# Mathematics

## Foster early math skills in your TK classroom

In your Transitional Kindergarten (TK) classroom, mathematics can be taught—and discovered—in the everyday environment of your young learners. For example, students can learn new concepts and relationships of numbers and quantities as they recite numbers in order, count objects, or visually compare groups of objects and express if they are the “same” or “more.” They can learn about measurement by comparing the length, weight, or capacity of objects by using words such as bigger, longer, heavier, or taller. Young children learn these important foundations of mathematics while engaging in imaginative play, exploring the environment and materials, making discoveries, or interacting with teachers or other adults.

“Mathematics learning at this level must be active, rich in natural and mathematical language, and filled with thought-provoking opportunities. Students respond to the challenge of high expectations and mathematics should be taught for understanding rather than around preconceptions around children’s limitations. This does not mean abandoning children’s ways of knowing and representing; rather it is a clear call to create opportunities for young students to learn new, important mathematics in ways that make sense to them.”1

### Elements of Mathematics Instruction

Instructional time in TK should focus on the following content:2

#### Numbers and Operations

• Develop an understanding of whole numbers, including concepts of correspondence, counting, cardinality, and comparison. Your TK students should know number names, the count sequence, and how to count to tell the number of objects.
• Represent, compare, and order whole numbers and how to join and separate sets. Students should compare numbers, understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

#### Geometry

• Identify shapes and describe spatial relationships.
• Describe shapes and space. TK students should analyze, compare, create, and compose shapes.

#### Measurement

• Identify measurable attributes and compare objects by using these attributes. Students should describe and compare measurable attributes.
• Order objects by measurable attributes.

## Role of the Teacher

As a teacher, you can foster the development of early mathematical skills by providing environments rich in language, where thinking is encouraged, uniqueness is valued, and exploration is supported. Teachers support young children’s diligence and mathematical development when they direct attention to the math children use in their play, challenge them to solve problems, and encourage their persistence. It is also important to incorporate strategies that connect new words with concept development for children who are Dual Language Learners (DLLs), aligning their English language development goals with support for the development of mathematical language and ability.

Encourage children’s strategies and build on them as ways of developing more general ideas and systematic approaches. By asking questions that lead to clarifications, extensions, and the development of new understandings, you can facilitate children’s mathematics learning. Ensure interesting problems and stimulating math conversations are a part of each day, and mathematical concepts are integrated throughout all learning centers. It is also important to honor individual children’s thinking and reasoning and use formative assessment to plan instruction that allows your students to connect new math skills with what they know.

It is imperative to provide all students with high-quality math instruction in a way that respects both mathematics and the nature of young children. This instruction should build on and extend students’ intuitive and informal mathematics knowledge and should take place in environments that encourage students to be active learners and accept new challenges.

The following principles can provide guidance for effective classroom practices in supporting early math development: (Adapted from the California Preschool Foundations Curriculum Framework Volume 1, 2010, p. 233-236)

• Build on children’s natural interest in mathematics and their intuitive and informal mathematical knowledge.
• Encourage inquiry and exploration to foster problem solving and mathematical reasoning.
• Use both intentionally planned experiences and everyday activities as natural vehicles for developing children’s mathematical knowledge.
• Provide a mathematically rich environment, which includes manipulatives, blocks, puzzles, number books, and board games, and incorporate the language of mathematics throughout the day.
• Use literature to introduce mathematical concepts then reinforce with hands-on activities.
• Establish a partnership with parents and other caregivers in supporting children’s learning of mathematics.

## Eight Mathematics Teaching Strategies

​​The teaching strategies below give concrete approaches for mathematics instruction in your classroom. They are designed to guide developmentally appropriate TK instruction, moving your students along a continuum of learning by bridging the Preschool Learning Foundations with the Kindergarten Common Core.

Strategy 1: Number Sense of Quantity and Counting
Strategy 2: Number Sense of Mathematical Operations
Strategy 3: Measurement
Strategy 4: Shapes
Strategy 5: Patterning
Strategy 6: Problem Solving
Strategy 7: Classification
Strategy 8: Integrated Approaches for English Language Development and Family Engagement