Algorithms: Making Sense For All Students - Week 2

Last week's math class opened with the question, "Why encourage Alternative Algorithms?" When I heard this question I instantly put my head down because I did not understand the concept of an algorithm. I shyed away from the word because I thought it was something extremely complex and out of my mathematical league. However, to my surprise and embarrassment this big word, "algorithm", is simply a step by step process for how to solve a problem.

In my opinion, teachers MUST encourage alternative algorithms because not every student learns in the same way. Algorithms promote creative thinking for how to solve a problem. This thinking might be understood in numerous ways depending on the student. One way of solving a problem might make total sense to one student but another way might make even more sense to a different student. As a result, I believe in promoting a classroom that encourages my future students to learn in a way that best suits them. There is no need for one right solution because there are thousands of right solutions. It is the responsibility of each individual student to find that one, or multiple right ways that best suits their learning.

Below is an example of Skip Counting presented in last week's class. Skip Counting is an algorithm that uses a number line to solve addition and subtraction problems. When using a number line it is important to remember that the line always increases to the right and decreases to the left. Skip counting can be used for students in all grades. I love this method because it makes sense. I am an extremely visual learner and this method appeals to me because I can see the process it takes in order to get the answer. The use of a number line helps students to keep track and visualize their math problem.

Problem: (Nathan's class goal is to sell 50 tickets, they have already sold 332 in the first week, how many will they have to sell to meet their goal?) 500-332=168 The 332 is broken down into 300, 30 and 2 across the number line. Younger students could break down the 300 into (100, 100 and 100) to better visualize the skip counting.

Helt, Courtney. 2016

As well, this picture is taken from last weeks math class. Below is an example of how to solve a multiplication problem using the concept, objects in an array. This is one way for understanding multiplication. Again, being a visual learner this solution makes sense to me. The problem is separated into a rectangular chart. Students can break down the process of multiplication through sections to further their understanding.

The multiplication equation 25x 28 is broken down into 20 + 5 and 20 + 8. Each number is multiplied by the adjacent number and the totals are added together. Therefore the equation is further broken down, and expanded to provide insight into the equation.

Helt, Courtney. 2016

Furthermore, it is crucial as new teachers to understand the importance of teaching our students how to solve equations in numerous ways. It is also crucial to show our students visually what we are doing in order for them to fully understand there math problems. Providing students with open problems will encourage interest and creativity. This will keep our students wanting more from math!

Jo Boaler couldn't have put it more perfectly when describing, Brain Crossing and it's importance to learning math, "Drawing, and visualizing and using symbols together in math is the most powerful math learning." Hence,it is key as future teachers to provide students with multiple ways to solve a problem and encourage the use of visual solutions.

https://www.youtube.com/watch?v=qZBjub36Bvs
Boaler, Jo. [S Lamb] 2015, August 25. "Day 2 - Brain Crossing" Retrieved from https://youtu.be/qZBjub36Bvs

Till next time,
Cheers, Courtney