The Impact of a Mathematical Mindset Approach on Learning

Abstract

Since the introduction of Carol Dweck’s landmark work in mindset, many scholars have studied the impact of a change in mindset on learning, behavior, and health. National and international large-scale studies have validated the consistent correlation between learners developing a growth mindset (knowing that they can learn and improve) and performance on learning outcomes and longer-term learning behaviors. Whilst mindset interventions can have a positive impact on student learning, recent years have shown the need for more than a change in messaging. For widescale and lasting improvements in mathematics learning, messages need to be specific to mathematics, and delivered through a change in teaching approach, with mindset ideas infused through teaching practices and through assessment. This paper shares the evidence on the need for a “mathematical mindset” approach and the wide scale benefits that the approach promises to bring about.

1. Introduction

Mathematics achievement has a powerful influence on lifelong opportunities. The development of quantitative reasoning ability helps young people move out of poverty and move towards greater prosperity and health [1] as well as many other benefits in jobs and in life [2]. But in most countries in the world, mathematics achievement is persistently low, and mathematics anxiety is widespread [3,4]. Many adults try to avoid mathematics in their lives as much as they can [1]. Research from mathematics education and from the learning sciences has provided valuable insights into why students often dislike mathematics and have outlined approaches to learning that have proved to be impactful [5,6,7,8,9]. Still, systemic change is slow, particularly as the recommendations that emerge from research are often undermined by the for-profit textbook and testing companies whose materials are used in most US school districts [10,11]. Procedural teaching, reinforced by frequent testing, remains the norm and continues to generate student disinterest and disaffection [12,13]. An additional barrier to change is the widespread myths about mathematics potential that prevail—with a persistent idea that some students have a “math brain” and some do not, with stereotypical views about those with mathematics potential [14,15,16]. Until recently, educational reforms have not focused on the need to change ideas about mathematics potential and have overlooked the importance of students’ beliefs and emotions as they learn mathematics [17,18]. This, and other barriers to change, have meant that gendered, racialized and social class patterns of participation and low overall achievement in mathematics continue [19,20,21,22].

This paper presents the idea of a mathematical mindset approach and also reviews the research that underpins the approach. It is proposed that a mathematical mindset approach can turn around the low mathematics achievement that is widespread across the world, as well as the mathematics anxiety and dislike that extends globally. As the term mindset suggests, the approach is concerned with students’ beliefs and ideas about mathematics and about their own potential, but we argue that these cannot change until the teaching and assessing of mathematics changes. This paper reviews key findings that illuminate the complex relationships among mathematical beliefs, mindset, teaching, assessment, and achievement.

2. Foundational Beliefs

2.1. Mathematical Beliefs

Students’ ideas about mathematics and their own potential are critical to their success. Contrary to the long-held view that learning and emotion operate separately, recent research shows a deep interconnection. Areas of the brain holding emotions about mathematics have been shown to be the same areas that are responsible for mathematical thinking [23]. Young, Wu & Menon [24] have shown that when people with math anxiety encounter numbers, the same brain area is activated as when people see snakes and spiders—at the same time the problem-solving centers of the brain shut down. The emerging neuroscience that is showing connections between understanding and emotion [23] adds to the substantial and more established research in motivation that has linked beliefs and achievement [25] with the research on students’ mindsets [26].

In early work on the impact of mathematical beliefs, Ernest [27] distinguished between three different beliefs about mathematics, which he described as instrumentalist, Platonist and problem-solving orientations. Those who hold an instrumentalist view regard mathematics as a fixed collection of facts, skills and procedures, which can be transmitted from teachers to students—leading to procedural teaching approaches. In contrast, those holding Platonist beliefs regard mathematics as an objective, unchanging system that exists outside of human influence and is waiting to be discovered. Teachers who hold these beliefs may encourage students to explore more than a teacher holding instrumentalist views, but only for the purpose of discovering mathematical truths. The third category of teacher beliefs describes teachers who regard mathematics as a problem-solving subject. These teachers regard mathematics as a subject of inquiry, and are more likely to engage students collaboratively, viewing students as active problem solvers. Ernest’s [27] conceptualization of beliefs has informed research on teacher’s beliefs about mathematics [28] as well as students’ ideas.

Schoenfeld [25] developed research on mathematical beliefs providing evidence that students’ beliefs about mathematics change their persistence, mathematical strategy use, and achievement. Other researchers [29] argue that beliefs act as lenses through which individuals interpret mathematical tasks, instruction, and problem-solving situations. They show that as learners encounter new mathematical ideas, their beliefs shift, which changes their mathematical understanding. Other researchers show that beliefs are dependent on teaching and teacher interactions and so are not fixed or measurable with surveys [30,31,32]. The field of mathematics education has a long history of studying the beliefs students and teachers hold about the nature of mathematics, which have been shown to influence the ways both approach the subject and any subsequent learning. In more recent years research has turned to a different aspect of beliefs; the ones students hold about their own potential, particularly during times of challenge.

