NEW REPORT! TIMSS 1995-2023: Zone Proxima charts investigate grade 4 math preparedness (on track for college- & career-readiness) across the globe.
—Debbie Denise Reese, PhD, CEO—Zone Proxima, LLC[ii]
Mathematics proficiency is important to personal, academic, and professional achievement. International, long-term, robust studies, such as the Trends in International Mathematics and Science Study (TIMSS), provide rich longitudinal portraits of mathematics achievement within the United States and across the World. When these portraits identify deficits in mathematics achievement, they motivate and inform intervention development and adoption.
The TIMSS has been conducted every four years since 1995. Results from 2023 testing were released in late 2024 and early 2025. These data afford comparison over all study years and participating jurisdictions. The International Data Explorer (IDE, https://nces.ed.gov/timss/idetimss/, International Association for the Evaluation of Educational Achievement) is an existing online reporting and analysis tool for TIMSS 1995 – 2019. IDE permitted comparison by testing year and jurisdiction for percentage of testees reaching benchmarks of students’ mathematics achievement. The TIMSS International Benchmarks categories are (1) Advanced, (2) High, (3) Intermediate, and (4) Low. A fifth category is assigned to student performance that is so poor it cannot be classified. Due to current United States federal funding priorities, 2023 updates to the IDE are halted (L. Malley, personal communication, February 24, 2025). The online IDE cannot currently conduct reports and analyses using 2023 data. To fill this gap, Zone Proxima prepared and plotted a combined dataset from the IDE TIMSS archive and the 2023 TIMSS data released by the U.S. Department of Education and the National Center for Education Statistics (2024).
State, national, and international testing results identify deficits in mathematics achievement by a troubling percentage of fourth grade students. It is realistic to assume those children lack foundational knowledge and skills. Foundational deficits often begin in early years. They compound over childhood and formal education, threatening personal, academic, career, and lifelong achievement and fulfillment:
Economic access and career opportunity depend on mathematics proficiency (Moses & Cobb, 2001).
Mathematics knowledge at age 7 predicts socioeconomic status at age 42 (even after controlling statistically for familial SES, IQ at age 11, reading achievement, and academic motivation, see Ritchie & Bates, 2013).
When family, caretakers, and educators prepare very young children with mathematical foundations, children find greater success. Even simple family activities such as counting songs, building with blocks and construction toys, drawing shapes, and measuring are associated with greater mathematics achievement. The frequency with which young children engage at home with older household members in these numeracy activities and various literacy activities is positively associated with higher fourth grade mathematics achievement (Mullis, Martin, Foy, Kelly, & Fishbein, 2020).
In general, Watts, Duncan, Siegler, and Davis-Kean (2014) found that preschool mathematics ability predicted mathematics achievement through age 15, even after accounting for early reading, cognitive skills, and family and child characteristics.
Imagine the achievement gains if the adults in a young child’s life were immersively present as they guided mathematics discovery? What if they could guide that discovery knowledgeably, actively, and effectively? What if the adults in a young child’s life could make mathematics meaningful, meaning-filled, intuitive, and autotelic? Humans use language all the time. Early childhood exposure makes language skills such as grammar and vocabulary more intuitive. For example, Hart and Risley (1995, 2003) discovered that the number of words used during a child’s household interactions from age 10 months to 3 years predicted rate of vocabulary growth and size at ages 9 and 10 and school achievement at grade 3. Just imagine a similar effect if adults routinely incorporated effective mathematics readiness activates as mutually engaging discovery during their interaction with young children. Zone Proxima investigates, develops, and disseminates practices and materials to make early childhood mathematics experience delightful, fulfilling, meaning-filled, meaningful, and effective (Reese, 2024a, 2024b, in press).
