Elementary math teachers, you may be interested. Key points from an article in today's Wall St. Journal (my summary) that I thought were interesting: National tests show nearly half of 8th graders aren't able to put three fractions in order by size. Building a conceptual understanding of fractions in 3rd and 4th grades much more valuable than rote learning of rules. Teaching fractions with a number line is more valuable than using circle graphs/pieces, particularly for division of fractions. Knowing how to place fractions on a number line is a better predictor of kids' fourth-grade fraction skills than calculation ability, working memory or the ability to pay attention (per a recent study of 357 kids by Nancy Jordan of Univ of Delaware). A child's knowledge of fractions in 5th grade predicts performance in high-school math, even after controlling for IQ, reading ability, working memory, family income and education, and knowledge of whole numbers (per a 2012 study of 4,276 students led by Bob Siegler at Carnegie Mellon Univ). Battleship Numberline on BrainPop (game) has helped students understand fraction concepts. One banana plus one banana is two bananas. One apple plus one apple is two apples. But, one apple plus one banana is not two banapples. Neat description to use in discussing addition of fractions with different denominators.
The article's at http://online.wsj.com/article/SB10001424052702303759604579093231122420774.html. (Warning: a number of the comments run to teacher-bashing.) Herewith some random thoughts: Remarkably many adults struggle with the concept of fractions and with the meaning of the concept "denominator". Teaching that the denominator "names" the fraction ties into the etymology of "denominator": de- 'from', nomin- 'name', -or 'one who or that which does something'. I've explained that the denominator is to the fraction as the denomination is to paper money: it tells you what a given single piece of the fraction is worth, compared to the whole. One of the reasons that fraction bars work better than circle graphs is the practical one that, for most fractions other than those with a denominator divisible by 2, accurate circle graphs are really hard to draw by hand. Fraction bars are a bit easier, though still challenging. (I've discovered, though, that very tidy fraction bars can be drawn by using a word processor's table function: to show the fraction 4/9, I can make a table 9 columns across by 1 row deep - it should automatically be generated to be as wide as the page AND with cells of equal width - and fill four of the cells with color.) But it just occurred to me to wonder whether another advantage of fraction bars might be that, unlike circles, they have defined beginnings and ends: the kid who's really unsure what's going on (and who isn't, at first, with fractions?) doesn't also have to wonder exactly which piece to start at in counting 4/9.
Thank you, TG. I didn't feel any teacher bashing when I read it. I think the issue with circle parts vs. linear parts had more to do with the concept of division in the point they made. I have always thought that we jump too quickly into rote practices in math, in general, and fail to provide enough concept activities.
The ARTICLE didn't teacher-bash at all, but the readers' comments? Oy. Other members of this community might want to stick to the article (and the site makes that easy). No argument from me that concepts are hugely important: if the concepts aren't there, the rote practice has, so to speak, no mental hook on which to hang - and at which to be found when it's needed.
This is really interesting to me, Upsadaisy. I just gave my grade 7s their first math quiz and I'm a bit shocked, and saddened, by the struggles some are having with basic number sense--place value, factors, multiples, etc. I'm nervous about fractions when we get there.
I taught that grade for many years, so I know what you are talking about. I also taught elementary, and I saw how easy it can be to do all the worksheets and still fail to prepare kids for the kind of thinking they will encounter later. Place value is such a fundamental cornerstone. Maybe you could go back to it with a base ten set.
I'll certainly be doing that with some of them; these skills are so fundamental (and should really be a review for them).
CCSS standards in third grade math reflect the key points of the article...fractions ona number line, ordering fractions,common denominators...:thumb:
