All you need to know about “Everyday math”
Everyday Mathematics certainly has some positive components. It allows for differentiated learning to meet the needs of a diverse student body – critical to any modern pedagogical approach. In addition, the emphasis on independent and critical thinking is important in helping children face unfamiliar problems and situations with confidence – or at least it should be. But confidence and accuracy are two different things; it matters little if a child thinks she knows how to solve a problem when the end result is, quite simply, wrong – or took her twice as long to arrive to as her peer. Despite its good intentions, the accuracy and reliability of the mathematical methods used in this program are questionable, as is the evidence supporting overall improvement of students in math achievement. The organization What Works Clearinghouse found that Everyday Math’s efficacy was only “potentially positive,” with no clear or definitive indicators that students taught math using this method did much better than the mean (students learning math under any other pedagogical approach).
When one examines the program itself, the reasons for this weak performance become clear. Students are taught many ways to approach a problem, known as algorithms. They may use whichever method they prefer, though the program identifies “focus” algorithms – those which are emphasized by the Everyday Mathematics curriculum. There are several problems with this pedagogy. First, is that none of the focus or alternative methods of solving problems have been shown to result in greater accuracy. Addition algorithms like the “partial sums” method, or the “column addition” methods (both of which work left to right) require a great deal of mental math, and are just as complex – if not more so – than the traditional method (known as the “fast method”, which is not even introduced until FIFTH grade). Common sense dictates that the more mental math involved, the greater the opportunities for error.
Then there are methods like the famous “lattice method” for completing multiplication problems – where two numbers are broken down into their places (hundreds, tens, ones) and set opposite each other in a grid format. The students then multiply each factor and then add the results. It is a method – like many of those which characterize Everyday Math – which creates many unnecessary steps to arrive at a correct answer. Conceptually, it is accurate – but in practice, it is unwieldy and tedious. Or what about the “partial quotients” method for solving division problems? In it, students pre-select “easy” multiples of the divisor and gradually subtract those from the number being divided until no more can be subtracted. The student keeps track of how many times he used the easy divisor to give the whole number, and what is left over is the remainder.
The same problem, done traditionally, would be completed in ONE column – the one used to do the operations. The “partial quotients method” requires two columns, both with their own set of operations – each of which introduces the opportunity for arithmetical error! In addition, it is unreasonable to assume that students who can barely stay in their seats for 40 minutes at a time will have the mental discipline to master not one, but two or more mathematical methods, each of which require extensive mental arithmetic, with any degree of proficiency. Setting up numbers in grids and attempting to align them properly is another issue – some children have serious issues with penmanship and staying in the lines to begin with – let alone deciphering problems in several stages, with multiple columns and different operations guiding each. Why make solving math problems any more difficult, laborious, or error-prone that it needs to be? It is true that these methods are meant to emphasize some of the guiding principles behind the way numbers work, how they can be broken down, and how they relate to each other. Certainly such practice is appropriate for students who have already mastered basic operations – and by basic, we mean to say the essential, time-tested, accurate, “traditional” algorithms which require a minimum of mental math, and the most efficient set-up on paper possible. But for most students, most teachers, and most grade levels – Everyday Math should be discarded.