In our keynote address at the 2025 National Numeracy Network Annual Meeting, we introduced the framework we developed for considering four domains of an institution’s quantitative skills/reasoning support ecosystem that includes bridge programs with a quantitative component, approaches to assessing readiness, curricular on-ramps, and supplementary support. We believe this ecosystem framework has the potential to help campus leaders coordinate institutional efforts around student success in areas connected to students’ quantitative preparation. This keynote highlighted the idea that coordination of stakeholders and their engagement with domains of the ecosystem fall along a spectrum. We provide approaches for using this framework to analyze the strengths and weaknesses of their institutional quantitative skills support ecosystem, no matter where efforts fall along this spectrum. We provide possible activities to advance conversations for strengthening the ecosystem including identifying collaboration partners, working toward a shared vision among project stakeholders, and examining initiatives past and planned. All of these approaches can help faculty and staff to leverage their skills and experiences in STEM classrooms or support centers to work together towards institutional change.
The United Nations Sustainable Development Goals emphasize numeracy as essential for quality education, and require its integration across the curriculum, including into civic education (CE). However, the integration of numeracy in CE in Indonesian universities has not yet been clearly mapped out. This study aims to analyze the need for numeracy integration in CE as a basis for developing a numeracy-based CE learning model. Using a mixed method with an explanatory sequential design, the study involved a convenience sample of 225 students and 10 lecturers from various universities through surveys, interviews, observations, and documentation studies. Quantitative findings show that numeracy is rarely used (65.3%), with 14.2% of students stating that it is never used in CE. This condition contributes to misperceptions, as evidenced by 71.56% of students considering numeracy irrelevant to analyzing citizenship issues. These findings are supported by qualitative evidence that learning has not integrated numeracy, thus affecting students' weak ability to analyze public discourse. Therefore, the results of this study indicate the importance of integrating numeracy into CE as a strategy to strengthen critical thinking, participation, and 21st-century competencies in order to shape informed, reflective, contributive, and thoughtful citizens. This study provides an initial empirical overview for researchers and institutions to develop a numeracy-based CE model that is adaptive to contemporary learning needs.
Numeracy has become an increasingly important 21st-century skill that, due to the relationship between math and science, is often formally developed at the college level in general education science courses. These courses serve a diverse group of students, many of whom have historically experienced science teaching, curriculum, and assessment on the margins. The well-documented biases of assessments in particular against Individuals of Color (IoC) have inspired us to approach numeracy for social justice in our work from this angle, and in this paper, we detail our efforts to revise our validated numeracy assessment to ensure it more fairly and equitably measures student knowledge, with particular attention to minimizing bias against students from racial/ethnic groups that have been marginalized in science, technology, engineering, and mathematics (STEM). We also discuss the implications of our work for assessment designers and describe why our approach to test creation is necessary precursor work to addressing the under-representation of IoC in STEM and science-related fields more broadly.
Traditional introductory statistics courses that focus on techniques are not engaging for many college students; this may be especially true for first-generation college students, who generally have more difficulty engaging in the college environment than continuing-generation students. We study first-generation college students’ experiences in a course-based undergraduate research experience called Passion-Driven Statistics. Passion-Driven Statistics is a multidisciplinary, project-based introductory statistics course where students develop their own research topics, analyze publicly available quantitative data, and focus on conceptual understanding of statistics rather than hand calculations. Using pre-course and post-course surveys from students taking Passion-Driven Statistics in colleges throughout the United States, we find both first- and continuing-generation students experienced gains in (1) interest in conducting research, (2) interest in pursuing advanced coursework in statistics, and (3) plans to use statistics in the remainder of their degree programs. These findings demonstrate the benefits of an inquiry-based course to students from different backgrounds. When compared to continuing-generation students, first-generation students were more likely to feel that they spent time doing meaningful research and to feel like they were part of a scientific community. Overall, these results imply potential to reduce social disparities in quantitative skills and related careers.
The special collection, “Teaching Numeracy for Social Justice: Educational Equity,” focuses on how quantitative reasoning (QR) can function as a vehicle for equity, empowerment, and democratic participation. Building on a longstanding tradition that treats numeracy as inseparable from social justice, these contributions highlight how progressive pedagogies (e.g., active learning, authentic research, and equity-oriented assessment) have the potential to broaden access for students historically excluded from quantitative fields. The studies span a variety of conceptual frameworks, introductory and advanced quantitative instruction, and interdisciplinary applications, showcasing how inclusive QR practices can build confidence, agency, and real-world understanding. These articles demonstrate that when students engage with socially meaningful data, numeracy becomes not only a cognitive skill, but a tool for personal transformative and civic engagement. By centering marginalized learners and advocating progressive approaches both for teaching and assessment, this collection affirms the importance of numeracy not only as a pedagogical approach but as a moral imperative for expanding educational opportunity.
