Math Test Performance: A Deeper Dive into the Data

Math Test Performance: A Deeper Dive into the Data

Abstract: Math test performance serves as a crucial indicator of academic achievement, influencing future educational and career opportunities. This article delves into a comprehensive analysis of math test data, examining various factors contributing to performance disparities. We explore the impact of socioeconomic status, prior academic preparation, teacher quality, curriculum design, and cultural influences on student outcomes. Furthermore, we investigate the role of test design, administration practices, and psychological factors, such as test anxiety, in shaping performance metrics. By critically examining the data through diverse lenses, this article aims to provide a nuanced understanding of the complexities underlying math test performance and inform evidence-based interventions to promote equitable and effective math education for all students.

Keywords: Math test performance, achievement gap, socioeconomic status, teacher quality, curriculum, test anxiety, educational equity, data analysis, educational interventions.

Introduction:

Mathematics is often considered a gateway subject, essential for success in science, technology, engineering, and mathematics (STEM) fields, as well as many other disciplines.[1] Proficiency in mathematics is not only crucial for academic pursuits but also increasingly important for navigating the demands of a technologically advanced society.[2] Consequently, math test performance is widely used as a metric to assess student learning, evaluate educational programs, and inform policy decisions.[3] However, relying solely on test scores can provide an incomplete and potentially misleading picture of student understanding and educational effectiveness.[4]

This article seeks to move beyond a superficial examination of math test performance by undertaking a deeper dive into the data. We aim to explore the myriad factors that influence student outcomes on math tests, recognizing that performance is not simply a reflection of innate ability or effort but rather a complex interplay of individual, social, and institutional influences.[5] By analyzing data from various sources and considering different perspectives, we hope to illuminate the challenges and opportunities for improving math education and promoting equitable access to mathematical literacy for all students.

1. The Landscape of Math Test Performance: A Statistical Overview

Before delving into the contributing factors, it’s crucial to establish a baseline understanding of the current state of math test performance. National and international assessments, such as the National Assessment of Educational Progress (NAEP) in the United States and the Trends in International Mathematics and Science Study (TIMSS), provide valuable data on student achievement in mathematics across different grade levels and demographic groups.[6]

Analysis of these assessments reveals several persistent trends:

• Achievement Gaps: Significant disparities exist in math test performance based on socioeconomic status, race/ethnicity, and gender. Students from low-income families and historically marginalized groups consistently score lower on standardized math tests than their more affluent and privileged peers.[7] While progress has been made in closing some of these gaps over time, significant inequalities remain.[8]
• Grade-Level Proficiency: Many students struggle to achieve proficiency in mathematics at their respective grade levels. NAEP data often show that a substantial proportion of students perform below the “proficient” level, indicating a lack of mastery of essential mathematical concepts and skills.[9]
• STEM Pipeline Concerns: Concerns persist about the pipeline of students entering STEM fields. Declining interest and participation in advanced mathematics courses, particularly among underrepresented groups, pose a challenge to meeting the growing demand for STEM professionals.[10]
• International Comparisons: International assessments like TIMSS allow for comparisons of math performance across different countries. While some countries consistently outperform others, these comparisons must be interpreted cautiously, considering differences in curriculum, educational systems, and cultural contexts.[11]

These statistical trends highlight the urgency of addressing the challenges in math education and promoting equitable opportunities for all students to succeed in mathematics.

2. Socioeconomic Status: A Powerful Predictor of Math Performance

Socioeconomic status (SES) is consistently identified as one of the strongest predictors of academic achievement, including math test performance.[12] The relationship between SES and academic outcomes is complex and multifaceted, encompassing a range of factors that can directly and indirectly impact student learning.[13]

• Access to Resources: Students from low-income families often lack access to the resources that support academic success. This may include limited access to high-quality early childhood education, nutritious meals, healthcare, and learning materials.[14] These resource disparities can create significant disadvantages from an early age, impacting cognitive development and academic readiness.[15]
• School Funding and Quality: Schools in low-income communities often face significant funding shortfalls, leading to larger class sizes, fewer resources, and difficulties in attracting and retaining highly qualified teachers.[16] These factors can negatively impact the quality of instruction and the overall learning environment, disproportionately affecting students from disadvantaged backgrounds.[17]
• Parental Involvement: While parental involvement is generally associated with positive academic outcomes, parents from low-income families may face barriers to actively participating in their children’s education. These barriers may include limited time due to work obligations, lack of transportation, and a lack of familiarity with the educational system.[18]
• Neighborhood Effects: Living in impoverished neighborhoods can expose children to a range of stressors, including violence, crime, and environmental hazards, which can negatively impact their cognitive development and academic performance.[19]

Addressing the impact of socioeconomic status on math test performance requires comprehensive and systemic interventions that target the root causes of inequality. This may include policies aimed at reducing poverty, increasing access to affordable housing and healthcare, improving school funding equity, and providing support services to families and communities in need.