Zone Proxima investigates long-term trends in mathematics achievement to motivate and inform its initiative addressing early childhood mathematics readiness. Grade four mathematics achievement is one indicator (and effect of) of early childhood readiness. The reauthorized Elementary and Secondary Education Act both required and funded state standards to produce young people who are on track for college- and career-readiness. It called for assessments to determine this preparedness. The U.S. Department of Education (2010) explained:
Why Focus on College and Career Readiness? Four of every 10 new college students, including half of those at two-year institutions, take remedial courses, and many employers comment on the inadequate preparation of high school graduates. (p. 4)
Under the National Assessment Governing Board, the Technical Panel on 12th-Grade Preparedness Research (2008) subdivided the concept of college- and career-readiness into (a) preparedness (academic qualifications that could be measured by standardized testing) and (b) behavior and affective components (e.g., time management, persistence, and interpersonal skills qualifications):
1. Preparedness for college refers to the reading and mathematics knowledge and skills necessary to qualify for placement into entry level college credit coursework without the need for remedial coursework in those subjects.
2. Preparedness for workplace training refers to the reading and mathematics knowledge and skills needed to qualify for job training; it does not mean that the student is ready to be hired for a job.
3. Preparedness does not mean success in postsecondary education and training. [The National Assessment of Educational Progress, NAEP,] can provide valuable information by reporting eligibility to enter postsecondary activities. Measuring success directly requires individual student scores on NAEP and longitudinal studies with these data. These research design elements are not compatible with the NAEP design or the NAEP legislation.
4. Preparedness in the NAEP context must be limited to academic qualifications for postsecondary education and workplace training.
5. Preparedness for job training is based on the assumption that similar jobs in both the military and civilian sectors require approximately equal reading and mathematics knowledge and skills to qualify for entry. (p. 3)
States and other organizations customized the definition. For example, within the West Virginia state standards “. . . college- and career-readiness refers to the knowledge, skills, and dispositions needed to be successful in higher education and/or training that lead to gainful employment” (West Virginia Department of Education, 2016, p. 1).
As early as grades three and four, U.S. state testing—for instance, North Carolina End of Grade assessment—identifies benchmarks of achievement that include the percentage of students who are and are not on track for college or career readiness (North Carolina Department of Public Instruction, 2022). In North Carolina, the college- and career-readiness achievement threshold divides between level 3 and level 4: (e.g., pp 1, 3):
Levels 1 and 2. Not proficient.
Level 3. Students at Level 3 demonstrate sufficient understanding of grade level content standards, though some support may be needed to engage with content at the next grade/course.
***
Level 4. Students at Level 4 demonstrate a thorough understanding of grade level content standards and are on track for career and college.
Level 5. Students at Level 5 demonstrate comprehensive understanding of grade level content standards, are on track for career and college, and are prepared for advanced content at the next grade/course.
Achievement Benchmarking—including preparedness benchmarks such as on track for college- and career-readiness—requires rigorous psychometrics and validation (e.g., Camara, 2013; McClarty, Way, Porter, Beimers, & Miles, 2013). TIMSS framework and benchmarks do not classify results for on track for college- and career-readiness. Zone Proxima analyses sought some perspective on readiness and preparedness by organizing the TIMSS data into two sets of charts reporting mathematics achievement benchmark percentages by jurisdiction and within year (1995 – 2023). Each table uses a different threshold assumption to classify mathematics preparedness. In one set, a high readiness threshold was set. The other used a low threshold.
TIMSS grade 4 mathematics benchmarks are categorized according to test score using statistical processes (Fishbein, Taneva, & Kowolik, 2025). TIMSS documentation provides both descriptions and examples of each benchmarked achievement level (von Davier et al., 2024)[iii] and list of anchoring items within each benchmark category (Khorramdel, Aldrich, & Bookbinder, 2024).[iv]
TIMSS Grade 4 Benchmark Categories Summary, Descriptions, and Examples
TIMSS Grade 4 Benchmark Categories Anchoring Item Descriptions
*Zone Proxima hosts this documentation with permission of IEA, granted March 28, 2025
The general summary definitions of the 2023 TIMSS Mathematics achievement benchmarks follow (Exhibit 1.1.3, von Davier et al., 2024, IEA permission to reprint granted March 28, 2025):
Advanced International Benchmark (score of 625 and above): Students can select and relate information to implement appropriate operations to solve problems. They can interpret the results of computations given in problem contexts, formulate a variety of expressions and patterns, and relate fractions and decimals. They can estimate and relate measures, apply knowledge of two- and three-dimensional shapes, identify simple properties of lines and angles, and show a basic understanding of surface area and perimeter in simple shapes. Students can interpret data and make choices about data given in numerous contexts.
