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EDUC 4274: P/J Mathematics

EDUC 4274: P/J Mathematics. Week Four----Session 1. Week 4: Oct. 7 - 11-- S7 Overview. Assignments: An Important Update Some Resources —MOE and Others Some marvelous stuff! Introduction to Early Counting and Number Next Class: What’s Coming Up.

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EDUC 4274: P/J Mathematics

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  1. EDUC 4274: P/J Mathematics Week Four----Session 1

  2. Week 4: Oct. 7 - 11-- S7Overview • Assignments: An Important Update • Some Resources—MOE and Others • Some marvelous stuff! • Introduction to Early Counting and Number • Next Class: What’s Coming Up..

  3. P/J Math Week 4 Session 1Into the Details…last assignment and resources • The final “assignment” (exam) • A change: from Exam week to In-Class last week • Review the change—see Course Outline • Download revised C.O. from flash drives circulating • Reminder: First presentation right after Study Week • Some Important Resources • See Franks’ Resource page, EDUC4274 • http://faculty.nipissingu.ca/dougf/EDUC4466/resources.htm • Esp. NLVM, NCTM (Illuminations), LearnAlberta, Math Central (U Regina) • MathGAINS: Check out--- (Brief Small Group Activity) • WINS • Guides to Effective Mathematics Instruction

  4. P/J Math Week 4 Session 1Early Number Sense Number Sense and Numeration... Some “Big Ideas”... • Numbers are related to each other through a variety of number relationships. The number 7, for example, is three more than 4, two less than 9, composed of 3 and 4, as well as 2 and 5. . . . • Number concepts are intimately tied to the world around us. Application of number relationships to the real world marks the beginning of making sense of the world in a mathematical manner. • Having number sense means that you can think about and use numbers and their relationships in many different ways. Van de Walle, Lovin, Karp, & Bay-Williams (2014) Teaching Student-Centered Mathematics: ... Grades Pre-K—2 (2nd ed.)

  5. P/J Math Week 4Session 1Early Number Sense NSN... First Principles and Early Concepts continued... • Counting Principles (from Marian Small, 2013, P. 140) • One-to-one principle: There is one and only one number said for each object. • Stable order principle: There is a consistent set of counting words that never changes. • Cardinal principle: The last number spoken tells how many. • Abstraction principle: It does not matter what you count; the process for counting remains the same. • Order-irrelevance principle: It does not matter in which order you count; the number in the set does not change.

  6. P/J Math Week 4 Session 1Early Number Sense • How many? . . . At a glance. . . • http://illuminations.nctm.org/ActivityDetail.aspx?ID=74 • http://www.classroomprofessor.com/wp-content/uploads/2011/03/Worksheets_Ten_Frames.pdf • SUBITIZING: • Van de Walle et al. (2014), p. 101: • “Quickly recognizing and naming how many objects are in a small group without counting. Young children can recognize and name quantities of objects that are less than four without counting” • Marian Small (2013), pp. 145-146. • “Students can recognize an amount even before they know its number name. It is a valuable skill for success in mathematics.”

  7. P/J Math Week 4 Session 1Early Number Sense • Progress through stages of counting... Research... • See Small (2013), p. 142 • From Van de Walle et al. (2014), p. 104 • Emergent Counting: Child is unable to count the collection of objects.... May be unable to coordinate one number word with one object ... Or not know correct number sequence. • Perceptual Counting: Child can count the collection of objects only if ...can be seen.... Counts from number 1 • Figurative Counting: Child can count collection even if objects blocked from view.... Able to visualize the objects.... Counts from the number 1, including imagined objects.

  8. P/J Math Week 4 Session 1Early Number Sense • Progress through stages of counting... Research... • From Van de Walle et al. (2014), p. 104, continued • Counting-on Counting: Child can start counting from a number other than 1; does not need to see objects to count. • Non-count-by-ones counting: Child does not count by ones; partitions and combines numbers involved. • E.g., 7 objects plus 6 objects may become: 6 = 3 + 3; I know 7 + 3 = 10, and then 10 + 3 more = 13 • [Small refers to this last stage as “facile number” counting]

  9. P/J Math Week 4 Session 1 • Next Class: • MoreNumber Sense and Numeration • Continuing with Problem Solving (TTPS)-- • Primary level NSN context

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