Mathematics and Science Standards
Fundamental concepts and their application to problem solving in mathematics and the sciences are interrelated. This idea is reflected in the current national standards for mathematics and emerging new standards for science that integrate knowledge and process skills in mathematics and practices in science and engineering while also placing increasing emphasis on technology in both disciplines.
In the early childhood classroom, the relationship between mathematics and science is evident in highly integrated activities and investigations. Suppose that children are helping the teacher make a snack mix. They may look for recipes in cookbooks or on the Internet to choose one they want to try. They may hypothesize or predict how well they think they will like it or what it might taste like.
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Critical Thinking Question
- Many prospective teachers have “math or science anxiety,” due to less than positive experiences with these subjects in their own schooling. How can this be overcome?
They will apply math concepts as they set up and count their equipment (“We need one big spoon, two bowls, three measuring cups”), sort/group ingredients (crackers, dried fruits, cereal, seeds), and follow ordinal (sequential) directions in determining what to do first, second, and so on and in using different size cups to measure. They apply operations to divide items (mix in one big bowl and divide into smaller bowls for serving) and one-to-one correspondence for serving (one napkin/scoop for each child).
They will also use science skills as they observe the process (“Look at all the colors we have in the bowl!”). They will decide when ingredients are fully mixed, and ask questions (“Why are the raisins and cranberries all wrinkly?”) that could lead to further investigation (drying fruits). They will evaluate the results of their recipe trial, perhaps graphing the preferences of children in the group.
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.
Doing Math and Science
The process standards for mathematics and practices for science focus on how children learn and apply concepts. Common to the disciplines is an emphasis on using concrete materials (Witzel, Ferguson, & Mink, 2012) for inquiry and problem solving, active involvement in the processes and practices used in mathematics and the sciences, developing and using critical thinking skills, and communication. Early childhood educators understand that developing dispositions and skills through first-hand experiences is essential to a firm foundation for mathematical and scientific thinking (NAEYC/NCTM, 2010).
Table 10.3 displays the interrelated nature of the mathematics process skills and the science/engineering practices. You can see how they reflect the different levels of Bloom’s taxonomy.
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