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.
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.A.ECa: Count with understanding and recognize “how many” in small sets up to 5.
6.A.ECb: Use subitizing (the rapid and accurate judgment of how many items there are without counting) to identify the number of objects in sets of 4 or less.
6.A.ECc: Understand and appropriately use informal or everyday terms that mean zero, such as “none” or “nothing”.
6.A.ECd: Connect numbers to quantities they represent using physical models and informal representations.
6.A.ECe: Differentiate numerals from letters and recognize some single‐digit written numerals.
6.A.ECf: Verbally recite numbers from 1 to 10.
6.A.ECg: Be able to say the number after another in the series up to 9 when given a “running start,” as in “What comes after one, two, three, four…?”.
6.B Add and subtract to create new numbers and begin to construct sets.
6.B.ECa: Recognize that numbers (or sets of objects) can be combined or separated to make another number.
6.B.ECb: Show understanding of how to count out and construct sets of objects of a given number up to 5.
6.B.ECc: Identify the new number created when small sets (up to 5) are combined or separated.
6.B.ECd: Informally solve simple mathematical problems presented in a meaningful context.
6.B.ECe: Fairly share a set of up to 10 items between two children.
6.C Begin to make reasonable estimates of numbers.
6.D Compare quantities using appropriate vocabulary terms.
Benchmarks: Goal 7
Goal 7: Explore measurement of objects and quantities.
7.A Measure objects and quantities using direct comparison methods and nonstandard units.
7.A.ECa: Compare, order, and describe objects according to a single attribute.
7.A.ECb: Use nonstandard units to measure attributes such as length and capacity.
7.A.ECc: Use vocabulary that describes and compares length, height, weight, capacity, and size.
7.A.ECd: Begin to construct a sense of time through participation in daily activities.
7.B Begin to make estimates of measurements.
7.C Explore tools used for measurement.
7.C.ECa: With teacher assistance, explore use of measuring tools that use standard units to measure objects and quantities that are meaningful to the child.
7.C.ECb: Know that different attributes, such as length, weight, and time, are measured using different kinds of units, such as feet, pounds, and seconds.
Benchmarks: Goal 8
Goal 8: Identify and describe common attributes, patterns, and relationships in objects.
8.A Explore objects and patterns.
8.A.ECa: Sort, order, compare, and describe objects according to characteristics or attribute(s).
8.A.ECb: Recognize, duplicate, extend, and create simple patterns in various formats.
8.B Describe and document patterns using symbols.
Benchmarks: Goal 9
Goal 9: Explore concepts of geometry and spatial relations.
9.A Recognize, name, and match common shapes.
9.A.ECa: Recognize and name common two- and three-dimensional shapes and describe some of their attributes (e.g., number of sides, straight or curved lines).
9.A.ECb: Sort collections of two‐ and three‐dimensional shapes by type (e.g., triangles, rectangles, circles, cubes, spheres, pyramids).
9.A.ECc: Identify and name some of the faces (flat sides) of common three‐dimensional shapes using two-dimensional shape names.
9.A.ECd: Combine two-dimensional shapes to create new shapes.
9.A.ECe: Think about/imagine how altering the spatial orientation of a shape will change how it looks (e.g., turning it upside down).
9.B Demonstrate an understanding of location and ordinal position, using appropriate vocabulary.
Benchmarks: Goal 10
Goal 10: Begin to make predictions and collect data information.
10.A Generate questions and processes for answering them.
10.A.ECa: With teacher assistance, come up with meaningful questions that can be answered through gathering information.
10.A.ECb: Gather data about themselves and their surroundings to answer meaningful questions
10.B Organize and describe data and information.
10.B.ECa: Organize, represent, and analyze information using concrete objects, pictures, and graphs, with teacher support.
10.B.ECb: Make predictions about the outcome prior to collecting information, with teacher support and multiple experiences over time.
10.C Determine, describe, and apply the probabilities of events.
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.