Student Misconceptions About Fractions And Decimals.

 

One issue I've seen in most of my classes has to do with remainders and how they relate to their placement in decimals.  So many of my high school students can begin the process correctly but then they mess up.  For instance, they divide 27 by 4.  They start it correctly and know that 4 goes 6 times into 27 so they write down the 6, multiply 6 times 4 and write 24 below the 27 before subtracting.  They get 3.  This is where their misconception arises.  They then put the 3 after the decimal and get 6.3 for the answer even though the answer should be 6.75.  I don't know if they are just trying to finish the problem as quickly as possible or if they honestly don't know how to take the problem all the way to its normal conclusion.

So I figured I would address several misconceptions when it came to changing fractions into decimals and fractions - decimals in general, that we, as teachers, are likely to run into.  One issue is that students often see fractions and decimals as two different types of numbers, hence they do not see 1/2 as equal to .5.  They believe that fractions and decimals cannot be equal representations of the same number.

Along the same lines, they don't see that both fractions and decimals are designed to express parts of a unit quantity.  Sometimes they see the decimal point in a decimal as separating two different numbers and this may be the issue my students are having.  They may see the 4 as one number so in their minds the remainder of 3 goes on the other side of the decimal thus they have the two different numbers listed.  

Another issue is when students don't see the relationship between decimals clearly.  When they see a fraction like 4/5, they know the denominator tells them how many equal units the whole is divided into.  In a decimal, the information on the denominator is hidden and they have to rely on their knowledge of place value in order to do things correctly.  If you divide the numbers correctly, you end up with 0.4 as the decimal equivalent but students don't always recognize 0.4 as four-tenths or 4/10.  

In other cases, they might see 2.6 as two and 1/6th reading the decimal as the denominator and this interpretation leads to students association a fraction with the wrong equivalent decimal. In addition, students might see decimals with the idea that the more places you have in the decimal, the larger that number is.  For instance, students look at .621 and interpret it as 621 parts so it has to be bigger than .7 which only has 7 parts. The equivalent of this in fractions is when students try to compare denominators as 4 being smaller than 8 so 1/8 is larger than 1/4.  

Furthermore, since they don't understand that the denominator in fractions refers to how many equal parts something is divided into, they don't "see" that when you cut something into 4 parts, the size is larger than if the same sized cake was divided into 8 pieces so each piece is half the size.  In regard to decimals, they don't see that place value helps tell you the size of pieces.  For instance, 0.7 means that you have 10 pieces with 7 of the pieces colored red where 0.621 says you have 621 pieces out of 1000 colored in so each of the 621 pieces is smaller.

In my day, we just learned it without understanding the sizes of the parts involved.  I believe many of the misconceptions involved with both fractions and decimals create issues for when students convert from fractions to decimals and vice versa.  These misconceptions often drive how students arrive at an answer as they convert from fractions to decimals so they more than not get the incorrect answer.  

Let me know what you think, I'd love to hear.  Have a great day.