Use Case 2 Brazil: Zone Proxima 1995-2023 TIMSS Grade 4 Math Charts

—Debbie Denise Reese, PhD, CEO—Zone Proxima, LLC

Corresponding author: Debbie Denise Reese, PhD, ceo@zoneproxima.com, Box 28, Marble, NC. 28905. 

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Well-designed charts and tables provide clear consolidation and presentation of data. The visualizations can be useful and efficient for validating and refuting claims. In 2025, the World Population Review Newsletter posted “Think School is Broken? Not in These Countries. Where the brightest futures are being shaped—and how to join them” (Saparov, 2025). Saparov lauded a number of countries for their academic initiatives and results. The section ‘Latin America’s Quiet Education Leap’ featured Brazil’s early childhood education policy: mandatory and free early childhood education starting at age 4, free childcare from birth. Did Brazil’s early childhood education policy increase mathematics achievement? What do the data reveal? Since 1995, the Trends in International Math and Science Study (TIMSS) has provided a rich, reliable, and validated source of mathematics achievement data. Worldwide assessments of mathematics achievement at grade 4 are an indicator of the academic effects of early childhood education. The Zone Proxima 1995-2023 TIMSS Grade 4 Math Charts report TIMSS test results by year, proficiency level, and testing jurisdiction. Jurisdictions are participating educational systems. These may be countries or smaller regions such as the province of Quebec.  The Charts are a quick go-to for investigating claims regarding countries of the World and mathematics academic achievement. What facts do the Zone Proxima TIMSS Charts provide about Brazil’s mathematics achievement by grade 4, between 1995 and 2023? What are the trends? Has achievement spiked? The charts provide a first look that might motivate deeper investigation.

It’s simple to check the Zone Proxima TIMSS Charts: Just download the two PDF files (see Figure 1 for links) and locate the Brazil pages and any others you wish to compare.

What Are the Zone Proxima TIMSS Charts?

The U.S. Department of Education’s web-based International Data Explorer supported investigation of grade 4 mathematics achievement as measured by the 1995 – 2019 Trends in International Mathematics and Science Study (TIMSS) assessment cycles. When the U.S. Department of Education announced it was not funded for the 2025 update to the International Data Explorer (L. Malley, personal communication, February 24, 2025), Zone Proxima’s research staff prepared the 1995 – 2023 Trends in International Mathematics and Science Study (TIMSS) grade 4 mathematics benchmarked achievement and proficiency charts (High Proficiency Threshold, Low Proficiency Threshold) and report to fill that gap. The Zone Proxima Charts extend functionality by investigating preparedness/readiness: What do the data tell us about grade four student preparedness/readiness? By grade four, what percentage of students are on track for academic and career preparedness/readiness? Two versions of the Charts are available for download. One uses a higher, more conservative threshold for readiness: only the TIMSS scores in the advanced and high TIMSS achievement benchmark categories were considered on track. This is the “High Proficiency Threshold” version. The other uses a more relaxed standard, with the threshold set between Intermediate and Low TIMSS categories: the Low Proficiency Threshold version.

Are the Charts Useful?

Are these Charts and the Zone Proxima report useful for examining claims about mathematics achievement such as Saparov’s (2025) claims for Brazil’s accomplishment?

1. If you haven’t already, please download the TIMSS 1995-2023 Charts (see Figure 1).

2. Review the report TIMSS 1995-2023: Zone Proxima Charts Investigate Fourth Grade Mathematics Preparedness via Benchmarks within Year and by Testing Jurisdiction (Reese, 2025). Within the report, the section “Case of Singapore” provided the first use case, an illustration of how a scholar or the public might use the Charts.  In this report, we describe another use case.

