Standard 3 promotes children “using models an relationships to explain their thinking and justify their answers and processes.” Both of these standards are well utilized by this article’s approach. The authors began by explaining why invented procedures promote understanding. Because children’s natural tendencies do not fit the traditional algorithms, the authors say that invented procedures promote math as an activity with meaning. In other words, they will focus on strategies and not just computation. Another reason given is that different problems are solved with different methods.
Second, the article focuses on ways to encourage algorithm invention. Among these is having manipulatives ready to support children’s thinking because when children begin school they are able to use objects to model before they have memorized math facts. The article also stresses encouraging kids to share their strategies. This allows children to learn from one another.
One teacher used this idea by having her students keep a “math log,” in which the student devises a particular strategy and explains it step-by-step.
Another example of this idea is allowing students to share their idea on the chalkboard. I think this method makes sense for many reasons. It would make kids more confident in their math abilities because they are starting out with a method with which they feel comfortable. I think it would probably be easier to relate a traditional algorithm to a child’s own strategy, than to try to form the child’s strategy by teaching the algorithm. The idea of manipulatives is good because the representation of a problem is often the difficult part for a child, not the math itself.
The only drawback I can see here are ones the author pointed out also. One, when a child is having difficulty with a problem, it may be hard to tell whether a teacher needs to intervene and show a child what to do or let the child continue. Two, other adults who are trained in traditional methods may try to steer the child towards traditional ways. However, these are small obstacles that do not significantly change the value of this method