High International Benchmark (score of 550 – 624): Students relate concepts or representations in extended contexts. They can apply knowledge of properties of whole numbers to justify a solution. They show an understanding of the number line, multiples, factors, rounding numbers, and operations with fractions and decimals. Students can resolve measurement tasks across numerous contexts. They can relate two-dimensional shapes to unfamiliar three-dimensional figures and demonstrate basic understanding of angles. Students can interpret features of data representations and represent data in a variety of graphs.
Intermediate International Benchmark (score of 475 – 549): Students demonstrate mathematical knowledge in simple situations and relate representations. They can perform computations with three-digit whole numbers in a variety of situations. They can add and order simple decimals. Students can measure straight distances and describe three-dimensional shapes. They can use data from multiple sources to relate representations.
Low International Benchmark (score of 400 – 474): Students demonstrate basic mathematical understanding. They can add and subtract whole numbers with up to three digits, multiply and divide single-digit whole numbers, and solve simple word problems. They can apply basic measurement ideas and properties.
The remaining students do not evidence sufficient knowledge to classify into a benchmarked level:
Knowledge Level Unclassifiable (score below 400): Student performance is inadequate, does not permit determination of a knowledge or proficiency level.
Zone Proxima’s charts combine data from the National Center for Education Statistics TIMSS International Data Explorer (1995-2019 datasets, International Association for the Evaluation of Educational Achievement) and the U.S. Department of Education, National Center for Education Statistics (2023 dataset, 2024). They report percentages of testees per Benchmark Achievement level of by jurisdiction (country-level or smaller region) within year. The charts plot percentages for five TIMSS Benchmark Achievement Categories:
Knowledge Level Unclassifiable: Scores below 400.
Low: Scores 400 to 474.
Intermediate: Scores 475 to 549.
High: Scores 550 to 624
Advanced: Scores at and above 625.
College- and career-readiness, with respect to preparedness, can be estimated by proficiency. Thus, fourth grade students who are not proficient are not currently on track for college- and career-readiness. Because TIMSS data do not report percentages of grade 4 testees on track for college- or career-readiness or preparedness, we posited proficiency thresholds to provide preparedness insights through both conservative and liberal data representations.
High Proficiency Threshold. The high threshold interpretation sets a proficiency threshold between Intermediate (not proficient) and high (proficient). Knowledge Level Unclassifiable, Low, and Intermediate Benchmarks plot to the left of the zeroing threshold. High and Advanced Benchmarks plot to the right of the threshold.
Low Proficiency Threshold. The low threshold interpretation sets a proficiency threshold between Low (not proficient) and Intermediate (proficient). Thus, Knowledge Level Unclassifiable and Low Benchmarks still plot to the left of the zeroing threshold. Intermediate joins High and Advanced Benchmarks to plot to the right of the threshold.
Two files report threshold representations of the 1995-2023 TIMSS Benchmark achievement within year by jurisdiction data: the Low Threshold PDF and the High Threshold PDF. Each file contains 29 plots (pages/charts). Each page report results for three or four jurisdictions or the averages across a year’s participating jurisdictions.
This section summarizes the characteristics of the Zone Proxima 1995-2023 TIMSS grade 4 mathematics reports. Figures 1 and 2 display high and low proficiency threshold versions for the report pages that include Singapore, the United States, and the annual averages across all of a testing year’s participating jurisdictions. In these figures, note the horizontal axis at the top of the graph and the individual data labels.
The label “0” indicates the location for the threshold for proficiency, either the high proficiency threshold or low proficiency threshold representation. A hyphen appended to numerical percentages indicates a percentage of testees who were not proficient. Hyphens indicate nonproficiency for both (a) the axis labels to the left of the proficiency threshold and (b) each Benchmark achievement category percentage plotted to the left of the proficiency.
The hyphens indicate nonproficiency for a positive percentage, not negative percentage number.
Data Labels. The data label on each benchmarked percentage within each year within each jurisdiction reports the actual percentage of testees within that year and jurisdiction scoring within that achievement level.
