## Key Ideas > [!abstract] Core Concepts > > - **False dichotomy between explicit and non-explicit**: Effective mathematics education requires explicit teaching for foundations before problem-solving applications > - **Progressive approaches cause cognitive overload**: Real-world contexts overwhelm novice learners who lack foundational knowledge > - **Explicit teaching as whole system**: Not just token instruction but comprehensive planning, teaching, and assessment approach ## Definition **Maths Wars**: Ideological divide between explicit instruction (systematic teaching of discrete skills) and non-explicit teaching (discovery through meaningful contexts) in mathematics education. ## Connected To [[Reading Wars]] | [[Explicit Teaching]] | [[Non-Explicit Teaching]] | [[Logical Fallacies]] | [[Cognitive Load Theory]] | [[Knowledge-Based Curriculum]] | [[Problem-Solving]] --- The term "maths wars" refers to the ideological divide between two primary approaches to mathematics teaching: [[Explicit Teaching|explicit instruction]] and [[Non-Explicit Teaching|non-explicit teaching]]. This debate often presents a [[Logical Fallacies|false dichotomy]]. Effective mathematics education does not require balance between approaches but rather appropriate sequencing: explicit teaching must lay the foundational knowledge before students can meaningfully engage in [[Problem-Solving|problem-solving]]. ## Historical development ### New Math era (1950s-1970s) Following the Soviet Union's 1957 Sputnik launch, the U.S. National Science Foundation funded development of new mathematics curricula as part of a broader science education initiative (Phillips, 2015). The 1958 National Defense Education Act provided additional funding for mathematics education reform. New Math curricula emphasised conceptual understanding of mathematical principles and de-emphasised computational skills. The approach featured set theory concepts and terminology as foundational elements, and transformation geometry replaced traditional Euclidean geometry. By the mid-1960s, over half of U.S. high schools had adopted some form of New Math curriculum, rising to approximately 85% of all schools (K-12) by the mid-1970s. Parents and teachers opposed New Math on the grounds that the curriculum was too abstract and removed from students' ordinary experience. The material placed new demands on teachers, many of whom were required to teach content they did not fully understand. A 1967 five-year study showing American students lagging in mathematics skills among Western nations damaged New Math's credibility. By the early 1970s, opinion polls indicated Americans favoured a "Back to Basics" approach emphasising computation, formulas, and mathematical laws. ### Back to Basics movement (1970s-1980s) The Back to Basics movement emerged as a direct reaction to New Math's perceived failures. Some states and school districts introduced minimum competency testing as requirements for grade promotion or graduation. Schools devoted more classroom time to language arts and mathematics, reintroduced phonics instruction, and required regular homework with emphasis on neatness and decorum. By the mid-1970s, New Math had fallen out of favour, as students' performance on standardised mathematics tests did not improve as expected. However, a late-1970s study of U.S. schools concluded that "there appears to be little change in mathematics instruction in grades K-12" and "the single textbook is still the primary source of mathematics curricula," suggesting limited implementation of either approach. ### NCTM Standards era (1989-present) In 1986, the National Council of Teachers of Mathematics (NCTM) Board of Directors commissioned the Curriculum and Evaluation Standards for School Mathematics, published in 1989. This document launched the current era of standards-based educational reform in mathematics. The NCTM employed a consensus process involving classroom teachers, mathematicians, and educational researchers. The 1989 Standards emphasised that students need to learn more mathematics, learn new kinds of mathematics, and learn mathematics differently, with problem-solving as the major thrust. The standards promoted equity and mathematical power for all students, encouraged calculator use and manipulatives, and de-emphasised rote memorisation. Education officials supported these standards, and the National Science Foundation funded several curriculum development projects aligned with the standards' recommendations. However, by the late 1990s, the 1989 standards generated considerable controversy, focused on specific instructional materials developed in alignment with the standards. These debates became known as the modern "math wars." ### California controversy (1997) In 1997, the group Mathematically Correct was created by educators, parents, mathematicians, and scientists concerned about reform mathematics curricula based on NCTM standards. Although the organisation had a national scope, much of its focus was on opposing mathematics curricula prevalent in California in the mid-1990s, making California the centre of the Math Wars. Mathematically Correct opposed most programmes developed from National Science Foundation-funded research projects. The group objected to the integrated approach taken by California's draft mathematics standards, arguing there was little research to support it and advocating for "only a proven, research-based curriculum." On 11 December 1997, the California State Board