3. Prior Academic Preparation: Building a Strong Foundation

Math education is inherently sequential, with each concept building upon previously learned knowledge and skills.[20] Therefore, students who enter a grade level with gaps in their prior academic preparation may struggle to keep up with the curriculum and achieve proficiency on math tests.[21]

• Early Childhood Education: High-quality early childhood education programs play a crucial role in developing foundational mathematical skills and preparing children for success in elementary school. Studies have shown that children who participate in effective early childhood programs tend to have higher math achievement scores in later grades.[22]
• Elementary Math Instruction: The quality of math instruction in elementary school is critical for building a strong foundation in number sense, arithmetic, and basic problem-solving skills.[23] Effective elementary math instruction should focus on conceptual understanding, mathematical reasoning, and the development of positive attitudes toward mathematics.[24]
• Remedial Support: Students who fall behind in mathematics require timely and effective remedial support to address their learning gaps and prevent them from falling further behind. Remedial programs should be individualized to meet students’ specific needs and should focus on building a solid understanding of foundational concepts.[25]
• Summer Learning Loss: Summer learning loss, also known as the “summer slide,” can exacerbate existing achievement gaps, particularly in mathematics. Students from low-income families are often more susceptible to summer learning loss due to limited access to enrichment activities and learning resources during the summer months.[26]

Addressing the impact of prior academic preparation on math test performance requires a focus on strengthening early childhood education, improving the quality of elementary math instruction, providing effective remedial support, and mitigating the effects of summer learning loss.

4. Teacher Quality: A Cornerstone of Effective Math Education

Teachers are arguably the most important in-school factor influencing student learning.[27] The quality of math teachers has a significant impact on student achievement, particularly in mathematics, where content knowledge and pedagogical skills are crucial for effective instruction.[28]

• Content Knowledge: Math teachers need a deep and thorough understanding of the mathematical concepts they teach. Teachers with strong content knowledge are better equipped to explain complex concepts clearly, address student misconceptions, and provide challenging and engaging learning experiences.[29]
• Pedagogical Skills: Effective math teachers possess a range of pedagogical skills, including the ability to differentiate instruction to meet the needs of diverse learners, use effective questioning techniques to promote critical thinking, and create a positive and supportive learning environment.[30]
• Professional Development: Ongoing professional development is essential for math teachers to stay up-to-date on best practices in math education, deepen their content knowledge, and refine their pedagogical skills. Professional development should be relevant to teachers’ specific needs and should be aligned with school and district goals.[31]
• Teacher Retention: High teacher turnover rates, particularly in low-income schools, can disrupt the continuity of instruction and negatively impact student learning. Efforts to improve teacher retention, such as providing competitive salaries, supportive working conditions, and opportunities for professional growth, are crucial for ensuring that all students have access to qualified and experienced math teachers.[32]

Investing in teacher quality is essential for improving math test performance and promoting equitable outcomes for all students. This includes strengthening teacher preparation programs, providing ongoing professional development, and creating supportive working conditions that attract and retain talented math teachers.

5. Curriculum Design: Aligning Content and Instruction

The curriculum plays a vital role in shaping student learning experiences and determining the content and skills that are assessed on math tests.[33] A well-designed curriculum should be aligned with national and state standards, be coherent and rigorous, and provide students with opportunities to develop a deep understanding of mathematical concepts.[34]