Recent commentary has featured a debate over whether urban homicide rates are rising or falling. This debate illustrates the complexities of trying to convey the significance of statistical data.
In this paper, we present a framework for understanding the multiple roles that mathematics can serve in the classroom towards social justice goals, developed through an analysis of 36 social justice mathematics curricular modules in college settings. The framework is grounded in Patricia Hill Collins's matrix of domination and consists of seven themes that represent the different roles mathematics can play: measuring inequality, illuminating conditions resulting in inequality, understanding the mechanisms of phenomena, challenging stereotypes and misconceptions, generating and evaluating solutions, communication and action, and criticizing quantification. Our framework supports the perspective that mathematics can serve important and distinct roles and purposes that contribute to addressing the multiple domains of power in Hill Collins’s matrix of domination. In addition, we argue that by explicitly naming these roles and purposes, this framework serves as a valuable resource for educators seeking to integrate social justice with mathematics curricula.
This paper explores the impacts of introducing quantitative literacy skills in an interdisciplinary Environmental Economics course typically taught as an issues and policy course without a quantitative component. The study examines the effects of infusing an engaging, student-selected data collection and analysis assignment on students' quantitative reasoning skills, as well as their interest in and attitudes about data analysis and quantitative information. Using data gathered from a set of pre- and post-assessment questions designed to measure changes in quantitative reasoning skills and attitudes, the findings point to significant attitudinal impacts, gains, but smaller, insignificant gains in quantitative reasoning skills.
This study examines the impact of integrating Quantitative Reasoning (QR) into a Calculus III course at a Hispanic-Serving Institution (HSI) on student engagement, confidence, and aspirations. The course is offered at Hostos Community College in the South Bronx. It incorporated QR-focused projects on economic inequality, environmental pollution, and access to healthcare. These projects allowed students to apply advanced calculus concepts to real-world social issues. A pre- and post-survey design was employed to assess changes in students’ mathematical confidence, perceptions of relevance, and career and educational goals. Results showed statistically significant gains in confidence and in the belief that advanced math supports their future success. Students, many of whom faced additional life responsibilities, showed robust improvements. Although no control group was included, the findings suggest that QR-infused pedagogy can meaningfully engage students from underserved backgrounds and help them view mathematics as a powerful tool for social understanding and personal growth. This paper contributes a replicable model for equity-focused math instruction and highlights the importance of contextualized QR in supporting student success in advanced STEM courses.
Numeracy is a critical competency for academic and everyday functioning. This study investigates the key factors associated with students' numeracy skills by employing decision tree algorithms as a data mining technique. The dataset used in this study is educational assessment data from Indonesia. Utilizing a dataset comprising 6,953 entries and 60 variables from Education Report, the research adopts an exploratory approach involving data preprocessing, exploratory data analysis, and decision tree model construction. The findings reveal that students' literacy skills serve as the most dominant predictor of numeracy proficiency, emerging as the root node in the decision tree structure. Additional associated factors include psychological well-being, quality of learning environments, teacher competence, and school inclusivity. The decision tree model achieved a classification accuracy of 89.82% at optimal depth, enabling the derivation of interpretable decision rules for categorizing numeracy proficiency into four levels: far below minimum competency, below minimum competency, meeting minimum competency, and exceeding minimum competency. These results demonstrate the potential of decision tree algorithms to uncover complex interdependencies and inform data-driven educational policy and instructional interventions. The code and data used in this study are available upon request.
In South Africa, university completion rates remain low, with only 23% of students finishing within the regulation time (three or four years). These completion rates continue to reflect racial inequalities, with 'White' students significantly more likely to complete degrees in professional fields such as engineering and commerce compared to their 'African' counterparts. To address these challenges, the South African higher education institutions, through their umbrella body, introduced the National Benchmark (NB) tests to assess students' academic literacy skills—including quantitative literacy, academic literacy, and mathematics—to identify those most at risk of struggling with the curriculum. The NB tests aim to evaluate students' readiness for higher education using scores and proficiency bands. This study examines the predictive validity of the NB Quantitative Literacy test scores and proficiency bands in science, technology, engineering and mathematics (STEM) programmes in the faculties of commerce, engineering and science. The analysis focuses on completion, dropout, and retention rates within one first-time entry cohort at a South African university. Among 2,493 first-time entering students, 15% dropped out after the first year, 22% left by the regulation time, and 23% exited within two additional years. Graduation rates were 34% within regulation time and 67% within two extra years. Findings highlight the predictive value of the NB Quantitative Literacy assessment, emphasizing its potential role in informing admission and placement decisions, curriculum design, and teaching and learning strategies to enhance student success in STEM programmes.
