Learning Leader

Early Mathematics

May 2021

Relevant Research

With the growing importance of STEM, recent studies that test the impact of early math curricula show that devoting time to specific math activities as part of the school curriculum is effective in improving children’s math learning before and at the beginning of elementary school.

Research evidence also suggests that children’s math achievement when they enter kindergarten can predict later reading achievement; foundational skills in number and operations may set the stage for reading skills (Claessens et al., 2009).

Informal Mathematics

Young children have the ability to learn mathematical terms and language through everyday experiences.

Research indicates that young children have a strong, intuitive understanding of informal mathematics. Toddlers understand the word “more”, enjoy lining up cars into a straight line to create a row, sort their goldfish crackers by color, and learn how to turn a puzzle piece to fit. These are examples of informal math activities that naturally occur in early childhood.

In addition, children may use math spontaneously during play with shape recognition, rotation of three dimensional shapes, and manipulating shapes to create structures. These play experiences can help children make strong mathematical connections and knowledge that can provide the right foundation to learn formal math.

Teacher assisting young students building with plastic blocks

Young Children are Natural Learners

Teachers should want to offer activities that are playful because young children are natural learners. They are inquisitive, curious, enjoy manipulating items, and experimenting with materials. Renowned Swiss psychologist, Jean Piaget, theorized that the experience creates dissonance, a mental conflict that the child seeks to resolve. As the children resolve their cognitive dissonance, they develop and assimilate their own knowledge.

Exposure to math opportunities should occur throughout the day. For example, snack time can provide real world math learning and a chance to practice subitizing. The teacher may spoon a small amount of goldfish crackers on the child’s plate to give them a chance to state how many crackers they see without counting.

How to Teach Mathematics

Math achievement of young children can be improved by placing more emphasis on math instruction throughout the school day.

When early educators understand that young children’s understanding of mathematics is built upon informal knowledge about quantity, then they can observe the children to look for opportunities to build upon that understanding and intentionally create opportunities and activities for children.

Adults can use children’s interest in quantity to begin communicating math-related ideas which will help foster children’s growth and interest in math. Our focus should be on helping children learn to problem-solve, ask thoughtful questions, use math language during real life moments, and have hands-on time to use materials throughout the day. Understanding the recommendations on how to teach math can help teachers be more effective in their instruction with the children.

Small group of students working with a counting frame

Five Recommendations for Teaching Math to Young Children

The Institute of Education Sciences (2013) has provided five recommendations for teaching math with young children that can help provide the essential foundation needed for students’ future success in school, and consider ways to integrate math language and materials into preschool classrooms.

  1. Teach number and operations using a developmental progression.
    Teachers should provide opportunities for children to practice subitizing, which is small number recognition. Next, promote accurate one-to-one counting as a means of identifying the total number of items in a collection. Once children can recognize or count collections, teachers can provide opportunities for children to use number words and counting to compare quantities. Then, encourage children to label collections with number words and numerals. Once children develop these fundamental number skills, teachers can encourage them to solve basic problems.
  2. Teach geometry, patterns, measurement, and data analysis using a developmental progression.
    This recommendation focuses on teaching geometry, patterns, measurement, and data analysis using a developmental progression, which includes a large variety of objectives to on work with the children.
  3. Use progress monitoring to ensure that math instruction builds on each child’s developmental progression.
    Progress monitoring is used to tailor instruction and build on what children know. The panel recommends that instruction include first determining children’s current level of math knowledge based on a developmental progression and then using the information about children’s skills to customize instruction. Monitoring children’s progress throughout the year in the beginning of year, middle of year, and end of the year can then be an ongoing part of math instruction where instructional goals and methods can be adjusted with the child’s existing math knowledge or level of understanding.
  4. Teach children to view and describe their world mathematically.
    Teachers should teach children to view and describe their world mathematically. This recommendation can be implemented by being aware of math language that can be used informally throughout the day and by encouraging the children to use informal methods to represent math concepts, processes, and solutions. Teachers can also help children link math vocabulary, symbols, and procedures to their informal knowledge or experiences by asking open-ended questions. This prompts children to apply their math knowledge and encourages them to recognize and talk about math in everyday situations.
  5. Dedicate time each day to teaching math, and integrate math instruction throughout the school day.
    Teachers should dedicate time each day to teaching math and integrating math instruction throughout the school day. Teacher planning for daily instruction should target specific math concepts and skills. One way to implement math throughout the day is for teachers to use books with math concepts during read alouds, highlight math during classroom routines and activities.

Teachers can help young children with foundational math concepts by providing engaging activities and helping children learn to use problem-solving skills. Building on children’s curiosity and imagination play an important role in mathematical development. Since math skills are used as part of everyday life, we know these are important skills for young children to begin developing.  As preschool teachers, you play a critical role in laying the foundation for children’s developing math skills. By providing materials in a math center for children to explore, by infusing math into everyday routines, and by planning focused math lessons, you can help lay the foundation for children’s future success in school and in life!


Claessens, A., Duncan, G. J., & Engel, M. (2009). Kindergarten skills and fifth-grade achievement: Evidence from the ECLS-K. Economics of Education Review, 28(4), 415–427.

Institute of Education Sciences, National Center for Education Evaluation and Regional Assistance, What Works Clearinghouse. (2013, November). Teaching Math to Young Children Practice Guide. https://ies.ed.gov/ncee/wwc/Docs/PracticeGuide/early_math_pg_111313.pdf

Teaching Tips

Using the Small Grouping Tool

We know from research that early identification of learning needs and grouping children according to those needs is known to maximize instructional impact. CLI Engage provides a feature called the Small Grouping Tool that divides children into small groups based on their assessment results. The tool sorts through the assessment results and provides a list of children that have not reached the satisfactory level for each skill. The children grouped by the tool are identified for the teacher as needing more practice with certain skills and would benefit from small group instruction.

Teachers can click on the “View Groups” button located on the student assessment screen to see the identified small groups and targeted intervention activities from the CIRCLE Activities Collection. Below is an example of the tool’s automatically selected results.

Small Grouping Tool report for Counting Sets

The links to recommended activities are listed in the “Classroom Activities” section. The text is hyperlinked directly to the CIRCLE Activity Collection to make it easy to access the lessons that target specific skill areas. Another way to add intentionality with children’s learning is to customize new groups to offer more support for them. As you work with the children, you can add observational notes to any group by clicking on the bubble button that will save the notes for future reference.

When analyzing your assessment data consider the tools that are available to help you develop a plan for children who are identified as in need of intervention:

  • Small Grouping Tool located within the assessment
  • CIRCLE Activity Collection
  • CLI Engage online professional development for teachers

Recommended Resources



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