4/27/15 Welcome to
Early Mathema,cal Experiences MNAFEE Conference April 16, 2015 Beth Menninga [email protected] Please sign in!
Why focus on mathema,cs? Personal consequences of poor numeracy •  Increased risk of living in poverty, school dropout, under or unemployment (interna?onal) •  Poorer health outcomes – poor health care risk assessment and decisions (e.g., Reyna & Bainard, 2007) •  Less effec?ve financial and social decision making skills (McCloskey, 2007 review) 1 4/27/15 Why Be Concerned
about Early Math?
Another Gap MDE School Readiness Study 2012
2 4/27/15 Source: Minnesota Compass www.mncompass.org (MDE data)
Source: Minnesota Compass www.mncompass.org (MDE data)
3 4/27/15 Why Be Concerned
about Early Math?
A strong predictor of school success “Early math concepts such as knowledge of numbers and ordinality were the most powerful predictors of later learning…..early math is a more powerful predictor of later reading achievement than early reading is of later math achievement.” (G. Duncan, et. al. 2007) 4 4/27/15 Less ,me on math • 8% of ?me on math • 21% of ?me on literacy Only small por,on of content Rote Coun,ng Number Recogni,on Simple Shape Recogni,on 5 4/27/15 Li[le Use of Math Language & Math Reasoning More Behind Beside Pa[erns How do you know? Math Anxiety Less ,me for instruc,on Less comprehensiv
e instruc?on 6 4/27/15 What messages have you heard about math? 7 4/27/15 You’re born with a math gene, either you get it or you don’t. Math is for males, females don’t get math! 8 4/27/15 I’m a crea?ve thinker so I won’t do well at math. Math is a cultural thing, my culture just doesn’t get it. 9 4/27/15 Research based national standards
say children need to
Charts & learn about….
graphs PaRerns Measurement Shapes and spa,al sense Numbers and opera,ons using these mathematical processes
10 4/27/15 To build mathematical skills
and knowledge, we
provide…
• 
• 
• 
• 
Environment Experiences Vocabulary Conversa?on Finding mathematics in the classroom
• Blocks • Art • Reading • Sensory • Music • Drama?c play • Manipula?ves • Meals • Outside • Transi?ons 11 4/27/15 use
voc mat
abu h
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ar
y
k
s
a ion
t
s
e
u
q
s
12 4/27/15 In preschool math
is not focused on
having the
“right answer”,
it’s about
encouraging
mathematical
thinking Numbers and operations
13 4/27/15 What children are learning
•  To quan?fy (amounts): v Global v One-­‐to-­‐one v Count v Cardinality •  The coun?ng sequence •  To recognize numerals and match to amounts •  Comparing sets •  Beginning to add and subtract: •  Take apart & put together •  Adding on “Subi,zing is a fundamental skill in the development of students’ understanding of number.” Baroody 1987 14 4/27/15 Number sense Three Three groups of countries 3 301  Maple Drive 612 -­‐ 624-­‐3123 Seigler, 2009 15 4/27/15 Playing numerical board games
•  Has demonstrated effects in Head
Start classrooms (Ramini, Siegler,
Hitti, JEP 2011)
•  Linear array appears superior to
circular array of numbers
•  Superior to unstructured number
activities
•  Works well in small group settings
with aide
•  May promote counting on strategy
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How you can help children learn about
numbers
•  Start small: Ø  Explore 1-­‐5 with lots of real things and experiences, then up to 10, then larger amounts •  Link numerals to amounts and magnitude (number line) •  Lots of playful coun,ng Ø  (games) start with 1-­‐3 then 1-­‐10 Ø  then the “tricky teens” 16 4/27/15 “The understanding of founda,onal concepts in three areas of geometry-­‐-­‐ two-­‐ and three-­‐dimensional shapes, spa,al rela,onships, and symmetry and transforma,ons – should be a focus of curriculum experiences for young children.” (Na,onal Council of Teachers of Mathema,cs, 2000) SHAPES
• Physical knowledge of shapes • Language related to shapes 17 4/27/15 SHAPES: stages
Visual See shape as a whole Example: rectangles look like doors Descrip,ve See a[ributes of shapes Example: triangle has 3 sides and 3 “points” Informal deduc,on (6+ years old) Form logical deduc?ons Understand why a square is always a rectangle but a rectangle is not always a square. Van Hiele, 1986 Exploration with shapes helps
children move from the VISUAL
to DESCRIPTIVE stage
VISUAL DESCRIPTIVE 18 4/27/15 Teaching attributes
• Rectangles and squares • Triangles •  A[ribute –the a[ribute is a characteris?c to describe an object. The a[ribute usually refers to the shape, size or color. •  Learning a[ributes of shapes: •  edge •  side/face •  angle/corner •  curved, straight •  flat (2 dimensional) and 3-­‐dimensional 19 4/27/15 RECTANGLES: Dos and don’ts
DO SAY: •  A rectangle has 4 sides with opposite sides the same length •  A rectangle has 4 right angles or corners •  All lines are connected and straight •  A square is a special kind of rectangle, where are the sides are the same length RECTANGLES: Dos and don’ts
DON’T say: •  Rectangles are long •  Squares are not rectangles (they are!) •  Rectangles have 2 long sides and 2 short sides •  Rectangles are like any 3-­‐D shapes such as a shoe box 20 4/27/15 TRIANGLES: dos and don’ts
DO say: •  Triangles have 3 sides or line segments •  Triangles have 3 points or corners •  All sides of a triangles are straight •  All sides of a triangles are connected •  Triangles may vary in orienta?on, size, symmetry or pointedness TRIANGLES: dos and don’ts
DON’T say: •  Triangles have 2 points on the bo[om and 1 on top •  Triangles have a point in the middle •  Triangles have a flat bo[om •  Triangles can be made from any 3 line segments (older children) •  Triangles are like the open triangle used in music or cone-­‐shaped clown hat 21 4/27/15 SPACE: manipulating shapes
• Children: • Compare and match • Take apart and put together • Move and reorient • Understand and use posi?onal words • Represent ideas and objects SPACE
“Thinking spa,ally—that is, visualizing objects in different posi,ons and imagining their movements—is important to young children’s development as mathema,cal thinkers” (Copley, 2010) 22 4/27/15 TRANSFORMATIONS
A transforma,on means that a shape has changed posi,on while retaining the same size, angles, area and line lengths. Symmetry
Symmetry refers to a similarity of form, arrangement, or design on either side of a dividing line or around a point. 23 4/27/15 What do we measure? Which is bigger?
