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Engaging Pyp Students In Mathematics
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Engaging Pyp Students In Mathematics

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  • PCK entails understanding the what, who, and how of teaching: What refers to understanding the key concepts or ideas in a specific content area; who means knowing about learners and their background knowledge, and how represents the repertoire of methods that are appropriate to represent and present specific kinds of content to students of a particular age (Shulman, The wisdom of practice: Essays on teaching, learning and learning to teach , 2004). Pedagogical content knowledge is a subset of subject matter understanding. It’s that part of subject matter knowledge that relates directly to teaching strategies – what is a good illustrative example of a key idea, which student questions are more likely to generate helpful discussion –AND That part of subject matter knowledge that is related to students’ developing understandings, behaviors, and interests (what are students likely to already know, what are typical early confusions). By the same token, both pedagogy and students’ development must each be filtered through the other two elements: pedagogical content knowledge resides only in the intersection of these three bodies of knowledge.

Engaging Pyp Students In Mathematics Engaging Pyp Students In Mathematics Presentation Transcript

  • engaging pyp students in mathematics hendra agustian sekolah victory plus teacher induction programme 2009 SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • essential agreements
    • active participation
    • open mindedness in the framework of international mindedness
    • silent gadgets
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • “ beauty in mathematics is seeing the truth without effort."  george polya (father of mathematics problem solving) SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • what we are going to do
    • philosophy of mathematics teaching
    • discussion of pyp mathematics by strands
        • data handling skills
        • measurement
        • shape and space
        • pattern and function
        • numbers
    • simulation of classroom activities
    • watch out for let’s do it and cool stuff
    • conclusion and further suggestion
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • mathematics teaching PCK pedagogical content knowledge WHAT content knowledge WHO knowledge of children HOW instructional methods Shulman, 1986, 1987 SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • counting is complex + SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • number is complex SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • mathematical knowledge...
    • begins in infancy
    • undergoes extensive development over the first 5 years of life
    • is a natural part of young children’s thinking
    this DOES NOT mean that any and all of maths instruction is appropriate. SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • discussion by strands SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • data handling skills
    • please bear in mind the 3 steps of maths learning:
    • concrete
    • representational
    • abstract
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • graphs always begin with real objects connect them with representation of the objects (pictorial graph) when pupils have grasped the sense of quantities, proceed to symbolic graph (ey 2) SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • let’s do it
    • have everybody take off one shoe, then sort all the shoes into two rows: with laces, without laces -> concrete graph
    • a pictorial representation of that relationship can be introduced at a later stage
    • still later (ey2), a symbolic graph could be made
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • create graphs of snack time choices or how many kids walk or ride the car
    • voting for the class leader
    • differences in food
    • comparing number of sunny days, cloudy days, etc.
    • hang pieces of yarn in front of the room and ask which is the longest or which is the shortest. Have the kids arrange the yarn by lengths from shortest to longest
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • prob a bility and statistics
    • why teach probability and statistics?
    • recent technological advances have made more statistical information available to us than ever before
    • statistics has never enjoyed a terrific reputation, yet, our society is increasingly making use of ideas found in statistics and probability
    • learning probability and statistics provides real applications of arithmetic
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • let’s do it again
    • tiles in the bag
    • place 10 tiles in a bag, some of two different colours. tell the pupils what you’ve done
    • go around the class, asking individual pupils to draw out a tile without looking, to note its colour, and then to replace it. record
    • do this for 10 draws, and then ask groups to look at the information and decide whether they can predict what is in the bag, or if they need more information
    • do 10 more draws again, then discuss and share
    • repeat as many times as needed for most of the class to feel they can predict which colour is more of in the bag
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • measurement
    • concepts and skills in this strand deal with making comparisons between what is being measured and some suitable standard of measurement
    • it is important to note the reality that measurement is never exact; even the most careful measurements are approximations
    • being able to measure connects mathematics to the environment
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • begins to make comparisons between several objects based on a single attribute
    • shows progress in using standard and non-standard measures for length and area of objects
    child indicators SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • what should be taught
    • making comparisons between objects by matching -> let’s do it
    • comparing objects with nonstandard unit (parts of the body, straws, cubes, books) -> let’s do it
    • comparing objects with standard units (later)
    • choosing suitable units for specific measurements (later)
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • let’s do it
    • foot cutout
    • trace your left foot (with your shoe off) on construction paper
    • cut it out
    • record your name, shoe size, and the length of your foot in centimetres
    • compare your shoe size and foot length with those of others
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • measure shoes, height, length of table, etc. with yarn or hands
    • sizes of containers
    • blocks to build towers with length or height equal to other objects
    • number of steps it takes to get somewhere
    • measure ingredients for cooking
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • shape and space
    • in their play experiences, children encounter relationships among shapes naturally
    • children needs experiences that relate geometry to ideas in measurement, number and patterns
    • although often regarded as a less important section, geometry is a significant branch of mathematics, the one most visible in the physical world
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • begins to recognise, describe, compare, and name common shapes, their parts and attributes
    • progresses in ability to put together and take apart shapes
    • begins to be able to determine whether or not two shapes are the same size and shape
