Sunday, June 23, 2013

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, rather the means to an end. The end being 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 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 being the students' prior knowledge. Throughout the chapter, Sammons makes it clear how important it is to link new knowledge to existing schema in order to provide for 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 own 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 dispels 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 it becomes automatic for students. As in reading, Sammons goes on to explain how important it is to focus on meaningful connections and not the distracting ones. This, I know from reading, is sometimes hard for students. And when introducing making connections in math, I feel caution needs to be taken so that the making connections does not steer learning away from the math concept at hand.I do feel making math to math connections is a place I want to focus on next year to help students see the bigger picture.

I took some of Sammons ideas and used them to create these reminders for thinking stems/questions related to making connections. I can make a copy, cut them out, and put them on a ring as a visual reminder to use them 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 you think 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. It is through these experiences that 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 different architectural structures, I am telling you 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 if you think you could use something like this with your students. Just something to think about...

What are your thoughts on making connections in mathematics? Leave a comment or link up and share your thoughts. The next chapter focuses on asking questions. Asking questions is indeed an art in itself. Hope you stop by after June 27 to see what new ideas I find. In the meantime, don't forget to visit the other blogs who are hosting this chapter to get some of their ideas too: Teaching with a Touch of Twang and Smiles and Sunshine. You can click on the schedule below to see other blog posts from previous chapters as well!

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