• Alignment with Standards: The curriculum should be aligned with national and state standards, such as the Common Core State Standards for Mathematics (CCSSM), to ensure that students are learning the essential mathematical content and skills that they need to succeed in college and careers.[35]
• Coherence and Rigor: The curriculum should be coherent, with concepts building upon each other in a logical and sequential manner. It should also be rigorous, challenging students to think critically, solve problems, and apply their mathematical knowledge to real-world situations.[36]
• Conceptual Understanding: The curriculum should emphasize conceptual understanding, rather than rote memorization of formulas and procedures. Students should be able to explain why mathematical concepts work and how they relate to each other.[37]
• Problem-Solving: The curriculum should provide students with ample opportunities to engage in problem-solving activities that require them to apply their mathematical knowledge and skills to solve complex and challenging problems.[38]
• Culturally Relevant Pedagogy: Incorporating culturally relevant examples and contexts can make mathematics more engaging and accessible for students from diverse backgrounds. Connecting mathematical concepts to students’ lived experiences can help them see the relevance and importance of mathematics in their own lives.[39]

A well-designed and implemented curriculum is essential for promoting student learning and improving math test performance. Curriculum developers and educators should work together to ensure that the curriculum is aligned with standards, coherent, rigorous, and engaging for all students.

6. Test Design and Administration: Ensuring Validity and Fairness

The design and administration of math tests can significantly impact student performance. It is crucial to ensure that tests are valid, reliable, and fair to all students, regardless of their background or learning style.[40]

• Content Validity: The test should accurately assess the mathematical content and skills that students have been taught. The test items should be aligned with the curriculum and should reflect the range of topics and skills covered in instruction.[41]
• Construct Validity: The test should measure the underlying mathematical constructs that it is intended to measure. For example, a test of algebra should measure students’ understanding of algebraic concepts and their ability to apply those concepts to solve problems.[42]
• Reliability: The test should be reliable, meaning that it consistently produces similar results when administered to the same students under similar conditions.[43]
• Fairness: The test should be fair to all students, regardless of their background or learning style. Test items should be free of bias and should be accessible to students with disabilities. Accommodations, such as extended time or assistive technology, should be provided to students who need them.[44]
• Test Anxiety: Test anxiety can significantly impact student performance on math tests. Creating a calm and supportive testing environment, providing clear instructions, and allowing students sufficient time to complete the test can help reduce test anxiety.[45]
• High-Stakes Testing: The use of high-stakes math tests for making important decisions about students, teachers, and schools can create undue pressure and anxiety, potentially leading to negative consequences such as increased test cheating and a narrowing of the curriculum.[46]

Careful consideration of test design and administration practices is essential for ensuring that math tests are valid, reliable, and fair to all students. Test developers and administrators should strive to create tests that accurately measure student learning and provide meaningful information about their progress.

7. Psychological Factors: The Impact of Attitudes and Beliefs

Psychological factors, such as attitudes, beliefs, and motivation, can significantly impact student performance in mathematics. Students who have positive attitudes toward mathematics, believe that they can succeed in mathematics, and are motivated to learn are more likely to perform well on math tests.[47]

• Math Anxiety: Math anxiety is a common phenomenon that can negatively impact student performance in mathematics. Students who experience math anxiety may feel nervous, stressed, or overwhelmed when faced with mathematical tasks. Math anxiety can interfere with cognitive processing and hinder problem-solving abilities.[48]
• Growth Mindset: A growth mindset is the belief that intelligence and abilities can be developed through effort and learning. Students who have a growth mindset are more likely to persist in the face of challenges, seek out learning opportunities, and view mistakes as opportunities for growth.[49]
• Stereotype Threat: Stereotype threat is the risk of confirming negative stereotypes about one’s group. Students who are members of groups that are stereotyped as being less capable in mathematics may experience stereotype threat, which can lead to decreased performance on math tests.[50]
• Motivation and Engagement: Students who are motivated and engaged in mathematics are more likely to invest time and effort in learning and to perform well on math tests. Creating engaging and relevant learning experiences, providing opportunities for students to collaborate and discuss mathematical ideas, and offering positive feedback can help foster motivation and engagement.[51]

Addressing psychological factors that impact math test performance requires creating a positive and supportive learning environment, promoting a growth mindset, reducing math anxiety, and addressing stereotype threat. Educators can also help students develop positive attitudes toward mathematics and foster their motivation and engagement in learning.

