Misconceptions - Geometry
Something here may be what is holding back your students' learning in mathematics.
Keep in mind that mistakes are made by some students but misconceptions are made by many students (and sometimes even teachers). Misconceptions happen repeatedly because students believe they are correct.
Click on the topic below.
Angles
Misconception 1: Students must use a 180° protractor. The type of protractor is not stipulated and it must be noted that the syllabus actively encourages the use of a 360° protractor.
Misconception 2: Angles are static. It must be noted that the measure of angles is based on the amount of turn from one arm to another. Angles have been taught in a static form due to limitations of the representation but now that there is access to dynamic geometry programs there is no need for this misunderstanding.
Misconception 3: Angles look like this: ∠ Too often students are only presented with angles in the anticlockwise orientation starting at a horizontal placement. Hence they cannot measure any angle represented in any other orientation, e.g. 〉⦦ ︿ ‹
Misconception 4: Let’s draw an angle. We don’t draw angles, we construct angles. To ‘draw’ suggests an estimation.
Misconception 5: Adjacent angles can overlap each other. Often students struggle with the definition of adjacent angles and confuse adjacent angles with angles that overlap each other.
Misconception 6: Right angles look like this: ∟ Ensure you change the orientation of the ‘right angle’ so students don’t always think it only faces in the right direction, e.g. ∟ â…ƒ â…‚
Lines
Misconception 1: What are lines that are neither horizontal or vertical? Lines that are neither horizontal or vertical are called OBLIQUE. Although this term is not in the Stage 1 syllabus. If discussed however, it is better to introduce it to the students and have them use the correct language than having to reteach “sloping” or “diagonal” in later years.
Misconception 2: Parallel lines can be curved. Parallel lines are straight lines so be extremely careful with your examples, e.g. Train tracks on a curved orientation. The tracks are simply equidistant, not parallel.
Misconception 3: Parallel lines must always be the same length. Again, if the examples are poor with all lines the same length, then students will create misconceptions like this.
Misconception 4: Parallel lines only come in pairs. Parallel lines occur in sets of two or more. Most examples present parallel lines as a set of two, which can encourage this misconception.
Misconception 5: Parallel lines must be the same thickness. Thickness has nothing to do with parallel lines - they must be equidistant. Again the misconception comes from a limited range of examples.
Misconception 6: Parallel lines are lines that never meet. WORST DEFINITION EVER! Every secondary Mathematics teacher curses this definition as they have to unteach this definition as skew lines also ‘never meet’.
Symmetry & Transformations
Misconception 1: Yes it is symmetrical! Not understanding that one side of a symmetrical shape/pattern is a reflection of the other, rather than a repeat in the same orientation. Students may have difficulty seeing symmetrical patterns, designs, pictures and shapes when the line of symmetry is not horizontal or vertical.
Misconception 2: Only have a horizontal or vertical axis of symmetry. Students may have difficulty seeing symmetrical patterns, designs, pictures and shapes when the line of symmetry is not horizontal or vertical.
Misconception 3: Students come with an understanding of ‘clockwise’ and ‘anticlockwise’. The digital age has reduced this understanding. Teachers will need to ensure students have a clear understanding of the terms.
Location & Position
Misconception 1: Is it referring to the intersection of the lines or the spaces between? This can become problematic for students. Cartesian planes refer to the intersection of the grid lines. Most maps refer to the spaces between the lines but not all. Students must be able to identify the type of grid referencing.
Misconception 2: Assuming students can connect between the physical and the representation (the map). Students will only master the skill of "translating" between a portion of the real world and a spatial representation of that same terrain by setting up circumstances in which students must repeatedly make connections between a school or park map and a video filmed in the school or community.