Exploring Patterns and Algebra

When you were a student in elementary school, did you think that patterns and algebra were two separate units in math that never really crossed paths? This is the misconception that I had as a student in elementary school. This week's class gave me the opportunity to delve into the topic of patterns and algebra and to discover some useful teaching strategies and resources to incorporate in my future math class.


Building Connections

We began our exploration of patterns and algebra with a matching exercise where several patterns were demonstrated in four different ways: a table of values, a graph, an equation, and a stage-by-stage block diagram. Our task was to group the four different illustrations which represented the same pattern. I found this task to be very helpful in demonstrating how patterns and algebra are so closely connected. As we collaborated to discuss how an equation, table of values, graph, and block diagram were linked together, I was able to understand how an algebraic equation forms from generalizing patterns to create a bigger picture of the relationship. This activity reminded me of the importance of encouraging my students to discover the connections between different areas of math. From my own experiences and observations, I think it is easy for students to get so caught up in the minute details that they lose sight of the big picture of how math concepts are connected. I find that when students are able to see the bigger picture, they are able to develop a deeper, more meaningful understanding of the math concept they are learning.

Olij, B. © 2016

Teachers as Facilitators

This week we were also able to gain a better understanding of the value of facilitation as one of our group members took on the role of facilitator during our matching activity. The second video of The Three Part Lesson in Mathematics describes how teachers can serve as facilitators in the classroom. The role of the facilitator is to ask questions that encourage students to make connections, make predictions, justify their answers, debate ideas, and explain their reasoning. The video provided some examples of open-ended questions that a facilitator might use such as "How did you do this?" or "How do you know...?" or "How else might you solve this?" Rather than give students the necessary information through direct instruction, the facilitator is there to guide and support students as they discover and explore the key concepts. This was another important reminder for me that as a teacher I need to create a learning environment where my students are active learners. It is not very beneficial for my students if I simply give students the information to memorize through rote learning. Rather, I want to facilitate a collaborative learning environment where my students take ownership of their learning as they explore, question, and share their ideas.


Gizmos 

Another helpful resource that allows students to explore patterns and algebra is the Function Machine found on Gizmos. In this app, students can create a table of values by dropping different numbers into a function machine. They can then look at the table of values to determine what the function or expression of the machine is. I would definitely encourage my students to use this app to become more familiar and comfortable with identifying patterns and forming equations as it allows students to experiment with patterns and equations in a fun, interactive, and engaging way.

Screenshot taken from the "Function Machines 1" app on Gizmos
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