Mathematics

The domain of Mathematics includes Preschool Benchmarks in: Sense of Numbers, Identification of Relationships in Objects, Concepts of Geometry, and Analysis of Data Information

Young children are natural mathematicians, fascinated by what is “bigger,” wanting “more” of their favorite things, and very concerned with whether the distribution of those things is “fair.” These kinds of observations of the world are mathematical at their core because they are about quantity and size. Preschool children’s experiences of the world are equally affected by ideas about spatial relationships and shape. They explore the concepts of geometry whether they are maneuvering through the living room, building a block tower, or choosing a puzzle piece. Such daily experiences are packed with mathematical concepts that fascinate and challenge young thinkers and can eventually prompt analytical thought, growing precision, and abstraction.

The major mathematical task of early childhood is to coordinate these natural interests and understandings with the beginnings of a useful knowledge of conventional math concepts and skills. Unfortunately, for many children, meaningful mathematical thinking is displaced too early by an emphasis on math “facts” (such as 2 + 2 = 4) and math “procedures” about what to do when. Too many young children learn how to say the counting words up to 20 without being able to successfully count out a set of five objects. While the procedures—such as the order of the count words—must be learned, it is crucial that they be meaningfully connected to things children understand and care about, such as “how many” children can fit at the play dough table or “how many” slices of apple they can have at lunch.

To effectively build on young children’s innate interests in quantity and space and move their thinking in conventional mathematical directions, the most important thing teachers can do is talk with them, helping them “see” the math in the world. When adults provide rich language to mathematical experiences, such as “thicker” or “longer” rather than simply “bigger,” children understand that there are many different types of attributes that can be compared and measured. When teachers ask, “How do you know the door looks like a rectangle?” they support children’s budding conception of geometric rules, such as a rectangle having four sides. When teachers count with one-to-one correspondence to find out “how many children are in the group today,” they demonstrate the use of whole numbers in a way that is very real to children and matters to them. These sorts of interactions, based on experiences that are a natural part of children’s everyday lives, are the best way to ensure the development of beginning mathematical understandings that inspire children to keep learning.

The mathematics standards in the IELDS are more detailed and developmentally informed than those in the previous version, reflecting our growing understanding of how children’s mathematical thinking develops during early childhood. We hope they will provide a useful guide to the kinds of mathematics experiences preschool children ought to have prior to their kindergarten year.

Math is a big part of every day in Ms. O’Brien’s Preschool for All classroom. She knows that understanding quantity for preschoolers goes far beyond reciting counting words, and she provides many opportunities for children to count in meaningful situations. Each day, the group counts how many children are present and how many are absent, how many steps from the door of their classroom to the playground, and how many plates and napkins are needed to set a table for snacks. They say the counting words in both English and Spanish. She provides many manipulatives that encourage children to use one-to-one correspondence as they sort, categorize, order, and build to create groups of objects and to connect numbers to quantities of objects. Shapes are everywhere in her preschool classroom, and Ms. O’Brien takes advantage of every opportunity she can to name the shapes for the children in both English and Spanish and to encourage them to explore, manipulate, and build with them. The children have also learned to love taking surveys. Ms. O’Brien has created clipboards with Yes/No graphs on them for children to interview each other about favorites. She loves to hear a child ask another, “¿Te gusta helado de chocolate?” (“Do you like chocolate ice cream?”) and see him note the answer under the Yes or No column. She makes sure to follow up on the results of his survey and have him present it to the class at large group time. Ms. O’Brien finds it easy to include math goals from the IELDS on her lesson plan for her play areas, daily routines, and group experiences because math is everywhere!

Benchmarks: Goal 6

 

Goal 6: Demonstrate and apply a knowledge and sense of numbers, including numeration and operations.

6.A Demonstrate beginning understanding of numbers, number names, and numerals.

6.B Add and subtract to create new numbers and begin to construct sets.

6.C Begin to make reasonable estimates of numbers.

6.D Compare quantities using appropriate vocabulary terms.

Benchmarks: Goal 8

 

Goal 8: Identify and describe common attributes, patterns, and relationships in objects.

8.A Explore objects and patterns.

8.B Describe and document patterns using symbols.

Notes

 

The Mathematics goals, standards, and benchmarks align with the following sections of the Kindergarten Mathematics Common Core:

  • Goal 6: Counting and Cardinality, 1-7, Operations and Algebraic Thinking, 1-6.
  • Standard 6.A: Counting and Cardinality, 1-7.
  • Benchmark 6.A.ECa: Counting and Cardinality, 4-5.
  • Benchmark 6.A.ECb: Counting and Cardinality, 4-5.
  • Benchmark 6.A.ECc: Counting and Cardinality, 3.
  • Benchmark 6.A.ECd: Counting and Cardinality, 3-4.
  • Benchmark 6.A.ECe: Counting and Cardinality, 3 & 7.
  • Benchmark 6.A.ECf: Counting and Cardinality, 1.
  • Benchmark 6.B.ECa: Operations and Algebraic Thinking, 1-5.
  • Benchmark 6.B.ECb: Operations and Algebraic Thinking, 1-2.
  • Benchmark 6.B.ECc: Operations and Algebraic Thinking, 1-4.
  • Benchmark 6.B.ECd: Operations and Algebraic Thinking, 4-5.
  • Standard 6.D: Counting and Cardinality, 6.
  • Goal 7: Measurement and Data, 1-3.
  • Benchmark 7.A.ECa: Measurement and Data, 2.
  • Benchmark 7.A.ECc: Measurement and Data, 1.
  • Goal 8: Measurement and Data, 1-3.
  • Benchmark 8.A.ECa: Measurement and Data, 1.
  • Goal 9: Geometry, 1-6.
  • Benchmark 9.A.ECa: Geometry, 1-2.
  • Benchmark 9.A.ECb: Geometry, 3-6.
  • Benchmark 9.A.ECc: Geometry, 2-5.
  • Benchmark 9.A.ECd: Geometry, 5-6.
  • Benchmark 9.A.ECe: Geometry, 4-6.
  • Standard 9.B: Geometry, 1.