8. Cultural Influences: Recognizing Diversity in Learning Styles

Cultural influences can also play a significant role in shaping student attitudes, beliefs, and learning styles related to mathematics. Recognizing and valuing cultural diversity is essential for creating inclusive and effective math classrooms.[52]

• Language: Language can be a barrier to learning mathematics for students who are not native English speakers. Providing language support, such as bilingual instruction or translated materials, can help these students access the curriculum and succeed in mathematics.[53]
• Cultural Values: Cultural values can influence students’ attitudes toward mathematics and their approaches to learning. For example, some cultures may emphasize collaboration and group work, while others may emphasize individual achievement. Educators should be aware of these cultural differences and adapt their instruction accordingly.[54]
• Cultural Relevance: Incorporating culturally relevant examples and contexts into mathematics instruction can make the subject more engaging and accessible for students from diverse backgrounds. Connecting mathematical concepts to students’ lived experiences can help them see the relevance and importance of mathematics in their own lives.[55]
• Representation: Ensuring that diverse cultural groups are represented in mathematics textbooks and other learning materials can help students feel more connected to the subject and see themselves as capable mathematicians.[56]

Recognizing and valuing cultural diversity is essential for creating inclusive and effective math classrooms. Educators should be aware of the cultural influences that can impact student learning and adapt their instruction accordingly.

9. The Role of Technology in Math Education

Technology has the potential to transform math education by providing new tools and resources for both teachers and students. Technology can be used to enhance instruction, personalize learning, and provide students with opportunities to explore mathematical concepts in new and engaging ways.[57]

• Interactive Simulations and Games: Interactive simulations and games can help students visualize mathematical concepts and explore them in a hands-on way. These tools can make learning more engaging and help students develop a deeper understanding of mathematical ideas.[58]
• Personalized Learning Platforms: Personalized learning platforms can adapt to students’ individual learning needs and provide them with customized instruction and practice. These platforms can help students work at their own pace and receive targeted support where they need it most.[59]
• Data Analysis Tools: Data analysis tools can help teachers track student progress, identify areas where students are struggling, and adjust their instruction accordingly. These tools can also help teachers identify patterns and trends in student data that can inform instructional decisions.[60]
• Online Resources: A vast array of online resources, such as videos, tutorials, and practice problems, can supplement classroom instruction and provide students with additional support.[61]

While technology can be a powerful tool for enhancing math education, it is important to use it thoughtfully and effectively. Technology should be used to support and enhance instruction, not to replace it. Teachers should be trained on how to use technology effectively and should carefully select tools that are aligned with their curriculum and instructional goals.

10. Evidence-Based Interventions: Promoting Equitable Math Achievement

Based on the analysis presented above, several evidence-based interventions can be implemented to improve math test performance and promote equitable math achievement for all students.

• Early Childhood Interventions: Investing in high-quality early childhood education programs is crucial for preparing children for success in mathematics. These programs should focus on developing foundational mathematical skills and promoting positive attitudes toward mathematics.[62]
• Targeted Remediation: Providing timely and effective remedial support to students who are struggling in mathematics is essential for preventing them from falling further behind. Remedial programs should be individualized to meet students’ specific needs and should focus on building a solid understanding of foundational concepts.[63]
• Professional Development for Teachers: Ongoing professional development is essential for math teachers to stay up-to-date on best practices in math education, deepen their content knowledge, and refine their pedagogical skills. Professional development should be relevant to teachers’ specific needs and should be aligned with school and district goals.[64]
• Curriculum Reform: Implementing a well-designed and aligned curriculum is essential for promoting student learning and improving math test performance. The curriculum should be aligned with standards, coherent, rigorous, and engaging for all students.[65]
• Addressing Psychological Factors: Creating a positive and supportive learning environment, promoting a growth mindset, reducing math anxiety, and addressing stereotype threat can help improve student attitudes and beliefs related to mathematics.[66]
• Family and Community Engagement: Engaging families and communities in supporting student learning in mathematics can have a significant impact on student achievement. Schools can provide resources and workshops for parents to help them support their children’s learning at home.[67]
• Culturally Responsive Teaching: Using culturally responsive teaching practices can make mathematics more engaging and accessible for students from diverse backgrounds. Connecting mathematical concepts to students’ lived experiences can help them see the relevance and importance of mathematics in their own lives.[68]

Implementing these evidence-based interventions requires a collaborative effort from educators, policymakers, families, and communities. By working together, we can create a system of math education that is equitable, effective, and empowers all students to succeed in mathematics.