In this study, we present evidence for the validity of a shortened form of the Quantitative Reasoning for College Science (QuaRCS) Assessment, a validated instrument assessing the numeracy and math-related affect of undergraduate students in general education/introductory science courses. Previously published analyses of QuaRCS data revealed that 1) roughly 30% of students found the assessment boring, leading to lower self-reported effort and 2) affective factors (e.g. numerical self-efficacy) were significant predictors of QuaRCS score. As a result, we reduced the length of the assessment from 25 to 15 quantitative items, and expanded the affective variable selection from three to eight to include math related anxiety, situational math affect, sense of belonging, growth mindset and metacognition. We administered the abbreviated assessment ("QuaRCS light") to roughly 15,000 students across 18 institutions and validated it with classical test theory and item response theory based methods. We found, despite a modest decrease in reliability, students' effort scores were significantly higher on QuaRCS light, justifying this tradeoff. In addition, we validated the new affective factors using exploratory and confirmatory factor analysis. When included in a linear regression model as predictors of QuaRCS score, these 8 factors explain 31% of the observed score variance, increasing to 49% when student confidence, effort, and calculator usage are included. Our findings emphasize the importance of affective factors in understanding and fostering numeracy, and this work informs the design of more holistic and effective assessments that are appropriate for assessing numeracy in diverse student populations.
We utilize concepts of numeracy including number sense, reading and interpreting graphs, basic probability and statistics, and reasoning to estimate guessing and verify our earlier findings on human self-assessment as replicable. Our field study employed a low-stakes paired measures assessment (11,229 scores from the validated Science Literacy Concept Inventory and postdicted global self-assessment ratings generated upon completion of the Inventory) in conjunction with a five-category taxonomy of self-assessment proficiency. We also simulated 11,229 random guessing responses, to model responses that disengaged, purely random-guessing participants should produce. At least 90% of participants sincerely engaged with the instruments of measure, self-assessed imperfectly but reasonably well, and exhibited equal tendencies to underestimate or overestimate their scores by modest amounts. Results contradict the prevalent claim that most people overestimate their actual abilities, with the least knowledgeable being grossly overconfident (ie, the Dunning-Kruger effect). In this study, disengaged, random guessers could account for nearly all participants who grossly overestimated. Confirming that significant numbers of low-scoring participants are aware of their poor performance removes support from the "dual-burden hypothesis," which states that low-scoring participants lack both the competence and metacognitive competence needed for accurate self-assessment. The amount of guessing in a populace does not attenuate the "effect," as claimed in recent psychology literature, but magnifies it. Studies of paired measures yielded a new understanding of guessing. The "effect" is better explained as an illusion produced by probability than as an accurate portrayal of human self-assessment.
Quantitative Reasoning (QR) competencies are increasingly vital for academic and professional success across disciplines. This study examines the QR proficiency of over 400 undergraduates through a mixed-methods approach, integrating survey-based self-assessments (n = 469) with direct evaluations of final exams (n = 80). This study took place at a public, primarily undergraduate, four-year state university in Northern California with approximate enrollment of 7,500 students. Although students reported frequent engagement in foundational QR tasks— such as calculation and interpretation—rubric-based scoring revealed inconsistent levels of mastery, particularly on higher-order skills like evaluation and coherence. Regression analyses linked confidence to calculation and data visualization abilities but suggested that interpretation may be underappreciated or conflated with other QR dimensions. Qualitative responses emphasized finance-related applications while overlooking broader contexts for quantitative literacy. Limitations of the study include data collection at a single institution, convenience sampling, and utilizing a single artifact type (final exams) for direct assessment. Overall, the findings highlight a need for more explicit instruction and assessment of complex QR tasks, along with curricular design that foregrounds real-world data analysis and problem solving. These results offer practical insights into reinforcing QR education, ultimately supporting students' ability to apply quantitative knowledge meaningfully across diverse contexts.
Understanding what knowledge mathematics teachers develop during lesson study is crucial for improving teaching practices and student learning outcomes. Despite widespread use of lesson study as a professional development approach, limited research has explored the specific types of teacher knowledge that emerge through this collaborative process, especially in secondary education contexts. This study explores the types of knowledge developed by mathematics teachers during the implementation of Lesson Study. Using a qualitative case study design, data were collected from three Lesson Study cycles involving four junior secondary school mathematics teachers. Data sources included classroom observations, video recordings of planning and reflection sessions, and teaching documents. Transcript-based lesson analysis was employed to examine changes in teachers’ knowledge across three key domains: mathematical content knowledge, pedagogical content knowledge (PCK), and awareness of student thinking. Findings indicate that participation in Lesson Study encouraged deeper conceptual understanding, more deliberate instructional decisions, and greater sensitivity to students’ learning processes and misconceptions. These outcomes highlight the transformative potential of Lesson Study in fostering collaborative, practice-based professional growth. The study concludes by recommending the strengthening of school–university partnerships and the institutionalization of Lesson Study as an effective and context-responsive approach to mathematics teacher development in Indonesia.
