Course DescriptionA course for early childhood educators focusing on math concepts appropriate for young children. Topics include patterns, sequencing, classifying, number systems and computation, functions, geometry, measurement, and basic concepts from statistics and probability. Interactive, activity-based methods are used guided by national mathematics education standards. Emphasizes conceptual understanding, connections among topics, and communication of mathematical thinking.

A. Problem solving strategies. B. Patterns, sequencing, sorting, and classifying. C. Numeration systems, place value, ordering. D. Operations with numbers, including with fractions, decimals, and percents. E. Relations, functions, and two-dimensional representations of them. F. Characteristics and properties of two- and three-dimensional geometric shapes. G. Systems of measurement. H. Area, perimeter, and volume. I. Collection of data and communication of results through graphical displays. J. Basic concepts of data analysis and probability. K. Communication of mathematical ideas and reasoning. L. Interconnections among mathematical ideas and connections with the world. M. National curriculum standards for math in pre K to grade 2.

Problem solving 1. Identify and describe problems; develop a plan for solving the problems. 2. Apply problem-solving strategies to problem situations, such as the use of models, pattern recognition, working backwards, “guess, check, and revise”, and organized tables. Patterns, sequencing, classifying, and sorting 3. Recognize and describe patterns, including those found in nature, sounds (music, rhythms), pictures, and objects. Create new patterns. 4. Create sequences of objects or numbers, extend existing sequences, and order events in sequence. 5. Determine and articulate characteristics or attributes that can be used to sort and classify objects, such as size, shape, color; order objects by measurable attributes. Number systems and operations 6. Discuss the components of our base 10 number system and a numeration system other than base 10, including symbols used, place value, methods of computation, and advantages and disadvantages of the system. 7. Describe and apply a variety of cognitive models and concrete materials (manipulatives) to explore, illustrate, and justify quantitative relationships and computational methods. 8. Compare and estimate magnitudes and quantities. 9. Use number sense, estimation, and reasoning to evaluate the reasonableness of solutions. 10. Demonstrate proficiency with operations with Real numbers, including fractions, decimals, and percents, without a calculator. 11. Apply properties of the real number system to justify reasoning and to solve problems involving whole numbers, integers, fractions, decimals, percents, and proportions. 12. Use correct order of operations to evaluate numerical expressions with several operations and parentheses. Functions, relationships 13. Explore and analyze patterns, relationships, and functions, for example using “Guess my rule” games. 14. Describe quantitative changes such as rate of growth. 15. Use two-dimensional graphs, such as coordinate geometry, to specify locations and describe relationships. Geometry, spatial awareness, and measurement 16. Analyze characteristics and properties of two- and three-dimensional geometric shapes, using correct vocabulary, and develop mathematical arguments about spatial relationships. 17. Build and manipulate representations of two- and three-dimensional objects using concrete models and drawings. 18. Use visualization, spatial reasoning, and geometric modeling to solve problems. 19. Recognize measurable attributes of objects. Explore and apply various units and systems of measurement, including nonstandard, U.S., and metric (SI). 20. Select and use appropriate measurement units, techniques, and tools to find length, perimeter, area, volume, capacity, and weight. Compare and contrast shapes and objects by size. 21. Determine area, perimeter, and volume of basic two- and three-dimensional geometric shapes. Statistics and probability 22. Design simple investigations and collect and organize data. 23. Display data in a variety of ways including graphs and charts. 24. Determine and analyze measures of center for sets of data (mean, median, mode). 25. Interpret data by observing patterns and departures from patterns in data displays. Discuss results. 26. Calculate the empirical probabilities of events after collecting relevant data. 27. Discuss the theoretical probability of simple events and the likelihood of real world events. Connections and Communication 28. Connect mathematical ideas to the real world. 29. Recognize how mathematical ideas interconnect and build on one another to produce a coherent whole. 30. Communicate mathematical thinking coherently and clearly (using correct vocabulary) to peers, teachers, and others by, for example, leading activities involving the concepts of this course or presenting lessons to the class using appropriate materials. 31. Collaborate with classmates in order to achieve some of the learning outcomes of this course. 32. Relate the National Council of Teachers of Mathematics (NCTM) standards for pre-K to grade 2 to mathematical content of this course.

Professional/Technical Computational Skills: OUTCOME 5. USING CONTENT KNOWLEDGE TO BUILD MEANINGFUL CURRICULUM Students apply their knowledge of developmental domains and academic (or content) disciplines to design, implement, and evaluate meaningful, challenging curriculum that promotes comprehensive developmental and learning outcomes for each child. Key elements of OUTCOME 5 5a: Explain content knowledge and resources in academic disciplines: language and literacy; the arts – music, creative movement, dance, drama, visual arts; mathematics; science; physical education – physical activity, health, and safety; and social studies. 5b: Recognize and apply the central concepts, inquiry tools, and structures of content areas or academic disciplines. 5c: Use their own knowledge, appropriate early learning outcomes, and other resources to design, implement, and evaluate developmentally meaningful and challenging curriculum for each child.