Chapter 3: Making Mathematical Connections (BMC Book Study)

As I was reading this chapter, I thought, is important not to lose sight that teaching students in the mathematics classroom to make connections is not the learning goal but rather the means to an end. The end is activating schema and opening entry points of learning to solidify mathematical understanding (105).

I like how Laney Sammons described making mathematical connections as building bridges from the new to the known (100). To many students, math is viewed as a textbook with isolated units of study and is not necessarily a part of their everyday lives. We need to take where students are at and build from there. Sammons spends some time talking about schema. Schema is the students' prior knowledge. Throughout the chapter, Sammons makes it clear how important it is to link new knowledge to existing schema to provide a richer learning experience. Prior knowledge, or schema, consists of:
  • attitudes: How do students perceive math? 
  • experiences: What role does math play in the daily lives of our students and the world around them?
  • knowledge: What mathematical concepts do students understand and know? (88-89)
There are three types of connections in math, much like reading: math to self, math to math, and math to world (92-94). Math to self connections focus on one's life experiences involving math (allowance, time, measuring). Math to math connections focus on connecting past mathematical concepts and procedures to current units of study. Students need to see how math builds on prior math. Math to world connections dispel the misconception that math is only taught in school with a textbook. Math to world connections help students to understand the bigger picture of math.

Once again, explicit instruction is needed to help students learn this process of making connections so that they become automatic. As in reading, Sammons explains how important it is to focus on meaningful connections and not the distracting ones. This, I know from reading, is sometimes hard for students. When introducing making connections in math, caution needs to be taken so that making connections does not steer learning away from the math concept at hand. 

I took some of Sammons' ideas to create reminders for thinking stems/questions related to making connections. I can make copies, cut them out, and put them on a ring as a visual reminder during modeling and think-alouds. I also can make them for students as bookmarks to help them practice making meaningful connections in the context of what we are currently studying in math. Click on the image above and see if this might be useful for your students.

As students begin to develop an understanding that math impacts and exists in their daily lives, incorporating real-world problems create authentic learning experiences. Through these experiences, math becomes more meaningful and relevant (104). This reminded me of an activity I did during a geometry unit, Architectural I Spy. Once we started talking about architecture and the different shapes we could find in the various architectural structures, students no longer looked at buildings in the same way. Talk about connecting to geometric shapes in the real world. Check out the activity below by clicking on the image to see if you could use something like this with your students. Just something to think about...

What are your thoughts on making connections in mathematics? The next chapter focuses on asking questions. Asking questions is indeed an art in itself. 

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