The following is an observation of Dr. Theodore Chao’s Early Childhood and Elementary Math Methods course, on a day when the students engaged in both a rehearsal teach and a problem-solving interview. The ideas expressed are from doctoral student Hochieh Lin’s perspective, with commentary following this observation by Dr. Chao.
During this semester, I am fortunate to have access to observing the Early Childhood Math Methods Course taught by Professor Dr. Chao. This course is taking place at a school so that pre-service teachers (PST) are able to take advantage of working with real students. I have been amazed at great things going on. Recently, PSTs started practicing rehearsal teaching and problem-solving interviews with children of grades K-3. These experiences have provided great learning opportunities for PSTs.
In doing rehearsal teaching, PSTs need to co-plan their lesson in advance and rehearse their lesson with classmates playing as children. Dr. Chao suggested five norms to this activity: (1) create and learn in a community; (2) teaching is public; (3) strategic intervention; (4) pause, rewind, revise; (5) teacher timeouts. This revision cycle enables PSTs to discuss in a group and reflect on their decision making before actually implement the instruction to real children.
I find the fifth norm particularly unique as anyone in the classroom can propose a timeout, asking questions or suggesting ideas. At first, I thought this might interrupt the flow of the lesson. However, later I found it very helpful. For instance, when someone spotted something and thought up a question, a timeout allowed the audience to pay attention to that incidence at the context. This practice called upon an experience I had before. It was during a soccer practice match, a coach asked for a timeout and asked all players to kneel and look around. This helped us recognize the positions we were at and immediately reflect on why we made the move to the positions. Therefore, I think this norm can benefit our decision-making process.
As to 1-1 problem-solving interviews, many PSTs had wonderful experiences as the child they worked with shared amazing thinking. However, I noticed a couple of PSTs showing frustration toward their experiences, particularly in working with children who they might not be able to relate to or have trouble engaging mathematically. I closely observed how one PST interacted with a boy who did not reply to her questions in a way that corresponded to the answer she was expecting. At first, the boy wanted to do his math problem rather than the PST’s problem. The PST let him work out his own problem and encouraged him to describe his thinking. However, the PST still did not seem to understand the child’s explanation and tried to provide some hints. Next, the PST redirected him to work on her problem. The boy tried to use manipulatives of chips in a way he wanted. The PST expressed her concern about his strategy and suggested him her way of using manipulatives. The boy did not adopt it. Rather, he wanted to complete trying his way. The PST sighed and looked frustrated. I noticed, that in exasperation, she told the boy his strategy would not work out. She grabbed the chips and directly showed the boy her way of using chips in solving the math problem. I noticed a large tension occurring between the boy and the PST.
Interviewing a student we are not familiar with is challenging. Multiple aspects about the many identities, experiences, and expectations that a child holds may clash with the expectations that a PST has. A child may interpret and respond the PST’s questions and directions in a way that is very different from the PST have previously thought of. Additionally, it is likely for many PSTs to expect a standard reply or explanation from a child. Learning to be an inquiry-oriented math teacher requires a mind-shift into the hard work of understand young children’s unique way of explanations. Therefore, this issue is worthy of me as a future teacher educator to contemplate on and find out ways to better support PSTs.
Dr. Theodore Chao
Hochieh brings up some strong observational points about activities in my methods course. My rehearsal teaching activity is very heavily based on the work by Kazemi, Ghousseini, Cunard, and Turrou (2016), particularly in how I do a quick run through of the lesson before the pre-service teachers engage in the teach. We are fortunate to teach our methods course at Highland Elementary School, so we invite real children to be in our rehearsal teaches. I think the presence of real children makes the rehearsals an incredibly powerful experience. I can see how pre-service teachers are forced to make difficult teaching decisions in the moment that they would not have predicted, based on the very real and very unpredictable mathematical thinking exhibited by the child.
The problem-solving interview that Hochieh mentions is from the Teach MATH work, specifically from their case study module. I got to pilot test this module as a doctoral student and have made many tweaks to it over time. First, I extensively use online video for pre-service teachers to focus on noticing mathematical thinking that happens during these interviews. Second, I heavily emphasize the construct of identity, particular how mathematics identity develops, as connected to the ways one is positioned not just mathematically, but also sociopolitically.
Mathematics education has a deep history of using mathematics to sort children based on gender, race, ethnicity, language, and socioeconomic status. It’s horrible. So I think what Hochieh is referencing here is that, as PSTs learn how to do the very, very hard task of listening to children’s mathematical thinking, they also have to pay deep attention to how children are positioned. And they have to pay extra special attention to children who come from communities historically marginalized in mathematics. This ability to pay attention to multiple things is really hard to do. Something I don’t think can realistically happen in a 1-semester Math Methods course. But I know it’s important. And so we try.
As you can read from Hochieh’s observation, both the PST and the child are deeply involved in trying to make sense of how to communicate with each other, how to reach a place where they are both listening to, respecting, and honoring each other’s mathematical thinking. To me, great mathematics teaching happens when this distance is reduced. And so I want to honor the PSTs and the children that are willing to go on this journey with us, because it’s not an easy one, especially at the beginning. And I also want to ask for advice. What are things we can do better in our mathematics teacher preparation, particularly in regards to honoring the many identities that children bring with them into our classrooms?