The Next Step in Middle School Mathematics Remediation

Parents,

If you followed my last post, you know that the first step in mathematics remediation is to check to see if your child has memorized his or her basic mathematics facts.  If you use the link above, you will be able to find links for the practice of each number table for multiplication.

The next step is obviously that your child also needs to be able to perform multi-digit multiplication and long division without difficulty.  If anyone needs for me to find some links to helpful websites for this, please let me know!

The next step that is critical is that your child needs to be able to fluently work with fractions.  This is another large cause of many children having problems with mathematics in middle school, high school, and beyond.   Van de Walle, Karp, and Bay-Williams (2013) stated that students not fully understanding fractions keeps them from succeeding in algebra and higher mathematics.

Fraction skills need to be built one upon the other.  Many students have quite a bit of trouble with fractions, because they were not taught fractions in a concrete manner first, then moved on to operations with fractions.  For example, the 4th and 8th grade NAEP national testing found that only 41% of eighth graders in the U.S. could place three fractions in simplified form in correct numerical order (Van de Walle et al., 2013).

Researchers such as Johanning (2011) are finding that middle school students often have learned procedures, but do not have a basic number sense of fractions and their size.  Students who learn mathematics as a collection of procedures without understanding the conceptual underpinnings of fractions in a concrete manner cannot estimate in order to determine if their answer makes sense.  They are less able to answer real world problems that involve fractions.  The new testing being developed will place a greater emphasis on real world problem solving with mathematics.

Many parents, finding their child is having problems with mathematics will turn to a “math wiz” to help their child.  This may or may not be helpful.  If their trained teacher was not able to help them, this must cast doubt on the local “math wiz” being able to help them either!  Unfortunately, adults in the U.S. have mostly been taught mathematics as a group of procedures.  Many of us admit to not really understand the concepts behind the procedures.  Many adults state that they, “… never really understood math.”

The types of lessons that I teach begin with students using either manipulatives (fraction bars, fraction strips, pies, number lines) or pictures that they draw.  They will solve a real world problem that will help them begin to understand why the rules for operations of fractions work (For example, why do we not add the denominators when we add fractions?).  Using manipulatives and carefully chosen problems, I move students to understanding of why these rules work through problem solving and discussion.  Then, students work to improve their understanding and move from the concrete and the conceptual to abstract problem solving with the traditional procedures and algorithms using carefully chosen problems.  In this manner, students understand the procedures they are using and why they work.  I also emphasize estimation skills, so students are always being asked, “Does this answer make sense?  Why?” Then, we utilize games in order to build speed of computation.  This is how the National Council of Teachers of Mathematics (n.d.) advocates that mathematics be taught, based upon mathematics education research.

References:

Johanning, D. I. (2011). Estimation’s role in calculations with fractions. Mathematics Teaching in the Middle School, 17(2), 96–102.

National Council of Teachers of Mathematics. (n.d.). Principles and standards for school mathematics. Retrieved from http://www.nctm.org/standards/content.aspx?id=26830

Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson Publication. 

an-equivalent-fraction

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