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Even before the pandemic slowed learning for many, only 39 percent of California students demonstrated proficiency on the state math assessment. During the pandemic, the proportion of math-proficient students fell to one-third. At the same time, the STEM workforce faces shortages and a lack of diversity, which call into question the longstanding practice of filtering the majority of students out of advanced pathways in math, often from a young age. To address these problems, a committee of California math educators proposed changing the approach to teaching math based on what research has revealed about what will improve math achievement and engagement. In 2021, California started the process of revising the framework that guides math instruction.

Babies and infants love mathematics. Give babies a set of blocks, and they will build and order them, fascinated by the ways the edges line up. Children will look up at the sky and be delighted by the V formations in which birds fly. Count a set of objects with a young child and then move the objects and count them again, and they will be enchanted by the fact they still have the same number. Ask children to make patterns with colored blocks, and they will work happily making repeating patterns--one of the most mathematical of all acts. We want to see patterns in the world and to understand the rhythms of the universe. The joy and fascination young children experience with mathematics are quickly replaced by dread and dislike when they start school mathematics and are introduced to a dry set of methods they think they just have to accept and remember. Successful math users have an approach to math as well as mathematical understanding that sets them apart from less successful users. They approach math with the desire to understand it and to think about it, and with the confidence that they can make sense of it. Successful math users search for patterns and relationships and think about connections. They approach math with a mathematical mindset, knowing that math is a subject of growth and that their role is to learn and think about new ideas. The outcome of the misguided school emphasis on memorization and testing can be seen in the numbers of students dropping out of mathematics and in the math crisis we currently face. This article discusses techniques to develop mathematical mindsets in students so that they are willing to approach math with sense making and intuition.

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 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 the current mathematics curriculum. The integration of data science can provide a more equitable mathematics pipeline than the calculus-focused pathway that has excluded most students from a future in mathematics. Through data science, students can learn to answer questions that are relevant to their lives and communities, to be critical consumers of the data that surround them every day, and to wield the power of data analysis.

Over the course of 18 months, teams at the University of Chicago and Stanford University joined with other leaders across the United States and world to consider the issue of the types of mathematics used in the classroom. It quickly became clear that all students--starting from the youngest in prekindergarten to those in college--need to learn the mathematics that will help them develop data literacy, to make sense of the data-filled world in which we all live. In this article, the authors explain the importance of a new initiative at youcubed, note the reasons it is so exciting for all teachers and students, and share some important resources for teaching with a data perspective across PK-12. This new data science PK-12 initiative is designed to counter this threat and offer resources for teachers that they can use to excite their students about data in the world.

Reasoning and problem solving are both critical acts in mathematics learning. The author has met many teachers who tell her they would love to highlight them more but feel they cannot because of the pressures of content coverage, pacing guides, and district tests. In this article, she describes a teaching intervention that highlighted problem solving and reasoning and resulted in changed mathematics pathways for students, whether they were at the low, middle, or high end of the achievement spectrum.

The number of students who leave U.S. schools mathematically underprepared has prompted widespread concern. Low achieving students, many of whom have been turned off mathematics, are often placed in low tracks and given remedial, skills-oriented work. This study examines a different approach wherein heterogeneous groups of students were given responsibility and agency and asked to engage in a range of mathematical practices collaboratively. The teaching intervention, which was introduced in the first paper, took place as part of a summer class on algebra, and it gave students the opportunity to participate with mathematics in changed ways. This paper will report evidence that the vast majority responded with increased engagement, achievement, and enjoyment. The students chose collaboration and agency as critical to their improved relationships with mathematics.

In this response, we consider the Rights of Learners, in particular considering the ways "assessment for learners" policies and practices may be woven into the rights. We also consider findings from neuroscience on the positive role played by mistakes and suggest adding such findings to the messages given in classrooms. [For "The Rights of the Learner: A Framework for Promoting Equity through Formative Assessment in Mathematics Education," see EJ1162636.]

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 approach had been successful in a diverse setting in California, the project team sought to implement and evaluate the possibilities of such reform in a context in which the need for a culturally responsive pedagogy was critical. Elements of complex instruction offered considerable possibilities in aligning with the cultures of the remote communities, but with recognition of the possibility that some elements may not be workable in these contexts. Complex instruction also valued deep knowledge of mathematics rather than a tokenistic, impoverished mathematics. The strategies within complex instruction allowed for mathematical and cultural scaffolding to promote deep learning in mathematics. Such an approach was in line with current reforms in Indigenous education in Australia where there are high expectations of learners in order to break away from the deficit thinking that has permeated much education in remote Australia. The overall intent is to demonstrate what pedagogies are possible within the constraints of the remote context.

