At our math night in November, many people were curious about algorithms and how we teach them at Prairie Creek. It's a question that might be more common for parents of older elementary children but even young children use algorithms to solve problems.
An algorithm is a process one employs to derive an answer. When we use the term in elementary mathematics, we usually mean a way to compute the answer to a math problem. It is a predictable, step by step procedure that always gives one the correct answer. For example, many of us learned to "carry a one" when we were adding in vertical columns and had a value greater than 10 of a place value.
The simplest of algorithms may be to count out objects one by one to combine amounts -- it's a procedure that always yields the correct answer. A student may then learn to count objects by groups of two or five - a more efficient approach. Students might take the largest addend and "count on" -- this is also an algorithm. We sometimes think of algorithms as something that are taught to children only once they are ready for multi-digit, written problems. However, even our kindergarteners learn different ways to approach simple addition and subtraction problems and these are algorithms, too. In fact, the flexibility to approach the same problem in multiple ways is key to developing as a mathematician.
Algorithms are culturally based -- ask a friend who grew up in another country to show you how to do multi-digit multiplication and you may be surprised by what he or she considers "traditional." Different algorithms can be used more effectively or efficiently in some situations. For example, many of us learned "borrowing" or "trading" when dealing with a subtraction problem in which the subtrahend in a place value was larger than the minuend (bottom number "bigger" than the top number). However, it's not an ideal algorithm when solving a problem like "100-89." In that case, a fluent, flexible mathematician might reason "Well, I'll add one to the subtrahend to get to a multiple of 10, do the subtraction and add one to the difference." Both approaches produce "11" but the latter does so much more efficiently (at least if you don't have to explain it!)
Which brings us to how we use algorithms at Prairie Creek. We watch children carefully and when they show a solid understanding of a concept such as combining (adding) we introduce algorithms to help them work with larger numbers efficiently. Some of the algorithms we teach are the "traditional" U.S. algorithms but others might be new to many parents. Ideally, children develop a math sense that enables them to manipulate numbers with ease, allowing them to naturally choose a procedure that will produce an answer quickly and accurately.
As an example, it is our goal that a child who is confronted with a problem like "300x15." Would approach it using the partial products algorithm -- (300x10=3000, 300x5=1500 combine the products to get 4500). This is much faster than the traditional U.S. algorithm and the "lattice" method. However, a problem like "12,399 x 4,351" is best approached with lattice which insures accuracy in the face of complexity. (Of course, I would argue that a calculator is the best way to do this last problem -- but that's the subject of another blog entry, I expect.)
No matter what algorithm a child is using, it is crucial that he or she understands "why" the procedure produces the correct answer. Too often, we (and here I use a general "we," not specifically Prairie Creek) just know "how" to do something like long division. But without a deeper understanding, it's hard to catch mistakes, make estimations, and use an algorithm efficiently.
To get a feel for the different algorithms your child might learn during her time at Prairie Creek, you can visit a site that Michelle created when she was teaching in Connecticut and using the Everyday Math program, elements of which we use at Prairie Creek. These are the algorithms that that curriculum teaches explicitly and that we often use with the students. Math CiderSites
If you have more questions about algorithms or have ideas for future blog entries, please comment below or share your thoughts with your child's teacher.
Blog entry author: Michelle Martin
