#### A Special Issue of Education Sciences with Guest Editor Professor Jo Boaler

Many students of mathematics are held back in their learning because of ideas about mathematics or mathematics learning, that are inaccurate. This Special Issue features a range of articles that tackle some different “myths” that restrict learning opportunities for students, and the ways they may be taken out of the learning equation to liberate students. Examples of myths that are tackled are the idea that only some students can learn high level mathematics – a range of articles tackle this faulty idea and provide evidence of change when this idea is dispelled. Other articles tackle the faulty idea that to be good at mathematics you need to calculate fast, or that mathematics is a set of disconnected procedures that need to be memorized, or that student “off task” conversations impede learning. Others consider the true nature of real mathematics, and the difference between mathematics as a discipline and the mathematics taught in schools. The Special Issue features research papers, reviews of research studies, technical reports, and conceptual pieces. The goal of the Special Issue is to conceptualize and raise attention to the myths that reduce students’ learning of mathematics and highlight interventions, and research with teachers and students, that has set students free and liberated their learning of mathematics.

Jo Boaler

*Guest Editor*

#### Achieving Elusive Teacher Change through Challenging Myths about Learning: A Blended Approach

**by Robin Keturah Anderson, Jo Boaler and Jack A. Dieckmann**

Abstract: The idea that success in mathematics is only available to those born as “mathematics people” has been challenged in recent years by neuroscience, showing that mathematics pathways develop in the brain through learning and practice. This paper reports on a blended professional learning model of online and in-person meetings during which 40 teachers in 8 school districts in the US learned about the new brain science, challenging the “math person” myth, as well as effective mathematics teaching methods. We refer to the combination as a Mathematical Mindset Approach. Using mixed methods, we conducted a one-year study to investigate teacher and student learning in a Mathematical Mindset network. We collected data on teacher and student beliefs, teacher instructional practice, and student learning gains on state achievement tests. The results from our quantitative analyses found statistically significant positive improvements in student beliefs, teacher’s instructional practice, and on students’ math test scores. The mindset approach particularly raised the achievement of girls, English learners, and economically disadvantaged students. Based on our qualitative analysis, we propose that the success of the intervention rests upon two central factors: (1) The different forms of PD served to eradicate the learning myths that had held up teachers and learners; and that (2) Teachers had space for identity work as mathematical learners.

#### The Myth That Only Brilliant People Are Good at Math and Its Implications for Diversity

**by Eleanor K. Chestnut, Ryan F. Lei, Sarah-Jane Leslie and Andrei Cimpian**

Abstract: A common misconception about math is that it requires raw intellectual talent or “brilliance.” Only students who possess this sort of brilliance are assumed to be capable of success in math-related subjects. This harmful myth has far-reaching consequences for the success of girls and children from ethnic-minority backgrounds in these subjects. Because women and minorities are stereotyped as lacking brilliance, the myth that success in math requires this trait is a barrier that students from these groups have to overcome. In the first part of this paper, we detail the pervasiveness of this myth and explore its relation to gender and race gaps in math and beyond. In the second part, we highlight some potential sources of this myth in children’s everyday experiences and offer some strategies for debunking it.

#### Myths of Early Math

**by Douglas H. Clements and Julie Sarama**

Abstract: Myths about early education abound. Many beliefs people hold about early math have a grain of truth in them, but as a whole are not true—they are largely myths. But the myths persist, and many harm children. In this article, we address ubiquitous math myths that may be negatively affecting many young students. We conclude that avoiding the myths and listening to the findings of research and the wisdom of expert practice will serve both teachers and children well.

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

**by Teresa K. Dunleavy**

Abstract: This article continues to challenge the robust myth that mathematical smartness is exemplified in individuals who consistently complete mathematics problems quickly and accurately. In so doing, I present a set of counterstories from three students in one ninth-grade Algebra 1 classroom. These students described transformative experiences in their perceptions of mathematical smartness. Analysis of interviews revealed four themes about their perceptions of mathematical smartness, including: (1) consistently and unapologetically affording time and space to value multiple solution strategies, (2) belief in mathematical justification and explanation as the goal for demonstrating mastery of mathematical content, (3) valuing mathematically valid ideas from all class members, and (4) valuing collaborative problem solving as a way to help group members, distribute mathematical knowledge and orient students toward learning with one another. I found that their interpretations of mathematical smartness are counter to the still-dominant myths around speed and accuracy. While the four themes that emerged have been previously studied in the frame of teacher practices, this research provides needed additional empirical evidence of students’ voices describing what mathematical smartness can and should look like.

#### Counteracting Destructive Student Misconceptions of Mathematics

**by Uffe Thomas Jankvist and Mogens Niss**

Abstract: In this article, we ask the question of what it takes for targeted efforts to be reasonably successful in altering students’ misconceptions and unproductive beliefs and ensuing myths about mathematics as a discipline and a school subject and about themselves in relation to mathematics, so as to pave the way for satisfactory learning. We attempt to answer this question through the analysis of three cases of upper secondary school students, who all struggled with mathematics-related difficulties due to myths resulting from misguided beliefs, erroneous proof schemes, or mistaken interpretations of the didactical contract, the three theoretical constructs we employ in the study. We describe how specially educated teachers, so-called “mathematics counsellors”, taking part in a professional development program conducted by the authors, were able, firstly, to identity these students, then to diagnose more precisely the nature of their difficulties, and finally to design targeted interventions in order to assist the students in actually overcoming (parts of) their difficulties and eventually dispelling some of the myths they were influenced by. We further offer an analysis of the elements responsible for the success of these interventions. More precisely, we identify five such elements. Finally, we zoom in on the role and intricate connectedness of the three theoretical constructs mentioned above.

