# Actualizing Change after Experiencing Significant Mathematics PD: Hearing from Teachers of Color about Their Practice and Mathematical Identities

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## Abstract

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## 1. Introduction

‘So I feel like I have gained so much confidence in my own mathematical skills by participating in the Institute because other people recognized that I have something to contribute, that my ideas are worth hearing, and somebody liked it or somebody said, ‘Wow, I really liked that model or I liked the way you explained that or I get it because I understand what you’re talking about ...’(Gloria, 7th Grade Mathematics Teacher)

‘We were spoon-fed when we were in elementary school … You do this, you line your numbers, you borrowed. We didn’t know what we were doing. Now, I am creating thinkers, not spoon-feeding, not telling them what to think or how to think. They are discovering their way of learning mathematics.’(Alana, 3rd Grade Teacher)

- How do elementary school teachers of color characterize their experiences in mathematics as pre-tertiary students?
- How do these teachers characterize themselves as teachers of mathematics after experiencing significant mathematics professional development?
- How do these teachers characterize their mathematical identities after significant PD experiences in mathematics?

#### 1.1. An Overview of the Institute

#### 1.2. Students of Color Lack Access to a Quality Mathematics Education

#### 1.3. Mathematical Identity

#### 1.4. Theoretical Framework: Sociopolitical Theoretical Perspective

## 2. Materials and Methods

#### 2.1. Research Context and Participants

#### 2.2. Data Collection

#### 2.3. Data Analysis

#### 2.4. Ethical Considerations

## 3. Results

#### 3.1. How the Teachers Characterized Their Experiences in Mathematics as Pre-Tertiary Students

‘When I was in high school, I was taught the procedural way and it worked, and I thought I was good. And I thought I would be great teaching that to other students and it didn’t work. In college I was pushed to learn the conceptual way and I resisted it a lot. So I stayed in that same mindset in college, because I didn’t have the real life experience to know that the procedural way didn’t work for everybody. So I resisted that change. I resisted that idea, that change, that math identity change until I went into the real world. And I noticed then that doing math procedurally didn’t work, but that’s what I was taught. That’s how I could do it.’

‘One thing that I remember as an elementary student was when it came to subtraction, I never understood. I don’t know if it was just the way it was explained to me, just that procedural process. Like when it came to subtracting zeros, the whole regrouping, I did not understand that process at all.’

‘When I got into junior high, I was placed in the lowest math class there was. So right there, I was like, oh, well, I’m really bad. I must really be bad at math if I got placed here. So, I guess that my math identity began. I thought I’m not good enough. I’m not smart enough. I don’t get it, and so I was afraid. When I entered college, I knew I wasn’t going to take high level math classes and tried to avoid anything that had to do with math.’

‘When I tested into the general math class, one of my classes ended up being a math lab. So it was kind of like the extra help that I needed. So I had two math classes. One was the regular math class and then a math lab. I would go to the math lab and I was getting worksheets. There’d be instructions on what to do. A lot of it was like percents, decimals and fractions. It was kind of a way for me to catch up, but I had to kind of catch up on my own because there wasn’t real direct instruction. It was more like worksheets and going at your own pace.’

‘In eighth grade, teachers were seeing that I was understanding. So, they bumped me into algebra. I went into Algebra I because that’s where they said I should be, but I didn’t have the pre-algebra foundation that I should have gotten in 7th grade. I was always trying to catch up. I still always struggle with fractions and percents and decimals, because I never really had instruction (in these areas).’

‘I just didn’t feel prepared. Even though I had taken calculus in high school, I just didn’t feel prepared. So that was kind of discouraging. And for me, that was a feeling of, I did not belong at my school, because I was not smart enough to get through those classes. So, I dropped the classes.’

‘So I get into middle school and it was the same thing (solving problems using procedures we had been taught). Why do I have to do this? And it was always because that’s just what you do it. I could follow procedures left and right. I could solve anything. I could memorize procedures. But a lot of times I just wouldn’t do my work because I thought, why am I going to have to do 50 problems using the same procedure when I already know how to do it? And I don’t really understand why I’m doing it. That cycle continued through high school … I remember really depending on my dad to help me make connections from what I was doing in school and how they would be applied in the real world.’

#### 3.2. How Teachers Characterized Themselves as Teachers of Mathematics after Experiencing Significant Mathematics Professional Development

‘He wasn’t writing it out, he wasn’t showing it. He was just verbally saying it, and I could totally follow and understood everything that he was saying. And so, then I thought about it later and (asked myself) could I, a few years ago, have followed and understood that conversation? I guess it’s obvious that you’ve grown in your understanding of math.’

‘As far as my math teaching, I think what has helped me is my confidence in my math skills and my understanding has improved so that I can help students that have difficulty. I’m not yet confident in teaching algebra, if I went above where I’m at right now, I think it would be a little scary for me, like high school math.’

