My math students struggle with planning their methods before working through problems. I always ask questions in class to help them create plans, to think about how to work through something. I will use a flow chart with my AP Calculus students to help them decide which derivative rules to use before finding the derivative. This entire activity revolves around making decisions without completing any computations. I provide instructions here and am excited to see what happens. 

     I teach many different types of learners and am always looking to find new ways to reach them. I like to have each student come into my classroom with a fresh start, but they do not always feel that way. Students struggle with math and struggle to make meaning of the math they learn in school. I want students to see that the content may not be the most valuable math lesson; learning how to learn and approach problems is the fundamental skill. Learning how to learn is individual and different for every student. So, while I show students one way to problem-solve, I always welcome new ideas, talking through them to ensure those methods work consistently. But many students will not make this effort. They try to fit new information into pre-existing schema instead of creating a new schema to make space for the latest information. (Walden University, 2015e)

    In my math class, I want students to work together to make sense of the content and develop personalized problem-solving methods. When I teach trigonometry, and we create the unit circle, students always ask if they have to memorize the information. I tell students that I want them to find ways to remember the material; memorization is temporary, and this is the knowledge we will need for the course and math courses to follow. I give them time to look over the unit circle, find patterns, and see what connections exist in the material. I have seen students color code their unit circles, underline certain information, and create phrases to help organize the material. I enjoy watching them make this personal and meaningful without my help. (Rob & Rob, 2018) This year, I shared a website with students to test their knowledge of the unit circle. As students felt ready, they clicked on the website I had posted in Google Classroom and tested themselves to determine how well they knew the unit circle. Some students competed against each other for the fastest time, and some competed against themselves. Through mistakes students made on this website, they could adapt their methods to remember the information better for the next time. Having computers ready and available for students to experiment, not just watch and listen, supports the constructivist learning theory. (Rob & Rob, 2018) Throughout this process, I act as a facilitator (ISTE, 2016), helping students become problem solvers, using technology to check and explore their methods. (ISTE, 2007)

    Today, my Calculus students learned how to find a derivative of an exponential function using the chain rule. Students were trying to identify the parts we needed to start the problem. I had a student who thought he had found another way to find the derivative of our first example. I let him work through the problem on his own and then challenged him with another to see if his method worked. It did not, and he was able to figure out why. Pitler, Hubbard, and Kuhn (2012) discuss this type of discovery as a way to deepen students’ understanding of the material. This student worked with another classmate to talk it through together; what a fantastic way to start my day!

    Constructivism and constructionism are closely related, and the differences are subtle. When trying to decide which theory best describes my classroom, I struggled - having multiple sources to read helped me identify both views within my classroom. In my pre-Calculus class, students are working on proofs that have numerous pathways. The focus is on the methods, and processes students use (Orey, 2001) as opposed to answers. I often give my Calculus students a challenging problem after we have practiced the necessary skills and have them work as a class to complete the work. I may ask a question as they work, but they are responsible for creating the process. This knowledge construction comes from conversations and interactions, as described by changingminds.org.

    My favorite discovery was that Seymour Papert, along with his theory of constructionism, developed Logo. I remember using the turtle on the computer screen to make shapes. Eventually, we used the Logo programming to connect vehicles made from Legos and were able to move the vehicles around the classroom using the Logo programming language. I did this in middle school, and I remember it so vividly. I want students to have this same experience from the projects they create during our Genius Hour time. I want students to explore and build on their knowledge, adapting as they move through the process. (blog.cccatconference.org)

    Each year, I want students to leave my classroom with a newfound respect for math. If I can have students move on to future endeavors with their own problem-solving methods and the ability to collaborate with peers to the same end, I will know that students found success in my class. 

References

Walden University, LLC. (Producer). (2015e). Constructionist and constructivist learning theories [Video file]. Baltimore, MD: Author.

Rob, M., & Rob, F. (2018). Dilemma between constructivism and constructionism: Leading to the development of a teaching-learning framework for student engagement and learning. Journal of International Education in Business, 11(2), 273–290. https://www.proquest.com/docview/2154592910?accountid=14872 https://doi.org/10.1108/JIEB-01-2018-0002

International Society for Technology in Education. (2016). ISTE standards for teachers. http://www.iste.org/standards/iste-standards/standards-for- teachers

Orey, M. (Ed.). (2001). Emerging perspectives on learning, teaching, and technology. http://textbookequity.org/Textbooks/Orey_Emergin_Perspectiv es_Learning.pdf

International Society for Technology in Education. (2007). ISTE standards for students. http://www.iste.org/standards/iste-standards/standards-for- students

Pitler, H., Hubbell, E. R., & Kuhn, M. (2012). Using technology with classroom instruction that works (2nd ed.). Alexandria, VA: ASCD.

Dave If you like what you are reading. (2022, October 7). Constructivism vs. constructionism. Connecting, Collaborating, and Celebrating the Art of Teaching. Retrieved November 29, 2022, from https://blog.cccatconference.org/2022/10/constructivism-vs-constructionism.html

Constructionism and constructivism. (n.d.). Retrieved November 29, 2022, from http://changingminds.org/explanations/research/philosophies/constructionism.htm