Instructional Dynamics II: Numeracy and Quantitative Reasoning for Diverse Learners - EDU-3266

What does it mean to think mathematically?

This was the guiding question for Instructional Dynamics II, a course which was centered around a 60-hour practicum in an upper elementary math classroom. My practicum was spent in a local fourth grade classroom, during which I designed and taught a lesson and helped out in the class as needed.

The course objectives were to:

1. Gain knowledge of how children think mathematically and respond to math instruction;
2. Acquire strategies for planning lessons that are contructivist, integrated, and standards-based, and meet the criteria for the licensure portfolio at JSC;
3.  Develop a broad perspective on mathematical instruction including how it is shaped by school and classroom culture;
4. Construct a vision of themselves as positive leaders in math instruction.

We had several great texts to use during this course, along with numerous relevant articles to reference both during our practicum and for future use in our teaching careers.

Our main text was Learning Mathematics in Elementary and Middle Schools by Cathcart, Pothier, Vance, and Bezuk. This book will be be invaluable to me as a practicing educator. It has so many tips and a lot of insight into how to build on children's existing knowledge to advance their mathematical understanding.

Another text we used, and a resource I am grateful to have is, How the Brain Learns Mathematics by David A. Sousa. As one might expect, the book focuses on brain development and how it applies to learning mathematics. It's a valuable tool for all teachers of mathematics who wants to base their instruction on brain research and how it applies to their students' current phase of development.

We spent some time discussing lesson plan development, and followed up in the next class by presenting our lessons to the group and getting feedback on what worked and what didn't. One thing, in particular, that I took away from our meetings was that questions during math should be more open-ended so as not to limit students' thinking. Another important thing to remember is to provide students with wait time. Don't worry or jump in right away if you ask your students a question and no one volunteers and answer. Give them time to come up with something. It's important, also to have students explain their strategies. They can do this with partners, or with the whole class by going to the board and working their way through a problem.

I believe I said this in an earlier post, but it remains just as important-- children must feel safe and protected and cared for in their classroom environment in order for them to take risks in learning. How important this becomes in math! Math is all about taking risks and making mistakes.

We discussed, too Pierre van Hiele, a Dutch psychologist who spent years gathering data on his middle school geometry students. He found that if students have the experiential base, with one skill building upon the previous understanding and so on, then they can be successful in understanding geometry.

I presented to the class a slideshow about Chapter 6 in Learning Mathematics in Elementary and Middle Schools, which focused on numeration and understanding place value in our base 10 system.

My practicum experience was so rewarding and has made me even more enthusiastic to have a class of my own. Through this process, I've learned more about who I am as an educator and also the things I still need to work on. I'll close this post with a reflection I wrote about my time in the classroom(s) this semester.

What are three strengths that you have demonstrated that have supported your development into a better teacher?

• During this practicum, I have been able to strengthen my skills in collaborating with other educators. It has been a pleasure working with other teachers, offering what I can to assist during lessons and instruction.
• I have also been able to strengthen my confidence in leading a class during a lesson. It was a good opportunity to prove to myself that I am capable of designing a lesson, teaching it while holding the kids’ interest, and following up after the lesson to check for understanding.
• This practicum has taught me that preparation and organization as a teacher are even more important skills than I had imagined. I worked hard to be well-prepared during this experience.

What are three areas that you need to improve upon to become a better teacher?

• I need to improve in the area of command of the classroom. My voice tends to be quiet and soft in nature, so I cannot rely on volume or voice projection to get children’s attention. I must find other ways to keep the kids on task and engaged.
• Although my confidence in leading a class has grown, I still have a ways to go before I am no longer nervous about it.
• I can see that I will need to grow a bigger “toolbox” of activities for times when my lessons go more quickly than I anticipated or when some students have finished the task and are waiting to move on.

How could you use your available resources (human and other) to improve in these three areas?

• I can seek out other teachers that I’ve known who have similar dispositions as mine to see how they’ve learned classroom management. In the end, though, I suspect that the best way for me to gain improvement in this area is to get real-life experience with my own students. I strongly feel, too, that gaining student trust and building relationships is the best way to “manage” your class. And while I value the experiences I had during this practicum, it was not enough time for me to solidly establish those relationships.
• Confidence will come with time and experience. It also comes from knowing a subject well, so preparation for lessons is key. In other words, I need to learn it before I can teach it!
• Again, I will seek out the advice of seasoned teachers whose methods I respect. Also, through the use of technology, including Pinterest and teacher blogs, I will be able to find a vast amount of tips and ideas for building up that toolbox.