ECE Study - Mathematics

help children learn to estimate by

use words related to estimation in conversations with children: around, about, approximately, near, more than, less then, between - ask children to estimate amounts of food, numbers of items, lengths of time - help children compare actual outcome with original estimate - with repetition, make more accurate estimates

knowing number names and understanding 1:1 correspondence

young children learn to name numbers in a way that is similar to how they learn to recite alphabet letters - learning to associate number symbols with concrete objects in real world environment is a major advance in cognitive development - 1:1 correspondence: matching number symbols to the quantities they represent - essential early math skill - grab bag game: pull card out of bag with number, count out corresponding number of items, put with card - can also include name of number of card to promote development of early literacy skills

Measurement of time

younger children typically do not have an understanding of abstract concept of time - can still help understand that time elapses, count/measure this process - who can stand on one foot longer? - still make references: you can play for five minutes longer: repeating will help eventually learn time passes - can time everyday activities, count ticks on clock - until children old enough to understand abstractions like today/yesterday/tomorrow, adults can use concrete references like after lunch or before bedtime

developing number sense and numeracy skills

- count real things and encourage children to count - sort objects by size, shape, color similarity , differences (bigger/smaller) - how numbers used to find street addresses, keep score during games - count on fingers - help children count without repeating or skipping any numbers

red rover game

can adopt to teach shape recognition by cutting out various shapes and pin to child's shirt: blue circles come over! - shape and color recognition skills - vary action verbs to support vocabulary development and comprehensive skills - develop gross motor skills

young children's thinking and learning

cannot understand abstract concepts - think in concrete ways - see, feel, manipulate to help understand math concepts - exploration and discovery activities: hands on learning

early math skills and sequencing/practice fine motor skills

ice cube necklaces - temperature at which water freezes - scientific observations by noting how long water takes to freeze - color patterned necklaces

making connections in children's early mathematical development

- children informally learn intuitive math thinking through everyday life exp. - one frequent problem: can come to see academic math as a collection of procedures and rules instead of as a means of finding solutions to everyday, real life problems: interfere with ability to apply formal math in practical way - prevent: establish connection between intuitive math and formal math: teach math through use of manipulative materials familiar to children

prerequisite abilities

- ability to identify, copy, expand, and create patterns - ability to count - paint six ping pong balls red on one side to make red/white balls; blue/white balls; ask child to make pattern in egg carton (two white, then two red)

effective problem solvers

- able to focus attention on the problem and its individual component parts - can formulate hypotheses about the problem/situation and then test them for veracity - willing to take risks within reason - persistent if they do not solve a problem right away and do not give up if their first attempt at solving a problem is unsuccessful - flexible, experiment with alternate methods - self regulation skills

games/activities

- adult/child conversations to play mental mathematics games - "if you have two plums and I give you two more..." - using children's favorite things in story problems, don't restrict types of problems presented based solely on their child's grade level: children can work with any situation if can form mental imagery - harder tasks: problems involving larger numbers, problems involving division with remainders, problems with negative number answers - use Socratic method: asking guiding questions to allow children to arrive to solution rather than telling them right answer

developing counting skills, numeracy skills, motor skills

- beanbag game - write number 1-5 on each can; fill tube socks with beans; number 1 on five beanbags, two on four, 3 on three, 4 on two, 5 on one; direct children to toss beanbags into cans - children devise games/rules - toss into cans - toss into a can with same number - develop imagination and decision making skills, create own games while learning number and set identification

mental math games

- better to ask children questions than give them answers - use turn taking: adult poses story problem, and then child gets to pose one - games should be fun, not strictly factual - at end of early childhood (around school age) children can handle the abstract algebraic concept of variables/unknown numbers (mystery numbers) and use this concept in games - x or n

communicating with children to promote mathematical reasoning skills

- express math concepts using pictures, words, diagrams, symbols - talk with peers and adults helps them clarify own thoughts - develops vocal, early literacy and reading skills - reading children's books that incorporate numbers - drawing pictures or diagrams and sing concrete objects to represent numbers and solve problems - words, charts, drawing, tallies

games that teachers can create for the practicing of practice number recognition

- fishing for numbers: cut fish shapes 10, write 1-10 on each fish, insert paper clip, make rods, assign child a number and they fish for it - can also do larger/smaller - letters instead of numbers - dolch word/sight word on each fish

clinical interview

- individual and family therapists, researchers - structured/semi-structured/open-ended questions and listen to responses and record for accuracy - find out what respondent thinking/feeling - how did you do this? what is happening now? can you tell me more about this? - flexible questioning helps uncover child's thought process - ask clinical-interview-type questions as part of instruction -ask shapes' names, how differ from one another, why they think shapes differ: help promote math skills and literacy development - promotes math communication skills - helps children learn to use language to explain thinking, share ideas, express themselves

