Reality Check on Mathematics and Constructivism

I had a conversation with a new colleague at the university. The new math colleague (we will call David) has been teaching high school for more than ten years and is one of the first students admitted into the new Mathematics Education Ph.D. program. David teaches in a high school 1/2 time with head teacher/homeroom responsibilities and is a university student the other 1/2 time. He is fully funded to do his work in both places. David’s arrangement reminds me of the Master’s Degree I earned from Syracuse University. They had a program where I completed a master’s degree in Education and was hired to teach in the Syracuse City Schools as my assistantship. I learned about teaching mathematics, but teaching math, but Syracuse University paid for 30/36 credits of my master’s degree. I wish I had taken better advantage of that opportunity.

My conversation with David was about the research study to bring Posa to regular kids. Currently, the Posa program requests that teachers recommend the talented ( mostly boys) to the weekend math camps. David is involved in a research project to bring Posa to schools in general. I said, “there is a lot of risk around doing this problem-solving, constructivist approach to teaching, math(s) to regular kids.” I said this because I wonder how hard it is to teach percieved talented mathematics to kids who would probably be successful with or without the math camp.

His response was refreshing. We are not very successful in teaching regular kids math, so why not try this problem-solving way? We sometimes lose many students to the love of mathematics, by instructing in the same mundane procedural only, memorization process, and with lower level repetitive thinking by doing many problems without conceptual understanding. Why not use the POSA method to teach critical thinking through mathematics to all secondary school children. There are jobs, not yet invented that might require problem-solving, so why not teach in a problem-solving way to produce the citizens of the future? By teaching kids how to learn in a constructivist way, we might have a jumping off point to contributing to our democracy.

It is about using the teaching of mathematics as a democratic act. By teaching kids how to learn in this constructivist way we might have a jumping off point to other larger democratic processes.

My Goodness. It was a wonderful to hear David, this seasoned teacher, talk about why he teaches. He mentioned that he approaches his teaching to build the fabric of mathematics for the next generation. He talked about how success in mathematics is a process that he enjoys witnessing in children. His explanation feels like the journey metaphor I am pushing. He seems to love the process of learning and helping the next generation of kids learn mathematics in a way that is it dynamic, creative and rewarding.

He made me smile. I realized that my work around helping teachers make a difference in the mathematical lives of all students is important, democratic, academic, emotional, and maybe even memorable. Why do I say memorable?

After visiting the Hungarian Parliament today, as an American tourist, I learned that the Hungarians had re-written their histories. The rewriting may have been with the Austrians, the Turks, the Germans, the Russians, and now the Europeans. Each time the Hungarians recover from some war or occupation, internal or the external occupying forces, they work to rewrite the version of history created for them by the occupiers. Some might say that the story (history) always goes to the victors. Some might say that the interpretations of history are therefore important and relevant for us to engage.

The interpretations about ensuring the access and success in mathematics for all is an ongoing journey with factors and people who have different visions for the future. Teacher expectations make a difference in student learning and helping teachers unpack their expectations might just be the work. Dr. Dolores Grayson, here you are again with the Generating Expectations for Student Achievement (GESA).

David, a talented (as perceived by his teachers) alumna of the POSA method is now teaching using the POSA method to his students in his school. He mentioned many of teachers who are teaching using POSA were taught POSA as children. The concern is that without Posa experiences a child, how difficult will it be to transform a teacher’s conceptual framework around teaching and learning mathematics this way. It might be better to concentrate on new teacher training. The research project is hoping to bring the POSA method to teachers who may not have been POSA students.

David uses the Posa method but not all the time. He mentioned that the time it takes to prepare a 1-hour class using the POSA method is 3 -4 hours. We agreed that this could be a resource issue. We talked about how to work with teachers to use this method when we know that there may not be enough time, or resources to accomplish this rigorous way of teaching for all. He said. “I use POSA sometimes and then the typical didactic methods other times. He made me smile because he was so honest about the POSA method. Another colleague (let’s call her Joanne) is working on a research project for creating sets of problems that will support a system of problem-solving. This other faculty member is investigating how these problem sets might scaffold problem-solving differently. How do we put math problems together so that students can use the discovery process? It has been wonderful to find a set of mathematics people interested in delving into this type of thinking.

I am an insignificant want to be mathematics educator person interested in ensuring that more students have access to good math teaching of the constructivist problem-solving type. These math people, in another country, have similar interests. What a privilege it is to talk with them. I could not have asked for more on my time away.

Marcia

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