Back to WHS!

This visit to WMS proved to be extremely beneficial by expanding my teaching practices and knowledge that I will be able to implement within my own classroom in the near future. During today’s lesson, the students were learning how to divide fractions. They were in the instructional phases of this mathematical topic, thus the students were instructed to divide whole numbers by fractions using diagrams. The teacher did not give students any algorithms, but rather presented application problems which included a specific scenario where a pizza shop has 6 blocks of cheese, and the workers need to know how many pizzas they can make with this cheese if it takes ¼ of a block of cheese to make a pizza. Thus, the students were trying to evaluate the problem of  6 divided by ¼ using diagrams and models. There were a variety of problems with different fractions that divided into the six blocks of cheese such as ⅓ and ⅕. All of the first few instructional, pizza shop examples had a 1 in the numerator to allow students to better see the pattern. Thus, students were taking their models, and asked to analyze how they might be able to find the answer without the use of models, but rather using an algorithm before moving on to more challenging problems.

I have seen this class struggle immensely in the past with relaying the mathematical ideas of a specific topic back to the teacher. However, during this particular lesson, the teacher flipped the classroom and asked the students to try to derive an algorithm from their basic knowledge of fractions. I was hesitant at first to see the effectiveness of this method because I assumed that students would not be invested in their learning as they normally become as the class persists. However, this was not the case at all. Students really began to analyze the models and create hypotheses and conclusions. Students were then asked to explain an algorithm if they found one, and many students concluded that to divide by a fraction is the same as multiplying by a reciprocal. This proved to be an extremely effective lesson for the students because not only were they thinking critically by solving the problems, they were also analyzing the mathematics behind their problem and further hypothesizing about the methods. This expands student learning and understanding immensely because it shows that students understand the material and the mathematical process so well that they can form further conclusions and analyze patterns. I was really impressed by the success, enjoyment, and level of engagement I witnessed as an effect of this lesson.

Having students analyze their work and develop further hypotheses is fundamental to the common core state standards. Flipping the classroom is a great way for students to really analyze and understand the mathematics in a way that works best for that individual student, while aligning with the state standards. This was the first truly successful middle school flipped classroom that I have ever been a part of, and it gave me great insight into the effectiveness of using such a method to further student engagement and understanding. This is a teaching strategy that I will definitely be using in the future.