Saparov’s (2025) analysis spotlighted Brazil as “quietly [building] the future of education.” Addressing the reader as an “inquisitive architect of the future!” Saparov declared that Brazil was one of the nations “where young minds are thriving, innovation is the norm, and learning actually prepares kids and youngsters for the world they're inheriting.” And specifically, Brazil was “reforming early childhood education through a bold national funding.” Saparov invited us to “dive in and take a closer look at the classrooms changing everything.” So I dove in. I asked if the TIMSS Charts indicate Brazilian young people are achieving the mathematics skills, knowledge, and habits requisite for a future of opportunity. Are they on track for college- and career-readiness? I also allowed for a brief follow-up investigation: I could consult the literature if additional information were necessary to contextualize the TIMSS results. Together, these should provide enough insights to support or invalidate Mr. Saparov’s claim. 

Brazil Mathematics Achievement

Brazil’s only recorded TIMSS grade 4 mathematics participation was 2023 (see Table 1 and see Figures 2 and 3 for TIMSS Charts). Based on TIMSS results, in 2023 Brazil’s children had not shown stellar academic performance in mathematics. In fact, 50% of their grade 4 testees performed so poorly, no knowledge level was detected and no level of achievement could be classified.  Using a high proficiency threshold, only 5% were proficient and 95% lacked proficiency. Using a low proficiency threshold, 21% were proficient and 79% lacked proficiency. By any standards, these children are not on track for college- or career-readiness.

In 2015 using Brazil’s own mathematics assessment—the Basic Education Evaluation System, only 43% of students met mathematics learning standards at the end of grade five, 18% in grade nine, and 7% by last year of high school (Raikes, Alvarenga Lima, & Abuchaim, 2023). Thus, the TIMSS findings of 2023 were echoed in the country-level testing eight years prior.

The PISA Trends

The Programme for International Student Assessment (PISA) is another prominent international assessment of countries and economies, conducted triennially (due to the COVID-19 pandemic the 2021 PISA was delayed a year and rescheduled to 2022, OECD, 2023a, p. 16). Overseen by the Organisation for Economic Co-operation and Development (OECD), “PISA measures 15-year-olds’ ability to use their reading, mathematics and science knowledge and skills to meet real-life challenges” (OECD, 2025). PISA assessments

. . . explore how well students can solve complex problems, think critically and communicate effectively. This gives insights into how well education systems are preparing students for real life challenges and future success. (OECD, 2023c, p. 1)

Furthermore,

PISA measures student performance as the extent to which 15-year-old students near the end of their compulsory education have acquired the knowledge and skills that are essential for full participation in modern societies, particularly in the core domains of reading, mathematics, and science. (OECD, 2023b, p. 50)

Over the recent decades, the states of the United States led the development of the Common Core Standards for College- and Career-Readiness (Common Core State Standards Initiative, 2019). Although psychometrics have not rigorously matched PISA items with the concept/construct of college- and career-readiness and preparedness (for definitions and development of college- and career-readiness and preparedness, see, e.g., Camara, 2013; McClarty, Way, Porter, Beimers, & Miles, 2013; Smarter Balanced Assessment Consortium, 2018; Technical Panel on 12th-Grade Preparedness Research, 2008), the parallel between PISA goals and readiness are evident:

Preparedness represents the academic knowledge and skill levels in reading and mathematics necessary to be qualified for placement into a job training program . . . or into a credit-bearing entry-level general education course that fulfills requirements toward a two-year transfer degree or four-year undergraduate degree at a postsecondary institution. (Technical Panel on 12th-Grade Preparedness Research, 2008, p. 3)

