# Jo Boaler's research while affiliated with Stanford University and other places

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## Publications (59)

After experiencing years of procedural teaching in K-12 mathematics classrooms, many students arrive at college with ideas about, and approaches towards, mathematics that are not helpful to their learning. Students’ prior experiences and misconceptions can then negatively impact their experiences in university STEM courses. This paper describes a s...

A wide range of evidence points to the need for students to have a growth mindset as they approach their learning, but recent critiques of mindset have highlighted the need to change teaching approaches, to transfuse mindset ideas throughout teaching. This shifts the responsibility from students themselves to teachers and schools. This paper shares...

The COVID-19 global pandemic has required everyone to make sense of data about community spread, levels of risk, and vaccine efficacy. Yet research shows that students are underprepared in data literacy. Tanya LaMar and Jo Boaler argue that data science education provides an opportunity to address this problem while providing much needed updates to...

Many school districts strive to achieve high mathematics achievement and equitable outcomes. This study examines the work of Gateside district, an urban district that had made great progress in the enactment of equity minded policies such as de-tracking and the availability of high-level mathematics to all students. A detailed, case study of teachi...

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...

This study reports on the impact of a “massive, open, online course” (MOOC) designed to change students' ideas about mathematics and their own potential and improve their mathematics achievement. Many students hold damaging fixed mindsets, believing that their intelligence is unchangeable. When students shift to a growth mindset (believing that the...

In a previous study of 2 schools in England that taught mathematics very differently, the first author found that a project-based mathematics approach resulted in higher achievement, greater understanding, and more appreciation of mathematics than a traditional approach. This follow-up showed that the young adults who had experienced the 2 mathemat...

A few weeks ago the silence of my Stanford office was interrupted by a phone call. A mother called to tell me that her 5-year old daughter had come home from school crying because her teacher had not allowed her to count on her fingers. A few weeks afterwards, when I told my undergraduate mathematics class that visual mathematics was really importa...

This department publishes brief news articles, announcements and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education.

Mathematics education researchers have produced many important research insights into how students learn mathematics, but relatively few of these insights have influenced the practice of classrooms. This chapter takes up Kilpatrick’s call for more “foxes” in mathematics education and considers the ways the field may move to work in more “foxy” ways...

This article draws on the outcomes of a 4-year project where complex instruction was used as the basis for a reform in mathematics teaching in remote Aboriginal communities in Australia. The article describes the overall project in terms of the goals and aspirations for learning mathematics among remote Indigenous Australians. Knowing that the appr...

An examination of gender, social class and ethnicity performance and participation patterns in different UK countries shows that inequities occur in relation to gender, class and ethnicity but that the patterns of inequity look quite different in the three domains. Achievement is equal for different genders but many more males take mathematics forw...

The National Mathematics Advisory Panel was given the task of reviewing research on the instructional practices that enable students to learn mathematics successfully. The authors argue that in conducting its review, which appears in Foundations for Success: The Final Report of the National Mathematics Advisory Panel (2008), the Panel imposed dange...

Equity is a concept that is often measured in terms of test scores, with educators looking for equal test scores among students of different cultural groups, social classes or sexes. In this article the term ‘relational equity’ is proposed to describe equitable relations in classrooms; relations that include students treating each other with respec...

Background/Context
School tracking practices have been documented repeatedly as having negative effects on students’ identity development and attainment, particularly for those students placed in lower tracks. Despite this documentation, tracking persists as a normative practice in American high schools, perhaps in part because we have few models o...

With Australia performing so poorly in terms of equity in mathematical achievement on the PISA scores, there is an increasing recognition for practices that may stem the inequities in education in this country. This paper explores an approach that has been found to be highly successful in the United States and links it to current issues in Australi...

A new project is underway to improve mathematical learning by Indigenous students in Western Australia's east Kimberley region. Six schools are taking part, all based in self-governing Indigenous communities. The project uses a learning model that was developed by Stanford University for use with disadvantaged low-performing students in the USA ada...

Equity is a concept that is often measured in terms of test scores, with educators looking for equal test scores among students of different cultural groups, social classes or sexes. As an alternative I will discuss the idea of 'relational equity', a term I use to describe equitable relations in classrooms.

