Five-Step Process: Step Three

by | Mar 31, 2023

The Algebra Project’s Five-Step Curricular Process has been at the center of our classroom and Professional Development pedagogy since the Project’s inception. Exploiting a more traditional work cycle, the five steps are meant to be taken in order, as well as repeated.

For the third step in the Algebra Project’s Five-Step Curricular Process, “People Talk” gives students the opportunity to verbalize their findings from the previous two steps, “A Shared Physical Experience” and “A Picture/Model”. They use their ordinary, everyday language as a testing ground for their ability to communicate ideas effectively among a crowd of their peers.

The third step utilizes small groups discussions, and aims to accomplish two things: empower students, and affect dialogue. A beneficial outgrowth is that it will also generate the data necessary for interpretation in the final two steps, “Feature Talk” and “Symbolic Representation”.

“Before we get to the actual work of equations or abstract mathematics, we need the voice of the students to have an opportunity to come out” says Alan Shaw, Associate Professor of Computer Science at Kennesaw State University. “And to come out in a way that is natural, that comes from their own experiences. Their own feeling of, ‘well this is what it meant to me.’”

People Talk gives each student the opportunity to voice their own thoughts. By fashioning into small groups, students have time to comfortably form their opinions and dissect their observations before verbally discussing them. In a more traditional lecture style classroom, too often the only students who speak are those who are confident in their answers or questions being the ‘correct ones’. By facilitating dialogue and discussion between peers, rather than a question and answer formula between student and teacher, there is no conception of being wrong.

Students from the June Jordan School for Equity//Marcus Hung

Alan, who wrote a paper about the importance of orality in the classroom alongside Algebra Project Director of Professional Development, Bill Crombie et al., explains the importance of the low-stress small group discussions, “If you get a chance to really talk and really get your ideas on the table, there’s a chance that that’s gonna start making you see that what you think is important.”

The method isn’t limited in its effectiveness to mathematics. In fact, its fruition didn’t stem from mathematics education in the first place. It came from the Civil Rights Movement.

In the 1960s, Black sharecroppers and day-laborers were systemically prohibited from receiving an education that gave them a high degree of literacy. Simultaneously and very much intentionally, a high degree of literacy was made a requirement in order to vote.

“Sharecroppers in Mississippi, they go from being people who know they’re going through some kind of oppression and they’re being treated unfairly, but they don’t see themselves as having the power to overturn that. They don’t see their voice as something that could make a difference. And so, how do you change that?” Alan explains how Bob Moses developed the third step during his 1960s organizing activity in the South, under the mentorship of Ella Baker, “Bob would call it an earned insurgency. So, what he would do is have small group discussions. Everybody knew that these issues existed in the South, but when you had these small groups, you could talk within that group. A smaller community could talk and uncover a way of presenting the ideas, becoming articulate about how to explain what your ideas are.”

The clarity that came from sharecroppers expressing ideas they may never have vocalized before, and the social empowerment of their peer’s response was a watershed moment that played one role in the 1964 Mississippi voter registration drive known as Freedom Summer.

Today, in the classroom, focusing so heavily on student voice similarly serves as an investment when, in later steps such as Feature Talk and Symbolic Representation, students have the social empowerment necessary to talk about the more abstract aspects of algebra. They have the ability and desire to voice concerns and questions, and to assist in explaining anything their peers might be struggling with.

But it isn’t just about confidence making. While the emotional empowerment is an important dimension here, so, too, is the data that they are generating and framing through their verbal observations. That observational data collectively generated provides a foundation for the abstract symbolic representations to come later – it’s a key component of sense making for interpreting the symbol system of mathematics.

Besides obtaining the clearance necessary for one to stand on the power of their own voice and ideas, it also opens another door. It teaches students the importance of dialogue.

Each student should now not only feel assured in their own thought process, but comfortable negotiating feedback and fielding questions as well. This allows that thought process, and the conclusions therein, to constantly evolve.

“The feedback you’re getting is helping you go deeper. You don’t wanna just stay where you are. You don’t wanna just assume that what your initial reaction was is where you’re gonna end up. So you go deeper. But you gotta get there from first getting engaged.” Alan says.

By verbalizing ideas among their group, students see real-time reactions to their own thoughts. They might be met with agreement, or confusion, or boredom, and this, in turn, leads to a deeper understanding of how to express their thoughts.

Eventually, armed with the confidence of having already articulated themselves, and revised and experimented with their ideas among their cohort, People Talk moves into its next phase which is large group discussion.

“You go from that smaller format to the large group where you have these breakout discussions and you are now kind of seasoned. You have a way of talking to the bigger group that you developed in the smaller group.” Alan tells me.

It’s not an academically exclusive conversation. And that is key in teachers allowing students to claim ownership of these mathematical concepts. Which is why the third step in the process has deep roots in the paradigm that Ella Baker established around community organizing; or trusting that leadership will emerge from local people.

Ella Baker, a behind-the-scenes mentor to activists coming through the Student Nonviolent Coordinating Committee (SNCC) where she was a lead strategist, was concerned with how you get ordinary discourse on the table. When sharecroppers came into the meeting, if they saw experts up there with degrees and suits, they were very hesitant to talk.

The problem that SNCC had was how to get the sharecroppers to talk about their deepest concerns. And the strategy they took was first to do it in small groups and then to have those small groups take it to the general meeting, which is why Bob rarely led a discussion. Bob just helped organize them.

Teachers utilizing the Five-Step Curricular Process, likewise, will find themselves taking a step back, especially in these early stages, and letting students take the lead. It is not the job of the teacher to lead the student to a correct answer, but to facilitate discussion and allow the group to deduce their own explanation and come to a shared understanding with the class.

Taking the time, in these early stages, to foster that kind of learning environment is, largely, what separates the Algebra Project from many math education initiatives. Every learning initiative is primarily concerned with outcomes. For the Algebra Project, that outcome is a student prepared to do college level mathematics. But the third step in the Five-Step Process brings to the forefront an education that focuses on the whole child, rather than one small aspect, such as their proclivity for rote memorization and algorithmic computation.

An Algebra Project classroom is not just about pedagogy and content. The traditional “educational trinity” consists of curriculum, assessment and instruction. With the Five-Step Curricular Process, it is expanded into a quartet: curriculum, assessment, instruction, and culture. The culture of the classroom is all about the relationships. Ideally, rich relationships that teachers build and facilitate with the students in the classroom, but also the relationship that students have amongst themselves.

Students from June Jordan School for Equity//Marcus Hung


This necessarily involves, for example, whether kids feel safe enough in the classroom to talk about the ideas that they have.

Alan reflects on a scenario all too familiar to teachers, “By the time they’re in 12th grade, you ask a question and nobody raises their hand. Everybody’s afraid to speak, they don’t wanna be wrong. They don’t want somebody to tell them that something they said or thought wasn’t valid. And so teachers, early on, gotta work against that. And People Talk is one clear approach on how to work against that.”

Read the next installment, Step Four – Feature Talk

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