| If you've ever taken an IQ test, you'll be familiar | | | | of these is the progression: |
| with the type of question in which you're | | | | 1 2 3 4 5 6 |
| presented with a sequence of numbers, letters, | | | | In which the common difference (the difference |
| shapes or symbols and asked 'What comes next?' | | | | between two adjacent numbers in the sequence) |
| In this series of articles we're going to | | | | is 1. |
| concentrate primarily on number series, since | | | | The common difference in an arithmetic |
| these are mostly math-based and address two | | | | progression can be either any positive or negative |
| important questions. First, is this type of 'number | | | | whole numbers or fractions, so that the following |
| series' question a measure of general intelligence, | | | | are all arithmetic progressions: |
| mathematical prowess or the ability to match | | | | 9 8 7 6 5 4 3 |
| patterns? Second, is it possible to learn techniques | | | | 1 3 5 7 9 11 |
| that will improve your performance in this type of | | | | 0.5 1.0 1.5 2.0 2.5 |
| number series question? | | | | 100 90 80 70 60 50 |
| The answers to these questions are important | | | | With common differences of -1, 2, 0.5 and -10 |
| because IQ tests are meant to measure innate | | | | respectively. |
| intelligence, rather than learned capabilities. | | | | Presented with a 'What comes next?' number |
| Increasingly, both children and adults are faced | | | | sequence of: |
| with taking IQ tests at key points in their lives. | | | | 1 2 3 4 5 6 7 _ _ |
| Their scores may have a major impact on their | | | | Most kids would complete the sequence without |
| academic or career progression, such as the | | | | any reference to math principles, because they |
| awarding of scholarships, placement in school, | | | | recognize it as the pattern of numbers used in |
| college entrance or a promotion at work. It isn't | | | | 'counting', as taught at home or in elementary |
| surprising that some parents consider it beneficial | | | | math. Many kids will be able to complete complex |
| to 'coach' their kids in how to take an IQ test in | | | | arithmetic sequences using the same |
| order to enhance their performance. However, | | | | pattern-matching approach, without apparently |
| there is a real danger that a 'coached child' with an | | | | calculating or appreciating the significance of the |
| artificially inflated IQ test score may find | | | | sequence's common difference. For children that |
| themselves placed in a situation where they are | | | | do not spot number patterns so easily, the math |
| destined to fail, as their true intelligence falls short | | | | approach is to calculate the difference between |
| of the promise of their measured IQ score. If | | | | two adjacent pairs of numbers in the series. If |
| you are going to encourage your kids to engage | | | | this is the same and appears to be consistent |
| with 'What comes next?' math games, it is best | | | | across the sequence, then it is indeed a simple |
| to approach them as a fun activity that can | | | | arithmetic progression. Further numbers in the |
| improve their math skills, not their IQ scores. | | | | sequence can then be calculated by adding the |
| Simple Arithmetic Sequences | | | | value of the common difference to the final |
| In mathematics, a sequence of numbers in which | | | | number in the sequence. |
| the difference between any two successive | | | | In the next article, we'll consider more complex |
| numbers in the sequence is the same (in math | | | | arithmetic sequences in which math becomes |
| terms, a constant) is called an arithmetic | | | | more significant than the ability to match patterns. |
| sequence or arithmetic progression. The simplest | | | | |