2.2. Self-Belief

One of the most influential areas of research concerning students’ beliefs about their own potential comes from research on mindset, pioneered by Stanford psychologist Carol Dweck. For decades, studies have shown that students hold different beliefs about their potential, falling broadly into “fixed” or “growth” mindsets. Students who hold a fixed mindset are those who believe that their intelligence is somewhat unchangeable and fixed. Students with this view often focus on proving their intelligence rather than developing it. In contrast, students with a growth mindset are those who believe that their intelligence is expandable and is developed through effort and learning. Students with this perspective embrace challenges, persist through setbacks, and learn from mistakes and others’ successes [26].

The research of Dweck and colleagues has shown that students with a growth mindset usually achieve at higher levels because they are focused on learning and improving rather than protecting their self-image. In a landmark study, Blackwell et al. [33] delivered a mindset intervention to students learning mathematics in seventh grade. Students who were predominantly from minority or economically disadvantaged backgrounds were randomly assigned to either intervention or control conditions. In both conditions, students attended eight 25 min sessions over about 8 weeks. Students in the intervention group learned about brain plasticity whereas those in the control group worked on activities. Before the transition into 7th grade, students in both groups were experiencing a decline in math grades, which is typical for students at that stage of their schooling. After the mindset intervention, the two groups’ trajectories diverged. Whereas the control group’s math grades continued to decline, the intervention group’s grades stopped declining, and started improving, nearly returning to the levels from the beginning of the year.

Following this study, other mindset interventions have been delivered with high impact. Yeager et al. [34] worked with a nationally representative U.S. sample of 9th graders with low prior achievement. In a brief, one-hour online intervention, delivered as part of a randomly controlled experiment, control students learned about brain function and neuroscience but did not get the message that intelligence is malleable or any other information pertaining to fixed and growth-mindset beliefs. The intervention students learned that brains grow from challenge and effort, reflected on their own challenges, and thought about how they could grow their brains through effort, persistence, and strategy. The study showed that students who received the intervention adopted more growth-oriented beliefs, improved their GPAs across subjects, and enrolled in more advanced mathematics courses the following year. Importantly for this summary, follow-up analysis showed that schools with classroom practices aligned to growth mindset principles saw the most sustained outcomes, underscoring the need to integrate mindset ideas into teaching and assessment practices.

Mindset interventions communicate to students that learning is a journey, and that times of struggle and challenge are valuable for student brain development and growth. Research on mindset suggests that mathematics classrooms should provide students with challenge, and teachers should value struggle and mistakes, reorienting them as “desirable difficulties” [35]. Kapur [36] investigated the impact of students grappling with complex problems before being shown ways to solve them. In the “productive failure” condition, students worked in small groups to generate their own solution methods to challenging mathematics problems. In the control group, students received direct instruction first and practiced worked examples, the more typical approach of mathematics classrooms.

Kapur [36] found that students in the productive failure groups developed a deeper understanding of mathematical concepts. On post-tests, productive failure students outperformed the direct instruction group on measures of conceptual knowledge, transfer, and flexible application—even though the direct instruction group performed better during learning.

Deslauriers et al. [37] conducted an important study on students learning calculus that involved students learning in different ways at different times, sometimes learning through lectures and sometimes learning through active engagement and intellectual struggle. The researchers found that students believed they learned less during active learning, because struggle made the process feel harder and was less comfortable, but they actually learned more, with assessments showing significantly higher conceptual understanding and retention. The researchers described the importance of classrooms creating conditions for “desirable difficulties”—learning opportunities that feel difficult but lead to deeper learning.

Anderson, Boaler & Dieckmann [38] led a professional development initiative in which teachers learned to value times of struggle and challenge in elementary mathematics and found that the approach led to significant changes in achievement. But the message from mindset research that struggle should be valued is often undermined by classroom practices that focus on correctness, which sometimes leads to mixed messages when teachers encourage students to learn from mistakes but then penalize them when they make mistakes. Dweck [39] described this contradiction as a “false growth mindset,” warning that praising mistakes or effort without changing evaluative practices sends mixed signals that can undermine student trust and motivation. Yeager et al. [40] found that growth mindset interventions were effective only in classrooms where teachers’ feedback and grading practices aligned with growth-oriented beliefs; when teachers encouraged students to learn from mistakes but continued to penalize them, the intervention’s effects disappeared. Similarly, Tulis et al. [41] showed that negative or punitive responses to student errors reduced persistence and learning, whereas supportive error responses promoted adaptive motivation.

