# High School Algebra Students Busting the Myth about Mathematical Smartness: Counterstories to the Dominant Narrative “Get It Quick and Get It Right”

## Abstract

**:**

## 1. Introduction to the Myth: Mathematical Smartness Defined by “Get It Quick and Get It Right”

## 2. Literature Review

## 3. Materials and Methods

#### 3.1. Site and Teacher Selection

#### 3.2. Participant Selection

#### 3.3. Data Collection

#### 3.4. Data Analysis

#### 3.5. Researcher Positioning

## 4. Results: Counterstories to “Get It Quick” and “Get It Right”

#### 4.1. Consistently and Unapologetically Affording Time and Space to Value Multiple Solution Strategies

Neesha’s explanation that she was required to explain her own method and also to listen to her partner’s method illustrates her belief that she was regularly encouraged to share her own method and to learn her group members’ ways of working on a problem.So, you do need to be able to explain thoroughly and [in] several different ways… So [that] everybody can get it. Or at least, if both of you have the right answer, you both have to explain how you got it, to each other. You might not have the same way, but you need to understand both ways.[31]

Helen’s reflection on how math was “different” indicated her belief that learning in this class was “outside the box” because students were learning in their “own way,” and they were not learning formulas from memory or by procedure. Helen’s comment also illustrates her belief that students should leverage their own strategies when doing mathematics.I know [Ms. Martin] teaches us differently. I know it’s more like you’re thinking for yourself. And you’re thinking outside the box or something. And instead of learning a formula or something, you’re learning it in your way, instead of like the structured way, or whatever.[32]

#### 4.2. Students’ Beliefs in Mathematical Justification and Explanation as the Goal for Demonstrating Mastery of Mathematics Content

Across the interviews, the students described these group interactions as consistently going beyond quickly confirming a correct answer. Because Helen shared at her first interview that she had previously “never had much confidence” in her mathematics abilities, the fact that she said she could ask questions to her group and “it just worked out,” pointed to the ways that students described groupwork as focusing beyond valuing speed and accuracy.We all made our statements, and it just worked out. And it helped. If they said something I didn’t understand, I could ask questions. And then they would say, “Oh no, it’s this…”.[32]

Jaelyn’s description of Shuffle Quizzes indicated the ways that she experienced the mathematical accountability an explanation that Shuffle Quizzes required [6,12,13,17]. In particular, Jaelyn described helping her group members to engage in mathematical justification by checking in with them about whether they are ready to explain on behalf of their group. Jaelyn also said that she should ask her group members, “Okay, what exactly didn’t you get?” if Ms. Martin suggested they needed to talk more about the mathematics so that they would each be ready to justify their mathematical thinking when Ms. Martin asked them to.Yeah, there’s some benefits. Because if I’m in a group with somebody, and I know they don’t get it, and then like, if the Shuffle Quiz comes to them, and they’ll be like… Oh, you know, a little like … Because … I don’t know, I feel like I can relate to it, because I was that person last year. So, if I see somebody struggling, I can be like, “Hey…” You know, when she [Ms. Martin] walks away and she’s giving us another chance she’ll be like, “Okay, what exactly didn’t you get?” “So, you know, when she comes back around, and she picks you again, will you be able to explain it?”.[33]

#### 4.3. Mathematically Valid Ideas Come from Everyone

Neesha’s reflection on Ms. Martin indicated her belief that Ms. Martin not only paid attention to how students solved mathematics problems, but she subsequently identified students’ smartness by allowing them to explain the mathematics to one another, then to follow up with statements like “I knew you would.” Helen said she noticed Ms. Martin tell her ways she was smart in mathematics by “not just complimenting her” but by drawing attention to what she understood:Ms. Martin, she’ll come toward you and talk with you. And she won’t give you the answer; she’ll walk away. But even if she walks away, you can tell she’s still listening, just by her posture. Like, she might be away, but she’s kinda slightly towards you, so she can definitely still hear your group’s conversation. And then, when you figure it out, she’s like, “I knew you would,” walking by … She just does things like that. So, you can tell that she’s paying attention to almost every group at the same time.[31]

Helen perception of Ms. Martin’s support explains how Ms. Martin assigned her competence [13,17] for solving mathematics problems in her own way.Ms. Martin points out what I know, and it’s not just like she’s complimenting me all the time or something. But it’s like, she’s more encouraging, in that she knows that I know how to do the problem. [She knows] I know enough information to put it all together.[32]

