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COPYRIGHTED MATERIAL Intentional Teaching As with all areas of the curriculum, children learn more effectively when teachers incorporate de- velopmentally appropriate practices when im- plementing activities in the STEM disciplines. The third edition of Developmentally Appropriate Practice in Early Childhood Programs Serving Children from Birth through Age 8 (Copple and Bredekamp 2009) emphasizes the importance of intentional teaching. This means that effective teachers are purposeful in all aspects of teaching. They plan the curricu- lum and environment with specific outcomes and children in mind. They remain alert for teachable moments as they occur throughout the class- room. Effective teachers understand the develop- mental learning trajectories for children in each area of the curriculum. They also know what in- dividual children understand based on the child’s development. This knowledge allows teachers to plan a multilevel curriculum that meets the learn- ing needs of a range of children. The teacher can intervene as children interact with the materials to structure the learning for each child. The following example illustrates how in- tentional teaching guides learning for a range of children. Ms. Ortega has introduced a collection of vari- ous sizes and types of pinecones into the science area. She expects that children will explore the similarities and differences among the pine- cones and also begin to measure them. When Anna interacts with the pinecones, Ms. Ortega notices that Anna groups the large pinecones together and moves the smaller pinecones into a different pile. Building on Anna’s interest in size comparison, the teacher helps her use direct comparison to put six of the pinecones in order based on their length. Later Eric and Wei visit the pinecone collection. They are older than Anna and have had more experience with measure- ment. For these boys, Ms. Ortega introduces a set of interlocking cubes and suggests that they use the cubes to measure the length of several pinecones. She even gives them a recording sheet (prepared ahead of time) so that they can notate their results. In the above example, the teacher was effective in working with all three children for several reasons: 1. She had identified measurement as one of her goals for the activity. 2. She knew the developmental trajectory for measurement concepts and where individual children in her class were likely to fall along this continuum. 3. She had considered how to implement the activity with various children as part of her planning. Teaching for Understanding In its Principles and Standards for School Mathematics, the National Council of Teachers of Mathemat- ics (2000) addresses effective teaching practices through its Teaching and Learning Principles. The Teaching Principle emphasizes that mathe- matics teachers must understand what students know, what students need to know, and how to support students in their learning. This principle applies equally to teachers of preschool through high school. Teaching for understanding is a focus of all of the activities in this book. The Learning Principle, which also relates to development, focuses on the importance of learning mathematics with under- standing. Regardless of age, students use their prior knowledge and experience to construct new knowledge. Conceptual understanding of mathematics is critical because students can then use their mathematical knowledge to solve new problems. Learning at the conceptual level, rather than simply memorizing facts, is equally important in science education. In both mathematics and science, teachers should encourage children to solve problems through their own thinking rather than supply- ing them with answers. This allows children to build upon their previous knowledge and deepen COPYRIGHTED MATERIAL st e m e d u c at i o n 5