Standard vs. Non Standard Algorithms & Teaching Students

Having to break down and figure out the way certain algorithm methods work was a brilliant way of putting us future teachers back into the students shoes. Many of these algorithms at first glance were not only completely foreign to us, but very unclear, even with our knowledge of how to add, subtract, multiply and divide. As a teacher it is extremely important to understand how the child is percieving the problem so that you can steer your explanation to the student in a way that is clear and helpful to them. These algorithms showed me that there are many ways that a child can correctly solve a problem that at a glance may seem incorrect or abnormal but actually result in the correct solution. The "Additon with Leprechaun's" video elaborates more on the importance of highlighting there are various ways to arrive to a solution. Like the teacher in the "Reasoning about Multiplication & Division" video states, it is important that we allow the students to first try and explain through their own understanding how algorithms like multiplication or division work. It is important for the students to first try and understand through their own methods how the algorithms work instead of being taught how to do these algorithms then just restating what the instructor tells them without actually understanding what they are explaining. When students explain their methods, it also gives them ownership and confidence.

The non standard addition, subtraction, multiplication and division algorithms, although very different, actually have very similar characteristics to the standard algorithm once broken down. Although set up in a non-traditional way to our standards, when worked out correctly the algorithms all produce the correct answer. Every algorithm, like the standard algorithm, distinctly arranges each digit in its correct place value spot. Through this, every digit produces a sum, quotient, or product with the correct digits in the correct place values. In doing this, when numbers need to be carried over or borrowed, every algorithm has its own unique way where the borrowing or carrying over will be conducted. All the additional algorithms, similar to the standard algorithm, account correctly for where each digit needs to be placed according to place value which allows for the correct answer to be produced through all of these methods.