5 Misconceptions in Elementary Mathematics
Elimination of Mistaken Beliefs about Math Concepts is Critical
Sep 15, 2008
Just like in other subjects, students have misconceptions in mathematics. These misconceptions are derived from their prior knowledge and experiences with numbers in their everyday lives. These misconceptions hinder the learning process, because they are tightly held by students. Their teachers need to provide tangible experiences to break these misconceptions.
Eliminating mathematic 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 a discussion on the misconception is important. Providing guiding questions using inductive reasoning is the best approach.
Math Misconceptions and Elimination Strategies
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.
- 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.
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.
- 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.
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.
- 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.
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.
- 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.
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.
- 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.
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