# * The spaces in between: fractions and decimals

The latest edition of Teaching Children Mathematics (TCM) is solely focused on teaching fractions and decimals.  And it’s a winner!  We don’t need a journal to tell us that many kids are struggling in this area of math.  Looking back over my own teaching history, it’s interesting to trace the evolution of teaching “between the wholes,” as TCM refers to it.  It’s a miracle that any of my students understood decimals and fractions back in the day.  I really didn’t.  It was considered a big leap when teaching supply companies created an abundance of pie- and strip-shaped manipulatives and games.  But these materials served to reinforce misunderstandings by focusing solely on area models of fractions.  Students memorized shapes and attached a meaningless value to them.  They rarely understood the relationship of fractional parts to real life.

One of the most powerful differences in this improved instruction is student exploration of part-whole relationships. My favorite article focuses on “French Fry Tasks,” where students are asked to “share” paper fries using estimation, with increasingly larger groups of people.  Some constraints are in place: no rulers and no folding the paper.  This strategy has a number of advantages, but a primary one is understanding that repeated sharing results in smaller sizes.  Should we tell kids that the denominator increases as the size shrinks or let them discover this through careful experimentation?  Duh.  TCM also includes two articles which provide excellent tools for assessing student understanding of fractions and decimals, along with strategies for improving their performance.

The strategies outlined in TCM are not unknown in the current teaching landscape.  So why aren’t they an integral part of math instruction?   Not all teachers DO know how to teach fractions and decimals effectively.  But I think the greatest deterrent is the clock.  It takes time for students to develop these understandings.  It takes a lot of student interaction and exploration.  It takes classroom management skills to keep these tasks meaningful.  It takes reasonably-sized groups of kids.  And it means slowing down the mighty rush to “get through” the curriculum before tests are administered.  Without administrative leadership, this lenghtier process of learning will not occur.  And for that administrative support to exist, it takes a broader (political) climate that rejects our current dash through the curriculum.  Let’s hear it for the french fries!