Making Sense of Number Sense Definition Number sense is “ … .good intuition about numbers Making Sense of Number Sense and their relationships . It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts , and relating them in ways that Jennifer Jansen are not limited by traditional algorithms.” Mississippi Bend (Howden, 1989) Area Education Agency Find someone whose card has the Perceptual Subitizing same quantity as yours Introduce yourself to your number soulmate You perceive the three or four dots intuitively & Ask your number soulmate … simultaneously. • What’s your favorite number? You “just know.” • Why? Conceptual Subitizing A Big Idea The quantity of a small set You perceive the parts and put together the whole can be intuitively perceived All of this happens quickly and often is not conscious - it is still subitizing without counting .
Learning about Number from Mitsumasa Anno
How many fives do you see? Number is Complex!!! A Big Idea Uses of numbers • Nominal or categorical numbers Numbers are used many • Referential numbers ways, some more • Cardinal numbers • Ordinal numbers mathematical than others. A Big Idea A Big Idea Quantity is an attribute of a set of objects. Quantity is an attribute of a set of objects. 3 elephants 3 mice
A Big Idea A Big Idea Quantity is an attribute of a set of objects. Quantity is an attribute of a set of objects. A Collection Can Have Many Attributes Numerosity • Pink color is an attribute • The quantity of things in a set • Round shape is an attribute • The “three-ness” of 3 • Nice smell is an attribute • Separate from number words and written • Quantity is another attribute: symbols. Words and symbols these vary there are THREE roses in this between languages – numerosity does not. collection • Humans seem to be biologically programmed to automatically perceive the numerosity of small sets. (The Early Math Collaborative, 2014) Numbers: Nouns or Adjectives? Big Ideas of Number Sense Counting, determining & naming quantity, telling “how many” ... all of these use number as an adjective, not a noun. Are there 3 dots? 3 fingers? 3 inches? 3 tenths? Developmental Levels for Recognizing Developmental Levels for Recognizing Number and Subitizing Number and Subitizing • Verbally labels arrangements to 6, then up to • Name groups of 1 or 2, sometimes 3 (2 yrs) • Match small collection (no more than 4, 10, using groups (5 yrs) • Verbally labels structured arrangements up to usually 1-3) (3 yrs) • Instantly recognizes collections up to 4 and twenty using groups (6 yrs) • Uses skip counting and place value to verbally verbally names the number of items (4 yrs) • Instantly recognizes collections up to 5 and label structured arrangements (7 yrs) • Uses groups, multiplication, and place value to verbally names the number of items (5 yrs) • Verbally labels all arrangements to 5 (5 yrs) verbally label structured arrangements (8+ yrs) (Clements & Sarama, 2014) (Clements & Sarama, 2014)
Developing Visual Number Sense Video Analysis: Focus on the Child Through Models While watching, consider: • Children’s understanding • Children’s learning • Evidence of thinking • Additional opportunities Recognizing Quantity Child 1, preschool Recognizing Quantity Child 2, preschool Matching Quantity Child 3, preschool Comparing Quantities Child 4, preschool Dot Cards Comparing Quantity Child 5, kindergarten Estimating Quantity Child 9, preschool Estimating Quantity Child 3, preschool Developing Visual Number Sense Developing Visual Number Sense Through Models Through Models Number Cards Dice Developing Visual Number Sense Developing Visual Number Sense Through Models Through Models Counting Frames or Rekenreks
Where’s the MATH? Where’s the MATH? Number All Around the Classroom Number All Around the Classroom In Art At Snack Time In the Block Area During Transitions In the Book Area In Dramatic Play Transition Activity Attendance Routine Why focus on developing Number Sense number sense? • Solid number sense is key to mathematically Hierarchical Inclusion healthy development & practice. Because each number • Number sense is not static. It continues to names a quantity one greater than the deepen & build as new relationships amongst number before it, each more numbers are established. number includes all the quantities named by those earlier numbers. (Kamii & Joseph, 2004) Poly-ominoes Poly-ominoes Dominoes (2-square shape) How many ways? • Tri-ominoes (3-square shapes)
Poly-ominoes Poly-ominoes How many ways? How many ways? • Tri-ominoes (3-square shapes) • Tetromiones (4-square shapes) Poly-ominoes Poly-ominoes How many ways? How many ways? • Tetromiones (4-square shapes) • Pentominoes (5-square shapes) Mathematics All Around: Poly-ominoes Exploring Number Subitizing is foundational. How many ways? • Subitizing relies on visual patterns. • Pentominoes (5-square shapes) – Not all arrangements of a number are equally easy to “see.” • How is subitizing different than counting? – Label small sets with number, without enumerating. • How does subitizing support counting? – Authentic reasons to count small sets. – When counting, restate the last count word to emphasize cardinality: “1, 2, 3, ... 3 cups.”
Mathematics All Around: Mathematics All Around: Exploring Number Exploring Number Subitizing is foundational (continued). Children learn about quantity even without exact numbers. • “Which pile has more?” • Subitizing & counting build understanding of • “Put one napkin on each plate.” cardinality. Smaller numbers are easier than larger. • Expect children to subitize small sets; avoid • With infants and toddlers, talk about “1” and “2” and “1 more” and “2 more” “counting to be sure.” • With preschoolers, spend a lot of time exploring “3” and “4” and “5” Fingers are great tools for understanding small numbers, then building to 5 & 10. Children need repeated exposure to amounts in order to associate number name and quantity. Video Analysis Finding Math in Great Books Mouse Count by Ellen Stoll Walsh Number Arrangements • About the Children Ten Black Dots by Donald Crews • About the Teacher Count and See by Tana Hoban • About the Activity Splash by Ann Jonas 1, 2, 3 to the Zoo by Eric Carle Five Creatures by E Jenkins How might this experience connect to other math? The Doorbell Rang by Pat Hutchins Ten, Nine, Eight by Molly Bang Making Connections to Making Connections to the Big Ideas of Number Sense the Big Ideas of Number Sense Iowa Early Learning Standards • Standard 7.1.PS Children understand counting, ways of representing numbers, and relationships between quantities and numbers. • Benchmarks: The child … 7.1.PS.1 recognizes small quantities (1-5) without counting them (subitizing). 7.1.PS.4 makes sets of 6-10 objects and describes parts. 7.1.PS.5 uses language such as more, less or the same amount to compare quantities. 7.1.PS.6 identifies numerals to 10 by name. (Early Childhood Iowa, 3rd ed., 2018, p. 202) (Heroman et. al., 2010, p. 107 )
Making Connections to Making Connections to the Big Ideas of Number Sense the Big Ideas of Number Sense NAEYC Early Childhood Program Standards & Iowa Quality Preschool Program Standards • Standard: – Curriculum • Criterion: – Children are provided varied opportunities and materials to build understanding of numbers, number names, and their relationship to object quantities and to symbols. (Heroman et. al., 2010, p. 108 ) Resources Questions??? Early Math Collaborative. (2014). Big Ideas of Early Mathematics. Boston: Pearson. Contact Information: Early Math Collaborative website Jennifer Jansen www.earlymath.erikson.edu jjansen@mbaea.org Follow on Facebook, Twitter, YouTube Young Mathematicians website http://youngmathematicians.edc.org/
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