Best Strategies for Eliminating Elementary Student Math Misconceptions

Eliminating math misconceptions is difficult and merely repeating a lesson or extra practice will not help. Telling students were they are mistaken will not work either.

Recognizing student misconceptions and immediately focusing on the misconception is important. Providing guiding questions using inductive reasoning is the best approach, along with the use of writing prompts which help reveal further student misconceptions.

In Fractions the Largest Denominator is the Largest Fraction

Students assume this is always true because they learned that a 6 is larger than a 3 for example.

For example – the best way to eliminate this misconception is to allow students to work with math manipulatives when beginning work with fractions. This allows students to visualize denominators and numerators broken down into their basic parts.

Multiplication Always Results in a Larger Number

This is true when working with positive whole numbers. However not true when working with fractions and negative numbers. Students latch on to this misconception because of earlier experiences with positive whole numbers.

For example – instead of using “one half times eight,” try using “one half of eight.” The use of the word “of” when multiplying a fraction times a whole number informs students the answer will be less than eight. Using math games is another part of this strategy.

Geometric Shapes are not Recognized Unless Held Upright

This is typically an inadvertent misconception passed on by teachers. If geometric shapes, such as triangles or rectangles, are held in one direction all the time students will not recognize it when viewed in a different direction.

Students can only find a diamond shape if pointed in the right direction. In reality there is no such thing as a diamond shape, it is either a square or a rhombus.

For example – the best ways to eliminate this misconception is to allow students to draw geometric shapes in any direction, provide examples of shapes in a variety of directions, and rearrange displays of geometric shapes to point in different directions regularly. This strategy helps students understand math shapes are everywhere and can appear in any direction.

To Multiply by 10 Just Add Zero

This is a common misconception students fall into because this is something they hear all the time from parents, siblings, students, and others. Students learn this from working with positive and negative whole numbers. However it is not true when working with decimals and fractions.

For example - the best way to eliminate this misconception is to have students work out problems with decimals and fractions being multiplied by 10. When they work out the problems themselves, they will internalize that multiplying by 10 does not always mean just add zero.

The Tallest Container Always has the Greatest Volume

This a misconception caused by visual perception. Also they learn this from eating in fast food restaurants and similar locations that display cup sizes. The tallest cup always holds more, because of the way they are displayed.

For example – the best way to eliminate this problem is to have students fill tall containers with water and then pour the water into a shorter container which has the same volume. This is a difficult misconception to break and even adults have issues with this misconception.

The most effective method of eliminating math misconceptions is to address them immediately when observed. This is imperative, so students do not carry these misconceptions any further and develop a better understanding of mathematics.