In my last post (Immersion Applies to Academic Fluency Too) I stressed the importance of immersing students in the unique language of a subject in order for them to master that subject. On a related note, it’s also important to anticipate and alleviate confusion related to words having different meanings in academic contexts than they have in everyday language.

In math, for example, we tell students to “reduce” fractions to lowest terms even though the process involves no reduction in value at all (e.g., 6/8 = 3/4). Unfortunately, you can’t just replace “reduce” with a more accurate word (such as “convert”) in your classroom unless the rest of the world is going to do so too. But what you can—and should—do is discuss with students how the meaning of “reduce” in this case is different from its usual meaning. Another thing you should do is refrain from shortening expressions when doing so might trigger confusion, as when teachers advise students to simply “reduce it” as opposed to spelling out, “reduce it to lowest terms.”

And finally, a great way to highlight and eliminate potential confusion resulting from language inconsistencies: True-False questions where you require students to explain why a statement is or isn’t true. Example: “When you reduce a fraction to lowest terms, the new fraction has a lower value than the original fraction.”

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This entry was posted on Sunday, March 7th, 2010 at 4:54 pm and is filed under General Instruction, Math. You can follow any responses to this entry through the RSS 2.0 feed.
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The problem here, as you know, is that you are not reducing the fraction, you are reducing the terms of the fraction. You can still introduce the term ‘reduce’ but I think you have to be more precise: “reduce the numbers on the top and the bottom of the fraction to the lowest numbers you can without changing the size of the fraction” is what is really meant. Once students get the idea of this, (and if you keep using that full sentence!), you could then say “We call this reducing a fraction”. Students do like to know the ‘big’ words, but I find it is better to give them the word after they demonstrate an understanding of the concept. A lot of them also like to know what level or criterion it is in the grading system or curriculum too!

Another stumbling block is the idea of equivalence of fractions like this, many students need to be convinced that 2/4 and 1/2 are the same size, even if they don’t look the same!

Thanks for your comments. Like you, I often defer giving names to concepts until students show they understand them (see https://ginsburgcoachingtt.wordpress.com/2010/03/06/immersion-applies-to-academics-too/). And I relate to the equivalent fraction stumbling block–I’ve seen a lot of students who’ve done better with this when they did the division(i.e. converting to decimals) first, then converted to fractions with common denominators.

Interesting, but I’m not sure that terms such as “reduce” are the source of the problem. In the standard (Hindu-Arabic) numeral system, every whole number has a unique name, so it is natural for students to think that fraction names are also unique. So they believe that 2/4 and 1/2 are different quantities, not because we call it reducing, but because they are written differently. Certainly one needs to make it clear that when we reduce a fraction we are not reducing its value.

I think that it’s important to make sure that students understand the concept of equality, because they often have misconceptions about it. The most common misconception is that the equals sign means “the answer is”, as if pressing the equals button on a calculator. Students should understand that 1/2 = 2/4 implies that 1/2 can always be replaced with 2/4 and vice versa, with no change in meaning.

Thanks for your comments, Dave. Point taken on kids thinking 2/4 and 1/2 have different values simply because they’re written differently. And thanks for emphasizing equality–this is huge in my experience, and not just w/fractions but when it comes to algebraic thinking, etc.

The problem here, as you know, is that you are not reducing the fraction, you are reducing the terms of the fraction. You can still introduce the term ‘reduce’ but I think you have to be more precise: “reduce the numbers on the top and the bottom of the fraction to the lowest numbers you can without changing the size of the fraction” is what is really meant. Once students get the idea of this, (and if you keep using that full sentence!), you could then say “We call this reducing a fraction”. Students do like to know the ‘big’ words, but I find it is better to give them the word after they demonstrate an understanding of the concept. A lot of them also like to know what level or criterion it is in the grading system or curriculum too!

Another stumbling block is the idea of equivalence of fractions like this, many students need to be convinced that 2/4 and 1/2 are the same size, even if they don’t look the same!

Thanks for your comments. Like you, I often defer giving names to concepts until students show they understand them (see https://ginsburgcoachingtt.wordpress.com/2010/03/06/immersion-applies-to-academics-too/). And I relate to the equivalent fraction stumbling block–I’ve seen a lot of students who’ve done better with this when they did the division(i.e. converting to decimals) first, then converted to fractions with common denominators.

Interesting, but I’m not sure that terms such as “reduce” are the source of the problem. In the standard (Hindu-Arabic) numeral system, every whole number has a unique name, so it is natural for students to think that fraction names are also unique. So they believe that 2/4 and 1/2 are different quantities, not because we call it reducing, but because they are written differently. Certainly one needs to make it clear that when we reduce a fraction we are not reducing its value.

I think that it’s important to make sure that students understand the concept of equality, because they often have misconceptions about it. The most common misconception is that the equals sign means “the answer is”, as if pressing the equals button on a calculator. Students should understand that 1/2 = 2/4 implies that 1/2 can always be replaced with 2/4 and vice versa, with no change in meaning.

Thanks for your comments, Dave. Point taken on kids thinking 2/4 and 1/2 have different values simply because they’re written differently. And thanks for emphasizing equality–this is huge in my experience, and not just w/fractions but when it comes to algebraic thinking, etc.