‘You feel that you can do math, you know, you feel like you’re validated in your thinking and your confidence, even if it’s in one little aspect of mathematics, you’ve owned it. I don’t say did it correctly because it’s not about doing something correctly. It’s about an idea, a strategy that can lead to an answer, and it may not necessarily be the right answer in the end, but your strategy got you to that point. And your way of thinking got to that point. So yeah, the confidence that you get from that math identity, whenever you, you feel like you did it … So, that creates that confidence.’

‘I’ve really brought kids out of their shell and had them think about mathematics in a way that they hadn’t thought about it before. I got them communicating with each other, sharing ideas, writing down their mathematical thoughts when they really couldn’t even express them in the beginning of our mathematics class. And just opening those conversations about why does the math work, what is the concept behind the procedure? I think I really opened up their mind to a world of mathematics that they hadn’t really been exposed to before. I think that’s what really made me successful is understanding that students really needed to know the why behind the math and understand the concepts rather than just knowing a procedure and memorizing a procedure.’

#### 3.3. How Teachers Characterized Their Mathematical Identities after Significant PD Experiences

‘I think that’s what led to their, um, huge gains on the standardized assessments because they could write a paragraph about how they completed a mathematical problem. And it wasn’t the steps. It wasn’t the procedures, it was the concepts. So, yeah, I saw a lot of students change throughout time and I’m seeing it even now that I’m teaching fifth grade. I’ve only had these students for four weeks … their mathematical identities have changed significantly already.’

‘I was exposed to that conceptual math and look at the concept behind the math. Instead of just the procedure, understand what the problem’s asking you to find and think about it deeply so that you can come to an understanding and figure it out instead of just looking for the clues. I was able to change the mathematics program there at the middle school to something that was more conceptual based. Um, so that was kind of a win for me because I had been doing a lot of work with them to kind of see that conceptual side of the mathematics. And there are a lot of great strategies that we’ve talked about over all the different professional developments that we had together.’

‘I’ve been able to experience for myself in the Institute that, that growth mindset of like, I don’t get it yet right now. I don’t get it right now, but I will through practice and through discourse and through experiences that I have with colleagues, you know, the way he groups us, the way he has us discuss our math thinking, and then being able to show our math thinking builds that concrete, representational and abstract in my mind. And that’s what builds that, that confidence, I think.’

‘I’m not sure that I would have been able to create that mathematical identity that I’ve created within myself, um, by myself, because I don’t know that I would have been able to understand how to do all that stuff or how to teach conceptually, how to learn conceptually. It really was a matter that I learned myself and then I taught it to my students. So if I didn’t have that support when I first came out of college ... I don’t think I would be as successful as I am … I really saw their mathematical identity changed significantly from when I got them in fifth grade to when they left in sixth grade … And I think that’s what led to their huge gains on the standardized assessments, because they could write a paragraph about how they completed a mathematical problem. And it wasn’t the steps. It wasn’t the procedures, it was the concepts.’

‘I got to say that that’s still not enough because I still get pushed to my limits with my, um, productive struggle. And with my productive struggle, I learned so much more of myself and I become more confident and I can build that mathematical identity for my students through that productive struggle in my own classroom.’

‘I think some of my strengths are that, you know, I allow my students to struggle. I know that has been difficult for me because it’s difficult to see them struggle. And many times I want to jump in and I want to save them right. I want to say, no, no, no, no, no, no, no, no, this is what we have to do. But you know, I have learned that struggle is very important. I also think a strength that when I’m teaching, I don’t do all the talking.’

‘I really enjoy, um, even still having that connection. So having [MSA staff] come in and, um, share a book or send an email that says, ‘Oh, you know, look at this.’ Or, you know, like to me, I feel like that still is that accountability. Like it still holds me accountable for I’m continually learning. Like I’m still improving in my math instruction.’

‘Had I not had the support of MSA and the Institute, I’m not sure that I would have been able to create that mathematical identity that I’ve created within myself, by myself, because I don’t know that I would have been able to understand how to do all that stuff or how to teach conceptually, how to learn conceptually, because it really was a matter of that I learned myself and then I taught it to my students. So if I didn’t have that support, when I first came out of college and I’ve got into the real world and I knew that it didn’t work, I don’t know. I don’t think I would be as successful as I am.’

