©2013 Cengage Learning. All Rights Reserved. Section I Concept Development in Mathematics and Science Unit 1 How Concepts Develop

Concepts Are the building blocks of knowledge Allow people to organize and categorize information Can be applied to the solution of new problems in everyday life Can be observed being constructed and used by children in everyday activities ©2013 Cengage Learning. All Rights Reserved.

Concept Development During the preprimary period –learn and begin to apply concepts basic to mathematics and science During the primary period –apply basic early concepts when exploring more abstract inquiries in science to help them understand more complex mathematic concepts such as addition, subtraction, multiplication, and division and to use standard units of measurement ©2013 Cengage Learning. All Rights Reserved.

Development Follows an individual timetable for each child Series of steps that each child reaches ©2013 Cengage Learning. All Rights Reserved.

Normal Range of Development Children who are the same age may be weeks, months, or a year or two apart in reaching various stages and still be within the normal range of development ©2013 Cengage Learning. All Rights Reserved.

Math and Science in Early Childhood Math and science are interrelated –math concepts such as comparing, classifying, and measuring are called process skills when applied to science investigations –other science process skills such as observing, communicating, inferring, hypothesizing, and defining and controlling variables, are used for solving problems in both science and mathematics ©2013 Cengage Learning. All Rights Reserved.

Principles of School Mathematics Six statements that reflect basic rules to guide high-quality mathematics education and describe the overarching themes of mathematics instruction. The principles address –equity –curriculum –teaching –learning –assessment –technology ©2013 Cengage Learning. All Rights Reserved.

Standards for School Mathematics Standards provide guidance as to what children should know and be able to do at different ages and stages of development ©2013 Cengage Learning. All Rights Reserved.

Standards for School Mathematics Ten standards are described for prekindergarten through grade 12 –first five standards content goals for operations, algebra, geometry, measurement, and data analysis and probability –last five standards processes of problem solving, reasoning and proof, communication, connections and representation ©2013 Cengage Learning. All Rights Reserved.

National Science Education Standards Coordinated by the National Academy of Science’s National Research Council. Developed with the major professional organizations in science and individuals who had expertise in writing standards. ©2013 Cengage Learning. All Rights Reserved.

National Science Education Standards Document Includes six major components –Science Teaching Standards –Standards for Professional Development of Teachers –Assessment in Science Education –Science Content Standards –Science Education Program Standards –Science Education System Standards ©2013 Cengage Learning. All Rights Reserved.

NAEYC Has developed guidelines for developmentally appropriate practice (DAP) in all areas of instruction in early childhood including mathematics and science ©2013 Cengage Learning. All Rights Reserved.

Jean Piaget Identified four periods of cognitive growth and development –sensorimotor period—birth to about age two –preoperational period—age two to age seven –concrete operations—age seven to age 11 –formal operations—age 11 through adulthood ©2013 Cengage Learning. All Rights Reserved.

Decide which of the following describes a child in the sensorimotor (SM), preoperational (P), or concrete operational (CO) Piagetian stages. 1. Leah watches as her teacher makes two balls of clay of the same size. The teacher then rolls one ball into a snake shape and asks, “Leah, do both balls still have the same amount, or does one ball have more clay?” Leah laughs, “They are still the same amount. You just rolled that one out into a snake.” 2. Michael shakes his rattle and then puts it in his mouth and tries to suck on it. 3. Aiden's mother shows him two groups of pennies. One group is spread out, and one group is stacked up. Each group contains 10 pennies. “Which bunch of pennies would you like to have, Aiden?” Aiden looks carefully and then says as he picks up the pennies that are spread out, “I'll take these because there are more.” ©2013 Cengage Learning. All Rights Reserved.

Piaget’s Division of Knowledge Physical knowledge Logic-mathematical knowledge Social ©2013 Cengage Learning. All Rights Reserved.

Lev Vygotsky Recognized both developmental and environmental forces in cognitive development Developed the concept of the zone of proximal development –area between where the child currently operates independently in mental development and where the child might go with assistance from an adult or older child assistance or scaffolding is provided by more mature learners ©2013 Cengage Learning. All Rights Reserved.

The Learning Cycle Constructivist approach Viewed as a way to take students on a quest for knowledge that leads to construction of knowledge Both a curriculum development procedure and a teaching strategy Thrust of each phase of the learning cycle –exploration –concept development –concept application ©2013 Cengage Learning. All Rights Reserved.

The Learning Cycle for Early Childhood Encompasses four repeating processes: –awareness –exploration –inquiry –utilization ©2013 Cengage Learning. All Rights Reserved.

Current Thrust in Mathematics and Science Instruction Reform classroom instruction –change from traditional drill and practice memorization approach –adopt the constructivist approach with more exploration and problem solving ©2013 Cengage Learning. All Rights Reserved.

National Standards Movement Common Core State Standards is a movement toward common curriculum standards for every state. NAEYC and InTask have developed Professional preparation standards ©2013 Cengage Learning. All Rights Reserved.