Mathematics Standards
The national mathematics and science standards differ in content and the ways in which strategies are applied and used for problem solving and inquiry. The National Council of Teachers of Mathematics (NCTM) developed the standards (2000) for math education from pre-K through high school. The NCTM describes principles on which math education should be based, content knowledge, and processes for development of mathematical competence. The 2010 revised joint position statement by the National Association for the Education of Young Children (NAEYC) and NCTM also stresses that high quality mathematics for young children is grounded in their natural interests, daily experiences, and opportunities for play. Children acquire informal mathematical knowledge and skills needed for understanding formal mathematics from daily life (Baroody, Lai, & Mix, 2006; Charlesworth, 2005; Sypek, 2017; van Hoorn, Nourot, Scales, & Alward, 2007). Common Core State Standards (CCSS) for education from kindergarten through high school were finalized in 2010. Although CCSS for mathematics are being used in 35 states, the standards do not address pre-K education (Ujifusa, 2017).
The development of mathematical concepts is cumulative, so informal knowledge is very important as a basis for intentional and systematic mathematics instruction. But because children’s experiences can vary significantly by socioeconomic context, the early childhood years provide opportunities for both informal and planned experiences with mathematics, which occur and develop concurrently. Research supports an approach to mathematics instruction that focuses neither on direct instruction nor unguided discovery but on guided discovery that includes both:
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- Adult-initiated experiences, such as games, tasks, and projects
- Child-initiated activity with guided adult responses, such as building upon a child’s questions during play (Baroody, Lai, & Mix, 2006; Campbell, 1999; Charlesworth, 2005; Rice, 2014)
The content standards identify what children should know and be able to do in five strands within mathematics:
- Numbers and operations
- Algebra
- Geometry
- Measurement
- Data analysis and probability
Emphasis on each of the strands varies over time, depending on where the children are developmentally and what they’ve already learned. But one thing is sure: future success in mathematics is based on sound foundations of conceptual and procedural understanding in the early years (Campbell, 1999; Linder, 2017; NAEYC/NCTM, 2010; Seefeldt, 1999; Witzel, Ferguson, & Mink, 2012).
Science Standards
The Next Generation Science Standards for K12 reflect and are guided by A Framework for K12 Science Education: Practices, crosscutting concepts, and core ideas, published by the National Research Council in July 2011. The framework emphasizes an approach for standards development that integrates three dimensions: science/engineering practices (the methods used in science and engineering), cross-cutting concepts (integrated understandings across the science disciplines), and core ideas within each of the four science disciplinesphysical science; life science; earth science; and engineering, technology and applications.