WEEK NINE: SPACE (GEOMETRY)
- cassbass
- May 24, 2016
- 4 min read
The BIG ideas covered and related concepts, skills and strategies:
What geometry is;
An organised, logical and coherent system for the study of 1D (lines), 2D (planes) and 3D (solid) shapes.
Concept: That objects and pictures can be classified into differing shapes and dimensions
Skills:
(Week 8 Lecture - Part One)
Strategies: Count the sides, does it roll or slide? pattern blocks, venn diagram, mark lines of symmetry, classification table
How children learn geometry:
- At the sensori-motor stage, children respond to stimuli (touch & sight) while playing with blocks & other 3D toys.
- At the ikonic stage children form mental images of shapes. They recognise shapes by touch & sight and can name them, relating them to real life objects. Their thinking is prototypical (e.g., all are equilateral, all quadrilaterals are squares).
- At the concrete-symbolic stage they can work with drawings of shapes if they have a concrete referent on which to base their reasoning. Paper folding, geostrips & 3D models are crucial.
(Week 8 Lecture - Part One)
Blooms Taxonomy for higher order thinking:
How can I use Bloom's Taxonomy?
Knowledge - What shape is this?
Comprehension - Why is it a triangle?
Application - Can you see any other triangles in this classroom?
Analysis - Why is this a square and this a rectangle, when they both have similar attributes?
Synthesis - If we look at this rectangle and know how to work out the area, how can we use that to work out the area of a triangle?
Evaluation - Lets us compare these three triangles, what is the same and what is different?
Classroom resource to aid teachers in using Bloom's Taxonomy
(Smart Tutor. (n.d.). A blooming butterfly [Digital image]. Retrieved from http://thinkonline.smarttutor.com/blooms-taxonomy-poster-for-parents/)
Space and geometry concepts in relation to 3 dimensional shapes (solids);
(Week 8 Lecture - Part Two)
Teaching Strategies for 3D shapes:
Teaching 3D Shapes:
- Sorting and classifying shapes
- Making shapes from play dough, clay, mud
- Matching shapes
- Look for shapes in nature - Tree trunks, rocks etc
Ask the students:
- How does this shape feel?
- Can this shape be moved? Does it roll?
- What shape does this look like?
- What attributes does the shape have?
Space and geometry concepts in relation to 2 dimensional shapes (planes);
(Week 8 Lecture - Part Two)
Reflection: What I found most interesting about this week's lecture is how many early mathematical concepts lead seamlessly into one another. For example, we use shapes in patterning and patterning can help us learn about attributes, whilst also being an early introduction to algebra. This means as a teacher, I will have to be aware of how I introduce early concepts as these will shape following concepts (and so on). This is why it is important to use concrete manipulatives, so students have explored their understanding in a way that creates a very firm concept in their mind, before moving through to the next concept.
The Language Model:
Misconceptions and strategies to remediate:
Misconception:
That the same shape in a differing size, has differing angle sizes. For example (as in lecture 9); A smaller kite has smaller angles - WRONG - We know that the sum of a quadrilaterals angles equals 360 degrees.
Strategies to avoid or remediate misconception:
- Direct comparison using paper cut-outs
(Week 9 Lecture - Part One)
Australian Curriculum and Scootle links:
ACARA Links to Foundation Year:
(http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?layout=1)
Scootle Resource:
Learn to draw shapes with Ziggy:
(https://www.scootle.edu.au/ec/resolve/view/M019176?accContentId=ACMMG009)
Seeing shapes:
(http://www.scootle.edu.au/ec/viewing/R10709/index.html)
Additional Resources:
Teaching Strategies and resources:
1. Playdough to Plato. (n.d.) Learning shapes with marshmallows [Photograph]. Retrieved from http://www.playdoughtoplato.com/learning-shapes-marshmallow-geometry/#_a5y_p=1933617
2. Kindergarten Kindergarten. (2012). Dimensional geometrical shapes [Photograph]. Retrieved from http://www.kindergartenkindergarten.com/2012/02/math-problem-solving-week-7-2-dimensional-geometric-shapes-.html
3. Craftaholics Anonymous. (2015). Geometry paddle pop sticks [Photograph]. Retrieved from http://www.craftaholicsanonymous.net/summer-crafts-for-kids
Chapter 16: Geometry
- Understanding the properties or attributes of objects and the relationship amongst differing geometric objects is important
- Students need concepts from 2D shapes in order to more completely describe 3D shapes.
- Describing and sorting - Children need to describe properties of 3-dimensional objects to explain how 2 or more objects are alike or different
- Activities - Who am I? Who stacks? How are we alike or different? Who doesn't belong? How many faces do I have?
- Exploring and discovering through construction - Often difficult for children to visualise 3D shapes. Construct 3D shapes from net cutouts etc
- Two-dimensional shapes - Children first recognise shapes in an holistic manner (Eg; that is a triangle because it looks like something in my room that is a triangle).
- Build vocabulary gradually and build upon it - When introducing triangle - Focus on what tri means (tricycle, tripod etc).
-Number of sides and vertices - One of the first properties children will focus on is the number of sides.
- Activities - How many sides? Less is best. Can you make?
- Symmetry - Have children explore symmetry with mirrors / Draw lines of symmetry across shapes
- The sum of angles:
- Triangle - 180 degrees
- Quadrilateral - 360 degrees
- Base angles of an isosceles triangle are equal
- Polygons:
- 3 sides: Triangles
- 4 sides: Quadrilaterals
- 5 sides: Pentagons
- 6 sides: Hexagon
- 7 sides: Heptagons
- 8 sides: Octagons
- 9 sides: nonagons
- 10 sides: Decagons
(Reys, Lindquist, Lambdin, Smith, Rogers, Falle, Frid & Bennett, 2012)
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