Whereas early studies of mindset interventions showed promise with mindset interventions sharing the value of self-belief and struggle, bringing about increased achievement [42], critics have pointed out that improvements are modest and do not justify attention from school leaders. Recent years, however, have shown that significant and lasting improvements come about when schools go further than brief interventions and develop what is termed as “growth mindset cultures” [3,42]. The remainder of this paper reviews research on efforts to integrate mindset ideas into schools and classrooms, developing mindset cultures, with particular attention to two central domains of teaching and learning—assessment and classroom tasks.

3. Educational Practices Supporting Growth Mindset Ideas

3.1. Educational Practice: Assessment and Grading

Mathematics is the most tested subject in schools, and the tests that are given usually communicate scores or grades to students. These are usually accompanied by frequent grading of work, also communicated as scores or grades. These practices have contributed to what is known as a “performance culture” in many mathematics classrooms, in which students often judge themselves according to external criteria, with little awareness of ways to improve. An alternative approach to student assessment that was first developed in the UK, but has been applied and studied worldwide, is called “assessment for learning” (also A4L) and recommends replacing scores and grades with meaningful feedback on ways to improve. Black and Wiliam [43] conducted an extensive literature review summarizing decades of empirical research on classroom formative assessment. Black & Wiliam found that when assessment was designed to provide frequent feedback to students on their learning substantial learning gains resulted. They moved from this literature review to conceptualizing the Assessment for Learning approach [44,45].

The A4L approach is consistent with mindset ideas as it communicates learning as a journey and sets out goals for students that they work towards. Teachers are encouraged to give feedback to students that communicate where students are now, where they need to get to, and ways to close the gap (See Figure 1). One of the practices recommended by A4L is giving students diagnostic feedback, pointing out what students have learned and what they need to work on to reach goals. Butler [46,47] conducted a series of seminal experiments demonstrating that the type of feedback students receive has a significant impact on their motivation, engagement, and achievement. Across multiple studies, she compared the effects of three conditions: numerical grades, grades accompanied by comments, and diagnostic comments alone. Butler consistently found that students who received only diagnostic, task-focused feedback showed the greatest gains in performance and intrinsic motivation. In contrast, grades—whether alone or paired with comments—reduced students’ interest and led to lower achievement, particularly on challenging or follow-up tasks. These effects were observed for both high-achieving and low-achieving students.

Building on this work, Pulfrey, Buchs, and Butera [48] replicated and extended Butler’s findings, showing that the presence of grades activates performance-goal orientations and heightens concerns about social comparison. When grades were removed and replaced with constructive, informational feedback, students’ achievement improved across the spectrum—from the top 25% to the bottom 25%. Their findings underscore that diagnostic feedback not only supports deeper learning but also reduces the competitive pressures and fixed-ability signals often conveyed by grading systems.

Together, this research highlights that feedback practices play a powerful role in shaping students’ mindsets, motivation, and willingness to engage with challenging tasks. Shifting from grades to diagnostic comments can strengthen learning for all students while fostering more growth-oriented classroom cultures. Figure 1 illustrates the information communicated by an assessment for learning approach.

Teachers using an A4L approach often communicate learning goals through rubrics that students can read and understand, showing students their mathematics journey, sometimes with opportunities for self-assessment. Hattie et al. [49] conducted several meta-analyses to measure the impact of different innovations upon learning and achievement. In a meta-analysis involving 70,000 studies with 300 million students, Hattie et al. found that the highest achievement gains came from students reporting their own progress. Cockett and Jackson’s [50] review of the literature on rubric use in higher education shows that rubrics tend to enhance students’ understanding of assessment criteria, help them self-assess, and promote self-regulation. Karaman [51] showed that when pre-service teachers used rubrics for self-assessment (with instructor feedback), students showed significant improvement in academic performance compared to a control group. They also reported increased use of learning strategies (rehearsal, planning, monitoring) associated with self-regulated learning. Vasileiadou & Karadimitrou [52] conducted a study with primary-school students (grades 5–6) and found that those who used self-assessment rubrics over a 2.5-month period significantly improved their scores in language, history, and writing, compared to a control group. Panadero et al. [53] conducted a meta-analysis that showed that rubrics are most effective when they are used formatively—not only for final grading, but as tools for self-assessment, peer-assessment, feedback, and revision.