Problem solving skills

- learn concept that question can have more than one answer and a problem can have more than one solution - explore problem, situation, and use logical reasoning - adults can discuss everyday challenges, asking children to propose ways to solve them and ask them to explain how they arrived at their solutions, propose problems

reasoning skills applying early mathematical and scientific concepts

- major component of problem solving: reasoning - think through questions and find usable answers - use logic to classify objects o concepts into groups: follow logical sequences to arrive at conclusions that make sense - use analytical abilities to explain their own thought processes - apply what they have learned about relationships/patterns to help them find solutions to problems - justify mental processes - adults: ask questions, give time to think about answers, listen, why something is as it is

mathematics and everyday life and other academic subjects

- math concepts inform other content areas: music, art, sciences - children comprehend math more easily when they can make connections

helping children learn geometry

- observe commonplace objects and paces in physical world - identify figures for them; asking them to name when encounter in future; ask them to describe, draw, trace - learn most effectively with hands on activities (involves many physical properties like shape, line, angle, abstract concepts) - boxes, containers, puzzles, blocks, shape sorters - children become better able to follow directions and navigate through space when develop geometric knowledge and spatial sense - as they mature, children can play games in which search for hidden shapes

using problem solving skills in daily life

- preschoolers: use math concepts to understand that they have three toys, to comprehend that three fingers equals three ays, understand that two cookies plus one more equals three cookies - abstract math: need two major skills: being able to visualize a scenario and being able to apply common sense thinking - thinking and planning to achieve goals within the constraints of the properties of the surrounding environment is natural behavior for young children - problem solving skill learned by doing; requires practice

developing shape recognition skills, fine motor skills, creatively, observational skills, general and early math vocabulary skills

- shape matching: game board like a tree: descriptive vocabulary words tall/short, thick/thin - cut 5-10 pairs of shapes teacher cuts - pairs should not match exactly (blue square can be paired with red square): see how quickly can match each shape to its partner on the tree - warmer/cooler distance clues - reinforcement each time child correctly matches - can use more shapes, match shapes of different sizes

collecting, organizing, displaying day

- shows children sticky notes, has them select favorite color - choosing: data collection - organized data they gathered by helping children arrange colored sticky notes into columns - displayed data once chart completed

reusing sectioned plastic trays from the grocery store

- supply beads, pennies, erasers, other small objects, dozen sticky notes - write number on each note: for older preschoolers, can write 7 and seven - younger: numeric symbol plus seven dots or other marks as a clue to that number symbol - one number note in each compartment - guide children to transfer correct number of each small object to correct compartment - count aloud while transferring

promoting pattern recognition skills, imagination, an understanding of symbolic representation, map reading skills

- treasure hunt: make sure can read map independently - make connections between symbols and images to corresponding real-world physical objects, begin learning to read maps

steps preparing young children to learn

1) understanding the problem 2) coming up with a plan to solve the problem 3) putting that plan into action 4) observing the outcome and reflecting on whether the solution was effective and whether the answer arrived a makes sense - learning series of steps and develop qualities needed to solve problems

concept of starting at zero rather than one

= explaining a ruler - zero means none/nothing. when we count: we start with one because we already have a least one of something - when you were born: began at zero - to get to one inch, need to start at zero

estimation

making an educated or informed guess about a measurement when no actual measurement is available - young children in process of learning concepts of sizes and numbers - must comprehend comparison and relativity (larger, smaller, more less) before able to make accurate estimates - helps them to learn math vocal: about, around, more than, less than - learn to make predictions, realistic answers - important for young children to learn how to make estimates, recognize when appropriate to apply estimation method, recognize when estimates reasonable

strengthening numeracy skills

adapt format of 20 questions, i spy to focus on numbers and help learn number concepts - I'm thinking of a number 1 to 10 - give cues like higher and lower - can increase number range, use larger numbers, reverse roles: adults guess - learn to describe numbers, compare them, sequence them - limit number of guesses allowed or set time limits to make more difficult