of Education approved the California Mathematics Academic Content Standards for Grades K-12. ## Contrasting approaches The two approaches differ in philosophy, sequencing, and cognitive impact. [[Non-Explicit Teaching|Non-explicit teaching]] follows progressive, discovery-based philosophy where novice mathematics learners encounter mathematics in meaningful contexts such as real-world scenarios. This approach introduces real-world contexts first, then addresses foundational skills. [[Explicit Teaching]] follows systematic, knowledge-building philosophy that teaches discrete knowledge and skills before asking students to problem-solve. This approach establishes foundational skills first, then applies them to contexts. Non-explicit teaching creates predictable [[Cognitive Load Theory|cognitive overload]] because students must simultaneously grapple with unfamiliar mathematical concepts whilst navigating complex contextual information. Explicit teaching manages working memory limits by separating skill acquisition from application. Non-explicit approaches disadvantage struggling students who lack compensatory support outside school, whilst explicit instruction benefits all students, especially those from disadvantaged backgrounds. The literature shows overwhelming consensus that mathematics knowledge must be explicitly and systematically taught, otherwise student outcomes suffer across the board, especially for children from disadvantaged backgrounds who lack compensatory support outside school. The more recent iteration of non-explicit teaching is "launch, explore, summarise", which incorporates token amounts of explicit teaching. This superficial inclusion allows advocates to claim they use explicit instruction whilst maintaining progressive structures that undermine systematic knowledge building. Genuine explicit teaching requires a whole system that incorporates planning, teaching, and assessment over the short, medium, and long term. The curriculum is [[Knowledge-Based Curriculum|knowledge-based]], not resource-based or activity-based, driven by what students need to learn rather than what materials or activities seem engaging. ## Research evidence Research on standards-based reform mathematics curricula has found that students using these curricula perform as well as students in traditional programmes on measures of computational skill and procedural knowledge. Students using reform curricula perform better on assessments of conceptual understanding and ability to use mathematics to solve problems (Schoenfeld, 2004). Communities that adopted reform curricula generally saw increases in students' mathematics test scores. However, correct implementation of reform curricula was essential to achieving these outcomes. Research demonstrates an iterative relationship between conceptual understanding and procedural skill. Children's initial conceptual knowledge predicts gains in procedural knowledge, and gains in procedural knowledge predict improvements in conceptual knowledge (Rittle-Johnson & Alibali, 1999). This finding suggests that procedural skill and fluency develop more effectively with a sound grounding in conceptual understanding. The 2008 National Mathematics Advisory Panel examined the debate and recommended a balanced approach between reform and traditional mathematics teaching styles, rather than continuation of ideological conflicts between proponents of the two approaches (National Mathematics Advisory Panel, 2008). ## Scientific vs political resolution The maths wars, like the reading wars, suffer from treating educational disputes as political rather than scientific questions (Stanovich & Stanovich, 2003). Educational practice has suffered because its dominant model for resolving disputes has been more political (with corresponding factions and interest groups) than scientific. The field's failure to ground practice in the attitudes and values of science has made educators susceptible to fads and gimmicks that ignore evidence-based practice. The "anything goes" mentality that characterises much progressive mathematics teaching represents a threat to professional autonomy. It provides a fertile environment for untested educational remedies that are not supported by an established research base. Teachers need quality control mechanisms to evaluate claims about teaching methods, and peer-reviewed research journals in educational psychology and mathematics education provide those mechanisms (Gersten, 2001). The converging evidence from multiple methodologies: experimental studies, quasi-experimental designs, meta-analyses, and classroom research, consistently supports systematic, explicit instruction in mathematics. Stockard et al. (2018) conducted a meta-analysis of a half century of research on direct instruction curricula, finding strong positive effects (effect size = 0.59) across diverse student populations and settings. This convergence gives educators confidence that explicit teaching represents research-based practice rather than ideological preference. When research findings are amalgamated through meta-analysis, clear patterns emerge that are obscured when looking at individual studies. Meta-analysis is useful for ending disputes that seem to be nothing more than a "he-said, she-said" debate, providing a way of dampening contentious disputes about conflicting studies that plague education (Stanovich & Stanovich, 2003). ## References Gersten, R. (2001). 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