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Curriculum Standards

Devon Radant

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As an elementary teacher, I am responsible for teaching all subject areas.  While I enjoy various aspects of all the content areas, I love teaching math because it’s so hands-on.  Growing up, math was never a favorite subject of mine so as I teacher I try to make math as fun as possible.  I also try to take the frustration away by simplifying it as much as I can.  I always try to offer students a concrete model of what we’re working on and give them multiple strategies for working each kind of problem.  I love the flexibility that elementary math offers.  Because of this, I chose to look into math standards for my discussion of curriculum standards.  Currently, I am teaching in Georgia.  However, I am moving to Indiana this summer and will hopefully be teaching there in the fall.  Therefore, I am very interested in comparing their third-grade curriculum with the current curriculum I am using. 

To begin, I looked at the National Council for Teaching Mathematics’ set of standards for 3-5th grades.  The NCTM stresses three major areas in mathematics for the upper elementary grades.  Those areas are multiplicative thinking, equivalence, and computational fluency.  They also suggest having a mathematics specialist for these age children.

In Gwinnett County where I teach, we use the Academic Knowledge and Skills as the basis for our curriculum.  The standards for third grade are included below.  Some important topics covered are: place value, money, time, multiplication, division, graphs and tables, geometry, measurement, fractions, and decimals.  We also continue to work on computation, estimation, and probability.  Most students come into third grade not knowing their multiplication tables.  This is a main focus of our mathematics instruction for several weeks.  Multiplication and division are relatively new concepts to students, whereas much of the remaining curriculum is building upon concepts they have learned in previous grades.

When comparing the NCTM and Gwinnett’s curriculum to the Indiana Standards, there seems to be a lot in common.  Indiana has divided their standards for students in Kindergarten-8th grade and students in high school.  While this is a more broad perspective when looking at curriculum, there are many similarities between the three, especially when you consider the areas of major emphasis.  Visit http://www.indianastandards.org/files/math/math_scope.pdf to see the scope and sequence of Indiana’s standards for each grade level.  There are few discrepancies between my current third-grade math curriculum and the standards listed here. 

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National Council for Teaching Mathematics offers the following standards for grades 3-5 (material taken directly from their Website http://www.nctm.org) 

Overview: Standards for Grades 3–5

Students enter grade 3 with an interest in learning mathematics. Nearly three-quarters of U.S. fourth graders report liking mathematics, seeing it as practical and important. If mathematics continues to be seen as interesting and understandable, students will remain engaged. If learning becomes simply a process of mimicking and memorizing, students' interest is likely to diminish.

Interwoven through the Content Standards for grades 3–5 are three crucial mathematical themes--multiplicative thinking, equivalence, and computational fluency. The focus on multiplicative reasoning develops knowledge that students build on as they move into the middle grades, where the emphasis is on proportional reasoning. As a part of multiplicative reasoning, students in grades 3–5 should build their understanding of fractions as a part of a whole and as division.

The concept of equivalence helps students learn different mathematical representations and offers a way to explore algebraic ideas. Students should develop computational fluency-- efficient and accurate methods for computing that are based on well-understood properties and number relationships. For example, 298 42 can be thought of as (300 42) – (2 42), or 41 16 can be computed by multiplying 41 8 to get 328 and then doubling 328 to get 656. When these three themes are emphasized, the expectations for grades 3–5 reinforce two major objectives of mathematics learning: making sense of mathematical ideas and acquiring the skills and understandings needed to solve problems.

In grades 3–5, algebraic ideas emerge and are investigated by children. For example, students in these grades are able to make a general statement about how one variable is related to another variable. If a sandwich costs $3, you can figure out how many dollars any number of sandwiches cost by multiplying that number by 3. In this case, students have developed a model of a proportional relationship: the value of one variable is always 3 times the value of the other, or C = 3 n.

Given their central role in shaping the mathematics learning of students in these grades, teachers must recognize the need to develop mathematical expertise. Some elementary schools identify a "mathematics teacher-leader," who can support other teachers in their instruction and professional development. Other schools use "mathematics specialists" at the upper elementary grade levels, which assume primary responsibility for teaching mathematics to larger groups of students. Each of these models needs to be explored to enhance the mathematics education of students in grades 3–5.

 

 

Gwinnett County’s 3rd Grade Mathematics Academic Knowledge and Skills (AKS).  (See http://www.gwinnett.k12.ga.us/aks.nsf/pages/AKSHOME for more information).

 

Mathematics

 

Curricular goals interwoven throughout the mathematics program are that all students will:

 

A - Estimation

 

B - Number Sense and Numeration

 

C - Whole Number Concepts and Computation

 

D - Geometry and Spatial Sense

 

E - Measurement

 

F - Statistics and Probability

 

G - Fractions and Decimals

 

H - Algebra

 

 

 

 

Indiana’s Academic Standards (found at http://www.indianastandards.org/ ) are as follows:

 

Standards Summary

The standards describe a connected body of mathematical understandings and competencies and are a comprehensive foundation that all students should learn. They describe the mathematical understanding, knowledge, and skills that students should acquire from
Kindergarten through Grade 8 Standards

Number Sense
Number sense allows students to combine or decompose numbers naturally and solve problems using knowledge of the base-ten system and the relationships among operations.

Computation
Students should become fluent at performing computations in different ways, including mental calculations, estimation, and paper-and-pencil calculations using mathematically sound algorithms.

Algebra and Functions
Algebra involves the understanding of patterns, relations, and functions, as well as the representation and analysis of mathematical situations and structures using algebraic symbols.

Geometry
Geometry involves relationships among shapes and their properties and offers ways to interpret our physical environment. Geometry allows the development of students’ reasoning skills.

Measurement
Students should understand measurable attributes of objects and the units, systems, and processes of measurement, as well as be able to apply appropriate techniques and formulas to determine measurements.