Mary Duden, EdD, has been teaching at OES for eight years. She started out teaching fifth grade and has been the math specialist in the Lower School for the last four years.
Duden started her teaching career in the public school system. She worked for Clackamas and West Linn-Wilsonville school districts and also taught for two years in El Salvador. While she was getting her doctorate in education at Portland State University she was hired by a nonprofit consulting firm that supports teachers across the country. “Teachers Development Group is a national nonprofit that supports effective math instruction, and my job was to go to different schools in Oregon, Salem, Albany, and Medford and coach or do professional development with the teachers. That’s what I was doing right before I came to OES,” said Duden.
So what does a math specialist do? “I support the Lower School teachers with their math instruction,” said Duden. My role is twofold: half of the job is to work instructionally with teachers to support their instruction, and the other half is working with students.”
“Working with the teachers here is really wonderful because they are already very skilled in teaching,” continued Duden. “For some, it is just a chance to be collaborative with me; for others, it might be more of a coaching aspect where we talk about what it is they want to work on, and I walk around with them in the classroom and we research what’s happening based on what the teacher tried.”
“The other half of the job is working with students, but we sort of describe it as working on the extremes: working with children that might need some support because they're not making sense of ideas, and working with some kids that might need extension because they’ve already made sense of most of the ideas, so they need something new to think about,” Duden said.
She also helps with the professional development of teachers during the summer and is an adjunct professor at Portland State University.
“When students are taught to understand math and really think about whether their answers are reasonable, they become very powerful mathematical reasoners. Reasoning refers to students’ abilities to think through problems by relying on what makes sense to them. We want our students to develop agency, and by agency, I mean the ability to own your own math understanding and to recognize your own capacity to make decisions about how you will tackle a math problem.”
When asked if math instruction has changed over the years, Duden answers, “I’m not going to say the change started with my career. Most of the changes started around the 1980s. The fundamental change is the procedural aspect. That’s still an important aspect of math, but it’s like a three-legged stool. In addition to knowing the basic procedures, you also need conceptual understanding and you need to be able to apply what you know to non-routine problems. We want students to be able to say, ‘I have this problem, I don’t know what to do exactly, but I can figure it out.’”
By conceptual understanding, Duden means how math works and procedures work. For instance, when children are taught multiplication, they are asked to visualize a rectangle that represents rows and columns of an array, with a dimension or length that measures one side and another dimension measuring the length of the other side. The area measure is the multiplication of these two dimensions. It’s all a rectangle. “And that goes all the way up to multiplying binomials; polynomial work is all based on this idea of this multiplicative rectangle,” said Duden. Another example of conceptual understanding is knowing how numbers relate to each other. For example, 9 x 8 can be thought of (10 x 8) – (1 x 8) because we know that 10 is one more than 9. That relationship can help with all x9 facts. Rather than only asking students to memorize things like multiplication tables, when conceptual understanding is a priority, it is important to teach students to develop those number relationship strategies, which are algebra-based. This then leads students to the automaticity of facts.
“The biggest value that math teachers are teaching students currently is to think about what’s reasonable,” said Duden. “To me, that’s where this applies to most of your life.”
She continued, “When students are taught to understand math and really think about whether their answers are reasonable, they become very powerful mathematical reasoners. Reasoning refers to students’ abilities to think through problems by relying on what makes sense to them. We want our students to develop agency, and by agency, I mean the ability to own your own math understanding and to recognize your own capacity to make decisions about how you will tackle a math problem. This only works because students have developed conceptual understanding. That is quite different from the way math was taught when I was a student. I didn’t make any decisions because I was just told to use the procedure given, so math really lacked thinking and decision-making. I see these skills as critical in our ever-changing world.”
Duden says she greatly appreciates teaching at OES. “This is the longest I have remained with one school. I think it’s because there’s a lot of trust in me and what I do, and I have trust in OES as well. I feel that people are really collaborative, and I’ve wanted that in my working life. I feel like that’s built into our system at OES. I also feel like the teachers here are learners. I have to be in a place where there are continual opportunities to learn and grow. Because to me, teaching is an art form. And I love to be in a place where other people feel that way too. I also think the last couple of years with our discussions about diversity, equity, inclusion, and some of the changes that have been made, that’s important to me too.”
Her son Jacob went to OES for his last three years of Upper School, and she enjoyed seeing how quickly the OES community welcomed him. “I thought it was beautiful that he could start his sophomore year here and walk away with probably his closest friends,” Duden said. “He formed a tight group, and that was such a great experience.” Like she did, Jacob decided to attend college on the East Coast. “I think it’s great to go away and experience a different environment. I grew up here but I went to American University in DC for college, and it helped me gain so much understanding of people in the world because of leaving Oregon for college. But it was also great to come back.”