Horizontal Axis Labels. The horizontal axis labels permit the reader to estimate the total percentage of testee scores classified as either proficient or nonproficient.
Figure 1. High proficiency threshold plots for Singapore, USA, and average across jurisdictions.
Figure 2. Low proficiency threshold plots for Singapore, USA, and average across jurisdictions.
Benchmark alignment to the left and the right of the thresholds (see Figures 1 and 2) highlights aspects of the information carried by the data. The following examples illustrate. Both visual and numerical representations reveal that threshold choice highlights a different perception of the information.
Advanced Benchmark Percentages. No matter which threshold representation is examined, the Singapore percentage for the Advanced Benchmark is clearly greater than the Advanced Benchmark percentage for the United States and for the average of jurisdictions. Visually, I find the high threshold representation most clearly reveals the higher percentage of Singapore fourth grade students achieving advanced proficiency.
Sum of Knowledge Unclassifiable and Low Benchmark Percentages. No matter which threshold representation is examined, the Singapore percentages for the Knowledge Unclassifiable and Low Benchmarks are clearly less than the percentage for the United States or the average of jurisdictions. Visually, I find the low threshold representation best reveals Singapore’s consistent accomplishment, 1995-2023, of 11% or fewer grade 4 mathematics students scoring within knowledge unclassifiable or low knowledge categories.
Intermediate. Within both high and low threshold figures and across years, percentages of United States and global (average among jurisdictions) testees achieving the Intermediate Benchmark are similar to each other and greater than the percentage of Intermediate Benchmark achievers in Singapore:
Thus, over the 33 years and seven rounds of TIMSS assessment, a greater percentage of grade four Singapore mathematics students have attained High and Advanced TIMSS Benchmarks than have students in the United States or globally (as represented by the average of jurisdictions percentages).
Table 1 contains data from Figure 1 and Figure 2, TIMSS Mathematics results from 1995-2023 for grade 4 mathematics. The table provides an average for Not On Track and On track percentages by jurisdiction over 1995-2023 scores for both low and high thresholds. Percentages to the right or left of the threshold within a jurisdiction and year were summed. Then the sums within a jurisdiction were averaged over the seven TIMSS administration years.
Low and high threshold representations use the same data but may reveal different stories due to the movement of the intermediate category from proficiency to nonproficiency.
Low Threshold for Proficiency. Most Singapore students are on track (about 9 out of 10). In the United States, 50% more students are on track than not. Across the globe, 26% more students are on track for college- and -career readiness than are not.
High Threshold for Proficiency. Using the high threshold, 3 of 4 Singapore students are on track for college- and career-readiness. In both the United States and within the average of jurisdictions across the globe, movement of the Intermediate category to nonproficient produced a greater percentage of students who are not college- and career-ready than students who are.
Math achievement is both gate and gatekeeper to financial and personal success and fulfillment. International testing such as TIMSS provides both longitudinal and cross sectional profiles of students’ mathematics achievement and readiness. The persistence of substantial nonproficiency within fourth grade student populations across the globe is an alarm the World should address with intervention. Effective early childhood mathematics preparation integrated within later mathematics instruction predicts financial and personal success across the lifetime (see sections above). Zone Proxima proposes an early childhood mathematics intervention whereby—as a component of social norms that nurture young children for flourishing lives—adults learn to effectively mentor mathematics preparedness. Working together, effective
instructional methods,
pedagogically appropriate concrete learning objects, and
competent, knowledgeable adults (family, caretakers, and educators)
can guide young children to discover and apply foundational mathematics. The Zone Proxima TIMSS 1995-2023 Charts (High Proficiency Threshold, Low Proficiency Threshold) provide a quarter century of information tracking fourth grade mathematics achievement across the globe. The charts provide percentages for Benchmark Achievement levels within jurisdictions, across jurisdictions, and over time.
Singapore provides an existence case demonstrating that—by design—a jurisdiction can successfully provide effective mathematics education. Granted, the Singapore island city state is about the size of New York City’s five boroughs. However, Singapore’s mathematics achievement success is self-made and, again, by design.