As we survey the landscape of gender and mathematics relationships in various countries of the world, it is clear that we have reached an interesting and important time. In many countries, differences in girls' and boys' mathematics achievement that used to prevail have been eradicated. This is a significant achievement reflecting, in part, increas...

In a four-year, longitudinal study conducted between 2000 and 2004, the author followed 700 students as they progressed through three high schools: a diverse, urban school as well as two suburban schools. Although incoming freshmen at the urban school scored significantly lower in mathematics than incoming students at the two suburban schools, by s...

This article describes the ways in which the mathematics department of an urban, ethnically diverse school, brought about high and equitable mathematics achievement. The teachers employed heterogeneous grouping and complex instruction, an approach designed to counter status differences in classrooms. As part of this approach teachers encouraged mul...

By revamping their school's entire mathematics program, the teachers at an urban high school were able to help their disadvantaged students attain high levels of mathematical understanding. Just as important, Ms. Boaler notes, the students learned to appreciate the contributions of all their peers, regardless of gender, ethnicity, or social class.

The low and inequitable mathematics performance of students in urban American high schools has been identified as a critical issue contributing to societal inequities. In an effort to better the field's understanding of equitable and successful teaching, we report results from a four-year longitudinal study of approximately 700 students as they pro...

Introduction During the last five years I have been conducting a longitudinal study in the US in which a team of graduate students 3 and I have monitored approximately 700 students through four years of three different high schools. The aim of the study was to monitor the impact of different teaching approaches upon students' understanding of mathe...

At ICME 9, the International Organisation for Women and Mathematics Education (IOWME) met for four different symposia gatherings at which women and men from 24 countries came together to consider issues of equity and social justice in mathematics education. Presenters from Australia, England, Germany, Greece, Hungary, Israel, India, Japan, Singapor...

In this chapter we consider what it takes to learn to conduct research in mathematics education. We argue that learning any
complex practice requires opportunities to unpack its components in order to see what underlies competence performance. Many
of the components of successful research remain implicit and are left to new researchers to glean fro...

The analytical stance taken by equity researchers in education, the methodologies employed, and the interpretations that are drawn from data, all have an enormous impact upon the knowledge that is produced about sources of inequality. In the 1970's and 1980's, a great deal of interest was given to the issue of women's and girls' underachievement in...

Some researchers have expressed doubts about the potential of reform-oriented curricula to promote equity. This article considers this important issue and argues that investigations into equitable teaching must pay attention to the particular practices of teaching and learning that are enacted in classrooms. Data are presented from two studies in w...

What proficiencies are brought tobear when students work on mathematicsproblems? And to what extent may these becaptured by
knowledge categories? These arequestions that I consider in this article,as I explore notions of competency, that gobeyond
knowledge to include themathematical `dispositions' that studentsbring to problems and the `practices'...

This article demonstrates the importance of expanding notions of learning beyond knowledge to the practices of mathematics classrooms. A three year study of students who learned through mathematical modelling is considered. This shows that a modelling approach encouraged the development of a range of important practices, in addition to knowledge, t...

This paper reports findings from the first two years of a four-year longitudinal study into the ways that students' attitudes towards, and achievement in, mathematics are influenced by ability-grouping practices in six schools. Through the use of questionnaires administered to the whole cohort of 943 students, interviews with 72 students and approx...

This article reports upon a study of students learning mathematics in six English schools. Interviews with 76 students from the schools are analyzed in order to understand the nature of the classroom communities in which students work; the students' perceptions of these communities, and the impact of their perceptions upon knowledge development and...

In this report I offer an exploration of the insights that may be provided by a situated perspective on learning. Through an extension of my previous analysis of students learning mathematics in 2 schools (Boaler, 1998), I consider the ways in which a focus on the classroom community and the behaviors and practices implicit within such communities...

In this paper I illustrate the use of a particular situated method of interpretation in my analysis of the data from 3-year case studies of two schools. The constraints and affordances provided by different environments are shown to be key analytical tools in understanding the ways in which students develop and make use of knowledge. Various classr...