    • shows growth in matching, sorting, putting in a series, and regrouping objects according to one or two attributes such as color, shape, or size
    • builds an increasing understanding of directionality, order, and positions of objects, and words such as up, down, over, under, top, bottom, inside, outside, in front, and behind
    child indicators SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • geometric presentation tray (ey1)
    • this activity is aimed at introducing the child to the basic three shapes: circle, square and triangle
    • further afield, children will develop an awareness of shape in the environment
    let’s do it SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • show how to carry the tray to the table
    • show how to remove the insets from the tray by holding the knob with three fingers
    • tell the child that you are going to put the insets back in the sockets
    • feel around the inside socket
    • invite the child to try when she has put all the insets in the their sockets
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • hunt for shapes throughout the room
    • pass around a shape and have children look at it and feel it with eyes open and closed
    • have children hunt for shapes in a magazine and paste them on a page
    • have the children make objects using a variety of shapes
    • have ten cutouts of all different shapes and envelopes with that shape in them, kids place shapes into their corresponding envelopes
    • trace shapes, then color them in
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • place one of each shape on a magnetic board or flannel board. Have the children look through a basket of shapes and place a shape next to its corresponding match
    • select several sheets of paper and draw one large shape (can also use numerals). Set out 20 inch long shoelaces or string. Invite the children to create the shapes or numerals by placing the laces on top of the shape or numeral on the construction paper sheets
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • let’s do it again
    • walking down the outline (ey2)
    • use pieces of masking tape to make large outlines on the floor of a circle, square, triangle, etc
    • let the children take turns walking, crawling or hopping around the edges of the shapes
    • alternatively, ask the child to first identify the shape before walking around it
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • patterns are key factors in understanding mathematical concepts
    • the ability to create, recognise, and extend patterns is essential for making generalisations, seeing relationships and understanding the logic of mathematics
    pattern and function SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • enhances abilities to recognise, duplicate, and extend simple patterns using a variety of materials
    • shows increasing abilities to match, sort, put in a series, and regroup objects according to one or two attributes such as shape or size
    child indicators SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • introducing patterns
    • early experiences should focus on recognising regularity, identifying the same pattern in different forms, and using patterns to make predictions
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • let’s do it
    • introduce a repeating pattern like clap, snap, clap, snap
    • have children join in
    • give them materials with which they can represent the pattern, by making a train of interlocking cubes (2 nd step of maths learning)
    • represent the pattern with letters, in this case ababab...
    • ask the children to predict what comes later in the sequence
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • looking for patterns in the relationships between two sets of numbers is a key way to develop students’ understanding of functions
    • tricycle case: (1,3), (2,6), (3,9), ...
    • this set of pairs of numbers form what is called function
    developing understanding of function SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • look for patterns on leaves
    • building patterns with two colours of Unifix cubes or pattern blocks
    • constructing a pattern with two colours of napkins at snack time
    • clapping the rhythms of their name
    • colouring every second or fifth or tenth day on a calendar of days in school
    • create patterns using sponge printing, collage materials, geometric shapes or wrapping or wall paper
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • children must be able to make sense of the various ways numbers are used
    • they need to develop a sense of number that enables them to recognise relationships between quantities; to use the arithmetic operations; and to apply their understanding to problem situations
    numbers SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • child indicators
    • demonstrates increasing interest and awareness of numbers and counting as a means for solving problems and determining quantity
    • begins to associate number concepts, vocabulary, quantities, and written numerals in meaningful ways
    • develops increasing ability to count in sequence to 10 and beyond
    • begins to make use of one-to-one correspondence in counting objects and matching groups of objects
    • begins to use language to compare numbers of objects with terms such as more, less, greater than, fewer, equal to
    • develops increased abilities to combine, separate and name “how many” concrete objects
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • what should be taught
    • emphasise the development of number sense
    • patterns in number -> to help the children discover and develop generalisations about number
    • use of numbers in problem situations
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • Select five index cards. On the left-hand side of each, write a numeral from 1 to 5. Then, on the right side, punch a matching number of holes with a hole punch. Let the children take turns counting the number of holes in the cards and naming the matching numerals
    • Cut five apple shapes out of cardboard. Cut one finger hole in the first shape, two in the second, and so on. Colour the apple shapes red and mark each one with the numeral that matches the number of holes in it. Let your children take turns choosing an apple shape, sticking their fingers through the holes and then naming the number of "worms" they see
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • Divide a paper plate into six equal sections and label the sections from one to six by drawing on sets of dots. Write a numeral from 1 to 6 on each of six spring-type clothespins. Let the children take turns clipping the clothespins to the matching numbered sections on the circle.
    • Make a blank book for each child by stapling 10 pieces of white paper together with a colored paper cover. Write "My Counting Book" and the child's name on the front. Number the pages in the book from 1 to 10. Let your children look through magazines or catalogs and tear or cut out small pictures. Then have them glue one picture on the first page of their books, two pictures on the second page and so on.
    SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • examples of problem solving tasks SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • which one has more? SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • which of the 3 shapes takes up the most space? SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • distribute the food so that both animals get the same amount to eat turtle frog SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • SVP/PYPMathsCo/PD-4/Hendra/Jun09
  • there is more to maths than just... SVP/PYPMathsCo/PD-4/Hendra/Jun09
    • t h a n k y o u