Geometry and Shape Learning Through Visual Resources
Monday Morning
Creating, Describing, and
Comparing Shapes
Making Shapes
•
Square piece of paper
•
Scissors
Tangram Puzzle
Perimeter and Area
•
How do the
perimeters
of the pieces
compare (Grade 3 – attributes of
shapes)?
•
How do the
areas
of the pieces
compare (Grade 4 – areas of
rectangles, Grade 5 – area and
volume)
Problems
Can you create shapes with certain
“dollar values”?
Ohio’s New Mathematics Standards
Geometry
Kindergarten
•
Identify and describe shapes
•
Describe, compare, create, and compose shapes
Grades 1, 2, and 3
•
Reason with shapes and their attributes
Grade 4
•
Draw and identify lines and angles, and classify
shapes by properties of their lines and angles
Ohio’s New Mathematics Standards
Geometry
Grade 5
•
Graph points on the coordinate plane to solve real-
world and mathematical problems
•
Classify two-dimensional figures into categories
based on their properties
Tuesday Morning
Mosaics of Shapes and How
Children Develop an Understanding
of Geometry
Geometry Mosaic
•
Cut out all of the pieces
•
Determine the most descriptive
name for each of the pieces
•
Let’s try putting pieces together to
form new shapes
A Little Psychology …
So, how do children come to know
and understand “shapes” and their
attributes?
The Van Hiele
The Van Hiele
Model
Model
Teaching and Learning
Geometry
Pierre Van
Pierre Van
Hiele (1959)
Hiele (1959)
Why do students
struggle so much in
geometry?
Stages of Development
Stages of Development
•
Level 0 – Visualization (whole
Level 0 – Visualization (whole
shapes)
shapes)
Stages of Development
Stages of Development
•
Level 1 – Analysis
Level 1 – Analysis
(characteristics/properties)
(characteristics/properties)
Stages of Development
Stages of Development
•
Level 2 – Informal Deduction
Level 2 – Informal Deduction
(interrelationships)
(interrelationships)
Stages of Development
Stages of Development
•
Level 3 –
Level 3 –
Deduction
Deduction
(postulates,
(postulates,
theorems,
theorems,
proof)
proof)
Stages of Development
Stages of Development
•
Level 4 –
Level 4 –
Rigor (other
Rigor (other
geometric
geometric
systems)
systems)
Properties of the Levels
Properties of the Levels
•
Development is sequential
•
Advancement is dependent upon
instruction
•
Linguistics typical of each level
•
Mismatch between instruction/textbooks
and the level at which students function
How many
How many
triangles
triangles
do you
do you
see?
see?
From
Focus on Reasoning and Sense
Making
(NCTM)…
“Thinking, questioning, and justifying should occur whenever
students encounter a situation that is new to them, both within
and outside of the school setting, and not only when a proof is
required in geometry class. We rarely need to line up statements
and reasons in our daily life, but we frequently need to provide a
rationale … as to why we do or say particular things. Reasoning and
sense making should be regular parts of the geometry curriculum,
with or without formal proof writing. All students … must be able
to reason and make appropriate decisions. Geometry provides an
environment that can allow and encourage students to ‘practice’
the process of reasoning and sense making, for the benefit of all.”
% of 12
% of 12
th
th
Graders?
Graders?
•
International
International
49%
49%
•
United States
United States
19%
19%
Discussion Question
Discussion Question
What are the implications of the Van
Hiele’s research on how we plan our
lessons?
Practice/Assessment
Let’s visit a tangrams puzzle online app
to practice manipulating shapes and
using them to create other shapes:
http://www.abcya.com/tangrams.htm
Ohio’s New Mathematics Standards
Geometry
Kindergarten
•
Identify and describe shapes
•
Describe, compare, create, and compose shapes
Grades 1, 2, and 3
•
Reason with shapes and their attributes
Grade 4
•
Draw and identify lines and angles, and classify
shapes by properties of their lines and angles
Ohio’s New Mathematics Standards
Geometry
Grade 5
•
Graph points on the coordinate plane to solve real-
world and mathematical problems
•
Classify two-dimensional figures into categories
based on their properties
Dive into a visually engaging journey of geometry and shape learning, exploring various concepts, activities, and standards. From creating and comparing shapes to understanding perimeters and areas, this content offers insights into how children develop their understanding of shapes. Delve into the Van Hiele Model, Ohio's new mathematics standards, and the psychology behind children's shape cognition, all accompanied by vibrant visuals and practical activities.
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Presentation Transcript
Monday Morning Creating, Describing, and Comparing Shapes
Making Shapes Square piece of paper Scissors
Perimeter and Area How do the perimeters of the pieces compare (Grade 3 attributes of shapes)? How do the areas of the pieces compare (Grade 4 areas of rectangles, Grade 5 area and volume)
Problems Can you create shapes with certain dollar values ?
Ohios New Mathematics Standards Geometry Kindergarten Identify and describe shapes Describe, compare, create, and compose shapes Grades 1, 2, and 3 Reason with shapes and their attributes Grade 4 Draw and identify lines and angles, and classify shapes by properties of their lines and angles
Ohios New Mathematics Standards Geometry Grade 5 Graph points on the coordinate plane to solve real- world and mathematical problems Classify two-dimensional figures into categories based on their properties
Tuesday Morning Mosaics of Shapes and How Children Develop an Understanding of Geometry
Geometry Mosaic Cut out all of the pieces Determine the most descriptive name for each of the pieces Let s try putting pieces together to form new shapes
A Little Psychology So, how do children come to know and understand shapes and their attributes?
The Van Hiele Model Teaching and Learning Geometry
Pierre Van Hiele (1959) Why do students struggle so much in geometry?
Stages of Development Level 0 Visualization (whole shapes)
Stages of Development Level 1 Analysis (characteristics/properties)
Stages of Development Level 2 Informal Deduction (interrelationships)
Stages of Development Level 3 Deduction (postulates, theorems, proof)
Stages of Development Level 4 Rigor (other geometric systems)
Properties of the Levels Development is sequential Advancement is dependent upon instruction Linguistics typical of each level Mismatch between instruction/textbooks and the level at which students function
How many triangles do you see?
From Focus on Reasoning and Sense Making (NCTM) Thinking, questioning, and justifying should occur whenever students encounter a situation that is new to them, both within and outside of the school setting, and not only when a proof is required in geometry class. We rarely need to line up statements and reasons in our daily life, but we frequently need to provide a rationale as to why we do or say particular things. Reasoning and sense making should be regular parts of the geometry curriculum, with or without formal proof writing. All students must be able to reason and make appropriate decisions. Geometry provides an environment that can allow and encourage students to practice the process of reasoning and sense making, for the benefit of all.
% of 12thGraders? International 49% United States 19%
Discussion Question What are the implications of the Van Hiele s research on how we plan our lessons?
Practice/Assessment Let s visit a tangrams puzzle online app to practice manipulating shapes and using them to create other shapes: http://www.abcya.com/tangrams.htm
Ohios New Mathematics Standards Geometry Kindergarten Identify and describe shapes Describe, compare, create, and compose shapes Grades 1, 2, and 3 Reason with shapes and their attributes Grade 4 Draw and identify lines and angles, and classify shapes by properties of their lines and angles
Ohios New Mathematics Standards Geometry Grade 5 Graph points on the coordinate plane to solve real- world and mathematical problems Classify two-dimensional figures into categories based on their properties
