Misconceptions of Geometry (Article 2 (Misconceptions In Geometry (NO 14:…
Misconceptions of Geometry
Misconceptions In Geometry
No 7: Types of Triangle
Students classify triangles based on angles but not sides.
Exp: Students are unable to identify a right-angled triangle as a scalene
SR: Teach students how to identify triangles based on sides and angles
No 8: Lines of Symmetry
Students draw lines randomly to divide shapes
Exp: Rectangle 4 lines
SR: a) Cut out shapes b) ICT
No 9: 'A rectangle is a long shape'..'A square is not a rectangle'
SR: Re- introduce Mathematical definition of rectangle at proper level
No 10: A rectangular shape is one that is common
Regular shapes like pentagon described in such a way not due to it being used all the time
SR: Exposure to examples and non-examples of polygons
No 11: Language
Great difference at different level of geometric thinking
Exp: Different level of language between teacher and student, Geometrical terms wrongly interpreted due to improper introduction
SR: Explain using geometrical terms, Students are aware of the reasons to changes in terms, Association of new terms with upgraded diagrams
No 12: The diagonal of a square is the same length as its side
Exp: Diagonal of square=lenght of sides
SR: Concrete shapes, Drawing
No 13: Using a protractor
Horizontal position, measure angles right to left
SR: Proper introduction to instrument & features, Practice, proper use, formative assessment
NO 14: In Transformations
Vertical or Horizontal Mirror line
SR: Mirror Image using mirror lines at different slopes, Mirror lines placed in different positions, Rotation at any point
No 6: Perpendicular Lines
Angles between lines oriented differently are not so easily
perceived as right angles.
SR: Teach students to mentally rotate perpendicular lines.
No 5: Orientation & Rotation of Shapes
Unable to identify a shape when it is not in a standard position/when it is rotated
SR: Teach students to recognize shape, then mentally rotate the shape
No 4: Shape Properties
Fail to identify examples of shapes that are not identical to their own mental image of
Triangles have one point at the top and two points at the bottom
The bottom of a triangle is flat
SR: - Introduce the properties that define a shape.
Provide both examples and non-examples
No 3: Angles
Larger space means larger angles
Differentiate between „larger turn‟ and a „larger space‟ between the two
lines making the angle.
Angle is defined as "amount of turn"
No 2: Conservation
SR: Using a geoboard and rubber bands, students can construct different rectangles of varying
dimensions but with the same perimeter and compare the resulting areas.
No 1: Identifying the Base and Height of a Triangle
Exp: Use the bottom line as the base and the height upwards from the base.
Examine different types of triangles.
-Turn their books to analyse shapes in case of spatial problems.
The relationship between Base and Height: their relationship of being perpendicular to each other.
Children's Misconception In Geometry
Rhombus in Different Orientations
Difficulty Understanding Non- Standard Orientation
Name Shapes > Describe Properties of Shape
Foundation of this study : Van Hiele levels of geometric thought
Two forms of classification of mathematical concepts :Partition classification & hierarchical classification
Partition Classification : categorized into different parts
Hierarchical Classification : subsets & sets
Instruments used : Manipulatives and Questionnaires
Method : Given one set of questionnaire with 5 tasks
Task 1 : Identifying and naming shapes
Task 2 : sorting of shapes into 2 groups
Task 3 : Sorting of class inclusion of shapes
Task 4 : Defining shapes
Task 5 : Class inclusion of shapes
Results : Students lacked vocabulary to distinguish shapes and their attributes
Describe properties of shapes by property of sides NOT angle properties
Misconception: All shapes with 4 equal sides are squares. (A rhombus has 4 equal sides)
Other properties to look at:
Why didn't you measure the angle?
Reason: 4 sides are equal = right angle
Van Hiele Level 1 thinking
Sorting shapes task: into triangles and quadrilaterals
Using: property of sides
Only a few were able to use correct terminology
'quadrilateral' = 4 equal sides
Sort into triangles and quadrilaterals: Van Hiele Level 0
Sort into distinct group of triangles and quadrilaterals & correct criterion (number of sides): Van Hiele Level 1
Sort all correctly + correct criterion / terminology = Van Hiele Level 2
Mayberry's Claim (1983)
"Different Van Hiele's level on different concepts"
Students either, lost, gained or remained on the same level on the two tasks
Sorting by class inclusion: to prohibit class inclusions
those attempting to form sub classes of shapes did so partitionally
the learners focus on only a single attribute
Many could not sort shapes into distinct classes
Class exclusion (forming distinct classes of triangles) was easier
Still not Van Hiele's Level 3
Defining shapes Task:
many imprecise visual qualities
reference to visual prototypes was common
Misconception: identifying and naming shapes task
Class inclusion Task:
perceiving a square to be excluded from classes of rectangles and rhombuses
A square is not a rectangle
Reason: "because all four sides of the square are equal"
Could not state partitional difference even at visual level
"look like" type definition
Use of imprecise geometrical terminology
(Clements and Battista,1992)
language problems (spelling problems)
conceptual misunderstanding (mostly)
Clements & Battista's List
Exploratory Analytical Method
Identifying and naming shapes task
Authors: Humphrey Uyouyo Atebe and Marc Schafer