PARENT TO PARENT

Q: My daughter was always good at math until middle school. She insists that she understands, but can't seem to get the right answers, especially in the Algebra part. She did well with the other parts, like geometry and statistics. What can I do to help her?
Cynthia

A One concept many students struggle with is the Order of Operations. I don't know when the switch took place, but since I was in high school (back in the dark ages, as my children say) the way the books teach it has changed. In short, it's wrong. If your child does what she is taught, she'll get a wrong answer about 30% of the time - and on a test, that's a pretty bad grade. Now, not all teachers teach it wrong, and it isn't the teacher at all so let's not get upset and angry; it's the textbook that's the problem. Many students are introduced to the Order of Operations one piece at a time, upside down and backwards, over a period of months or even years, depending on the curriculum. Then there are the mnemonics (memory tricks) used to remember the order - they suggest a wrong order as well.

Here is what many students do: First they do parenthesis, then exponents, then multiply, then divide, then add, then subtract. This is only correct some of the time. The Order of Operations is as follows: 1. Powers and Roots (note there are two operations, not one. Most students are completely unaware that roots are also exponents). 2. Multiply and Divide. 3. Add and Subtract. Notice that the operations are in pairs. Adding and subtracting are, essentially, the same thing, as are multiplying and dividing; also powers and roots. The operations in each pair have equal status, so you do the math, from left to right, as it appears. For instance, you do not always add before you subtract; you add or subtract, in the order they appear in the equation. An example would be 8 - 3 + 2 =. If you add before you subtract, your answer would be 8 - 5 = 3. However, working from left to right, your student should subtract first, then add: 8 - 5 = 3; 3 + 2 = 5, which is correct. Notice the different answers - it's a minor detail, but it makes a huge difference.

Finally, notice the absence of parenthesis in the order I gave. This is a technicality, but an important one. Parentheses are not operations; you cannot "parenthesis" a number; it does not keep order; parentheses undo the order of operations. In short, they mess it up and force you to do the operations out of order, and therefore should be listed after the order of operations, as an aside. "By the way, you do the operations inside the parentheses first", is not part of the order, but is instead of the order.

So - your daughter does the math inside the parenthesis first, then goes back and works any powers and roots in the problem, then goes back and does any multiplication or division, in order, left to right, as they appear. Finally, she goes back and does the adding and subtracting, again in order, left to right, as they appear. This answer will be correct.

Q: My son is going into 4th grade. He did fine for the first few years, but last year started having problems with reading. He reads fine, but has a problem with comprehension. His teacher suggested that he may have an information processing problem and wants me to have him tested. He's really smart and doesn't have problems understanding most of the time, so I'm a little concerned about this. Is there anything I can do to help him with his reading?

A: Your son sounds like many students I see at the tutor center - he reads beautifully, but when he's finished he has no idea what he just read. The first thing you can do is check his reading style. Have him read a page out of a book for you, out loud. Make sure the book is simple enough so he doesn't struggle with a lot of words. Also, be sure he has not read the book recently. A simple chapter book for second or third grade should work well. Do not interrupt, correct, or in any other way comment about his reading until he is finished. Read silently along with him, watch him as he reads and look for the following: Does he skip words? Does he paraphrase simple sentences? Is he misreading words that are similar, such as 'take' for 'tack'? These are all very common problems, and students who make these mistakes will have difficulty understanding the text. Finally, a huge problem is monotone reading. Many students rush through a paragraph or page, as if reading quickly makes them a good reader. They don't stop at periods, don't pause at commas, totally ignore quotation marks, and treat questions the same as statements. Punctuation is there to give meaning. It must be used. A child's comprehension can often be dramatically improved simply by having them slow down, pay attention to details, and read with punctuation. Set aside a few minutes, three or four evenings a week, to read with your son. Have him read out loud to you, and help him learn to read 'properly'. Slow him down, make sure he stops or pauses at punctuation, discuss the use of commas in different sentences, etc. This may be all your son needs to become a truly excellent reader, since he already has the skills to read words. Don't forget to look for topic sentences at the beginning or end of paragraphs.

I hope this helps, Michele.

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