In 1965, when Singapore achieved independence from Malaysia, its GDP was 1/6 of the United States GPD. In 1975 Singapore conducted cohort studies with the following findings (Goh & The Education Study Team, 1979):
At least 25% of its primary 6 (final year of primary school) did not meet Singapore’s minimum numeracy level.
65% of its cohort students did not pass the high school ordinary level exams,
50% of those 65% could not pass the primary leaving exam, even in 3 attempts,
Young recruits, educated in English, did not have sufficient English literacy skills for their military positions. Only 11% of recruits were “able to handle fairly well work/training situations in which English was the sole means of communication” (p. 3-4).
The society was not homogeneous, with English and three mother tongues and cultures.
Under Mr. Goh (Deputy Prime Minister and Minister of Education) and Mr. Lee (Prime Minister) the country’s leadership proclaimed its people—its human capital—as its natural resource and set about designing effective literacy and mathematics education. The country designed norms and expectations for its youth, their families, and the overall health of their society: Singapore was to flourish and so were its people. Singapore mathematics education prepares children, especially young children, with substantial concrete learning experiences before they work with abstract representations (Ministry of Education, 2022, 2023). Singapore’s preschool curriculum framework explicitly promotes norms and expectations for children and for their caretakers and educators (Ministry of Education, 2023, p. 4):
Beliefs about Children
Children are joyful, curious, active, and competent learners.
Children play, learn and grow with others in a diverse and multi-cultural community.
Values
Respect
Responsibility
Care
Social and Emotional Competencies
Self-awareness
Self-management
Social awareness
Relationship management
Responsible decision-making
Learning Dispositions
Perseverance
Reflectiveness
Appreciation
Inventiveness
Sense of wonder and curiosity
Engagement
As the TIMSS study results show, the Singapore Ministers and the Ministry of Education were successful. Because of Singapore’s explicitly planned and executed investment in its human capital—in literacy and mathematics achievement, social and personal values, social and emotional competencies, and learning dispositions—Singapore has built one of the World’s leading economies and education systems (beginning with early learners). Specific economic models produce results that differ slightly in detail but tell the same story regarding Singapore’s success. Here, the World Population Review tables provided the numbers, but the story is evident in Figure 3.
Singapore’s gross domestic product (GDP) per capita rivals or exceeds that of the United States (2025: Singapore = $93,956, fourth highest in the world; United States = $89,678, 7th highest in the world; calculated by the International Monetary Fund using US dollars, World Population Review, 2025a).
Singapore’s gross national income (GNI), which includes GDP and income by citizens from sources outside the country, per capita led the world in 2023 (Singapore = $118,710, first in world; United States = $82,190, ninth in world, calculated using the Purchasing Power Parity (PPP) method, World Population Review, 2025b).[v]
Figure 3. GDP per capita 1974-2023: Singapore and United States
Singapore’s success is an existence proof; and this proof inspires faith. Instructional, educational, and societal interventions can improve mathematics achievement throughout the World. Like the 79% in Singapore, a majority of the world’s youth can achieve high and advanced mathematics capacity. Like the 92% in Singapore, almost all can achieve intermediate to advanced mathematics proficiency. Worldwide mathematics achievement is possible.
The Singapore early childhood curriculum (ages 4-6) is a framework for (a) values, social and emotional competencies, and learning dispositions that produce individual and collective flourishing, (b) guided-discovery and application of numeracy (identify and use numbers, understand the relationships between numbers, count accurately and recognize patterns, shapes, positions, and directions), and (c) instruction that is grounded in concrete experience and advances toward the abstract according to individual readiness (Ministry of Education, 2023). However, it appears the Ministry of Education may be unaware of the value of a consistent, core, coherent, and relationally isomorphic system of apt and effective manipulatives as a core component of early years that integrates within elementary education (for characteristics of effective mathematics manipulatives, see Uttal, Scudder, & DeLoache, 1997). In addition, it appears the Singapore early years frameworks focuses on caregivers and educators. Any parental support seems targeted; its focus limited to assisting parents to find effective childcare and/or education.
Strategic Response Action Item: Zone Proxima Math provides just such a solution. The TIMSS Charts and then Singapore case study inspire a path, an intervention targeting the parents of children ages 4-6 with Cuisenaire-Gattegno Rods and their curriculum (Chambers, 1964; Gattegno, 1970; Reese, in press).
