Math + (Talk) = 4 + All

June 4, 2019
Laurie Busby Teaching Middle School

Spartan scholar collaborates with teachers to make math more meaningful for students through discourse

By Nicole Geary

Laurie Busby and Dean Hanton felt they were very good teachers. 

They have been teaching middle school mathematics for over 30 years. They know their content, and they have attended many forms of professional development. 

When they agreed to participate in ongoing research through Michigan State University, they were cautiously eager to learn something new. 

Early in their partnership with Professor Beth Herbel-Eisenmann, who leads the project, they began to see their longstanding classroom approach through an entirely different perspective. 

“I realized … it’s terrible,” said Busby, who teaches eighth grade. 

Like many math teachers, they were using mostly direct instruction—asking students questions, getting answers and responding to them. They were doing most of the talking.

“What I was seeing were students who were successful with that model,” Busby said. “However, the majority of students were not comfortable with that and didn’t stand out. They were quiet and they didn’t have an opportunity to do anything else.” 

Busby, Hanton and fellow math teachers at East Lansing’s MacDonald Middle School spent the next six years honing a set of discourse moves shown to improve student learning and identity. The moves have transformed their classroom discourse—in other words, how they communicate with students and how students communicate and make meaning about math. 

“What this has done for us is completely opened up that old model,” said Hanton, a 1987 graduate of the Spartan Teacher Preparation Program. “It’s knocked down all those walls, so that students are actually the center of the instruction. 

“They raise ideas and respond to each other, build on each other’s thinking and share ideas with one another instead of just with me. 

I’m there to … help them get to that point, not to tell them the right answer.” 

The discourse moves and professional development model to help teachers use them successfully, called Mathematics Discourse in Secondary Classrooms, or MDISC, has now been published for schools and districts to purchase. 

MSU’s Herbel-Eisenmann, a pillar in the mathematics education field, has been learning from and with the teachers throughout the entire journey. 

“She has been more supportive than I could ever imagine her to be,” Busby said. “It’s because her passion is helping teachers help students.” 


Herbel-Eisenmann has nurtured long-term partnerships with secondary math educators throughout her career. The first was with a group of teachers in Iowa, who piloted her ideas for improving discourse over five years starting in 2004, with funding from a prestigious National Science Foundation CAREER grant. 

Leah Jones and Beth Herbel-Eisenmann
Leah Jones, an eighth grade mathematics teacher at MacDonald Middle School in East Lansing, discusses her practice with Professor Beth Herbel-Eisenmann.

More recently, teachers in seven different locations across Delaware and Michigan—which includes the East Lansing group—participated in the MDISC project, which had over $2 million in funding, also from NSF. These pilots were used to revise and improve the materials before they were published. 

The teachers’ willingness to explore different approaches alongside researchers, and reflect on their practice through systematic investigation of data they collect, resulted in the completed curriculum which became available to other teacher teams across the nation in 2017. 

Michelle Cirillo of University of Delaware and Michael D. Steele of University of Wisconsin-Milwaukee, who was formerly at MSU, were the co-principal investigators. 


Few were working to make math discourse more meaningful when Herbel-Eisenmann started her own instructional journey as a junior high school math teacher in 1990. She taught in North Dakota and Minnesota. 

Making her way to Michigan, she first became a Spartan as a doctoral student and completed her Ph.D. in Curriculum, Teaching and Educational Policy at MSU in 2000. Her advisor was David Pimm, now retired from University of Alberta. 

When she was recruited to the MSU College of Education to join the faculty eight years later, she was a well-established scholar in the field who was focused on changing norms and discourse in math classes to support students to participate more fully, especially in ways that make teaching in the subject matter more equitable across diverse groups.

Even now, with growing research and standards like the Common Core emphasizing the value of deeper, interactive classroom discussions about mathematical concepts, few teachers are doing it, Herbel- Eisenmann says. 

“As mathematics teachers, we rarely have an opportunity to step outside of the more typical interaction patterns like lectures and the [Initiate-Respond- Evaluate or] IRE pattern to examine these critically and try alternative discourse moves,” Herbel-Eisenmann said. “This is necessary, however, if we want to open up more space for students to participate in mathematics classrooms. 

“Research around formative assessment would say that having teachers learn about what their kids think is the most important thing for teacher decision-making. If students aren’t talking, teachers can only assume what they know or don’t know about things.” 

Outdated textbooks and increased focus on testing only exacerbate the issue, and teachers are rarely given the time and support to systematically reflect on their practice. Before MDISC, there were few resources to help secondary teachers collaborate around changing discourse patterns, Herbel- Eisenmann said. 


The MDISC professional development materials were still under development when Herbel-Eisenmann approached the MacDonald Middle School teachers in East Lansing. 

Dean Hanton works with students at their desks in the classroom.
“Don’t worry about being right or wrong. Think about something you can try and then we’ll chat about it,” MSU College of Education graduate Dean Hanton tells his math class.

They went through an intensive process that first year, putting in 36 hours for a professional study group then putting what they learned into action when they were teaching. It was a lot.

“We said, ‘This is crazy. There is so much work involved here.’ And we were ready to stop,” said Hanton, who teaches seventh-grade. 

The summer before the second year, Hanton and Busby met with Herbel-Eisenmann and were prepared to end the partnership. Instead, they walked out with a list of tasks to prepare to continue the following school year. 

“We could not say no,” said Busby. She was engaging in more collegial discussions with colleagues than ever before. Using the discourse moves, she was also learning more about her students than in any prior years. 

