J. Matt Switzer's article "Bridging the Math Gap" addresses the fact that there is a discontinuity between the math that is taught in elementary school and the math taught in middle school. Switzer states that there are many times when teachers within middle schools don't understand specific algorithms and mathematical methods that students had been taught in elementary school. The teacher then cannot understand exactly what students are thinking, and how they are solving problems. This creates a large gap in the students transition between the two schools, because the teacher cannot make connections to what students have already learned. Switzer then goes on to give a proposed solution to this problem, stating that teachers should strive to learn and understand what is being taught in the elementary schools, and then tie those ideas into the newer concepts that they are teaching. In this way, students are taught for understanding, and are better able to see the connections in mathematics between what they already know, and the new things that they are being taught. To demonstrate, Switzer then uses the concept of partial products to illustrate his point.
Switzer's observations on the transition between elementary school and middle school are very well stated. Middle school math teachers have a huge responsibility of connecting what students already know to the things that they need to teach them. This would help to eliminate the thoughts among Middle School students that they are doing an "entirely different kind of math." To accomplish this, three main things would need to happen. First, teachers from elementary schools and teachers in middle schools would need to get together and work with each other in order to facilitate a smooth learning experience for the students, as Switzer states in his article. Second, teachers would also need to be flexible and able to adapt quickly. When teachers come across something that they have never seen before, they must study it and understand it so that they can make better connections with students who already have that knowledge. Third, teachers would need to consistently seek out new algorithms and methods of teaching the concepts that they need to teach in order to find the best way to connect with the minds of the students. Switzer's article does an excellent job of demonstrating these facts, and his points are valid for anyone teaching transition math classes.