Wednesday, April 27, 2011

Teaching Patterns

            Patterns are a part of every Math program, particularly in the elementary ages.  Many teachers – whether public school, private school, or homeschool – quickly teach a pattern and then go on to another topic.  Others will use the lessons of patterns as an art activity and not connect the lesson to any other form of math.   Is patterning really worth teaching? 
            In a word, my answer is ABSOLUTELY!  Patterning is the basis of algebra, which, in turn, teaches logical reasoning, which is vital in adulthood.  Skipping patterning skills, or only regulating them to an occasional art project, is missing a cornerstone in mathematics.
            In the beginning, patterning should include simply recognizing a pattern.  These lessons include something like looking at a set of squares of different colors and the child must recognize that the pattern is “red, blue, red, blue,” and then tell that the next square should be “red.”  Developmentally, these lessons should really begin with concrete objects, like stuffed animals, different colored candies or cereal pieces, toy cars of varying sizes, colors, number of tires, etc.  The second step should be pictures on a paper, which is what most math programs include.  Colors, shapes, and pictures of objects are frequently used to demonstrate patterning skills.  Children should be able to tell what the pattern is and then be able to continue that pattern.
            This is a good beginning, but this is not where patterning lessons should end.  One step that is frequently skipped by teachers, particularly homeschool moms/teachers, is called patterning “transference.”  Once a child can recognize the pattern, the objects should be labeled with a letter or number.  For example, a “red, blue, red, blue” pattern can be transferred to an “AB” pattern.  A “square, circle, triangle, triangle” pattern can be called an “ABCC” pattern.  This is an important step because then the child can then transfer the pattern to a similar pattern, using different objects.  A “square, circle, triangle, triangle” pattern, once labeled “ABCC,” can then be connected to a “red, blue, yellow, yellow” pattern.  This is an essential step to developing logical reasoning.
            After a child is able to recognize a pattern, then transfer the same pattern to other objects, the next step is recognizing number patterns.  Numbers are more abstract, so that is why it is not in the beginning.  Patterning, like every other lesson objective, should be developmentally appropriate. Children should be able to explore different patterns, with increasingly more difficult steps.  Having children using number patterns of “add three” or “divide by 2” are examples, but you have to give them time to explore and create their own  number patterns before they are able to do more abstract patterns, such as find the rule of a table.
            When I taught fourth grade, we were required to teach something called a “function machine.”  For abstract thinkers, a function machine, or a table which lists numbers based on a set rule, makes it much easier to understand more complicated patterns.  An example of a pattern inserted in these tables would be, “2, 4, 6, 8.”  The recognizable pattern in this case is “add 2.”  The pattern is not stated – it must be recognized.  Then you can transfer this pattern, beginning with any number.  However, as stated in my article, “Not Just a Little Adult,” a fourth grader (generally ages 8 – 9) is firmly in the “Concrete” stage of development.  They are not ready for these non-stated patterns.  As a result, fourth and fifth grade teachers are very frustrated in teaching these concepts.
            To combat objectives the students were not developmentally ready for when I was a teacher and had no choice what to teach, I had to find a way to take this “abstract” idea and make it “concrete.”  What I did was teach the children that if the number pattern went up, the two choices were either addition or multiplication.  If the number pattern went down, the choices were subtraction or division.  Then they had to see what was needed to get from the first number to the second number.  I had them write the problem either above or below the number pattern, so they could physically see the pattern.  As you can tell, the above number pattern goes up, so my choices are either addition or multiplication.  Then I see what I can do to the first number to get to the second number.  2+2=4, so I can try to add 2.  However, 2x2=4 also, so then I have to check the next number.  If the pattern is add to, then 4+2=6.  Is 6 my next number?  Yes, so this is probably the answer, but I always need to check the other option.  4x2=8.  Is 8 my next answer?  No.  That means “add 2” is my pattern.  I took an abstract concept and made it concrete, so my students could understand it and do it.
            As a homeschooling mom, I recognize it’s a waste of my daughter’s time to teach her something she is completely not developmentally ready for.  At age 12, my daughter will probably be ready for this abstract concept, and it won’t take nearly as long for her to understand what she is doing.  If she is developmentally ready, she won’t have nearly the frustration level that she would have if it were taught too early.  In fourth grade, I will be teaching my daughter more complex, concrete problems which she will transfer to other objects, colors, or shapes.  I will not just check off a list that she understands it, but I will give her opportunities to explore these concepts so that she is ready when we start algebra and other more difficult concepts which rely on these base concepts.
            Patterning is a vital step in any mathematical program because it teaches logic.  Children should be able to transfer a pattern to other media, and they should be able to create their own patterns which they can then transfer.  Number patterns, tables, and function machines should be taught once a child is in the abstract level of comprehension.  These tables greatly simplify the concepts taught in algebra, so they should not be skipped, but they should be taught when the child is ready to learn.

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