understanding and applying mathematics standards for young children 7
game table may be very interested in finding enough plastic worms for
each of his friends’ fishing poles in the dramatic play area. Later, when
he has become more confident, he may apply the same concepts used in
quantifying the fishing bait to a game in the math center, especially if it’s
a fishing game.
What is universal design, and how does it apply to mathematics?
The concept of universal design originated in architecture to designate
designs that accommodated the broadest spectrum of possible users. The
term has become widely adopted in education to refer to inclusive learning
environments that support all learners, including those with specific dis-
abilities, as full participants (Salend 2008, 328–31). Universal design for
learning (often referred to as UDL) adheres to three important principles:
1. Instruction should provide multiple ways for students to
2. Students should have many different means to demonstrate
what they know.
3. Educators should employ many different methods to engage
In preschool and kindergarten classrooms, well-designed math activities
are often open-ended, so they already accommodate a wide range of devel-
opmental levels. For example, a game in which children roll a die to deter-
mine how many counters to take supports children at three distinct levels
of thinking: (1) global, in which children know that they need to take some
counters and may distinguish between a few and a lot; (2) one-to-one cor-
respondence, in which children align one counter with each dot on the die;
and (3) counting, in which children count the dots to determine how many
counters to take. Other children might play the game with two dice and
add the quantities. The important point is the material itself is designed to
accommodate this range of students.
Integrating mathematics throughout the classroom provides further sup-
port for UDL principles. Children can engage in mathematical learning
and communicate what they understand through art, music, building, and
other play activities.