The U.S. standards were developed “to ensure that all students are learning what they need to succeed,” and standards were to be based upon “evidence regarding what students must know and be able to do at each grade level to be on track to graduate from high school college- and career-ready (U.S. Department of Education, 2010, p. 2). The U.S. development teams often specified academic preparedness as a subset of readiness. Readiness was to also include habits of mind requisite for success, such as persistence, time management, and interpersonal skills (Technical Panel on 12th-Grade Preparedness Research, 2008). Development of the U.S. readiness standards was done with full consideration of the efforts and accomplishments of international scholars. In addition, the U.S. National Governors Association (NGA), Council of Chief State School Officers (CCSSO), and Achieve, Inc., specifically provided U.S. states “a roadmap for benchmarking their K-12 education systems to those of top-performing nations” (Technical Panel on 12th-Grade Preparedness Research, 2008, p. 33).  The U.S. identified five steps toward building a globally competitive education system (Jerald, 2008, pp. Table of Contents, 23-36):

1.  Adopt a common core of internationally benchmarked standards for mathematics, reading, and science.

2. Ensure textbooks, digital media, curricula, and assessments are aligned to the standards and “draw on lessons from high-performing nations and states.”

3. Revise policies for educators to reflect human capital practices of top-performing nations.

4. Ensure accountability for schools and systems.

5. Examine achievement in an international context, so students can compete in a “21st century economy.”

So, while the psychometrics to correlate the TIMMS, PISA, and college- and career-readiness are not reported (and most probably have not been conducted), the U.S. college- and career-readiness assessments and the PISA assessments work toward the common goal of measuring and predicting (a) college- and career-readiness and (b) lifelong personal and economic success for individuals, economies, and countries; that is, key knowledge and skills essential for full participation in social and economic life (OECD, 2023a, p. 38). The TIMSS Charts provide two possible thresholds for college- and career-readiness estimates.

Figure 4 plots PISA mathematics scores for Brazilian 15-year-olds from 2003 – 2022. To provide context, longitudinal scores are also plotted for the United States (a mid-range scoring educational system, OECD, 2023a, p. 52, Table I.52.51), the average of 23 OECD member countries,i and Singapore (the highest scoring country). On average, mathematics achievement on the PISA has been relatively stable over the past two decades, although achievement losses did coincide with the gap in face-to-face classes due to COVID-19. 

The Brazilian 15-year-olds tested in 2022 (see Figure 4) were the first cohort to complete PISA testing under Constitutional Amendment 59: obligatory preschool (Raikes et al., 2023). The law requiring four-year-olds to attend preschool passed in 2009. This is the timeline of events:

• 2007: PISA 2022 cohort born

• 2009: Constitutional Amendment 59—starting age for school = 4 (obligatory preschool)

• 2011: all children 4 years old were required to attend preschool (some locales were unable to provide these services)

• 2014: National Education Plan—by 2016 all schools were required to offer two years of preschool, enforcing Constitutional Amendment 59

• 2022: cohort reaches 15 years old and complete PISA

Even with the factors of COVID and Brazil’s Constitutional Amendment 59, PISA scores for Brazil were largely consistent from 2003 to 2022. The scores for USA, Singapore, and the PISA OECD average were also relatively consistent.

The TIMSS charts and the PISA results tell the same story. Brazil’s 15-year-olds are not academically on track to be prepared for a life of academic or personal success in a globally competitive economy. By grade five, at least half of the Brazilian students are not on track for education or career preparedness. Indeed, according to the 2023 TIMSS results, by grade four over 50% of Brazilian students do not score well enough to even reach a knowledge level category. Academically, at least, Brazil’s universal preschool does not appear to have increased mathematics preparedness. At this point, Brazil is hardly a poster child for shaping the brightest futures.

Contextualizing Legislation

Brazil guarantees free childcare and education from birth to age six (Jamet, Figueroa, & Tamassia, 2024; Raikes et al., 2023). In summary, the 1988 Brazilian Constitution of the civilian government, the Federal Republic of Brazil, legally specified early childhood education. The Federal Constitution declared early childhood education a right and a duty of the state (Raikes et al., p. 4). It designated the Ministry of Education responsible for the education of all children ages zero to six. In 2005, Brazilian Law 11.114 lowered the legal school starting age to six. In 2009 constitutional amendment 59 lowered the starting age to 4 years, legislating universal, mandatory preschool. In 2014, the National Education Plan required all schools to offer two years of preschool by 2016. 