In this article I describe two different models of teaching mathematics and the different forms of knowledge that students developed in response to these. Five different assessments were used to assess students in two schools, as part of a longitudinal, ethnographic study of mathematics learning. The outcomes of these assessments are reported along...

This paper presents case study data from two schools which taught mathematics in completely different ways. One of the schools followed a traditional, procedural approach which caused many girls to underachieve. The girls in this school related their underachievement to the closed nature of their working environment. The second school followed an o...

This paper reports on 3-year case studies of 2 schools with alternative mathematical teaching approaches. One school used a traditional, textbook approach; the other used open-ended activities at all times. Using various forms of case study data, including observations, questionnaires, interviews, and quantitative assessments, I will show the ways...

This paper reports on 3-year case studies of 2 schools with alternative mathematical teaching approaches. One school used a traditional, textbook approach; the other used open-ended activities at all times. Using various forms of case study data, including observations, questionnaires, interviews, and quantitative assessments, I will show the ways...

The question of whether students should be grouped and taught in classes according to their perceived ‘ability’ during their school careers is one of the most controversial issues in education. This is partly because the issues that surround setting, streaming and mixed ability teaching are relative, both to ideology and personal values. Decisions...

This paper considers the experiences of two sets of students who attended schools that taught mathematics in completely different
ways. One of the schools used a traditional, textbook approach, and the other used an open, project-based approach. The latter
approach produced equity between girls and boys whereas the textbook approach prompted many o...

ABSTRACT In this paper I consider what appears to be an emerging feminist perspective within mathematics education that suggests that theories such as 'attribution theory' lay too much 'blame' upon girls and women for their underachievement in mathematics and not enough blame upon the wider school system. I attempt to extend this theoretical positi...

In this paper I present some of the results of a three-year case study of a mathematics department in a UK school that taught in setted' groups. Interviews, observations, questionnaires, and assessment data are used to show the way in which high ability students, particularly girls, underachieved and became disaffected as a result of being in the t...

“Back‐to‐basics” policies fit easily within many mathematics classrooms. Features such as order, control, rule following, uniformity, and conformity are relatively commonplace and are now more generally in demand with the current political backlash against progressive forms of schooling. This paper examines some of the influences of these tradition...

This article considers the move in mathematics education, away from abstract calculations and toward ‘mathematics in context’, particularly in relation to female underachievement in the mathematics classroom. It is suggested that ‘unreal’ contexts, which require students to view school mathematics as useful only in the make‐believe world created in...

This paper reports upon a research project which considered the transfer of students' mathematical understanding across different task contexts. The research involved two groups of students from contrasting learning environments. The first environment was characterised by the complete integration of mathematical process and content using open ended...

## Citations

... On the other hand, a growth mindset sees intelligence ("intelligence") as a moldable trait that is not fixed and could be improved through effort and intervention ("intervention") (Macnamara and Rupani, 2017;Zhu et al., 2019). Additionally, the theories and intervention methods related to mathematical beliefs could also be applied to other STEM-related ("STEM") disciplines (Boaler et al., 2021). ...

... A data-driven world implies the essentiality of data practices (We prefer data practices to "data literacy," because we recognize there is a history of racialized and discriminatory uses of the term "literacy" (Philip & Rubel, 2019) or to data skills, because we view learning data science as a process of participation in situated practices with tools (Gutiérrez & Rogoff, 2003).). Accordingly, an enthusiasm for data science (DS) education-that is, education that leverages computer science, statistics, and mathematics knowledge for learning data practicesnow extends to K-12 schools (e.g., LaMar & Boaler, 2021). The preK-12 Guidelines for Assessment and Instruction in Statistics Education (GAISE II; Bargagliotti et al., 2020), for example, present "statistical literacy for all" as an "ultimate goal" (p. ...

... From Fig. 2.6, Cylindrical clay pots that teachers can use to teach various shapes teachers can formulate questions around the value of beds, the number of trees that have been cut, the different implements used to make the beds, different colours that the beds can be painted and how many learners chose the various colours of the beds. Such knowledge is what Boaler et al. (2021) call data science. However, such questions and the ability to represent the ordinary market artefacts into living Figure 2.6 can be used in other subjects such as commerce; one can teach about the value of beds, the cost of making a bed, and the demand and supply of beds and link that to the population and employment. ...