Conclusion:

This article has provided a deeper dive into the complexities of math test performance, highlighting the multitude of factors that influence student outcomes. It is clear that math test performance is not solely a reflection of individual ability but rather a complex interplay of socioeconomic status, prior academic preparation, teacher quality, curriculum design, test design and administration, psychological factors, and cultural influences. Addressing the challenges and promoting equitable math achievement requires a comprehensive and systemic approach that targets the root causes of inequality and provides all students with the resources and support they need to succeed. By investing in high-quality early childhood education, providing targeted remediation, supporting teacher professional development, implementing a well-designed curriculum, addressing psychological factors, engaging families and communities, and using culturally responsive teaching practices, we can create a system of math education that empowers all students to reach their full potential. Moving forward, it is essential to continue to collect and analyze data on math test performance, critically examine the factors that contribute to disparities, and implement evidence-based interventions that promote equitable and effective math education for all. The future demands mathematically literate individuals, and it is our collective responsibility to ensure that all students have the opportunity to develop the mathematical skills and knowledge they need to thrive in the 21st century.

References:

[1] National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. U.S. Department of Education.

[2] Steen, L. A. (2001). Mathematics and democracy: The case for quantitative literacy. National Council on Education and the Disciplines.

[3] Au, W. (2009). Unequal by design: High-stakes testing and the standardization of inequality. Routledge.

[4] Kohn, A. (2000). The case against standardized testing: Raising the scores, ruining the schools. Heinemann.

[5] Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32(3), 465-491.

[6] National Center for Education Statistics (NCES). (n.d.). National Assessment of Educational Progress (NAEP). Retrieved from [Insert NCES Website Here] TIMSS & PIRLS International Study Center. (n.d.). Trends in International Mathematics and Science Study (TIMSS). Retrieved from [Insert TIMSS Website Here] [7] Reardon, S. F. (2011). The widening academic achievement gap between the rich and the poor: New evidence and possible explanations. In G. J. Duncan & R. J. Murnane (Eds.), Whither opportunity? Rising inequality, schools, and children’s life chances (pp. 91-116). Russell Sage Foundation.

[8] Hanushek, E. A., & Woessmann, L. (2011). The economics of international differences in educational achievement. In E. A. Hanushek, S. Machin, & L. Woessmann (Eds.), Handbook of the economics of education (Vol. 3, pp. 89-200). Elsevier.

[9] National Center for Education Statistics (NCES). (n.d.). NAEP Data Explorer. Retrieved from [Insert NCES NAEP Data Explorer Link] [10] National Science Board. (2010). Preparing the next generation of STEM innovators: Identifying and developing our nation’s human capital. National Science Foundation.

[11] Mullis, I. V. S., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics. International Association for the Evaluation of Educational Achievement.

[12] Sirin, S. R. (2005). Socioeconomic status and academic achievement: A meta-analytic review of research. Review of Educational Research, 75(3), 417-453.

[13] Brooks-Gunn, J., & Duncan, G. J. (1997). The effects of poverty on children. The Future of Children, 7(2), 55-71.

[14] Duncan, G. J., & Murnane, R. J. (Eds.). (2011). Whither opportunity? Rising inequality, schools, and children’s life chances. Russell Sage Foundation.

[15] Hackman, D. A., Farah, M. J., & Meaney, M. J. (2010). Socioeconomic status and the brain: Mechanistic insights from human and animal research. Nature Reviews Neuroscience, 11(9), 651-659.

[16] Kozol, J. (2005). The shame of the nation: The restoration of apartheid schooling in America. Crown Publishers.

[17] Darling-Hammond, L. (2010). The flat world and education: How America’s commitment to equity will determine our future. Teachers College Press.

[18] Hoover-Dempsey, K. V., & Sandler, H. M. (1997). Why do parents become involved in their children’s education? Review of Educational Research, 67(1), 3-42.

[19] Sampson, R. J., Morenoff, J. D., & Gannon-Rowley, T. (2002). Assessing “neighborhood effects”: Social processes and new directions in research. Annual Review of Sociology, 28(1), 443-478.

[20] National Research Council. (2001). Adding it up: Helping children learn mathematics. National Academies Press.

[21] Riccomini, P. J., & Witzel, B. S. (2010). Response to intervention in math. Corwin Press.

[22] Schweinhart, L. J., Montie, J., Xiang, Z., Barnett, W. S., Belfield, C. R., & Nores, M. (2005). Lifetime effects: The High/Scope Perry Preschool Study through age 40. High/Scope Press.