#### 4.4. Valuing Collaborative Problem Solving as a Way to Help Group Members, Distribute Mathematical Knowledge, and Orient Students toward Learning with One Another

Neesha’s perspective of collaboration this early in the year is particularly striking because her comments emerged from the context of a class full of students who had not had prior success with mathematics and whose peers were often taking Geometry or Algebra 2. Because this was a typical response of students in this class, Neesha’s perspective provided evidence for the ways that Ms. Martin developed a classroom in which that being a mathematician was about collaboration, willingness to learn, and believing in each group member.I really like our class … I feel like … they’re really hard workers, or, if they’re not hard workers, then they’ll ask a lot [of questions], so they can get the answers, and they’re willing to learn. Ms. Martin knows that we’re all talking. And I feel like that all talking thing really helps, like she wants to make sure everybody gets it. … I feel like our class is extremely positive. [The students] seem to get the problems, and they can go up on the board and do the problems and get the right answer.[31]

Neesha reflected that “thinking out loud” with her group was helpful. Her comments reveal how she was oriented to work with her classmates and how groupwork allowed everyone to make sense of the mathematics in a way that working it out alone (“on paper”) would not, thus distributing the mathematical knowledge across group members.Talking out loud, or thinking out loud really, it like helps you … so then you know. Cuz’ that’s something I struggle for, because I could do it on paper, but then, when I have to present to somebody else, the table group or in front of the class, it gets a lot harder. Cuz’ you’re like, “Wait, how did I do that, in the first place?”.[31]

Helen concluded that groupwork in Ms. Martin’s class helped make her a better student because she did not have to “get things” on her own. Jaelyn also talked about how Ms. Martin oriented students to help group members, saying, “Ms. Martin will make everyone in your group help you out and stuff.” Jaelyn also talked excitedly about how receiving her first “A” on a mathematics test was related to her work in groups.This year, I think I’m a better math student. Because the other math environment I was in was more independent, and you had to get things on your own. This year, I think it’s the thing they do in the math department: We’re sitting in a group, and I think that really helps me.[32]

Once I got the hang of it down, for the first time in years, when we took our linear equations test, I got an A on it. And then I was like, running home, and I was like telling my mom, because I never get A’s on math tests.[33]

The more I asked Jaelyn to reflect on the connection between “getting A’s” and groupwork, the more examples she offered, linking group members to mathematics understanding.Even like, yesterday, I think it was yesterday, I was like, “Ms. Martin, I give up!” and then Ms. Martin was like, “No, no, no! You don’t.” And then to Qianna, Ms. Martin was like, “Qianna, help her. Explain!” You know. “Explain it to her!” And she was like explaining. And then I was like, “Oh, okay, I get it now!”.[33]

## 5. Discussion

## Supplementary Materials

## Conflicts of Interest

## References

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Student | Grade | Racial-Gender Identity | Initial Self-Perceptions | End-of-Study Perceptions |
---|---|---|---|---|

Neesha | 9 | Black female | I used to shut down. | Math is one of my favorite classes [31]. |

Helen | 9 | white female | I’ve never had much [mathematics] confidence. | Well now I can explain it to everyone I know [32]! |

Jaelyn | 10 | Black female | Last year, I didn’t like to go to class. | I was curious to get to class and see what everybody else’s answer was [33]. |

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**MDPI and ACS Style**

Dunleavy, T.K. High School Algebra Students Busting the Myth about Mathematical Smartness: Counterstories to the Dominant Narrative “Get It Quick and Get It Right”. *Educ. Sci.* **2018**, *8*, 58.
https://doi.org/10.3390/educsci8020058

**AMA Style**

Dunleavy TK. High School Algebra Students Busting the Myth about Mathematical Smartness: Counterstories to the Dominant Narrative “Get It Quick and Get It Right”. *Education Sciences*. 2018; 8(2):58.
https://doi.org/10.3390/educsci8020058

**Chicago/Turabian Style**

Dunleavy, Teresa K. 2018. "High School Algebra Students Busting the Myth about Mathematical Smartness: Counterstories to the Dominant Narrative “Get It Quick and Get It Right”" *Education Sciences* 8, no. 2: 58.
https://doi.org/10.3390/educsci8020058