A Small But Significant Decimal Point
A simple suggestion to help students who have difficulties with decimals. Read Full Post >
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December 24, 2012
July 15, 2012
Procedural Fluency: More Than Memorizing Math Facts
Procedural fluency or conceptual understanding--math educators have debated for years which is more important. I sided with conceptual understanding until my colleague Angela McIver helped me see the value of procedural fluency in terms of stamina. Like all of us, students have finite energy. The mo... Read Full Post >
June 30, 2012
Common Core State Standards: Math Instructional Shifts
The fate of the Common Core State Standards (CCSS) for Mathematics will depend on how we teach more so than what we teach. It's great, for example, that teachers will now have time to explore topics in greater depth. But unless they're prepared to go deeper with those topics, the extra time will be ... Read Full Post >
March 31, 2012
The Dreaded F Word: Fractions
Just hearing the F word can cause kids (adults too) to freak out. And if you think about it, there are lots of reasons students feel flummoxed by fractions. For one thing, there's the misleading vocabulary, as when we reduce a fraction to lowest terms even though it doesn't involve a reduction in va... Read Full Post >
March 05, 2012
Spiraled Instruction, Stifled Learning
My first teaching experience was as a substitute teacher in Chicago assigned to an 11th grade Algebra 2 class for ELL Polish students. I began by giving students an assignment their teacher had left for them. But no one attempted it, so I asked a boy who understood English if he and his classmates n... Read Full Post >
November 08, 2011
Combining Integers Instead of Adding and Subtracting Them
"Man, I didn't do nothing," students often said to me when I spoke with them about their behavior. "My point exactly," I replied. "If you didn't do nothing, you must have done something." It was after one of those exchanges when it occurred to me that the English language might provide a better way... Read Full Post >
September 14, 2011
Foiled by the FOIL Method
I observed an Algebra class recently where students were trying to multiply two polynomials, (x + 5) and (3x2 - 5x - 4). And as I roamed the room, I noticed several students who were stuck because they couldn't "FOIL it." Others, meanwhile, did FOIL it and came up with an incorrect product, 3x3 + 15... Read Full Post >
June 25, 2011
Math or Magic?
It's important when demonstrating mathematical procedures to stress the mathematics behind those procedures (i.e., the "why" behind the "what" or "how"), since failing to do so can cause or reinforce students' misconceptions. Take, for example, multiplying fractions such as 3/5 x 5/8, where teachers... Read Full Post >
May 25, 2011
Prevent Confusing Language From Confusing Students
In Academic Fluency: A Key to Academic Proficiency, I wrote that proficiency in an academic subject depends in part on fluency in that subject's language. Now, here's a key to helping students achieve such fluency: anticipating and alleviating confusion when words have different meanings in academi... Read Full Post >
April 10, 2011
Fractions: Divide and Conquer
A lot of students begin by finding a common denominator for the dividend and divisor when dividing by a fraction. And a lot of teachers intervene by saying, "Remember, you only need a common denominator for addition and subtraction. For division, just flip and multiply." Technically these teachers... Read Full Post >
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