However, these goals for education are set within the context of Brazilian socio-economic challenges. The Gini Index is a measure of equity, examining the distribution of family income in a country. The Gini reports on a scale

·      0 (worst) to 1 (best) or

·      0 (worst) to 100 (best) or

·      0% (worst) to 100% (best).

A Gini index of 0 would indicate perfect income equity, and an index of 1 or 100 or 100% would equal perfect inequity (e.g., one person holds all a country’s wealth). Brazil’s Gini Index,iii is 52% as calculated by either the U.S. CIA or the World Bank (see Table 3). Brazil has one of the World’s highest levels of socioeconomic disparity (Central Intelligence Agency, 2024).

Further investigation reveals that economic disparity, rural isolation, quality of local early education, and ineffective infrastructure plague an education path with noble legislative laws and processes (Jamet et al., 2024).

Curriculum: Play and Guided Discovery Learning

The Organisation for Economic Co-operation and Development (OECD) has taken a strong position that effective early childhood education will support a country’s global competitiveness (Jamet et al., 2024). OECD evaluates education systems via PISA. OECD also provides assistance throughout the World via policy reviews, country-specific reviews and notes, and international survey results through its early childhood education and care (ECEC) program. The ECEC recommends to Brazil that its economic revitalization requires initiatives that

. . . increase productivity, labour market participation and fiscal responsibility across government sectors while addressing gender disparities and social inequalities. A strategic investment in early childhood education and care (ECEC) can support achieving these goals [emphasis added]. (Jamet et al., 2024, p. 1).

To this end, Brazil had already established a National Common Core Curriculum in 2017 and set learning goals for Brazil’s childhood education (Raikes et al., 2023, p. 12):

1. Get along with other children and adults, developing a respect for other cultures and differences between people;

2. Learn through play;

3. Actively participate and have choice in activities;

4. Explore and learn concepts of art, language, mathematics, science and technology through multiple means and modalities and in various contexts;

5. Learn to express oneself through developing opinions and asking questions; and 

6. Develop a positive image of oneself and others.

This curriculum is proclaimed a child-centered policy for nurturing physically, cognitively, and affectively wholesome young children; and it seems Brazil’s early childhood education policy has set a path that privileges “play” (Raikes et al., 2023).

While it is laudable that the country of Brazil intends for young children’s natural curiosity and joy of learning to drive their early education, it seems absurd to think that the typical child could discover for himself or herself the mathematics that took the greatest minds of civilizations centuries to develop (Ausubel, Novak, & Hanesian, 1978, p. 475). Instead, during early childhood, children should discover mathematics foundations through guided discovery using apt concrete manipulatives and educators who have been trained and mentored to feature these manipulatives appropriately (e.g., Stern & Stern, 1971; Uttal, Scudder, & DeLoache, 1997).  That is, early childhood mathematics education providers should not expect their young children to recreate mathematics by themselves during unstructured free play. Instead, teachers or parents should guide children’s exploration of mathematics through sound, apt manipulatives and an equally sound guided-discovery curriculum (Gattegno, 1970; Stern & Stern, 1971; Uttal, 2003). This guided discovery is designed to provoke a child’s curiosity, and curiosity fosters academic achievement—especially for lower socio-economic youth who lack academically enriching environments and resources (National Association for the Education of Young Children (NAEYC) & National Council of Teachers of Mathematics (NCTM), 2002; National Council of Teachers of Mathematics, 2022; Shah, Weeks, Richards, & Kaciroti, 2018). Furthermore, these same manipulatives should be integrated throughout the years of elementary mathematics, building on the discovered foundations. New knowledge must build on older knowledge. Teachers should use the manipulatives (e.g., Cuisenaire Rods) to review old knowledge (gained during the early childhood mathematics guided discovery) and make connections to new knowledge. For example, Cuisenaire Rods can introduce fractions in early childhood and constantly reinforce and enhance understanding throughout elementary years (Gattegno, 1970, 2010).

