Consider the following examples of details versus big picture:
• Detail: What’s the answer? Big Picture: What’s the question?
• Detail: How much is 9 x 6? Big Picture: 9 x 6 is somewhere less than 10 x 6.
• Detail: Do I add or multiply? Big Picture: What does add mean? What does multiply mean?
• Detail: Is this inches or square inches? Big Picture: How are perimeter and area different? Similar?
• Detail: How do I add 2/7 + 3/7 ? Big Picture: What does 2/7 mean?
• Detail: What is 3/4 as a percent? Big Picture: What does percent mean?
• Detail: Is it true that 5 + 3 = 2 x 4? Big Picture: What does the equal sign mean?
• Detail: Is 11 x 13 equal to 93? Big Picture: Since 10 x 10 = 100, then 11 x 13 should be more than 100.
• Detail: (5 x 2 – 10) x 172 is a long problem. Big Picture: (5 x 2 – 10) is 0, and 0 times anything is 0.
Too often, kids learning math can be sidetracked to focus primarily on the details of math. Such details include the exact values of basic facts, the placement of the decimal point in a multiplication exercise, or converting fractions to percents.
Such details are important. As important as they are, however, details are not the only thing that’s important in math.
It’s also important that kids learn how to see the big picture, the larger perspective. Seeing the big picture requires non-math skills, such as overfamiliarity, impulse control, knowing definitions, practicing patience, knowing multiple ways to think about how much a number is or how to solve a problem, etc.
So what helps kids learn how to think with the big picture in mind? Here are some suggestions:
– Teach definitions of things, but keep definitions brief. Add means put together with. Equal means is the same value as. Percent means out of 100 or for every 100.
– Use those definitions. Ask your child regularly and repeatedly for the meaning of key terms like add, divide, equal,
– Aim for overfamiliarity – shoot for your child becoming overly familiar with, not just acquainted with, basic facts. Teach and play lots of math-type games – games involving lots of counting and calculation (more on those kinds of games in the next blog).
– Ask kids questions that go beyond details. See all of the Big Picture questions above. Encourage them to ask questions too.