One might consult the Zone Proxima 1995-2023 TIMSS Benchmark Percentage Charts to ask for many other stories. Some examples might be
What are the TIMSS stories of the other top GDP and GNI per capita performers?
Which jurisdictions have been consistent mathematics achievers?
Which jurisdictions have consistently failed to produce achievers?
Have any jurisdictions experienced discontinuities after which a jurisdiction’s Benchmark Percentiles profile changes?
Across the Globe, many young people fail to achieve mathematics proficiency or readiness. Averaged across participating jurisdictions for 2023 TIMSS, a mean of 37% (median 30%) of grade 4 students performed within the low or unclassifiably low levels of mathematics achievement benchmarks. Using a high threshold estimator, a mean of 66% (median = 65%) grade 4 students across all jurisdictions failed to benchmark as proficient and prepared (college- and career-readiness) during TIMSS 2023 mathematics assessment. The Zone Proxima 1995-2023 TIMSS tables provide visually accessible longitudinal profiles, illuminating cross-sectional and longitudinal trends within and across jurisdictions. Profiles inform identification of jurisdictions with exemplary success. They also identify needs. Thus, TIMSS 1995-2023 plots support intervention designed to improve mathematics achievement.
The literature concerning mathematics achievement is clear: readiness begins in young childhood. New knowledge builds on existing knowledge structures. Home-based (Mullis et al., 2020) and effective early childhood mathematics experiences predict mathematics achievement (e.g., Institute of Education Sciences (IES), 2023; Mullis et al., 2020; T. W. Watts, Duncan, Clements, & Sarama, 2018; Tyler W. Watts et al., 2014), economic prosperity (Tyler W. Watts et al., 2014), and access to opportunity (Moses & Cobb, 2001). Young children have the time to explore aptly designed concrete mathematics challenges, to discover and apply foundational mathematics concepts and processes they need for mathematics achievement, for preparedness: college- and career-readiness. There is some misconception that every young child needs to discover mathematics on their own, by independently playing with assorted manipulatives (for example, see discussion of this misconception in Clements & Sarama, 2014). But most children need parents and older family members, caregivers, and early childhood educators to guide them through that discovery. The Singapore framework (Ministry of Education, 2023) provides curricular models and methods for early childhood educators and caregivers. Theorists, educational scientists, and advocates have advised for over 75 years that young children require guided discovery experiences and concrete manipulatives that “make the structure of these new numbers and numerals visible” (Stern, 1953, p. xiiii). Manipulatives must be apt analogs of the mathematics they model (Uttal et al., 1997). Young children must develop healthy mindsets that recognize the joy of learning (Ministry of Education, 2023).
Together, the 1995-2023 TIMSS plots and research over three-quarters of a century suggest effective and appropriate guided discovery experiences during early childhood can increase mathematics achievement worldwide. Furthermore, the Cuisenaire-Gattegno manipulatives and curriculum are designed to make this happen (Chambers, 1964; Gattegno, 1970). Just like children, adults require mentorship to learn how to use the Gattegno curriculum and Cuisenaire Rods to guide mathematics discovery and application. “It is generally recognized that it takes years to make a teacher really expert in directing learning with the Cuisenaire [Rods and curriculum] (Brownell, Ruddell, Law, & Allan, 1967, p. 223). If educators require this training (National Council of Teachers of Mathematics, 2022), parents and childcare givers certainly do.
Singapore provides a model of norm setting for personal, academic, and societal flourishing (for definition of flourishing, see Zhang, 2022): the values, social and emotional competencies, and learning dispositions. These are very important. But even Singapore might benefit from bringing mathematics readiness discovery into the home. In jurisdictions such as the United States, mathematics readiness could be improved if the adults who parent, care for, and educate very young children would learn the habits of nurturing the values, social and emotional competencies, and learning dispositions while guiding young children through discovery and application of foundational mathematics using Cuisenaire Rods and the Gattegno curriculum. Zone Proxima offers this training. Effective early childhood preparation could make a difference throughout the World. In the future, perhaps a discontinuity caused by early childhood mathematics intervention could produce international trends across nations that duplicate the mathematics preparedness exhibited by Singapore’s grade four students.
