Why is it important to teach subtraction as difference and not just take away?
One of the most profound ways I have learned to improve my approach to math instruction is to always keep the longterm in mind. What concepts and skills will the students need to build their foundation for higher level math?
It is easy for teachers to focus their math instruction simply on methods for teaching their grade level standards, but it is important to think through areas that will gain importance later.
One area that sticks out is the way subtraction is taught to young children solely as “take away.” Taking away, or decomposing groups, is an important aspect of subtraction.
However, it is also of utmost importance that kids understand subtraction as the difference between two numbers on the number line. When you teach this to a child, you are building the foundation for their later success with many concepts.
These include subtracting fractions, subtracting decimals, and subtracting negative numbers (all concepts that have traditionally been difficult to teach.) The number line also connects operations with measurement, as a ruler is a number line which includes fractions. Finally, using the number line builds understanding of the inverse relationship between addition and subtraction. This will also eventually build understanding of the relationship between multiplication and division.
This picture shows clearly a time in middle school math when subtraction needs to be seen as difference:
Practical Methods for Practice:
Play board games. As Think Math writes, “Kids used to gain the interval idea (in a slightly different form) from their experience playing board games. They knew that when they rolled a 5, they had to count their five spaces beginning with the next space. That is, they were counting moves, not positions. Today’s children have had far less board-game experience, so they need to get that idea in school.”
Make and play with large number lines. You can use masking tape on the floor or have kids put numbered cards in order. With young children you can use numbered paper plates, or attach paper numbers to the connecting foam squares to make “paths.” Roll a dice and jump, hop, skip along the number line. Get or make an operations dice (addition/subtraction symbols) and move forward and backward on the number line. Have two kids stand at different numbers and ask what is the difference between them.
If you are working with only one child, use stuffed animals or dolls.
Make a small paper character (or use one such as a lego person or counter) to move along the desk number line. Use your child’s interests to add a fun aspect- I have made ballerinas dance along the number line, frogs hop along the number line, cats pounce along the number line.
Make opportunities to ask kids in real world settings the difference between two numbers.You want kids to know that they subtract to find difference, and have lots of practice in real settings. When you play a game with points, figure out the difference between the high score and low score.
Ask how much the winner won by. Figure out the difference between yesterday’s temperature and today’s temperature. Figure out the difference between two prices at the store.
Goals
In conclusion, remember that our goals in math are:
- for kids to be able to apply their skills to real situations,
- to see the value of learning mathematical concepts,
- to build their foundation for higher level math.
Teaching subtraction as difference is a very important strategy to accomplishing all of those.