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 forward to advanced levels; social class differences persist in both achievement and participation; and ethnicity shows a varied pattern with some groups performing and participating at particularly high levels and some particularly low. This paper identifies some critical issues that we face in making mathematics and science equitable and begins to analyse some of the barriers that stand in the way of students who are female, and from some ethnic and social groups. (Contains 1 note, 7 figures and 7 tables.)

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 respect and responsibility. This concept will be illustrated through the results of a four-year study of different mathematics teaching approaches, conducted in three Californian high schools. In one of the schools--a diverse, urban high school--students achieved at higher levels, learned good behaviour, and learned to respect students from different cultural groups, social classes, ability levels and sexes. In addition, differences in attainment between different cultural groups were eliminated in some cases and reduced in all others. Importantly, the goals of high achievement and equity were achieved in tandem through a mixed-ability mathematics approach that is not used or well known in the UK. (Contains 2 tables.)

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 of how departments and teachers can successfully organize instruction in heterogeneous, high school mathematics classes. This paper offers one such model through a qualitative and quantitative analysis. Focus of Study: In an effort to better the field's understanding of equitable and successful teaching, we conducted a longitudinal study of three high schools. At one school, Railside, students demonstrated greater gains in achievement than students at the other two schools and higher overall achievement on a number of measures. Furthermore, achievement gaps among various ethnic groups at Railside that were present on incoming assessments disappeared in nearly all cases by the end of the second year. This paper provides an analysis of Railside's success and identifies factors that contributed to this success. Participants: Participants included approximately 700 students as they progressed through three California high schools. Railside was an urban high school with an ethnically, linguistically, and economically diverse student body. Greendale was situated in a coastal community with a more homogeneous, primarily White student body. Hilltop was a rural high school with primarily White and Latino/a students. Research Design: This longitudinal, multiple case study employed mixed methods. Three schools were chosen to offer a range of curricular programs and varied student populations. Student achievement and attitudinal data were evaluated using statistical techniques, whereas teacher and student practices were documented using qualitative analytic techniques such as coding. Findings/Results: One of the findings of the study was the success of Railside school, where the mathematics department taught heterogeneous classes using a reform-oriented approach. Compared with the other two schools in the study, Railside students learned more, enjoyed mathematics more and progressed to higher mathematics levels. This paper presents large-scale evidence of these important achievements and provides detailed analyses of the ways that the Railside teachers brought them about, with a focus on the teaching and learning interactions within the classrooms.

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 senior year, 41 percent of the urban school's students were taking calculus, compared with approximately 27 percent of students in the other two schools. The urban school's approach encouraged both relational equity and high achievement. Important dimensions of the mathematics teachers' work included working collaboratively to design curriculums and teaching methods, a shared commitment to equity, heterogeneous classes, and a teaching approach in which students worked on complex conceptual problems in groups. These positive and respectful intellectual relations--which the author refers to as "relational equity"--depended on students' committing to the learning of others, respecting the ideas of others, and learning to communicate. (Contains 1 figure.)

The poor performance of students in America's urban high schools, both in absolute terms and in comparison with their more economically secure counterparts in suburban schools, is a critical issue for the country, and the opportunity for all students to learn mathematics has been heralded as the new "civil right." In a recent study of mathematics teaching in different schools, the author and a group of graduate students at Stanford found that students at Railside High School (a pseudonym), an urban school in California nestled within a few feet of the train tracks, performed better in mathematics than students at other schools and that differences in achievement among Railside students of different cultural groups were reduced in all cases and eliminated in some. Railside was one of three schools in which they spent four years following cohorts of students from their freshman to their senior years as they experienced different approaches to mathematics instruction. As part of the study, they documented the teaching practices of the Railside mathematics department--practices focused upon equity. In this article, the author considers some of the most important aspects of Railside's reform-oriented approach to mathematics instruction--an approach that transformed students' lives by helping them to see mathematics as a part of their future and by providing them with the quantitative reasoning capabilities needed to function in an increasingly technological and global economy.

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 multidimensional classrooms, valued the perspectives of different students, and encouraged students to be responsible for each other. The work of students and teachers at Railside School was equitable partly because students achieved more equitable outcomes on tests, but also because students learned to act in more equitable ways in their classrooms. Students learned to appreciate the contributions of students from different cultural groups, genders, and attainment levels, a behavior termed relational equity. This article describes the teaching practices that enabled the department to bring about such important achievements.

In stark contrast to the recommendations of the current White Paper, Jo Boaler's recent research suggests that the radical progressive state school commitment to mixed ability teaching has, in the case of this landmark study, led to better results and better life-chances than its more traditional counterpart whose ability grouping practices created, in the words of one ex-pupil, "psychological prisons" that "break ambition" and "almost formally label kids as stupid." If ability grouping reproduces social class inequalities, any political party that really cares about social justice must look again at the norms of ability segregation that blights so much of contemporary practice. In their stead, we need equitable and effective grouping polices that promote high achievement for all.