Foster [54] highlights that feedback supporting students to understand where they are in their learning and what they can do next leads to significant improvements in achievement across diverse subjects and age groups. Similarly, Xuan, Cheung, and Sun’s [55] meta-analysis shows that assessment for learning approaches—particularly those that include clear learning intentions, criteria for success, and opportunities for students to revise work—produce consistently positive effects. These approaches work because they help students build a sense of control over their learning, increase motivation, and reduce anxiety associated with evaluation.

In mathematics, specifically, Boström and Palm [56] provide important evidence that formative assessment supports deeper conceptual understanding and more flexible problem solving. Their work shows that when teachers use strategies such as eliciting student thinking, providing targeted feedback, and integrating opportunities for students to try again, students not only perform better but also develop stronger mathematical reasoning. The studies also underscore that formative assessment is most impactful when embedded in regular classroom routines and paired with an instructional stance that treats mistakes and partial thinking as valuable information for learning.

The literature base on the effectiveness of A4L and formative assessment is extensive and is central to a Mathematical Mindset approach as it shows that assessment is not merely a measurement tool: when used formatively, it becomes a central driver of learning, motivation, equitable participation, and students’ developing sense of themselves as capable learners. The link between mindset and assessment was confirmed by an important study by Yeager et al. [40], who showed that the effectiveness of growth mindset interventions depends heavily on feedback and assessment approaches. In classrooms where teachers gave feedback that emphasized progress, strategies, and improvement—and where grading practices signaled that ability can grow—students were more likely to internalize the mindset messages and show improved achievement. In classrooms where feedback or grading suggested that ability is fixed (for example, by focusing only on correctness, ranking students, or offering little opportunity to revise work), the mindset intervention had little or no effect.

There is broad recognition, supported by extensive research, that assessment practices shape student mindsets. Less widely acknowledged—but equally important—is the evidence showing that the tasks and questions used in classrooms also convey powerful messages about whether ability is fixed or can grow.

3.2. Educational Practice: Open Mathematical Problems and Tasks

Boaler et al. have argued that mindset messages of growth are undermined by short narrow mathematics questions that do not allow students to see or experience growth [57]. They suggest that when mathematics questions are more open and allow multiple solution pathways, and collaboration, they encourage students to progress and take on growth mindset messages. This message is supported by decades of research in mathematics education, showing that changing mathematics problems from short, closed questions to more open problems that invite students to engage in problem solving, critical thinking, and reasoning [58] bring about improved outcomes [59,60,61,62]. These outcomes encompass higher academic achievement, stronger interest in STEM fields, and more equitable learning results.

As an example, many students are invited to “add to ten” a Kindergarten grade standard in the US, by being given short exercise questions, such as 8 + 2, 6 + 3, or 4+ 2. A more open task that targets the same mathematics is to ask students to make foot parades with animals. (See Figure 2).

In the more open task, students have visuals to use as resources, there are many different answers, and the topic is engaging for young learners. The principle can be applied to any grade level; an ideal way for students to learn about equivalent algebraic expressions is to investigate the borders of different-sized squares and describe them algebraically, using visuals and words as well as algebraic symbols [64]. Figure 3 provides an illustration of the solutions.

Open tasks provide important opportunities for students to reason about ideas, consider why methods work, see ideas visually and physically [66,67] and make mathematical connections [2,68,69,70]. Overall, this change in mathematics experience is often described as students learning conceptually.

In Hiebert and colleagues’ [59] classic text on ways to teach mathematics conceptually, the authors review research showing that students who learn through more open problems develop deeper conceptual knowledge, greater procedural flexibility, and better long-term retention than students taught through memorization and isolated procedures. Hiebert & Grouws [60] also find that open, problem-based lessons promote students’ conceptual understanding and their ability to apply ideas to new problems—especially when problems are aligned with students’ zone of proximal development and are supported by classroom discourse and teacher questioning. Schoenfeld [71] has shown that teaching students to solve problems and to think mathematically, including attention to self-monitoring and reflection, produces improved student outcomes. Schoenfeld [72] has also provided evidence that when students, including those from marginalized communities, are given opportunities to engage with rich, open mathematical tasks and reasoning, they perform at higher levels.

Boaler and colleagues have conducted a series of quasi-experimental investigations in both the UK and US, comparing schools that emphasize traditional, procedure-focused mathematics instruction with schools that engage students in open problems, problem solving, and reasoning [61,62,73,74,75,76]. Across these studies, consistent patterns have emerged. Classrooms organized around memorization of methods and repetitive exercises tended to produce narrow procedural proficiency but also higher levels of anxiety, wider achievement gaps, and limited transfer to unfamiliar problems. In contrast, the schools that taught mathematics through open tasks, inquiry, and reasoning developed students’ conceptual understanding, mathematical flexibility, and engagement. Students in more open classroom environments learned to make sense of ideas, justify their thinking, and collaborate productively. The impact was not only an overall improvement in achievement: the benefits were especially strong for students who had previously been marginalized or labeled as “low attaining”. These students showed substantial gains when given opportunities to engage in rich problem solving rather than being confined to procedural worksheets.