... Några kommer ihåg detta som roligt och sporrande, andra kommer ihåg det med en rysning, som det tidsbegränsade testet som varje fredag slog fast att man inte kunde matematik, som till slut gjorde att man valde att inte studera mer matematik än nödvändigt. Tabelltesterna är kanske inte den enda aktivitet som skapar ångest men det är en av dem (Boaler, 2014) och om man frågar eleverna så är matematikängslan den främsta orsaken till att de inte presterar tillfredsställande i matematik (Karlsson, 2019). En tradition i svensk skola riskerar alltså att utestänga eleverna från att prestera i matematik och i förlängningen från att studera matematik. ...

Reference: Tabelltest på tid

... However, some of the research has been based on mindset interventions that deliver these messages but do not change the teaching that surrounds them, with students often receiving counter messages through educational practices [31]. When students are told they can learn anything, but are then presented with closed questions, requiring one method and one answer, the positive messages regarding mindset often fall flat [32]. This has led to criticism of the idea of mindset [33] and to research studies that show no impact [34]. ...

... Rich mathematical tasks also support the development of autonomous learners, as students are not dependent upon reproducing the teacher's example to gain the correct solution, rather they are encouraged to follow their own creative thinking and ideas (Silver and Stein, 1996;Silver, 1997). Several studies have shown the connection between the use of open tasks and the development or strengthening of students' growth mindsets (Boaler, 1998;Stohlmann et al., 2018;Sun, 2018). ...

... In this study, the porous structure design of the monolithic catalyst was mainly carried out at the bottom of the reactor and the surrounding area of the magneton, as shown in Fig. 1(b). Inspired by the natural spiral porous structure of nautilus [42][43], the bionic scaffold pattern was simplified and based on the four-grid pattern, as shown in Fig. 1(c). ...

... This has led to criticism of the idea of mindset [33] and to research studies that show no impact [34]. In contrast, studies that consider the impact of delivering mindset ideas and infusing them through teaching practices show significant impact [10,[35][36][37]. When questions are open-ended and engage students in meaningful contexts [28,38], students can see that they can learn and grow, and mindset ideas can more readily take root. ...

... Many growth mindset interventions additionally encourage students in the treatment group-but not the control group-to practice, study, pursue challenges, persevere, find optimal learning strategies, and/or seek help (e.g., Blackwell et al., 2007;Burnette et al., 2019;Paunesku et al., 2015;Yeager et al., 2018). Interventions often additionally teach students in the treatment group, but not the control group, strategies for learning course content and overcoming setbacks (e.g., Boaler et al., 2018;Yeager et al., 2018) and include role models or inspirational stories (e.g., Burnette et al., 2019;Foliano et al., 2019). ...

... Whether thinking about and searching for activities or problems for an assessment, disseminating information via email, or using the class whiteboard for students to solve problems, each action attempted to promote and support a sense of belonging in the mathematics classroom for their students. Specific participant comments and assertions that illustrate an image of promoting and supporting their students' sense of belonging in the classroom, included (Boaler & Selling, 2017;Dweck, 2006;Goldin et al., 2016;Hannula et al., 2019;Philipp, 2007;Rott et al., 2018): mathematical identity -"I want to make sure each student believes they can be . . . they are a contributor to the mathematics classroom . . . to view themselves as mathematicians" (Instructor 2, Week 6 meeting); motivation and persistence -"I usually focus on motivation and persistence as a way to promote students' beliefs in their ability to contribute to class discussions" (Instructor 1, Week 5 meeting); interest -"pair and small group activities are useful to support student interest and promote a sense of togetherness" (Instructor 1, Week 3 meeting); growth mindset -"students need to believe they can not only be successful in my class, but have the abilities to be successful in their future math courses" (Instructor 1, Week 5 meeting); and values -"since most of my classes have both traditional and nontraditional students, I have to make certain to provide activities that encourage each group to value mathematics " (Instructor 2, Week 9 meeting). ...