R-15 - R-27

Information about Connected Mathematics................................................. R-28 - R-32

 

Elementary and Middle School Instructional Resources by Grade

 

Elementary and Middle School Assessments

Plan for 2001-2002

Student Assessment Summary Records

 

High School Outcomes         

Algebra I.............................................................................................. O-69 – O-70

Algebra II............................................................................................. O-71 – O-74

Advanced Algebra and Trigonometry................................................. O-75 – O-76

Geometry............................................................................................. O-77

Pre-Calculus......................................................................................... O-78 – O-79

Calculus................................................................................................ O-80 – O-82

Integrated Math I................................................................................ O-83

Integrated Math II............................................................................... O-84 – O-85

Integrated Math III............................................................................. O-86

 

 

 

 

 

 

 

Contributors to Development of the Math Program Guide

 

 

 

Claudia Albert, Assistant Superintendent, Central Office

Joyce Birtcher, Stonington High School

Robin Bressette, Deans Mill School

Ann Crouse, West Vine Street School

Natalee Denard, Mystic Middle School

Susan Dumas, Mystic Middle School

Leslie Fleury, Math Committee

Sandra Grasso, West Vine Street School

Betty Henry, West Vine Street School

Charles Henzy, Board of Education

Debbie Janes, Deans Mill School

Joseph McKernan, Stonington High School

Michael McLaughlin, West Broad Street School

Francis McSweeney, Stonington High School

Leah Pittle, Pawcatuck Middle School

Susan Prentis, Pawcatuck Middle School

Sharleen Rustici, Stonington High School

 

 

 

 

 

 

 

 

 

 

 

 

 

Philosophy

 

Numeracy and literacy are of equal importance. Numeracy is the knowledge, skills and dispositions that enable students to represent physical events with data, reason, communicate mathematically and make connections within mathematics and to other content areas and to the world in order to solve problems.* The teaching of mathematics must focus on building a conceptual understanding of number; the basic four operations; fractions, decimals, and percents; spatial reasoning; and, data analysis and probability. Conceptual understanding is the goal of instruction and should be developed by students' active involvement in problem solving and opportunities to apply mathematical principles to real-world situations. Mathematical discourse that encourages students to explain their mathematical thinking is essential. This ability to speak and write about mathematics insures that the learning of mathematics, includes, but goes beyond, computational ability. Mathematical concepts should be introduced in a developmentally appropriate sequence and taught to mastery. Assessment must be ongoing and used to inform instruction as well as summative and used to ascertain mastery.

 

All students should be provided, through the Stonington Public Schools' Mathematics Program, with the learning experiences that will insure that:

 

"By the end of the 12th grade, students will apply proficiently a range of numerical, algebraic, geometric and statistical concepts and skills to formulate, analyze and solve real-world problems; to facilitate inquiry and exploration of real-world phenomena; and to support continued development and appreciation of mathematics as a discipline."**

 

 

 

 

Quoted from:

* Connecticut Guidelines for the Issuance of CEUs Required for Certification"

** Connecticut's Common Core of Learning

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Beliefs and Mathematical Thinking

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MAJOR TRENDS IN MATHEMATICS EDUCATION

 

 

How are our students doing?

 

·                    NAEP

·        Updated Testing – Increase of about one grade level between 1990 and 1996 of average placement on grade 4, 8, and 12 tests (CT students ranked #1 in the US)

·        Long Term Testing – Performance for today’s students (on the same test, emphasizing traditional concepts) significantly higher than students of 1973

 

·                    TIMSS

·        Comparing Results to Other Countries

·        4th Graders – Above Average

·        8th Graders – Slightly Below Average

·        12th Graders – Near the Bottom

·        Comparing Curriculum and Instruction to Other Countries

·        Too much focus on arithmetic skills

·        Too much review

·        Not enough focus on important topics for each grade

 

What is school mathematics?

 

·        Recommended Changes

 

·        K-12 – From emphasis on numerical facts and operations to emphasis on problem solving and reasoning

·        K-12 – Increased teaching of geometry, data analysis and algebra at all grades and for all students

·        College Level – Broaden Mathematics departments to Mathematical Sciences departments to reflect growth in statistics, research, application of math in other areas and advances in technology

 

 

·        Other Recommendations

 

·        Have students conjecture, test, revise and justify their actions, broadening the concept of what is part of mathematics

·        Clearly identify the concepts and processes that students need to know and be able to do

 

 

 

B-1

 

 

·                    How should instruction be conducted?

 

·        “Knowing” mathematics is “doing” mathematics.

·        Instruction should use a broad range of instructional practices that go beyond teacher-directed learning and include active student construction of meaning.

·        Teachers must be able to weave together in-depth knowledge of mathematics and “best practice” teaching methods.

 

 

·                    How should students be assessed?

 

·        In a variety of ways

·        To collect information for the purpose of improving student performance (diagnosing strengths and weaknesses to design instruction) and for the purpose of ranking and grading

·        To make math make sense to students

·        By crossing discrete categories

·        Through the use of open-ended problems that require students to construct responses (essay questions in math)

·        Using rubrics to evaluate responses

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

B-2

 

 

 

 

 

“Balanced” Mathematics

 

 

 

Valuing Traditions

AND

Embracing New Directions

 

 

 

Skills

AND

·        Problem Solving

·         

Use of basic operations

AND

·        Understanding of basic operations

·         

Learning the vocabulary of math

AND

·        Understanding processes, recognizing essential information and breaking down complex problems

 

Exposure to standard algorithms

AND

·        Use of multiple strategies to solve problems

 

Facility with basic facts

AND

·        Writing in math to justify answers and explain solutions

 

Periodic testing to verify what is or is not understood

 

AND

Continual, daily assessment to diagnose and guide instruction

·        Curriculum built on previously taught concepts

AND

·        Fewer concepts each year, but taught in greater depth and to a mastery level

 

·         Course grouping (late in middle school and in high school)

 

AND

·        Flexible grouping at all levels

·        Paper and pencil

AND

·        Variety of teaching/learning tools including technology

 

·        Algebra and advanced mathematics

AND

·        Starting earlier and for more students

 

·        Math texts

AND

·        Applications of math in "real life" situations

 

 

 

 

 

 

B-3

 

 

 

 

 

 

+  -  x  ¸  +  -  x  ¸  +  -  x  ¸  +  -  x  ¸  +  -  x  ¸  +  -  x  ¸  +  - 

 
 

 

 

 

 


Additional Important Concepts in Renewing the Math Curriculum

 

 

 

·                    Four steps need to be considered in teaching math:

 

Understanding the Concept

 

Developing the Needed Skills

 

Putting the Concept in Context (Application)

 

Using the Knowledge of the Concept to Learn More

 

·                    Concepts need to be presented in a developmentally-sound sequence.

 

·