Across both national contexts, Boaler and colleagues’ findings reveal that teaching using more open tasks that give students the opportunity to learn conceptually is a powerful lever for equity. Schools that adopted more open pedagogies saw narrower achievement gaps, more positive learner identities, and more students—including those from historically underserved groups—achieving at high levels. The research underscores that the nature of mathematical experience matters profoundly: when students are invited to reason, explore, and make sense of mathematics, more of them succeed.

Maher has, over decades, conducted studies that highlight how students are capable of reasoning and constructing mathematical arguments when given the opportunity—both inside school and in out-of-school contexts [58,77]. She and colleagues studied how middle-school students engage in mathematical reasoning and discourse in an informal, after-school program, finding that students worked collaboratively on open-ended tasks, co-constructing arguments and justifications, as well as questioning and building on one another’s ideas. The study documented not only the mathematical ideas and forms of reasoning students developed, but also how their conceptions of mathematics—and of themselves as mathematical thinkers—changed over time [77].

Cognitively Guided Instruction (CGI) is a research-based approach to teaching mathematics that begins with understanding how children think about and solve mathematical problems. Rather than teaching set procedures first, CGI recommends that teachers build on students’ existing ideas and strategies so they can develop deep, flexible mathematical understanding. Research from Remillard, Karp, Carpenter, Fennema, Franke and other members of the CGI community [78,79,80,81,82,83] converges on the finding that teaching through problem solving strengthens students’ conceptual understanding, improves teachers’ ability to notice and act on students’ thinking, and can support greater equity in mathematics outcomes when paired with teacher learning and curriculum supports. Verschaffel and colleagues [84] have shown that engaging students in realistic, real-world problem solving strengthens their mathematical understanding in several key ways, including bringing about improved modeling skills, more robust mathematical reasoning, greater flexibility and improved transfer.

Darling-Hammond et al. [85] synthesize research on effective teaching and conclude that high-quality instruction provides learning experiences that are active, meaningful, and intellectually engaging. Rather than emphasizing rote procedures, effective teaching immerses students in challenging, authentic tasks that promote deeper understanding and sustained inquiry. Forms of effective teaching that they highlight include inquiry-based learning, project-based learning, problem solving and exploration, as well as opportunities for students to apply knowledge in varied contexts, sharing that such approaches deepen understanding and support learning transfer.

While many mathematics education researchers have studied the impact of more open problems on student achievement, Daly, Bourgaize, and Vernitski [86] took a different approach, studying their impact on student motivation using electroencephalography (EEG). The researchers compared college students solving standard procedural problems with those working on open mathematical problems. Students tackling standard problems reported declining interest, while those solving open tasks grew increasingly motivated. Electroencephalography (EEG) studies revealed stronger activity in brain regions associated with motivation and engagement for students working on open-ended problems—activity that usually declines during difficult tasks. The findings of Daly, Bourgaize, and Vernitski [86] indicate that open, visual, and flexible tasks foster more positive and motivating mathematical experiences for students.

Decades of research have shown the importance of moving away from procedural mathematics teaching, giving students the opportunity to reason and problem solve through more open tasks. In recent years, this approach, as well as research informed approaches to assessment, have been combined with mindset messaging to create a Mathematical Mindset approach.

4. Findings: The Impact of a Mathematical Mindset Approach

4.1. Conceptualizing of Mathematical Mindset Approach

The Mathematical Mindset approach was launched as a summer camp on Stanford University campus in 2015 [87]. Over four weeks, 83 middle school students from under-resourced schools experienced a Mathematical Mindset approach, which included mindset messaging, encouraging struggle and celebrating mistakes, and teaching through open tasks, that encouraged collaborative problem-solving, with actionable feedback provided to students. The effectiveness of the approach was measured using a pre-and-post design that showed significant increases in mathematics tests, equivalent to 2.8 years of learning.

Following this pilot, camps expanded across the U.S. and internationally. In 2021, camps in ten school districts engaged 536 students in grades 5–7. A mixed-method study with matched comparisons found significant increases in growth mindset beliefs, mathematics achievement, and student grades [88]. Importantly, participating teachers also carried growth mindset practices back into their regular classrooms, including the sharing of mindset messages, and the use of more open mathematics tasks [89].

