Precursor Concepts
What are the precursor concepts?
Just as the foundation of a building anchors it in the earth and provides essential support for the growing structure, in the first three years of life children engage in a very fundamental way with concepts that anchor a child’s mathematical thinking and are essential for the growth of further mathematics.
We call these Precursor Concepts and each concept includes three key ideas. Precursor literally means “to come before,” and we believe that deep and meaningful engagement with these concepts must come before a child is ready to attend to the early mathematical Big Ideas in preschool.
Attributes
Are properties or qualities that allow us to describe and classify the world around us.
- We perceive attributes of the world around us through our senses.
- Attributes can be used to group.
- Language allows us to describe attributes with increasing precision.
Comparison
Is noticing sameness and difference.
- Comparison depends on recognizing attributes.
- Recognizing attributes makes it possible to notice sameness and difference.
- Noticing sameness and difference allows for matching, sorting, ordering and problem-solving.
Pattern
Involves rhythm, sequence, and regularity that allows for prediction.
- A pattern involves a set of defining elements.
- Regularity occurs when the defining elements recur in sequence.
- When a regular sequence begins, there is an expectation that it will include the defining elements.
Change
Means something becomes different.
- Change may be qualitative or quantitative.
- The difference may be the result of joining, separating, or of transforming.
- To respond to change, the difference between the initial condition and the changed condition must be recognized.
Beginning in the Earliest Years
We all know babies are born wonders! While they may look helpless, newborns arrive hard-wired to perceive quantity and magnitude as well as spatial relationships, regularity, and sequence. Projects we have that focus on the ages 0-3 are built around our Math All Around Me (MAAM) programs and philosophy.
Math All Around Me
These innate mathematical capacities in the earliest years only develop into specifically mathematical understandings and skills such as counting or creating patterns if they are nurtured by loving caregivers, using the highly effective strategies and practices the MAAM program calls CAIR (Closely Attend & Intentionally Respond). Through a series of professional development learning labs and on-site coaching, MAAM:
- Develops caregivers’ conceptual understanding of four Precursor Math Concepts: Attribute, Comparison, Pattern and Change. The term precursor means what comes before: in the earliest years, the child’s understanding of these four concepts develops so that they enter preschool primed to use the Big Ideas of Math as they count, measure and create sets
- Supports caregivers in using strategies and practices that are highly effective in developing understanding of the PMCs through playful everyday interactions; in other words, MAAM builds mathematical understanding from the ground up.
A Library of Ideas
In our Idea Library we have collected, categorized, and curated the best resources for early math thinking and teaching.
Precursor Concepts
“Building up” versus “pushing down”
Published in the Zero to Three Journal, authors Jie-Qi Chen, Mary Hynes-Berry, and others examine the mathematical thinking and experiences that are unique to infants, toddlers, and 2-year-olds.
Join the Collaborative
Together, We Can Change the Way Math Is Taught
Join a hub of educators, administrators, and professionals reframing the way we think about and teach math.