Monday, November 16, 2015

1+1 = ? Remember to Explain Your Answer

I am meeting more and more children who are having difficulty with basic arithmetic. Many of them are finding 1st and 2nd grade math difficult, if not impossible. Their parents are dealing with crying, frustrated, bewildered children. Parents, not sure of what the problem is, are turning to tutors for help. Often I find the child is struggling not with math but with language requirements. Many of these children can do simple arithmetic, but they can't explain how they do it. They also cannot explain how gravity takes them down a slide or explain the difference between the words a and the in a sentence. Children manage, however, to play on a slide and to use correct articles when speaking.

The new standards for math demand explanations. The mantra is, "We want students to understand math." One would hope that those who create tests reported to measure a child's "understanding" of a subject would themselves have an understanding of child development. 

There are many things in life a child does before being able to explain them. There are many things an adult does that he may have difficulty explaining. How many drivers can explain in detail what happen mechanically in a car when they hit the brakes? How many can explain the physics involved as the car stops?

A recent Atlantic article about the push for students to explain math was one of the few articles I have seen that discusses the problems some students have with this process. Although this article referred to middle school I have found that the push to explain one's answer starts in elementary school. Students on the autism spectrum, students with language problems, and students with delayed speech are put at a disadvantage when asked to explain, even with they can quickly and accurately find the answer to several of the same types of math problems.

Many younger children may not have yet developed the thought process which gives them the ability to explain the abstract. Some young students have problems with the eye hand coordination needed to circle or created the tiny lines and blocks needed to show regrouping in addition and subtraction. It is important to allow children to use concrete items when learning arithmetic. The fact that many children need these items makes one question their ability to then verbalize let alone write about an abstract algorithm. The other reality is that sometimes it is very difficult to explain in words something very simple. Some ideas are so simple that it takes a philosopher to make it convoluted through an explanation. 

Too often teachers are asked to encourage math discussions with children who get confused by the various suggested methods. While middle schoolers may have an aha moment when a peer discusses a math shortcut, a 7 year old may tune out because they haven't mastered the method, and don't have a true foundation to understand shortcuts.

Some students hit a math wall when introduced to fractions. Others hit a wall when introduced to algebra. I would be interested to see how many are hitting the wall when learning addition and subtraction today compared to a few decades ago.

There are many adults who claim to be "bad at math." Because of demands placed on them to "understand the math," some children who may get the process, and later with practice and maturity might understand the underlying concepts, decide early on that math is too hard. What good does it do to work one's way through a math problem, get the correct answer, and then be deemed ignorant because you can't give an adult explanation of how you got that answer?

We are not even going to touch the problem of children who can explain what they did in math (perhaps through memorization) and get credit for that explanation; but who seldom get the correct answer to a basic arithmetic problem. While it is true they will be using calculators someday, one wonders at the ability to explain without the ability to produce.

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