[23] Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. National Academies Press.

[24] National Council of Teachers of Mathematics (NCTM). (2014). Principles to actions: Ensuring mathematical success for all. NCTM.

[25] Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morvant, M., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79(3), 1202-1242.

[26] Cooper, H., Nye, B., Charlton, K., Lindsay, J., & Greathouse, S. (1996). The effects of summer vacation on achievement test scores: A narrative and meta-analytic review. Review of Educational Research, 66(3), 227-268.

[27] Hattie, J. (2009). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. Routledge.

[28] Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371-406.

[29] Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407.

[30] Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.

[31] Guskey, T. R. (2000). Evaluating professional development. Corwin Press.

[32] Ingersoll, R. M. (2001). Teacher turnover and teacher shortages: An organizational perspective. American Educational Research Journal, 38(3), 499-534.

[33] Schmidt, W. H., Wang, H. C., & McKnight, C. C. (2005). Curriculum coherence: An examination of US mathematics and science content standards from an international perspective. Journal of Curriculum Studies, 37(5), 525-559.

[34] Porter, A. C. (2002). Measuring the content of instruction: Uses in research and practice. Educational Researcher, 31(7), 3-14.

[35] Common Core State Standards Initiative. (2010). Common core state standards for mathematics. National Governors Association Center for Best Practices, Council of Chief State School Officers.

[36] Webb, N. L. (1999). Alignment of science and mathematics standards and assessments in four states (Research Monograph No. 18). University of Wisconsin-Madison, National Institute for Science Education.

[37] Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K., Human, P., Murray, H., … & Wearne, D. (1997). Making sense: Teaching and learning mathematics with understanding. Heinemann.

[38] Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.

[39] Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32(3), 465-491.

[40] American Educational Research Association, American Psychological Association, & National Council on Measurement in Education. (2014). Standards for educational and psychological testing. American Educational Research Association.

[41] Messick, S. (1995). Validity of psychological assessment: Validation of inferences from persons’ responses and performances as scientific inquiry into score meaning. American Psychologist, 50(9), 741.

[42] Cronbach, L. J., & Meehl, P. E. (1955). Construct validity in psychological tests. Psychological Bulletin, 52(4), 281.

[43] Nunnally, J. C. (1978). Psychometric theory. McGraw-Hill.

[44] Thompson, B. (2003). Score reliability: Contemporary thinking on reliability issues. Sage.

[45] Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181-185.

[46] Nichols, S. L., & Berliner, D. C. (2007). Collateral damage: How high-stakes testing corrupts America’s schools. Harvard Education Press.

[47] Dweck, C. S. (2006). Mindset: The new psychology of success. Random House.

[48] Tobias, S. (1978). Overcoming math anxiety. W. W. Norton & Company.

[49] Dweck, C. S. (2006). Mindset: The new psychology of success. Random House.

[50] Steele, C. M. (2010). Whistling Vivaldi: How stereotypes affect us and what we can do. W. W. Norton & Company.

[51] Ryan, R. M., & Deci, E. L. (2000). Intrinsic and extrinsic motivations: Classic definitions and new directions. Contemporary Educational Psychology, 25(1), 54-67.

[52] Gay, G. (2010). Culturally responsive teaching: Theory, research, and practice. Teachers College Press.

[53] Moschkovich, J. N. (2002). A situated and sociocultural perspective on bilingual mathematics learners. Mathematical Thinking and Learning, 4(2-3), 189-212.

[54] Hofstede, G. (2001). Culture’s consequences: Comparing values, behaviors, institutions, and organizations across nations. Sage publications.

[55] Ladson-Billings, G. (1995). Toward a theory of culturally relevant pedagogy. American Educational Research Journal, 32(3), 465-491.

[56] Zevenbergen, R., Dole, S., & Wright, R. J. (2004). Teaching mathematics in primary school. Allen & Unwin.

[57] National Council of Teachers of Mathematics (NCTM). (2011). Strategic use of technology in teaching and learning mathematics. NCTM.

[58] Clark, D. B., Tanner-Smith, E. E., & Killingsworth, S. S. (2016). Digital games, design, and learning: A systematic review and meta-analysis. Review of Educational Research, 86(1), 79-122.

[59] Pane, J. F., Steiner, E. D., Baird, M. D., & Hamilton, L. S. (2015). *Continued