Hello my name is Marcia Burrell. I am from SUNY Oswego in Northern NY on Lake Ontario. I come to this conference because there is support for my ideas about teaching mathematics to all populations. This talk has a U.S. context, but I realize that our concerns in the US are similar to those of yours across the world.
There is nothing new here, but one of my jobs is to help educators who teach mathematics realize that we are in control of who can and cannot do mathematics. This is a large responsibility.
Before I forget, please consider following my Blog. https://wordpress.com/posts/ajourneytomathematics.blog
I will be posting my thoughts about my observations over the next several weeks, while observing in classrooms in Budapest. My interest is in how teachers approach their teaching in this Hungarian system.
I am collaborating with BSME (Reka) and with two other maths teachers Emese Gyorgy and Ödön Vancsó
For today, the small study is about how we prepare pre-service and inservice teachers who teach math to all learners. I hope to reveal their thinking, after what I deem to be my interventions through my class teaching. The paper is about what teachers say about clearly established approaches to teaching and learning mathematics. The revelations are the interesting part of this discussion, but I want to set up so you understand my approach to ensuring that those who teach mathematics have an understanding of the perceptions, expectations and behaviors that often reinforce the good teaching in the classroom and sometimes the not so good things that happen in the classroom.
There are very good data about how people learn, and more importantly how people learn mathematics. We are not confused about what is good teaching. The constructivists have it. There is a Hungarian way of teaching, and they have the corner on the market. There is research on math anxiety, but I think this may be about disaffection as quoted by Lewis, 2013. Is it really about how we socialize certain audiences to love, struggle, hate, or have some other passion for the subject? We have many research studies, which help us understand about procedural and concept attainment.
Using the history of Mathematics (as echoed by Douglas Butler this morning), as a means to humanizing mathematicians is also important. The personal stories about who we are as mathematicians is an important part of helping students learn the difficult concepts.
Donavan documented the research about learning mathematics through 3 basic principles. There are specific things that teachers can do to help students learn. I have to give Hilary Povey credit for her presentation this morning, because her list clearly explicated the list of things that can be done. Thank you Hilary.
But there are hidden things that reveal themselves (called dispositions by Hovey) around culture and stratification and misunderstandings about who can and should learn mathematics.
While in Benin West Africa, as part of a study abroad program for students at SUNY Oswego I had the honor of observing teachers, with almost no resources, except chalk, explain difficult mathematical concepts to eager students. Now I am not naive about the fact the mostly boys in that classroom had the personal, financial and cultural resources to succeed. The Girls I saw in these classrooms were amazing, and no one was saying that they did not have the capacity. They demonstrated the capacity and the teacher expected students to succeed. Yes I know these students know how to suffer through the standardized exams, so already are considered the top of their populations. I get it. I witnessed no disaffection for mathematics at this level. In the US as soon as students begin to struggle with mathematics, we separate students into distinct categories. Again, as Butler said, “there are things that all students should learn. There should not be a divide between those we believe have the capacity and those we believe to not have the capacity.
It appears, at least in the research that outside of the US that struggle is a part of learning. Struggle appears to be a part of any learning process.
Our Master’s degree students in mathematics education were required to take a diversity course. I spent the summer creating a course, “Math for Diverse Learners”. I gathered articles on Math learning and proficiency. Many of the articles are references, but this is a limited list. One of the ongoing assignments for the course required students to read about mathematics pedagogy. Part of the assignment was for them to write brief reaction papers with the following headings, cognitive, affective and conative. I then mapped their writings to Perceptions, expectations and Behaviors. I pulled the comments from their papers. I was hoping that students could reveal to me and to themselves the kinds of behaviors that assist students (k-12) in their learning.
I set up an elaborate scheme to summarize how good teaching could create a new generation of mathematics learners. I hoped to unpack the perceptions, expectations and behaviors through their writing.
These writings are from a small group of students writing for an assignment. I wondered, are they writing what they think I want to hear, or are they giving real accounts of their understandings.
I want this group of pre and in-service teachers to reveal to themselves their ability to be the gatekeepers for learning. I want the course to provide a window to access, through their writings. It Is important for my teachers to see themselves as gatekeepers. Take a look at gates here as barriers, but there are many gates such as the “Door to no return”, the Brandenburg Gate, the Golden Arch, which is a gate to the west. All openings. The mathematics writings I had students produce were an effort for them to see themselves as gatekeepers, not the barrier gates.
So let’s divert our thoughts a bit to contradict my intentions…
So I do believe that we have a way of looking at things that reveal what we have to do, but our hidden expectations have to be engaged in order to see changes in our mathematics teaching systems.