What Does the Common Core Mean for Preschool Math?
Julie Sarama and Douglas H. Clements
University of Denver, Morgridge College of Education
Carmen had almost filled her pretend pizzas with toppings. As she got ready to roll
the number cube, she said, “I’m going to get a high number and win!” “You
can’t,” replied her friend, “You have 4 spaces and the number cube only has 1s,
2s, and 3s on it.” (from Clements & Sarama, 2009)
In our last Brief, we showed that early mathematics is surprisingly important. Not
only is mathematical thinking important in its own right, it is also a general cognitive
competence. Further, gaps in mathematics achievement are large, both between the U.S.
and other countries, and between those from lower- and higher-resource communities.
Good mathematics curricula and teaching can help close these gaps. We need better
mathematics for every child, and special support for those who lack resources. In this
Brief, we will ask, what mathematics is better mathematics for the young child?
Think First: What Mathematics?
What mathematics is most important to teach? The Common Core (CC,
CCSSO/NGA, 2010)) describes mathematics standards for grades K-12, but what about
preschool? Fortunately, The National Council of Teachers of Mathematics’ previously
published Curriculum Focal Points (CFP, National Council of Teachers of Mathematics,
2006) includes preschool, with standards that connect well with the Common Core. In the
following sections, we describe the two components of all high-quality standards:
mathematical processes and mathematical content.
Promote Practices and Processes
Both the CC and the CFP begin with an emphasis of on mathematical practices or
processes. Consistent with high-quality early childhood education, all mathematics
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curricula and teaching should include and promote problem solving, reasoning,
communicating and constructing viable arguments, making connections, and looking for
and making use of structures and patterns. In the opening story, Carmen’s friend showed
important mathematical reasoning and communication skills. Her thinking might be
summarized as follows.
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To win, Carmen must get at least a 4.
The number cube has only 1, 2, and 3.
These numbers are less than 4.
Therefore, Carmen cannot win on her next roll.
Focus on Pre-K Mathematics Content
With these processes firmly in mind, we can now focus on content. Number is a
key building block of mathematical content but so is geometry and spatial reasoning. As
an example of the latter, research in Israel and the U.S. shows early focus on geometry
leads not only to higher mathematics achievement, but also to higher writing readiness
and higher IQ scores in the primary grades (Clements & Sarama, 2007; Razel & Eylon,
1990). Upon these two domains, number and geometry, we can build the foundation for
early and later mathematics.
The first building block is number and numerical operations. Research shows that
this development begins with two methods of quantification, or assigning a number to a
set of objects. The first, counting, is the main and most easily extended method. Although
it is common, it is also commonly underappreciated and misunderstood. Counting is the
most extensible method of quantification and is the first and most basic mathematical
algorithm of mathematics. The development of counting spans years and years of a
child’s life (that development will be described in our next Brief). Here, suffice it to say
that misconceptions of early counting as “merely rote counting” limit our vision of what
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children can learn about counting. They learn about patterns in verbal counting,
cardinality and ordinality, and using counting strategies to solve a wide variety of
problems.
As important as counting is, there is a second method of quantification that is also
important and is often overlooked. This is unfortunate, because it is most children's first
method of quantification and it supports the development of number sense, counting, and
arithmetic. Subitizing is the ability to quickly recognize and name the number of
elements in small sets without counting. When children count, subitizing the number in
the set encourages and reinforces understanding of the cardinal principle: the last number
word is the same as the number the child recognizes.
As part of geometry and spatial sense, children observe and talk about shapes in
the environment. This goes beyond the simple naming of a typical circle, square, or
triangle. For example, they learn to recognize different shapes of triangle (that is, not
only equilateral or isosceles) and to discuss their attributes. They also describe the
relative positions of objects, using important vocabulary such as "above" and "next to." It
is easy to see how such deep, extensive use of language supports children's development
of general cognition and literacy.
The third focal point for prekindergarten involves foundations for measurement.
Children identify measurable attributes and compare objects directing using those
attributes. For example, children identify objects as "longer" or "shorter" and learn to
differentiate whether "bigger" means length, area, weight or some other attribute.
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Take the Next Steps Toward Implementing Standards
To learn more, download the Curriculum Focal Points from www.nctm.org. Ask:
How can teachers organize now to make use of this information regarding what topics to
focus on and the developmental sequences in which they grow? What unnecessary topics
might be deleted or de-emphasized? What ideas in number and geometry might educators
develop at deeper levels than in the past?
Read the Next Brief on Learning Trajectories
What may not be as clear is how the CFP also suggests a learning trajectory for
each of these topics. Similarly, many are surprised to learn that the CC was first written
as learning trajectories. We will address this important issue in the next Brief.
References
CCSSO/NGA. (2010). Common core state standards for mathematics (Vol. 2010).
Washington, DC: Council of Chief State School Officers and the National
Governors Association Center for Best Practices.
Clements, Douglas H., & Sarama, Julie. (2007). Early childhood mathematics learning. In
F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and
learning (Vol. 1, pp. 461-555). New York, NY: Information Age Publishing.
Clements, Douglas H., & Sarama, Julie. (2009). Learning and teaching early math: The
learning trajectories approach. New York, NY: Routledge.
National Council of Teachers of Mathematics. (2006). Curriculum focal points for
prekindergarten through grade 8 mathematics: A quest for coherence. Reston,
VA: Author.
Razel, Micha, & Eylon, Bat-Sheva. (1990). Development of visual cognition: Transfer
effects of the Agam program. Journal of Applied Developmental Psychology, 11,
459-485.
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