4.2. Studying a Mathematical Mindset Approach

Since the Mindset Mathematics camps have been implemented and studied, several experimental studies have highlighted the potential of a mathematical mindset approach to student learning. Boaler and colleagues [90] conducted a randomized controlled trial in which middle school students completed a six-session online course introducing growth mindset ideas and presenting mathematics as an open, visual subject that can be approached using different strategies. Students in the intervention group, who took the free online course at the start of the school year and were taught by the same teachers as the control group, scored significantly higher on standardized tests at the end of the year, obtaining 0.33 standard deviation gains in Smarter Balanced Assessment Consortium (SBAC) math tests overall scale score, as well as more positive mathematical beliefs and a growth mindset. Teachers also reported that the students who took the online course were 68% more engaged in mathematics class discussions across the year.

In a more comprehensive approach to sharing a mathematical mindset, fifth grade teachers took an online course with over thirty hours of professional development, met in groups to discuss possible teaching changes with leaders, received support from administrators and colleagues, and were guided by a “Mathematical Mindset Teaching Guide”. Anderson, Boaler & Dieckmann [38] reported impressive results. Teachers first improved their own mindsets about mathematics, they were then able to shift their instructional practices, leading to significant improvements in student beliefs, teaching quality, and standardized mathematics scores—particularly for girls, English learners, and economically disadvantaged students. Regression analysis revealed overall scale score point estimates on California state assessments increased for girls, English learners, and economically disadvantaged learners, all statistically significant at the one percent level.

In another grade-specific study of mindset-based teaching, Wang et al. [91] found that combining fraction instruction with growth mindset and self-regulation strategies significantly improved outcomes for struggling 3rd graders. Results confirmed that at-risk students who receive interventions with a growth mindset can succeed in challenging mathematics standards. Similarly, Bonne and Johnston [92] documented gains in growth mindset, self-efficacy, and achievement among 7–9-year-olds in New Zealand when teachers adopted mindset-consistent practices.

In another effort to bring math mindset to scale through teacher training, Hecht et al. [3] offered an intervention with 150 teachers to see if students would benefit if teachers learned about mindset boosting practices, such as allowing students to revise and resubmit work. The online intervention, 45 min long and self-administered, was designed around teachers’ core value to inspire student enthusiasm for learning while dispelling the notion that these practices involved sacrificing academic rigor. The intervention was given to high school teachers in the US as a randomized controlled trial, and found that teachers who received the intervention reported using more mindset-oriented practices, and student achievement significantly improved in classes with higher proportions of students with socioeconomic disadvantages.

In another professional development context, Boyd and Ash [93] collaborated with early-grade teachers in England implementing Singapore math. Over two years of joint work, teachers shifted their beliefs, viewing mathematics as more creative and collaborative, and they reduced ability grouping, moving to heterogeneous classrooms. Researchers show how the teacher collaborators began seeing mathematics as collaborative problem-solving and deep thinking, rather than emphasizing speed, memorization, and calculation to reach a single right answer. Researchers contended that “it is as much a shift in cultural beliefs about the subject of maths and of ‘ability’ within maths as it is about changing beliefs about the malleable nature of intelligence” [93] (p. 221).

As the lens widen on math mindset on motivation, identity and achievement, researchers have studied the interplay of mindset and gender beliefs in mathematics. Lee and colleagues [94] studied the effects of a Grade 4 intervention in South Korea that promoted both growth mindset in math, as well as gender-fair beliefs about math. The 40 min long teaching intervention was given at Grade 4, when the cognitive complexity of the curriculum increases sharply and when interest and confidence in math start to fall. Students participated twice a week for six weeks over three months, and all sessions were conducted during regular school hours. Results showed that growth mindset, perceived competence, persistence, and achievement of the intervention group increased, while the control group decreased on those measures. Path analysis revealed growth mindset after the intervention predicted math persistence and math achievement for students.

Growth mindset in math has also been a design principle in educational games, set within specific mathematical content such as fractions. Research by O’Rourke and colleagues [95] showed that an online game with a conceptual approach to fractions can also incorporate mindset messages. By adjusting incentive structures to promote growth mindset ideas, math games can foster a growth mindset and that players’ intelligence is malleable. The researchers followed 15,000 elementary students, observing that the group receiving such incentive modifications, particularly the low-performing students, persisted longer in the game, employed a wider range of strategies, and maintained engagement despite challenges. In a follow-up study, the same researchers [96] studied 25,000 students playing planned variations in the original fractions game with different forms of mindset messages and incentive structures. Results showed that students increased not with random brain points, but, importantly, when the brain points were associated with specific mindset behaviors such as productive struggle and use of math strategies.

Not all math mindset interventions have yielded clear positive results, even those that are thoughtful, well-planned and innovative. We examine two illustrative studies in the following sections that explore interesting connections with deliberate practice [97] and technology-enhanced interventions of mindset. We point out some features of both studies that may shed light on the modest levels of impact or no impact, providing insights for future math mindset studies.