Brownell, W. A., Ruddell, A. K., Law, M. L. F., & Allan, R. J. (1967). Arithmetical computation: Competence after three years of learning under differing instructional programs. (ED022703; Bureau No-BR-6-1077). University of California, Berkeley. Retrieved May 5, 2025, from http://files.eric.ed.gov/fulltext/ED022703.pdf.
Camara, W. (2013). Defining and measuring college and career readiness: A validation framework. Educational Measurement: Issues and Practice, 32(4), 16-27. doi: 10.1111/emip.12016.
Chambers, C. E. (1964). The Cuisenaire Gattegno method of teaching mathematics: A course for teachers volume 1. Reading, England: Educational Solutions Worldwide.
Clements, D. H., & Sarama, J. (2014). Play, mathematics, and false dichotomies. Preschool Matters . . . Today. Retrieved January 14, 2023, from https://nieer.wordpress.com/2014/03/03/play-mathematics-and-false-dichotomies/
Fishbein, B., Taneva, M., & Kowolik, K. (2025). TIMSS 2023: User guide for the international database. Boston College, TIMSS & PIRLS International Study Center: Boston College, TIMSS & PIRLS International Study Center. Retrieved March 15, 2025, from https://timss2023.org/data.
Gattegno, C. (1970). Gattegno mathematics: Text-book 1. New York: Educational Solutions.
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Hart, B., & Risley, T. R. (1995). Meaningful differences in the everyday experience of young American children. Baltimore: Paul H. Brookes. Retrieved January 20, 2025 from https://archive.org/details/meaningfuldiffer0000hart/page/n9/mode/2up.
Hart, B., & Risley, T. R. (2003). The Early Catastrophe. The 30 Million Word Gap. American Educator, 27(1), 4-9.
Institute of Education Sciences (IES). (2023). Annual reports: Kindergarten readiness. Retrieved January 13, 2023, from https://nces.ed.gov/programs/equity/domain_a.asp
International Association for the Evaluation of Educational Achievement. Trends in International Mathematics and Science Study (TIMSS), 1995, 2003, 2007, 2011, 2015, and 2019 Mathematics and Science Assessments. Washington, DC: Retrieved from National Center for Education Statistics TIMSS International Data Explorer, February 24, 2022, website: http://nces.ed.gov/timss/idetimss/
Khorramdel, L., Aldrich, C., & Bookbinder, A. (2024). Using scale anchoring to interpret TIMSS achievement results, Appendix 14A: TIMSS 2023 Scale Anchoring Item Descriptions – Grade 4 Mathematics. In M. v. Davier, B. Fishbein, & A. Kennedy (Eds.), TIMSS 2023 Technical Report: Methods and procedures (pp. 14.11-14.17). Boston: Boston College, TIMSS & PIRLS International Study Center. Retrieved from https://timss2023.org/wp-content/uploads/2024/11/1-1-3-8_ach-g4m-bmk.xlsx. doi: https://doi.org/10.6017/lse.tpisc.timss.rs6460
McClarty, K. L., Way, W. D., Porter, A. C., Beimers, J. N., & Miles, J. A. (2013). Evidence-Based Standard Setting: Establishing a Validity Framework for Cut Scores. Educational Researcher, 42(2), 59-108.
Ministry of Education. (2022). Nurturing early learners: A framework for a kindergarten curriculum in Singapore. Singapore: Retrieved from Pre-school Education Unit, Ministry of Education on February 2, 2025, website: https://ncm.gu.se/media/kursplaner/andralander/singaporeforskola.pdf
Ministry of Education. (2023). Nurturing early learners – A curriculum framework for preschool education in Singapore. Singapore: Retrieved from Ministry of Education, Republic of Singapore, on January 3, 2025, website: https://www.nel.moe.edu.sg/qql/slot/u143/2022/EG2022/Nurturing%20Early%20Learners%202022%20Educators%20Guide%20Numeracy.pdf
Moses, R. P., & Cobb, J., Charles E., . (2001). Radical equations: Civil rights from Mississippi to the Algebra Project. Boston, MA: Beacon Press.