Conclusion and Discussion

As the case of Brazil demonstrates, early childhood day care and preschool access and participation are not enough to prepare young children for mathematics learning and college- and career-readiness. Where the mathematics curricular focus is, as in Brazil, free play, then educators and caregivers desperately need an alert. A childhood of engagement and joy in mathematics discovery does not require that play lack direction or purpose. Early childhood mathematics learning requires guided discovery.  Renowned early childhood mathematics education experts Douglas H. Clements and Julie Sarama (2014) counsel that play versus early childhood mathematics education is a “false dichotomy”. Children should be guided to “play with mathematics” (p. 2). This requires adults–whether parents, educators, or caregivers–who are knowledgeable about effective pedagogy. Clements and Sarama decry the harm done to children when they are left to play and discover mathematics on their own. 

Zone Proxima research has identified effective pedagogy and concrete manipulatives (especially Cuisenaire Rods) and developed programs to mentor adults–parents, caregivers, and educators–to successfully guide young children to discover and apply foundational mathematics. The program is offered only in English, but it is available world-wide to individuals, to organizations, and governments at the local, regional, national levels. The Zone Proxima goal for this initiative is a universal norm whereby adults engage young children in effective and joy-filled mathematics discovery as an integral component of childrearing. Children prepared for mathematics are on track for college and career-readiness.

iOCED member countries: Austria, Australia, Belgium, Canada, Chile, Colombia, Costa Rica, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Korea, Latvia, Lithuania, Luxembourg, Mexico, the Netherlands, New Zealand, Norway, Poland, Portugal, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, Türkiye, the United Kingdom, and the United States.

iiSources. “PISA 2020 Results: Fact Sheets Brazil,” by OECD, 2023, PISA 2022 Results (Volume I and II). Copyright 2023 by OECD. Retrieved from https://www.oecd.org/content/dam/oecd/en/publications/reports/2023/11/pisa-2022-results-volume-i-and-ii-country-notes_2fca04b9/brazil_764ee0aa/61690648-en.pdf.

“PISA 2020 Results: Fact Sheets Singapore,” by OECD, 2023, PISA 2022 results (Volume I and II). Copyright 2023 by OECD. Retrieved from https://www.oecd.org/content/dam/oecd/en/publications/reports/2023/11/pisa-2022-results-volume-i-and-ii-country-notes_2fca04b9/singapore_604d4933/2f72624e-en.pdf

“PISA 2020 results: Fact Sheets United States”, by OECD, PISA 2022 results (Volume I and II). Copyright 2023 by OECD. Retrieved from https://www.oecd.org/content/dam/oecd/en/publications/reports/2023/11/pisa-2022-results-volume-i-and-ii-country-notes_2fca04b9/united-states_243107b0/a78ba65a-en.pdf

iiIThe Gini index measures

the extent to which the distribution of income (or, in some cases, consumption expenditure) among individuals or households within an economy deviates from a perfectly equal distribution. A Lorenz curve plots the cumulative percentages of total income received against the cumulative number of recipients, starting with the poorest individual or household. The Gini index measures the area between the Lorenz curve and a hypothetical line of absolute equality, expressed as a percentage of the maximum area under the line. Thus a Gini index of 0 represents perfect equality, while an index of 100 implies perfect inequality. (World Bank & Poverty and Inequality Platform, 2025, tab "metadata indicators")

 Concerning the “World Bank, Poverty and Inequality Platform:”

Data are based on primary household survey data obtained from government statistical agencies and World Bank country departments. Data for high-income economies are mostly from the Luxembourg Income Study database. For more information and methodology, please see pip.worldbank.org.” (World Bank & Poverty and Inequality Platform, 2025, tab "metadata indicators")

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