## Key Ideas > [!abstract] Core Concepts > > - **Evolved vs learnt knowledge**: Primary knowledge (language, walking) develops naturally without instruction, whilst secondary knowledge (reading, mathematics) requires deliberate teaching > - **Different instructional approaches needed**: Primary knowledge emerges through exposure and play, secondary knowledge needs explicit systematic instruction > - **Foundation for educational method selection**: Understanding this distinction helps teachers choose appropriate pedagogical approaches for different types of learning ## Definition **Biologically primary knowledge** refers to skills humans evolved to learn naturally through exposure, such as spoken language and walking (Geary, 2007). These abilities develop without formal instruction. **Biologically secondary knowledge** includes skills that emerged later in human history, such as reading, writing, and mathematics (Geary, 2008). These skills require deliberate teaching due to working memory limitations (Cowan, 2001; Sweller et al., 2019). The distinction informs educational method selection: teaching approaches suitable for primary knowledge (play-based exploration) may not be effective for secondary knowledge, where explicit, systematic instruction is most effective (Kirschner, Sweller, & Clark, 2006). ## Connected To [[21st Century Skills]] | [[Non-Explicit Teaching]] | [[Explicit Teaching]] | [[Cognitive Load Theory]] | [[Problem-Solving]] | [[Schema]] | [[Reading Wars]] | [[Situated Cognition]] --- ## Knowledge types ### Biologically primary knowledge Biologically primary knowledge and skills are those humans have evolved to learn (Geary, 2007). Most people learn to walk and acquire their native language without formal instruction. These abilities develop through natural exposure and interaction, appearing universally across human cultures at predictable developmental stages (Geary, 2007). Speaking a native language, walking, social interaction patterns, and general problem-solving strategies all develop without systematic instruction. General skills such as [[21st Century Skills]] are considered biologically primary. ### Biologically secondary knowledge Biologically secondary knowledge emerged later in human history, such as reading, writing, and mathematics (Geary, 2008). These skills are not naturally acquired and require conscious, deliberate effort to learn. Unlike primary knowledge, secondary knowledge does not occur naturally across cultures. Reading and writing, mathematical procedures and concepts, scientific principles and methods, and complex academic disciplines are cultural and historical products that require explicit, systematic instruction (Geary, 2008). The principles of [[Cognitive Load Theory]] apply when learning these skills, as working memory limitations constrain how much new secondary knowledge can be processed at once (Sweller et al., 2019). ## Biologically primary knowledge relevant to mathematics education ### Means-end analysis Means-end analysis involves comparing the current state of a problem with the desired outcome (Sweller, 1988). This innate problem-solving ability is evident in the Still Face Experiment, where infants try various strategies to regain their mother's attention (Tronick, Als, Adamson, Wise, & Brazelton, 1978). Whilst general problem-solving skills are biologically primary, teaching domain-specific knowledge is necessary for solving specific problems (Geary, 2007). ### Enumeration (subitising) Human infants and many animal species can enumerate or quantify small sets of items (three to four) without counting, a process known as subitising (Feigenson, Dehaene, & Spelke, 2004). This ability is automatic and quick, providing a foundation for number sense development in early mathematics education (Geary, 2007). ### Magnitude comparison Determining which of two numbers or quantities is larger or smaller becomes slower as the numbers increase in magnitude but faster and more accurate as the distance between the numbers increases (Moyer & Landauer, 1967). This natural ability provides a foundation for understanding number relationships and ordering. ### Addition and subtraction Human infants, preverbal children, and even chimpanzees can add and subtract items in small sets (up to three or four) (Wynn, 1992; Boysen & Berntson, 1989). Whilst this primary knowledge provides a foundation for school-based arithmetic, most formal arithmetic skills, such as partitioning and understanding the base-10 system, are biologically secondary and require explicit teaching (Geary, 2008). ## Educational implications The primary-secondary distinction provides practical teaching guidance when teachers use it to select appropriate