Charts and graphs

almost every daily activity can be charted in some way - how many pieces of fruit they ate by charting stickers peeled off of fruit - some children better able to understand math by viewing/making graphs - involves representing quantities visually instead of just listing numbers

button board

by gluing buttons of various sizes/colors to piece of cardboard, teachers can initiate a number of activities that help preschoolers learn math concepts while having fun - preschoolers commonly learning shapes and how to drawn them: teachers can give children lengths of string/twine/yarn or long shoelaces and show them how to wrap them around different buttons to form shapes - counting and 1:1 correspondence: wrap string around a given number of buttons - spoken to concrete objects - sorting, classifying objects into groups based on common characteristic: all big buttons, red buttons

cardinal, ordinal, nominal, real numbers

cardinal: numbers that indicate quantity: seven butters, three kittens - ordinal: numbers that indicate the order of items within a group or a set: first, second, third, fourth, fifth - nominal: numbers that name things: area code numbers along with telephone numbers to identify geographical calling areas, zip code numbers: categorize, serve as labels, not related to actual mathematical values of numbers, do not indicate quantities/operations - real numbers: all rational and irrational numbers - may or may not be cardinal numbers

counting

common practice: counting on fingers - blind finger counting: must learn to count mentally instead - concrete to abstract thinking - takes practice - box of blind objects, reach in and count

What is one of the earliest numeracy skills that young children develop?

counting - even before learned name of all numbers, young children learn to count to three, then five, etc.

mathematical milestones

counting: math skill milestone for young children - four year olds enjoy counting aloud - three levels of counting: 1) 1-12: memorization 2) 13-19: memorization and understanding of the more unusual rules for teen numbers 3) counting from 20+: at this level, children discovering regular math pattern which is base ten and number between 1 and 9 added (2 tens, 3 tens, 4 tens...) - process consistent - encouraging children as young as 4 to learn to count up to 100: helps children learn about and explore patterns in depth

making math fun

create grid on floor with numbers 1-10 using masking tape, construction paper, markers: ask children if can name, throw beanbag into squares, name number where it lands - hop from numbered square to square, collecting beanbags, and then hipping back - write onto scoreboard - count using number words, name selected numbers, throw accurately

integrating math into everyday activities

example: children line up - ask them who is first, second, third - 1:1 correspondence: plane one snack on each plate - some educators maintain insufficient when used on own because in larger classes not always possible to take advantage of teachable movements with every child - cannot be applied systematically in addition, use curriculum - HighScope, Creative, Big Math for Little Kids - combine, select parts of different programs

selecting one of three colors of sticky notes, organizing them, displaying them

had ten children each choose one of three colors of sticky notes: basic data collection - organized children;s choices - displays the collected and organized data - asks children which color chosen the most, least, most popular to least popular, count ten children, asks which color half of the children chose

pasta necklace making as a learning activity

hand-eye coordination: need for writing and everyday activities - create patterns: pattern recognition and pattern creation abilities - repetition, rhythm, categorization, sequencing skills

learning game that involves writing numbers, identifying numbers, running

number dash: small or large groups; write large numbers on paved area with sidewalk chalk - one of each number for each child: six 1s, 2s, 3s, if six children; tell children to run to whichever number you call out and stand on it until you call another number - call out randomly - help classmates - gross motor skills, number writing skills, number recognition skills - playing organized games, following rules, following directions, cooperating with and helping others - letters, colors, shapes

Number sense and number operations

number sense: includes understanding the various applications of numbers - conveying and manipulating information, describing quantities, characterizing relationships - able to count with accuracy and competence - given specific number, count upwards and backwards, break down number and reassemble it, recognize relationships between/among numbers - add and subtract

sorting and categorization

one of the major learning accomplishments is being able to identify similarities and differences among objects - enables children to sort like objects into groups, place objects into categories based on differences - compare and contrast: early step in development of critical thinking, analytical and problem solving skills - guess item with a hint - if guess correctly, allowed to look into a bag - preschoolers need three 1/2 cup servings of fruit and three 1/2 cup serving of vegetables daily - food rainbow project - glue food to corresponding stripe on rainbow - at bottom, draw and color one box for each food they eat to create bar graph - try to eat entire rainbow every week

fractions

parts or pieces of a whole - children in the pre operational stage of cognitive development cannot perform logical or mathematical mental operations - focus on one property of an object rather than all of its properties: centration - believe that several apple pieces more than one apple - cannot yet comprehend the logical sequence of dividing apples into fractions: must know what a whole unit consists of, how many pieces unit is divided into, whether the pieces are of equal size - help understand through informal sharing activities: slicing up food, dividing chores and play materials

