CURR 383CURR 383

Tuesday September 29, 2009Class 4

Mathematics and the Young Child: Developing Number Sense

Administrative DetailsAdministrative Details• Address an envelope. Watch the mail! p

• Independent Study Chart• Independent Study Chart

• Group Facilitation Rubric

• Document the learning curve on your prac!

AgendaAgenda• Openers

• Hundreds Board JigSaw• Tricky Track• Number Tiles

• Mathematics & the Young ChildF bi h K• From birth to pre-K

• Subitizing: What is it? Why is it important?• Building on Subitizing in the Classroom• Skip Counting on the Calculator

Hundred Board JigsawHundred Board Jigsaw• moving across or back one

ddispace means adding or subtracting one from the starting number; g ;

• moving up or down one row means adding or

bt ti t f thsubtracting ten from the starting number;

•

Tricky TrackTricky Track

Number TilesNumber Tiles

eWorkshop.on.caeWorkshop.on.ca• Counting & Representation

• Tell me• Show me• Let me tryy

Overview

h h h lMathematics and the Young Child:Putting Mathematical Brains to Work in the Primary Classroom

When was your first mathematical h hthought?

Did you know? f hEvery Brain Is Hardwired for Math

• at age 3 or 4 days, a baby can g y ydiscriminate between collections of 2 and 3 items

• by four and one half months a baby • by four and one half months, a baby “can tell” that one plus one is two and that two minus one is one

• by age 7 months babies can recognize the numerical equivalence between arrays of objects and drumbeats of hthe same number

How do we know this?How do we know this?

Elizabeth Spelke Harvard Baby Lab

This does not mean that there is an actual "math gene" but rather "an innate facility for mathematical thought"y g

So then … we all start with the same basic mathematical brain …

• all of us have an abstract understanding of numerical knowledge, before we develop the language skills necessary to articulate that knowledge (and by age two-and-a-half all children realize that number words are and y ag and a a a d n a a n d adifferent from other words ... )

• all of us can automatically recognize very small numbers, match up the objects in small collections tell which of two small collections is larger objects in small collections, tell which of two small collections is larger

• all of us have an innate capacity for recognizing visual patterns

• during a child's development the large area of the brain controlling finger movements becomes linked to the specialized circuits of the part of the brain that controls number, and the fingers come to represent numbers numbers.

The Brain’s Innate ArithemeticThe Brain s Innate Arithemetic• the capacity for basic

arithmetic is separate from arithmetic is separate from the capacity for rote memorization of addition and multiplication tables

• the part of the brain associated with intuitions about arithmetic is an area where neural connections from vision, sound and touch come together

Practice Really Does Make PerfectyJust as Einstein's brain has been found to have unusually densely packed cells in the left parietal lobe so musicians have the left parietal lobe, so musicians have been shown to have a bigger and more elaborately connected motor cortex -the region of the brain that controls the region of the brain that controls hand and finger movements - than non-musicians. This is not just a sign that these people are predisposed p p p ptowards music, but simply that practice makes perfect, i.e., the brain directs more cells towards those parts that are

hin most use. When pianists stop practising, their motor cortices go on a diet.

There’s nature … but the rest is up t tto nurture

i l hi t b d thi any numerical achievements beyond this are a result of our slowly mastering various representations of numbers supplied by the

d lt Th l d b d t surrounding culture. These include body-parts (fingers primarily), external aids such as tallies and abaci, and written symbols such as Roman or Arabic

l h b h by

numerals. This process begins at home … but, happens primarily in school

Building on innate strengthsBuilding on innate strengths

Subitizing: what is it? Why h i ?teach it?

Discussion Questions (key points)Discussion Questions (key points)1. What is subitizing?2. What is the difference between perceptual and

conceptual subitizing?3. What factors influence the difficulty level for

students in subitizing?4. What are the implications for teaching?5. What are some strategies that teachers can use to

promote subitizing?

All children can learn mathematics

• the ability to subitize is inborn … so how do we support that in the classroom and build on it?in the classroom and build on it?

• perception of simple arithmetic relationships is innate … so how do we support that in the classroom and build on it?

• a sense of approximate numerical magnitudes is inborn … so how do we support that in the classroom and build on it?

• the ability to track up to 3 or 4 objects in parallel appears to the ability to track up to 3 or 4 objects in parallel appears to be innate … so how do we support that in the classroom and build on it?

Ten Frames + Subitizing = Good Mental Models for Addition and Mental Math

Strategies

10-Frames and Basic Facts1 F am s and Bas Fa s

Dot Cards, Dot PlatesDot Cards, Dot Plates

Representation Cards & DominoesRepresentation Cards & Dominoes

Guess What??Guess What??Materials: Blank ten-frames, counters, a large hard-cover books to form a barrier between pairs of children.

Rules: One player secretly arranges some counters on a tenRules: One player secretly arranges some counters on a ten-frame. The other player asks questions that can be answered yes or no, trying to gain enough clues to work out the arrangement of counters. For example: Is the top row full? Are there 8 counters? Is there an empty box in the bottom Are there 8 counters? Is there an empty box in the bottom row?

Variations/Extensions:Va a /E1. As players become more skilled, the number of questions can be counted. The player asking fewer questions wins.

Skip CountingSkip Counting• Did you know?