Entry #5: Common errors in geometry 👦👧

 Common errors in geometry

Learning is such a whole complex process which requires effort and commitment. However, it is a fact that, when we are learning, there are other factors which have a significant influence. Between those factors, we find the mistakes or errors 😀. As Barrantes and Zapata (2008) state, errors are another element of the learning process. Sometimes because they are useful in order to learn and other times because they are internalised before the own teaching-learning process, which will condition the development of it. Due to all of this, I consider that teachers must know those errors beforehand in order to correct them if they appear during the lessons, to have an adequate explanation for them and not to persist in them. Therefore, some of those errors have their origin in the visual representations made by textbooks and by teachers (Barrantes & Zapata, 2008), so it is not a bad thing to be aware of them in order to tackle them without problems. Having said this, let's see some of those common errors! 👀

ERROR #1: TWO ROTATED PERPENDICULAR LINE SEGMENTS ARE NOT PERPENDICULAR

This common error, exposed by Cabello et al. (2014), consists of not being able to recognise two perpendicular line segments which are rotated. In other words, if the two line segments are not parallel to the edges of the paper or book, students have difficulties when trying to recognise them 😮. In addition to this, Barrantes and Zapata (2008) say that it also happens with parallel ones. 

In fact, I am sure that most of us need to move the paper in order to see if two rotated line segments are perpendicular or not! Or at least, that happens to me 😳, so we must take it into account. 

ERROR #2: A RHOMBUS IS A ROTATED SQUARE

This was a common mistake that I used to commit when I was a student. However, we must say that a square is a particular case of rhombus, but a rhombus is not a square 😲. As a consequence, a rhombus is not a rotated square. But why is a square a case of rhombus? Well, a rhombus is considered to be a parallelogram with four equal edges, consequently, a square is a particular case of it whose four angles are equal (the angles of the rhombus are equal two by two). For all of this, although a square is a kind of rhombus, a rhombus is not a rotated square. Thus, a rotated square... is still a square 😅.

ERROR #3: CONFUSION BETWEEN THE APOTHEM AND THE RADIUS OF A REGULAR POLYGON

There are students who have difficulties in this situation (Cabello et al., 2014). On the one hand, the reality is that the apothem is the perpendicular line segment between a side of a regular polygon and its centre. On the other hand, the radius is the line segment that goes from a vertex of a regular polygon to its centre. Actually, it is the radius of the circumscribed circle of the regular polygon 👇.

ERROR #4: A RIGHT TRIANGLE MUST REST ON THE SIDE WITH THE RIGHT ANGLE

According to Barrantes and Zapata (2008), students have many difficulties recognising a right triangle whose 90-degree angle is not in the lower side of it. It is important to know it, since the right triangle can be rotated, which implies many difficulties for students. As well as this, students also have many difficulties to recognise a rotated rhombus 👦👧. 

Well, that has been all! Of course, there are more common errors, but here I have given you four of those mistakes in order to learn them. If you know more errors, write them in the comments! See you! 😀

References

Barrantes, M., & Zapata, M. A. (2008). Obstáculos y errores en la enseñanza-aprendizaje de las figuras geométricas. Campo Abierto, 27(1), 55-71. https://mascvuex.unex.es/revistas/index.php/campoabierto/article/view/1985

Cabello, A. B., Sánchez, A. B., & López, R. (2014). Errores de conceptos geométricos persistentes en alumnos de 1º de ESO: detección y metodología de corrección. Épsilon, 31(1), 21-36. http://funes.uniandes.edu.co/18324/1/Cabello2014Errores.pdf