Balan and Sjöwall [98] studied growth mindset, math growth mindset, deliberate practice and grit in an extended intervention of 14 weeks with 7th grade math students (n = 237), with teachers randomizing students to different treatment groups and an active control group. The intervention design also included a one-time advisory session as a mentoring component. Researchers found no difference on surveys on growth mindset, growth mindset for mathematics, grit, deliberate practice, nor on math achievement. However, on mathematical behaviors observed, students in the intervention opted to retake the math test more often than students in the control group, indicating perhaps differences in persistence. This study had a theoretically informed design, extended duration, conducted in a real-world context, and with high fidelity. Furthermore, the study took place collaboratively with school partners. So, a closer look is warranted to understand the results.

In terms of sampling for the study [98], most students evidenced relatively high scores on the pre-measures suggesting a ceiling effect, and the relatively homogeneous group in terms of socioeconomic levels, where effects may have been detectable for a more socioeconomically diverse group. But perhaps more crucial is that the context in which students had to apply their deliberate practice was a standardized math test given repeatedly as a measure of their improvement. Likewise, students did not have opportunities to enact their math growth mindset in the context of more open problems, with multiple pathways and solutions. In this case, the selection of the context of performance (taking a standardized math test repeatedly) may have worked against a growth mindset. As the authors note, “It is possible that students need to put their new knowledge and behavior into practice for a longer period before differences in performance can be detected”(pp. 556) [98]. We contend that not only a longer period, but also a more authentic and sustained teaching context such as their daily math lessons, where lessons are designed to give students opportunities to enact their math growth mindset, would show impact.

Star and colleagues [99] used a randomized control trial to explore different inductions, pairing different technologies with motivational constructs. Induction 1: Virtual reality game set in space exploration, designed to improve self-efficacy. Induction 2: Abridged version of a commercial software program designed to increase implicit theories of general ability, but not math-specific. Induction 3: PBS-type videos illustrating math patterns in nature, meant to help students see math as applicable to the outside world. We found this study particularly interesting because, unlike other studies, it contained a math-rich teaching component, along with the more typical aspects of decontextualized mindset interventions. The intervention was for four days with students from Grade 5 to Grade 8 (n = 18,628). The students had one day of specific induction experience in self-efficacy, mindset or math applications, then two days of rich algebraic reasoning activity, concluding with the same technology intervention as in their first day. The study found only modest positive changes in math learning, and no change in self-efficacy nor student values (interest in math, perceptions in its utility, value of attainment). There were also only modest improvements in students’ mindsets, more so for students in higher grade levels. As the authors note, lack of stronger results may been due to the non-random loss of 53% of the data, short duration of the intervention, and the low-reliability of the math learning measures, which was not their principal focus. All studies face similar challenges, but an additional design feature may also explain the modest results for math mindset.

Despite the two-day lesson being mathematically rich, the growth mindset intervention itself was a commercial software package giving general, rather than math specific ideas about growth mindset. Here again, these results reaffirm that generic growth mindset messages are not as effective as those that are discipline specific and actionable with math classroom settings. Furthermore, key messages given to students by teachers about effort and persistence would have likely had more of an effect during the two-day math lesson, where students could see opportunities to enact their nascent math mindset.

To summarize across an ever-expanding research literature, we note the findings of two meta-analyses to identify important features and commonalities. Sarassin and colleagues [100] conducted a meta-analysis of mindset interventions that specifically included neuroplasticity as a rationale to students for how their intelligence can grow. Their sample of 10 studies examined motivation, math achievement, and brain activity. Five motivational scales were examined across the group of studies: academic enjoyment, goals, response to failure, helplessness attributions and effort beliefs. Results showed positive results for four of the five scales. Students in the intervention group reported higher levels of academic enjoyment than those in the control group. At-risk students in the intervention had significant increases in positive beliefs about the importance of academics and about goal-setting. Small but meaningful gains were found in students’ responses to failure, with those in the intervention group adopting more positive coping strategies than control students. For helpless attributions—tendencies to attribute difficulty to fixed traits—positive effects were observed specifically for at-risk participants. No differences emerged between groups in effort beliefs.

When examining effects for math learning and achievement across the sample of studies, consistent positive small-to-medium effects were observed, with gains being more pronounced for at-risk youth. The authors speculate that ceiling effects may be dampening the effect of non-at-risk students.