“I knew my students in the first two weeks. A lot about them. I could hear their voices every day,” she said. “After our second year, we were in 100 percent. We saw the return on our investment.” 

The group grew over time from four to nine teachers. Currently that includes Leah Jones, Samantha Wolfer-Dilno, Heidi Nussdorfer, Kaitlyn Chen, Cyndi Goff and Jodi Wheeler. 

“Our long-term partnership has allowed us to develop trust and we have been able to talk about some difficult things,” Herbel-Eisenmann said. “When you have these kinds of relationships, you want to keep working together because you can celebrate the successes together.” 

By exploring case studies, videos and student work from the Iowa teachers, then going through cycles of action research in their own classrooms, the MacDonald teachers became more purposeful about using the six Teacher Discourse Moves outlined in MDISC: waiting, inviting student participation, revoicing, asking students to revoice, probing students’ thinking and creating opportunities to engage with others’ reasoning. These moves (see below) were adapted from the “talk moves” described by Chapin, O’Connor and Anderson (2009) and tested in real classrooms by about 150 teachers. 

Herbel-Eisenmann and her graduate assistants also encouraged educators to think about two key areas, or conceptual lenses, to understand what happens when they use those practices: 

  1. Language Spectrum. How does the context (i.e. small group, whole class reporting out, writing a solution, reading a textbook) influence the language used? How do the various representations (i.e., graphs, tables, equations, drawings, story contexts) shape the way students communicate? How might teachers guide students toward more precise mathematical communication, while also valuing and respecting more informal ways of using language? 
  2. Positioning. How can discourse in the classroom contribute to how students see themselves and each other as learners? How am I, as a teacher, supporting students’ positive self and math identities? What might students say it means to ‘know’ mathematics in my classroom?  

The goal? Make math learning more productive and powerful. That can’t happen without an eye toward equity. 

“We have to see ourselves as people who are supporting students to learn to explain and justify their thinking while simultaneously thinking about whether we’re honoring students’ thinking and ways of interacting,” Herbel-Eisenmann said. “If we don’t constantly think about both of these things, it’s hard to create equitable spaces where every student feels valued and sees themselves as capable of making sense of mathematics.” 


For the MacDonald teachers, looking through those lenses led them to develop new norms for math teaching shared by the whole department. For many, it also forced them to examine their own implicit biases. 

“The point of the norms is to make it possible for all kids to participate in ways that maybe they didn’t even see themselves able to do before they walked in the door,” said Hanton. 

Using a web application called EQUIP created by Assistant Professor Niral Shah and Daniel Reinholz of San Diego State University, many of the teachers also reviewed data from classroom observations to examine their own questioning of students and differences in student discourse based on, for example, gender, socioeconomic status, race or perceived mathematical ability. 

“What kind of practices do we all have that are just hidden?” said Hanton, who is now in his 31st year of teaching. “We are trying to open up as many doors as possible instead of leaving some closed—or closing some myself.” 

Their concerted, collective efforts to change teaching practices have shown not only in daily classroom life, but in test scores, other subject-area classes and beyond. 

The group has heard from teachers at East Lansing High School who notice students explaining their thinking and taking risks in math more so than before. When a MacDonald social studies teacher asked where students learned to debate ideas—a skill they will need in many aspects of their future—the answer was surprising: math class. 

Through sales, the MDISC materials are being used by an increasing number of district-level math specialists, math department chairs and university teacher preparation programs— including at MSU where Herbel- Eisenmann is the subject-area leader for secondary math. 

“I’m pleased that one thing I’m doing in the classroom can be taken back and shared with fellow Spartans who were in the position I was in 30 years ago,” Hanton said. He also earned his master’s degree in Curriculum and Teaching from MSU in 1997. 

The MacDonald teachers have shared their work alongside Herbel-Eisenmann by co-writing a book chapter and presenting at local, state and national conferences on math education. 

“This professional development will change everything … It has directly impacted my practice and directly impacted the success of my students,” said Busby. She was on the cusp on retiring when the project started. Now she is in her 34th year of teaching and feels newly reinvigorated by what she learns from her students every day. 

“I could not wait to start another year with this, and I felt like I could not do it without the support of this group and our partnership with Michigan State.” 


    Providing students with time to process teacher questions and think about their responses. A less known form of wait time involves waiting after a student responds. When this occurs, responses can become more complex and students may be more likely to respond directly to peers’ contributions. 
    Using participation to make more diverse solutions available for consideration, and/or to be more social, such as by inviting multiple students to join the discussion. 
    Restating or rephrasing a student’s contribution. Full revoicing occurs when the teacher checks back with the original speaker and offers an opportunity for students to respond to questions such as “Did I get that right?” 
    Similar to Revoicing except that students are asked to do the revoicing. It requires that students listen to each other and creates opportunities to revoice ideas in their own words. 
    Following up with an individual student’s solution, strategy or question. The goal is for the student to elaborate on or clarify his or her ideas. 
    Asking students to engage with another person’s thinking. For example, a teacher might ask the class to use a particular student’s strategy to solve a similar problem or to agree or disagree with a solution. 


“Mathematics Discourse in Secondary Classrooms (MDISC): A Case-Based Professional Development Curriculum” can be purchased through Math Solutions (use code BOOKS30 for a discount). The package includes a published facilitator’s guide with seven learning modules called Constellations, downloadable participant guides, video and audio clips and presentation slides. The Constellations take about 36 hours to engage with, followed by a recommended action research component in which teachers enact and systematically study changes in their practices over at least two years. BUY ONLINE.