patterns and relationships

patterns: things that recur or are repeated regularly - images, sounds, numbers, events, actions, movements - Relationships: connections or associations between things that are identified or described using logic or reasoning - being aware of patterns and relationships among aspects of the enviro help us comprehend fundamental structure of these aspects - predict what will occur next in a series of events - confidence in environment - understand repetition; rhythm; categorization - look at pictures and designs; movement activities; hands on activities (necklaces with simple pattern making)

measurement

process of determining how long, wide, and tall something is physically and how much it weighs by using measuring units such as inches, feet, yards, square feet, ounces, pounds - used to quantify time using units like seconds, minutes, hours, days, weeks... - not just a formal means of quantifying size, area, time; also important for young children to see and identify relationships between and among things they encounter outside of school in everyday life - comparative sizes, how little/big something is - can let children initially choose own measurement units: three teddy bears tall

Rational numbers and irrational numbers

rational: numbers that can be written as ratios or fractions - fraction that has a whole number as the numerator and denominator - all whole numbers are rational numbers b/c can be written with denominator of 1 - irrational: can be written as decimal numbers but not as fractions because numbers to the right of the decimal point that are less than 1 continue indefinitely without repeating: pi, square root of 2 - infinite number of irrational numbers between 0 and 1 - not used as commonly in everyday life as rational

cooking baking activity

shape recognition, measurement, sorting, categorization - prepare cookie recipe: children help measure ingedirents, use cookie cutters: select, name, recognize shapes; adults mix cookie shapes and have children separate cookies with like shapes into groups: sorting skills - having children identify similar/different shapes, sizes, colors promotes categorization skills - arranging cookie shapes into patterns for children to identify: pattern recognition skills

creating collages

shape recognition: fundamental math skill - create collage of familiar figure - help children name each shape, trace shapes onto paper and cut out, arrange and glue - can subsequently teach additional shapes (octagons, ovals)

geometric shapes and their properties

shows squaresquaresquaresquare - how many rectangles are in the figure? - students answers one: incorrect because a square is a rectangle - figure has four - entire figure is itself a rectangle - there are five rectangles: also incorrect, two adjacent squares also form a rectangle - three additional! - three adjacent squares also form a rectangle: two additional - total of 10 rectangles! - analyzing visual information, synthesizing visual information, recognizing patterns/shapes, identifying the properties of shapes

Spatial sense and geometry

spatial sense: individual's awareness of one's own body in space and in relation to the objects and other people around the individual - allows young children to navigate environmental spaces without colliding with objects and other people; see and hear adequately; be aware of whether others can see and hear them; develop and observe a socially and culturally appropriate sense of their own and other's personal space - geometry: area of math involving space, sizes, shapes, positions, movements, directions; gives descriptions and classifications of our physical environment

probabilities and statistics

statistics: present them in graphs or charts to organize them, interpret them, make it easier to see relationships among individual statistics - graphs: visual alternative that depict math info and show relationships among inidivudal statistics, esp. changes over time; comparisons - probabilities: indicate the likelihood that something will happen: use to predict things, behaviors or outcomes - statistics: show numbers and proportions of responses or results obtained in research studies

Representation Skills

symbolic representation: the idea that objects, written letters, words, symbols used to represent other objects or concepts - developed at an early age (pretend play, written language and connect to spoken) - count on fingers, create tallies, draw pictures, make graphs - math vocabulary: ask child how categorizing rocks

spatial awareness

the relationships of objects to each other and within space - serve as foundation for principle of geometry and physics - build structures with blocks, pieces of puzzles - when moving around, begin to notice how other people/objects positioned in space and how own bodies move through space in relationship to objects and other people - gross motor skills, coordination, social skills - Numbers Plus preschool math curriculum: number symbols and names, counting, shapes, spatial awareness, relationships of parts to the whole

identifying shapes

three levels of perceiving shapes: seeing, naming, analyzing - seeing: very young children can recognize simple shapes like circles, squares, triangles - as cognitive and language skills develop: learn names for shapes, use names to identify single shapes - third level: analyzing each shape to understand its properties: more abstract: shape can have number of diff. appearances - triangle has three sizes, not necessarily equal in length - significant mark of progress in early math skills development: ability to not only identify various shapes but to draw them - once develop, typically want to practice all the time - pattern resist: paint over crayon of shapes