## 4. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Individual Teacher Interview Protocol

- (1)
- How many years have you been teaching?
- (2)
- What grade level are you currently teaching?
- (3)
- What grade levels have you taught and where have you taught?
- (4)
- When you think back about your successes as a math teacher, what are those successes? PROBE: Based on the teacher’s response, ask questions to elicit specific information related to a success or successes that the teacher names.
- (5)
- How would you generally characterize your experiences in math in grades K-12? Can you share a story with us about something that happened to you as a math student that really impacted you in a big way? PROBE: Based on the teacher’s answer, ask specific probe questions such as: “You said that your experiences in math were good in the elementary grades, but not so great in high school. What made your math experiences in the elementary grades better than your math experiences in high school?” OR “You just shared that not so happy story with us about what happened to you in Algebra class in high school. How has that impacted the way you approach teaching your students math?” etc.
- (6)
- Can you tell us about the math content courses that you took in your teacher education program? How many courses did you take and did these courses help prepare you to be an effective teacher of mathematics?
- (7)
- How would you characterize yourself as a math teacher? What are your greatest strengths as a math teacher and what areas of your math teaching would you’d like to improve in? PROBE: Could specifically ask about the teacher’s beliefs about math teaching. For example, ask: “What teaching strategies do you use to help students learn math?”
- (8)
- How comfortable are you understanding the math concepts typically taught at your grade level? How about math concepts typically taught a grade level or two above the grade you teach?
- (9)
- What are some reasons you might hesitate to implement something new in math? For example, you have participated in the Institute for the past ___ years. In those sessions, you have learned about inquiry-based instruction that involves actively engaging students in math lessons. Have you tried to implement ideas related to inquiry-based instruction with your students? Why or why not? PROBE: What are some challenges you have faced associated with implementing inquiry-based instruction in your math classes? What have you done to help you feel prepared to implement inquiry-based instruction? What sort of supports do you need to use inquiry-based instruction in your math classes?
- (10)
- In the Institute, one of the goals has been to demonstrate the value of including participants’ mathematical ideas in instruction. As you may recall, participants are regularly called on to share and explain their solutions to problems in both small group and whole group. A reason to do this is to help participants realize that they have wonderful math ideas that need to be shared with their peers. Hopefully, this leads to participants developing positive mathematical identities. Can you talk about your mathematical identity and how your participation in the Institute has impacted your mathematics identity? PROBE: What challenges have you found may be associated with you having a positive mathematical identity? What sort of supports do you need to have a positive identity as a math teacher?
- (11)
- How important is it to you that your students develop a positive mathematics identity? What are some practical strategies that you use to help your students develop a positive mathematics identity?
- (12)
- We’ve discussed challenges that you’ve faced to change your instruction to be more inquiry-based. If we haven’t already discussed it, can you talk about your interest in potentially changing your instruction in these ways? What supports exist in your district or school to try and change your instruction in these ways? POTENTIAL PROBES: How important is it to you to change your instruction in these ways? How might you and/or your students benefit from making these instructional changes?
- (13)
- We’ve discussed challenges that you’ve faced to have a more positive mathematical identity. Is there anything that you’d like to add to this conversation that we haven’t already discussed?
- (14)
- Is there anything that you’d like to add to our conversation about your experiences in the Institute and potential challenges/barriers you’ve faced to change your math instruction?

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Pseudonym | Gender Identity | Ethnicity/Race | Role | Years Teaching |
---|---|---|---|---|

Gloria | Female | Hispanic | Middle school math teacher | 22 years |

Suzie | Female | Hispanic | 4th grade teacher | 8 years as teacher, 7 years as teaching assistance |

Alana | Female | Native American | 3rd grade teacher | 21 years |

Camila | Female | Hispanic | 5th grade teacher | 21 years |

Silvia | Female | Native American | 2nd grade teacher | 15 years |

James | Male | Native American | 4th grade teacher | 14 years |

Adriana | Female | Hispanic | 6th grade math teacher | 13 years |

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## Share and Cite

**MDPI and ACS Style**

Kitchen, R.; Martinez-Archuleta, M.; Gonzales, L.; Bicer, A.
Actualizing Change after Experiencing Significant Mathematics PD: Hearing from Teachers of Color about Their Practice and Mathematical Identities. *Educ. Sci.* **2021**, *11*, 710.
https://doi.org/10.3390/educsci11110710

**AMA Style**

Kitchen R, Martinez-Archuleta M, Gonzales L, Bicer A.
Actualizing Change after Experiencing Significant Mathematics PD: Hearing from Teachers of Color about Their Practice and Mathematical Identities. *Education Sciences*. 2021; 11(11):710.
https://doi.org/10.3390/educsci11110710

**Chicago/Turabian Style**

Kitchen, Richard, Monica Martinez-Archuleta, Lorenzo Gonzales, and Ali Bicer.
2021. "Actualizing Change after Experiencing Significant Mathematics PD: Hearing from Teachers of Color about Their Practice and Mathematical Identities" *Education Sciences* 11, no. 11: 710.
https://doi.org/10.3390/educsci11110710