Mullis, I. V. S., Martin, M. O., Foy, P., Kelly, D. L., & Fishbein, B. (2020). TIMSS 2019 international results in mathematics and science. Retrieved February 14, 2024, from https://timssandpirls.bc.edu/timss2019/international-results/
National Council of Teachers of Mathematics. (2022). Mathematics in early childhood learning Retrieved January 14, 2024, from https://www.nctm.org/Standards-and-Positions/Position-Statements/Mathematics-in-Early-Childhood-Learning-2146936947/
North Carolina Department of Public Instruction. (2022). EOG mathematics achievement level ranges and descriptors. Retrieved March 26, 2025, from https://www.dpi.nc.gov/documents/accountability/testing/eog/eog-mathematics-achievement-level-ranges-and-descriptors/open
Reese, D. D. (2024a). About: How Zone Proxima Math works. Zone Proxima, Retrieved March 12, 2025, from https://math.zoneproxima.com/about/how-it-works
Reese, D. D. (2024b, December 3, 2024). ROOT(math success) = childhood + concrete analogs + challenges. Gathering 4 Gardner 15. Retrieved December 3, 2024, from https://g4gexchangearchive.omeka.net/items/show/1672
Reese, D. D. (in press). Aha! moment identification: Building the early childhood mathematics library for mentor and AI training.
Ritchie, S. J., & Bates, T. C. (2013). Enduring Links From Childhood Mathematics and Reading Achievement to Adult Socioeconomic Status. Psychological Science, 24(7), 1301-1308. doi: 10.1177/0956797612466268
Stern, C. (1953). Children discover arithmetic: An introduction to structural arithmetic. London: George G. Harrap & Co.
Technical Panel on 12th-Grade Preparedness Research. (2008). Making new links: 12th grade and beyond. Retrieved March 17, 2025, from https://files.eric.ed.gov/fulltext/ED507257.pdf
U.S. Department of Education. (2010). College- and career-ready standards and assessments. Retrieved March 4, 2025, from https://www.ed.gov/media/document/college-careerpdf-101084.pdf
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[i]This report compiles TIMSS fourth grade mathematics benchmark achievement percentages from 1995 – 2023, by year and testing jurisdiction (e.g., country). Initially, I wanted to update Zone Proxima presentation and publication materials (1995 – 2019) with the most recent TIMSS data (2023) using a relatively quick process via a Department of Education analysis and reporting tool. However, the tool had not been updated to include 2023, and federal funding for updates is currently unavailable. So, in January 2025, I began the work of replicating the reporting tool’s functionality to produce my own version of an updated product. At the same time, I had been investigating data from North Carolina end-of-grade mathematics testing and National Assessment of Educational Progress (NAEP) testing. The education assessments, federal and state practices, and laws stressed measurement/assessment and importance of college- and career-readiness: readiness at graduation from high school and on track for college- and career-readiness at younger grades. National data and state data reveal that many students’ prospects and fulfillment are threatened because they are not academically prepared to be on track for the academic components of college- and career-readiness: they lack preparedness. This report organizes grade 4 1995–2023 data by proficiency thresholds to explore the state of academic preparedness for college- and career-readiness. In jurisdictions across the globe, what percentages of fourth grade students test as prepared/on track for college- and career-readiness? Two threshold scenarios are provided. One sets a higher threshold for preparedness/on-track (between low and intermediate TIMSS benchmarked achievement). The other sets a lower threshold (between intermediate and high TIMSS benchmarked achievement). The charts support longitudinal analysis and comparisons among jurisdictions.
[ii] Corresponding author: Debbie Denise Reese, PhD, ceo@zoneproxima.com, Box 28, Marble, NC. 28905.
[iii] Zone Proxima hosts this documentation with permission of IEA, granted March 28, 2025.
[iv] Zone Proxima hosts this documentation with permission of IEA, granted March 28, 2025.
[v] The Purchase Power Parity (PPP) method “converts each country’s data into International Dollars (INT$), an imaginary currency designed to make country-to-country comparisons easier” (World Population Review, 2025b). Tax laws and other factors could inflate some GDP measures. Considering both GNI and GDP calculations may provide a more accurate representation.