What are you asking them to compare? 24 4/27/15 Which is bigger?
Which is heavier?
How do you know?
25 4/27/15 How do we measure?
• Comparing • Ordering Comparison strategies
(Copley 2010)
Percep?on-­‐based (visual) Direct comparison Quan?ta?ve (number) 26 4/27/15 Measurement Tools:
to be fair
• Non-­‐standard • Standard 27 4/27/15 What is a Pattern?
• Repe??on • Equality & symmetry • Analysis of change (what is the rule?) Children Learning Patterns
•  Sor?ng and Classifica?on •  Recogni?on of a pa[ern •  Copying a pa[ern •  Extending a pa[ern •  Crea?ng a pa[ern 28 4/27/15 Ini?ally, children sort before they count the number of items in each group (Clements, 2003) Children sort objects into groups before they can describe them with a label (Russell, 1991). Patterns
• Repea?ng pa[erns • Growing pa[erns • Analyzing Change 29 4/27/15 Charts, Graphs and
Estimation:
using data to find answers
What Skills are developed?
•  Sor?ng •  Coun?ng •  Collec?ng specific informa?on •  Looking for pa[erns and meaning •  Es?ma?on •  One to one coun?ng, quan?fica?on, set comparison, addi?on and subtrac?on 30 4/27/15 The normal developmental progression of graphic representa?on is concrete (i.e. using physical objects like toys, to make the graphs) to pictorial (i.e. using pictures of objects, like drawings of toys) to symbolic (i.e. using le[ers to present the color of toys, like b for a blue car and r for a red car) (Friel, Curio, & Bright, 2001) Communication matters…
Study on learning shapes highlights guided play strategy Girls are influenced by spa?al language use AND math artudes Use specific math vocabulary and ask ques?ons 31 4/27/15 Talking about numbers of things
(Ramscar et al 2011)
• 3 of ???? • Study: •  “What can you see? I see bears. There are three.” (Set-­‐before-­‐number) •  “What can you see? There are three bears.” (Number-­‐before-­‐set) Paying a?en@on to what ma?ers 32 4/27/15 Interactions are KEY
CLASS Tool: • Instruc?onal Support domain (concept development, quality of feedback, language modeling) • Teacher sensi?vity • Regard for Student Perspec?ves • Instruc?onal learning formats Interactions are key during….
• Play • Games • Explora?on 33 4/27/15 Board games• Math teach…
concepts: numbers, shapes, paRern and measurement • Math processes: reasoning, communica,on, connec,ons, problem-­‐solving, representa,on games you can make
Board
• Grid games • Short and long path games • Con?nuous path games (from More than Coun@ng Standards edi?on, Moomaw & Hieronymus, 2011) 34 4/27/15 Let’s play!
One person from your table comes up and chooses a game 2-­‐3 Players: • Play the game, make your own rules • Think about what math-­‐related vocabulary could be used • Think about what ques?ons you might ask to promote mathema?cal thinking Families
• Math talk • Games provide a natural opportunity for math talk 35 4/27/15 Some themes to remember….
Coun,ng Comparing Ordering Composing/decomposing Rela,onships between things ARributes: gekng specific Early Math and Numeracy Lab
Current research projects concern: •  mathema,cal thinking in early childhood and the school age years; •  math learning, math learning difficul,es, math and execu,ve func,on skills; •  parents’ and teachers’ roles in enhancing early mathema,cal thinking; •  access to support for early math learning in urban vs. rural child care sekngs Michele Mazzocco, Ph.D. Ins,tute of Child Development Research Director, CEED [email protected] 36