This study aims to develop a Project Based Learning (PjBL) model integrated with Higher Order Thinking Skills (HOTS) and the scientific approach to enhance high school students’ mathematical literacy skills. The research employed a research and development (R&D) design based on the Dick & Carey model. The participants were 32 eleventh-grade students at SMA Dharma Pancasila Medan, selected using total sampling. Research instruments included expert validation sheets, mathematical literacy tests, student response questionnaires, observation sheets, and interviews. Expert validation results indicated that the developed learning model was highly valid with an average score of 89.7%. The implementation results revealed a significant improvement, with students’ average pre-test scores increasing from 51.4 to 83.5 in the post-test, and a gain score of 0.66 categorized as moderate–high. Indicators of mathematical literacy, namely formulating situations mathematically, employing concepts, facts, procedures, and reasoning, and interpreting and evaluating outcomes, all showed significant improvements. Students’ responses to the learning model were highly positive, with more than 87% stating that the learning process was more engaging, facilitated concept understanding, and enhanced critical thinking and collaboration skills. Therefore, the PjBL-based HOTS model integrated with the scientific approach has been proven effective in improving students’ mathematical literacy while supporting the achievement of 21st-century competencies and the Sustainable Development Goal 4: Quality Education.
his research was conducted at MTs Negeri 2 North Lampung in class VIII 2. which was conducted on July 21, 2025-July 31, 2025. The type of research used was Classroom Action Research (CAR) which was conducted in 2 cycles, each cycle consisting of 4 stages: (1) Planning, (2) Implementation, (3) Observation, and (4) Reflection. Data collection can be done through three steps, namely data reduction, data presentation, and drawing conclusions. The results of the study showed that the classical completeness of students' interests in Cycle I reached 82%, increasing by 7% in Cycle II to 89%. Student learning outcomes in the cognitive domain of Cycle I classical completeness reached 73%, increasing by 1% in Cycle II to 74%. Thus, it can be concluded that the application of the Discovery Learning learning model can increase the learning interest of class VIII 2 students at MTs Negeri 2 North Lampung.
The purpose of this article is to discuss the curriculum that must be developed to address challenges and seize opportunities in the era of Golden Indonesia 2045, with a focus on critical thinking skills, technology integration, and contextual approaches. The method used is library research. Data sources were obtained from relevant literature, including books, journals, and scientific articles on the selected topic. The discussion results show that technology-based learning innovations, such as software and adaptive learning systems, can be a solution for improving students' mathematical literacy. In addition, a contextual approach that integrates mathematical concepts with other fields can prepare students to address real problems in the digital era. The conclusion of this article is that developing a mathematics curriculum for Indonesia Emas 2045 must focus on improving critical thinking skills, contextualizing material, and integrating technology into learning. By overcoming challenges such as the technology gap, teaching quality, and prior curriculum implementation, mathematics education is expected to produce a generation that is superior and competitive in the era of globalization.
The main objective of this study is to identify and explain students’ errors in solving PISA questions on Space and Shape content using Newman’s Error Analysis. The errors analyzed include five categories: reading errors, comprehension errors, transformation errors, process skill errors, and encoding errors. This study employs a descriptive qualitative approach with data collected through tests and interviews. The research subjects are ninth-grade students at SMP Negeri 7 Muaro Jambi. The results show that students frequently made errors in the stages of understanding the questions, modelling the questions into mathematical forms, and process skills. These errors were by weaknesses in processing information, limited mathematical skills in real-life contexts, and a lack of experience in practicing PISA questions. These findings highlight the importance of familiarizing students with contextual problems as an effort to minimize errors in solving PISA questions.
This qualitative classroom study explores how collaborative learning (CL) supported by Python (SymPy) can strengthen university students’ understanding of partial fraction decomposition and its application to integration. Thirty‑two second‑year mathematics majors participated in four weekly sessions that blended manual problem solving with computational checking. Students worked in six small groups with defined roles (problem solver, coder, recorder, presenter), engaged in real‑world tasks (e.g., economic growth, fluid flow, and motion analysis), kept reflective journals, and delivered group presentations evaluated with an analytic rubric. Data sources comprised observations, journals, and presentation assessments. Thematic analysis indicates improved participation, clearer conceptual linking between algebraic manipulation and integral calculus, and more systematic error‑checking when Python was used to validate manual work. Groups demonstrating stronger within‑group communication tended to employ Python more effectively and reached higher rubric scores. The study discusses practical design choices for CL tasks that combine traditional and computational approaches, and reflects on limitations such as heterogeneous prior programming experience and the absence of pre–post achievement testing. Implications for practice include structuri