In a detailed literature review of 16 math-specific growth mindset interventions, Bui and colleagues [101] posit that the notion of “having a growth mindset” will lead to success may be too abstract without a supportive environment. In mathematics education, the most effective key to a growth-mindset intervention appears to be math domain specificity rather than general mindset messaging about effort and confidence. Across the studies reviewed, math domain-specific interventions consistently yielded greater gains in students’ mathematics achievement than generic interventions, regardless of their focus, content, or method of delivery. By embedding the core principles of growth mindset directly within mathematical learning—and by giving students time and space to engage meaningfully with mathematical tasks—interventions created conditions for transformative shifts in beliefs and, subsequently, improved learning outcomes. We summarize that, for growth-mindset interventions to be effective, students must experience a growth mindset culture [3,42] in which they have opportunities to engage with mathematics through deeper, more open mathematical problems and receive opportunities for revision of work with feedback.

Table 1. Assessment Practices Supporting Mindset Messages.

Study	Focus	Method	Key Findings	Mindset Relevant Implications
[43]	Assessment and Learning	Review	Formative assessment strongly improves learning	Feedback and student agency matter more than grades
[44]	Assessment for Learning	Classroom synthesis	A4L improves achievement & motivation	Emphasizes growth, not performance ranking
[46,47]	Feedback types	Experiments	Task-focused feedback boosts motivation; ego-focused harms	Praise effort/process, avoid normative comparison
[54]	Formative assessment	Meta-analysis	Significant gains across ages & subjects	Clear guidance supports growth beliefs
[53]	Rubrics	Meta-analysis	Improves performance & self-regulation	Clarifies learning goals, supports self-belief
[48]	Grades & motivation	Quantitative	Grades trigger avoidance goals	De-emphasize grades to support growth

,

Table 2. Open Mathematical Problems and Tasks.

Study	Focus	Method	Key Findings	Implications
[74,75]	Reform math approaches	Longitudinal & comparative	Higher achievement & equity with open tasks	Rich tasks promote flexible thinking
[62]	Mixed Ability Teaching using Open Tasks	Case study	Strong achievement without tracking	Challenges fixed-ability beliefs
[78,79,80]	CGI	Longitudinal & Professional Development studies	Conceptual understanding improves	Student thinking drives instruction
[71,72]	Problem solving	Theoretical & empirical	Sense-making is central	Open problems develop agency
[68]	Understanding types	Conceptual	Relational > instrumental learning	Deep understanding counters fixed views

,

Table 3. Isolated Math Interventions.

Study	Focus	Method	Key Findings	Limitations
[33]	Growth mindset	Longitudinal + intervention	Improved trajectories	Effects context-dependent
[34]	National mindset trial	Randomized Control Trial (RCT)	Small but significant effects	Stronger when context supports
[98]	Math mindset	Quasi-experimental	Modest gains	Limited without pedagogy change

and

Table 4. Mathematical Mindset (Mindset Integrated into Teaching and Assessment).

Study	Focus	Method	Key Findings	Implications
[90,92]	Integrated mindset courses	Large-scale studies	Improved beliefs & achievement	Mindset most powerful when embedded
[38]	Teacher change	Mixed methods	Shifts in pedagogy & beliefs	Challenging myths enables reform
[101]	Mindset in math	Systematic review	Integrated approaches most effective	Tasks + assessment matter
[3]	Mindset culture	Large-scale analysis	Cultural shifts reduce disparities	Whole-school approach needed

summarize the research reviewed above.

5. Conclusions

Research across psychology, education, and neuroscience converges on a central message: students’ beliefs about mathematics and their own potential profoundly shape their achievement. These beliefs influence how students persevere through challenge, how they interpret mistakes, and whether they see themselves as capable mathematicians. While stand-alone mindset interventions can yield meaningful gains, the strongest and most enduring outcomes arise when mindset principles are woven into the fabric of teaching and assessment. This occurs through tasks that invite exploration, feedback that emphasizes progress and strategy, and classroom cultures that normalize struggle as part of learning.

When these elements work together, students not only achieve at higher levels but also develop the motivation, confidence, and intellectual agency needed for long-term success. A Mathematical Mindset Approach strengthens students’ problem-solving abilities, expands their creativity, and cultivates persistence in mathematics—outcomes that are especially powerful for students who have been historically marginalized. By integrating these practices systemically, schools and systems can open the door to richer, more rigorous, and more inclusive mathematics learning worldwide.

As researchers continue to study the complex relations between subject content, teaching approaches, assessment and messaging, we call for attention to the cultural context of learning. Just as we know that teaching is deeply cultural [102], so too are beliefs about learning, ability and growth. Each context holds complex relationships between individual beliefs about intelligence, cultural norms and expectations, and recognized markers of student achievement. We call for more nuanced studies that consider not only the disciplinary specificity of mathematics, but the cultural contexts in which studies are conducted.