#### “Indefensible, Illogical, and Unsupported”; Countering Deficit Mythologies about the Potential of Students with Learning Disabilities in Mathematics

**by Rachel Lambert**

Abstract: This paper describes two myths that circulate widely about the potential of students with Learning Disabilities to learn mathematics: (1) that students with Learning Disabilities cannot benefit from inquiry-based instruction in mathematics, and only from explicit instruction; and (2) that students with Learning Disabilities cannot construct their own mathematical strategies and do not benefit from engaging with multiple strategies. In this paper, I will describe how these myths have developed, and identify research that counters these myths. I argue that these myths are the unintended consequences of deficit constructions of students with Learning Disabilities in educational research. Using neurodiversity to frame disability as diversity rather than deficit, I assert that students with Learning Disabilities can learn mathematics to the highest levels, and that these limiting mythologies hold them back.

#### Productive Disruptions: Rethinking the Role of Off-Task Interactions in Collaborative Mathematics Learning

**by Jennifer M. Langer-Osuna**

Abstract: This paper confronts the myth that all off-task interactions in mathematics classrooms is detrimental to learning. To do so, this paper first explores links between participation, learning, and identity in mathematics education research that points to the importance of positional resources. Positional resources are related to identity processes and carry central functions that regulate learning and doing mathematics together. The paper then frames off-task behavior as an important positional resource in collaborative mathematics learning environments. With these ideas in mind, the paper then closes with new questions for research.

#### Against the Odds: Insights from a Statistician with Dyscalculia

**by Katherine E. Lewis and Dylan M. Lynn**

Abstract: Students with dyscalculia are typically thought of by both researchers and educators as having deficits. The deficit language permeates studies of dyscalculia as well as assessments and documentation of students in schools. In this paper, we offer an alternative to the dominant narrative. We understand disabilities, and dyscalculia specifically, as resulting from cognitive differences—not deficits—which lead to issues of access. We provide a case study of Dylan (second author), an individual with dyscalculia who decided to major in statistics at University of California, Berkeley and become a statistician. Although she experienced significant issues of access—both in the standard tools used to do mathematics, and in navigating the structures at the university—she developed systems to enable her to compensate. She collaborated in this research enterprise in order to share with researchers, teachers, parents, and students her experiences with dyscalculia and how she was able to succeed in higher level mathematics. Informed by previous empirical work, we collected video recordings of Dylan’s deliberate efforts to share insights and strategies with another student with dyscalculia. In this work, Dylan challenges dominant and problematic myths about ability and mathematics.

#### Rejecting Platonism: Recovering Humanity in Mathematics Education

**by Frederick A. Peck**

Abstract: In this paper, I consider a pervasive myth in mathematics education, that of Plato-formalism. I show that this myth is ahistorical, acultural, and harmful, both for mathematics and for society. I argue that, as teachers, we should reject the myth of Plato-formalism and instead understand mathematics as a human activity. This philosophy humanizes mathematics and implies that math education should be active, cultural, historical, social, and critical—helping students learn formal mathematics, while also learning that mathematics shapes their lives, that this shaping is a result of human work and choices, and that students are empowered to shape those choices.

#### M Is Not Just for STEM: How Myths about the Purposes of Mathematics Education Have Narrowed Mathematics Curricula in the United States

**by Kate Raymond**

Abstract: When public schooling was first introduced in the United States, early proponents emphasized the need for mathematics as critical for an informed citizenry in a democracy. Half a century later, this purpose of mathematics has been almost entirely overshadowed by the push for mathematics to maintain technological and economic advantages. The belief that preparation for technological careers is, and has historically been, the only purpose for school mathematics in the US has become a myth widely believed by the public and policymakers alike. As this myth took hold, mathematics curricula were narrowed, incorporating only the mathematics, and applications of mathematics, that supported this specific purpose. Not only does this narrowing of school mathematics negatively impact the development of informed citizens, but it limits the extent to which mathematics can be studied in ways that engage all learners. The emergence of mathematics for social justice is thus—in part—an attempt to recapture the broader purposes of school mathematics.

#### Teach the Mathematics of Mathematicians

**by Peter Taylor**

Abstract: The secondary-school mathematics curriculum is narrow in scope and technical in character; this is quite different from the nature of the discipline itself. As a result, it offers little inspiration to both students and teachers, and provides students with poor preparation for university mathematics courses and indeed for life. Over the past century, recently more than ever, there have been calls for change, for a curriculum that is true to the subject of mathematics as the creation and study of patterns and structures. While there are hopeful responses to this at the elementary level, there is almost nothing at the secondary level. Ironically, it is felt that in order to prepare students for university calculus, the secondary curriculum simply has to be what it is. This is a special case of a myth that needs to be destroyed.