As a teacher, I remember endlessly talking about squares in the same breath as saying “squares are a special type of rectangle”. I often designed activities that resulted in pupils producing tree or Venn diagrams to show the family classifications of quadrilaterals. Whether it was angles, dimensions, measures, constructions, or to represent unknown quantities, shapes could regularly be seen in lessons.
As I design the geometry waypoints in the Cambridge Mathematics Framework I have found a large amount of research concerning the classification of quadrilaterals. Much of this research identifies issues that we’re all too familiar with: pupils not recognising that a square is a type of rectangle and a rectangle a type of parallelogram; the necessary and sufficient properties a quadrilateral and the characteristics of the shapes to list a few. Pupils rarely fully understand or know a true mathematical definition for each quadrilateral, and instead tend to list their characteristics, four sides and all.
A few specifics stick out. Some muddy the waters while others help us to clear up the problems. With that in mind, here’s a small selection of important issues to think about when you’re working in this area.
What is the definition of a trapezium? Is it a shape with exactly one pair of parallel sides or at least one pair of parallel sides? Or maybe even none at all! Different cultures define a trapezium slightly differently and many have the term trapezoid too. In the US (for some) a trapezium is a four sided polygon with no parallel sides; in the UK a trapezium is a four sided polygon with exactly one pair of parallel sides; whereas in Canada a trapezoid has an inclusive definition in that it’s a four sided-polygon with at least one pair of parallel sides - hence parallelograms are special trapezoids.
Now I’m not in a position to make a definitive decision on this – but pointing out that these issues exist (especially in the multicultural classrooms in which we teach) is essential, as is pointing out to those who search the internet when lesson planning that some care, attention and scepticism is often needed!
Euclid, the forefather to much of our school geometry curriculum, defined (Book 1, Definition 2) a square to have equal sides and right angles, an oblong to have four right angles but not four equal sides, a rhombus to have four equal sides but no right angles, a rhomboid to have equal opposite sides and equal opposite angles but without right angles and without four equal sides. All other quadrilaterals were trapezia.
Even just making sense of this is a great opportunity to really think about what these shapes look like and their familiar relationships as Euclid implies that there are in fact no intersections at all between shapes. Each is either a square, an oblong, a rhombus, a rhomboid or trapezia. Now wouldn’t that make life simpler?
Well yes and no. A question to ask yourself is why do we have the inclusive definitions we do? What’s the point – surely they just daze and confuse?
It all comes down to what we can deduce and infer from one shape to another. A square is a special type of rectangle and rhombus and therefore a special parallelogram. These hierarchical definitions lead to more economical definitions of concepts and formulation of theorems, simplify the deductive systematization and derivation of the properties of more special concepts, provide useful conceptual schema during problems solving, can suggest alternative definitions and new propositions and provide useful global perspectives (De Villiers, 1994).
In other words: a theorem you prove for a parallelogram holds for squares, rectangles, and rhombi as they are all types of parallelogram. Yet a theorem that holds for a square may not hold for all parallelograms as not all parallelograms are squares.
At this point it’s really interesting to look at the restrictions needed as you pass around the family of parallelograms; to consider what remains invariant and how this interacts with the theorem in question. It may be that your proof based on the square doesn’t rely on these tightened restrictions that make it square not just parallelogram, hence actually your proof will work for all parallelograms.
When searching through the wonders of the web, Wikipedia offers this wonderful diagram:
![](data:image/png;base64,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)
https://upload.wikimedia.org/wikipedia/commons/9/9a/Euler_diagram_of_quadrilateral_types.svg
You may not completely agree with the names being used, but what’s wonderful is how you can identify the tightening or loosening restriction as you take a walk around. Leave a region and you loosen, enter another layer and you tighten. It also highlights that actually, you know what, maybe oblong isn’t such a nasty word – oblongs and squares make up the rectangle family and ‘oblong’ might help with the whole squares are rectangles confusion. Alternatively, Clements and Sarama (2009) suggest using the double name square-rectangle. Would this mean we would also have rhombus-parallelograms? It would be nice to consider if some regions are actually empty and as a team we have a question as to whether ‘darts’ here should be encompassed in the kite region too?
The whole conversation just highlights how confusing defining quadrilaterals can be. Crucially we need to decide on what we consider to be necessary and sufficient conditions, and therefore familiar relationships, whilst at the same time being ready to state them explicitly. Maybe once we’ve done that we can draw our own Wikipedia diagram for our definitions. I’ll leave that once with you, but I would be interested in what you design! Can I uncover your definitions from your diagram?
References:
Clements, D.H., Sarama, J., 2000. Young Children’s Ideas About Geometric Shapes. Teaching Children Mathematics 6, 482–488.
De Villiers, M., 1994. The role and function of a hierarchical classification of quadrilaterals. For the learning of mathematics 14, 11–18.
Sarama, J., Clements, D.H., 2009. Shape, in: Early Childhood Mathematics Education and Research, Learning Trajectories for Young Children. Routledge, New York, pp. 199–246.
SOMETHING TO TRY:
KS1: What does each set of shapes have in common? What makes each one different?
![](data:image/png;base64,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)
KS2: A rectangle is a special type of parallelogram. Why?
KS3: Draw a tree diagram to link the family of quadrilaterals. Explain the links you have made.
KS4: Construct a cyclic parallelogram.
KS5: Van Aubel's theorem states that: If squares are constructed on the sides of any quadrilateral, then the line segments connecting the centres of opposite squares are equal and perpendicular. What shape would these centres form if the original quadrilateral was a parallelogram? Using hierarchical classifications show why. Consider the proofs of the original theorem here.
|