Last week, I talked about the worthwhile workshop I attended on the topic of math and language. There is so much more to share! Thank you again to Karen Tzanetopoulos, M.S., CCC-SLP, for sharing her expertise. Here is the link to last week’s post: http://www.wordfindingforkids.com/math-and-word-finding-an-unlikely-combination/
More on the important language basis of math…
Think of how many ways we say “approximate” – about, around, approximately, almost, roughly, close to, nearly, barely, maybe, just about, just over, more or less, not more than, -ish. And how does a student know when it is appropriate to choose one term instead of another? Yet learning to approximate is an important communication skill. Not only does it help us make predictions and solve problems more quickly, but it also helps us know if our answers make sense.
Our American measurement system is not the logical, predictable metric system used by most of the world. Inch, foot, yard, and mile are totally arbitrary. How about ounce, pound, and ton? Children in the U.S. have a huge disadvantage in learning to measure when compared to their peers in other countries.
Words used in a math context have very different meanings than words used outside of math. Negative numbers, fractions, remainders, proper numbers, mixed numbers, point, and reduce are just a few of the terms that mean something very different outside of the math room. And even within math class – does “eighth” mean eighth in line, or does it mean one-eighth of a whole?
Karen’s solution is to use concrete manipulatives and a physical number line. She has a great list of resources and materials, which you can ask her about at email@example.com. Sadly, the toys with which kids learn these concepts are disappearing from preschool and early elementary classrooms. Remember when young kids could play in the grocery store and “buy” a dozen eggs or piece together a wooden pie or a pizza divided into sixths or eighths? Our attempts to push kids ahead in math have resulted in many children who can’t conceptualize the meaning of numbers and formulas that are written on a page.
Fractions and decimals bring their own set of challenges. What does “point” mean? And why do the numbers to the right of the decimal point have different values and different names than the numbers to the left? Instead of multiplying fractions, kids first need to experiment with concrete objects and understand what the numbers represent.
We compound the difficulty when we get to word problems. The syntax of word problems can be very confusing! Here’s an example from Karen’s presentation:
Jose took the 26 baseball cards he no longer wanted and gave them to Brian.
Now Jose has 71 baseball cards left. How many baseball cards did Jose have
to begin with?
If we use the common strategy of encouraging a student to look for the key words “how many are left?,” the child will immediately assume it is a subtraction problem. But in this case, he needs to add! And what about that imbedded clause, “he no longer wanted”? A child with syntax difficulties is likely to miss a problem like this because of his language deficit, not because he can’t do the math. If he is further asked to “explain his answer,” he will probably put his head on his desk in frustration and give up.
I googled “first grade word problems” and came up with the following example common core problem:
Jen has 7 apples. Pat has 10 apples. How many fewer apples does Jen have than Pat?
First grade! So a child is just learning to read, and he has to figure out “how many fewer than…?” But if I give him a basket of apples, one with 7 apples and one with 10 apples, he can play with them, feel them, and count them. He is much more likely to figure out that lucky Pat has 3 more apples than Jen.
I have proposed more problems than solutions with my synopsis of Karen’s presentation. She brought blocks, physical number lines, and other manipulatives to demonstrate many ways to support our language-disordered students as they tackle the complex language of math. She proposed schema that help students organize and understand their information. By providing accommodations and scaffolding complex information, we can help them be successful in all levels of their math education.
Math can be a real challenge! Let’s do our part to parse out the language that is compounding our kids’ difficulties.