instructional methods for different content types. Primary knowledge emerges through natural exposure and play-based learning. Social skills, for instance, develop through interaction during play. In contrast, secondary knowledge requires explicit, systematic instruction because it demands conscious learning effort. Teaching multiplication algorithms, for example, needs direct instruction rather than discovery approaches. ### Early years considerations [[Non-Explicit Teaching|Play-based learning]] may be effective in the early years when students draw on biologically primary knowledge such as subitising and adding or subtracting small quantities. As children progress, however, biologically secondary knowledge should be [[Explicit Teaching|explicitly]] taught to overcome the limits of [[Cognitive Load Theory|working memory]]. ### Common misconceptions No one is a "natural" mathematician (Geary, 2008). If some students grasp new concepts more quickly, it is likely because they have pre-existing [[Schema|schema]] to draw from, not innate mathematical ability (Chi, Feltovich, & Glaser, 1981). Attempts to teach biologically secondary knowledge through primary methods (discovery, exploration) often fail because they ignore the learning differences between the two knowledge types (Kirschner et al., 2006). ## Research connections ### Reading development The [[Reading Wars]] exemplify this distinction (Geary, 2007). Children naturally acquire oral language through exposure, as speaking is biologically primary. Reading, however, is biologically secondary and requires explicit phonics instruction and systematic practice (National Reading Panel, 2000). ### Mathematics education Young children naturally develop small number recognition (subitising) (Feigenson et al., 2004), basic quantity comparison (Moyer & Landauer, 1967), and simple addition and subtraction with small numbers (Wynn, 1992). These abilities form the biologically primary foundations of mathematics (Geary, 2007). Formal mathematics, however, requires explicit teaching of place value systems, algorithmic procedures, abstract mathematical relationships, and complex problem-solving strategies (Geary, 2008). ### 21st century skills debate [[21st Century Skills]] like creativity, critical thinking, and collaboration are largely biologically primary. They develop naturally through appropriate experiences rather than direct instruction (Geary, 2007). Applying these skills in academic domains, however, requires substantial biologically secondary knowledge (Willingham, 2007). ## Practical examples Language development illustrates the distinction clearly. Children naturally learn to speak (primary) but need explicit instruction for reading and writing (secondary). Similarly, children naturally subitise small quantities (primary) but need systematic teaching for place value and algorithms (secondary). Problem-solving follows the same pattern: children naturally use trial-and-error strategies (primary) but need explicit instruction in domain-specific mathematical procedures (secondary). ## References Boysen, S. T., & Berntson, G. G. (1989). Numerical competence in a chimpanzee (*Pan troglodytes*). *Journal of Comparative Psychology*, 103(1), 23-31. https://doi.org/10.1037/0735-7036.103.1.23 Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. *Cognitive Science*, 5(2), 121-152. https://doi.org/10.1207/s15516709cog0502_2 Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. *Behavioral and Brain Sciences*, 24(1), 87-114. https://doi.org/10.1017/S0140525X01003922 Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. *Trends in Cognitive Sciences*, 8(7), 307-314. https://doi.org/10.1016/j.tics.2004.05.002 Geary, D. C. (2007). Educating the evolved mind: Conceptual foundations for an evolutionary educational psychology. In J. S. Carlson & J. R. Levin (Eds.), *Psychological perspectives on contemporary educational issues* (pp. 1-99). Information Age Publishing. Geary, D. C. (2008). An evolutionarily informed education science. *Educational Psychologist*, 43(4), 179-195. https://doi.org/10.1080/00461520802392133 Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. *Educational Psychologist*, 41(2), 75-86. https://doi.org/10.1207/s15326985ep4102_1 Moyer, R. S., & Landauer, T. K. (1967). Time required for judgements of numerical inequality. *Nature*, 215(5109), 1519-1520. https://doi.org/10.1038/2151519a0 National Reading Panel. (2000). *Teaching children to read: An evidence-based assessment of the scientific research literature on reading and its implications for reading instruction*. National Institute of Child Health and Human Development. Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. *Cognitive Science*, 12(2), 257-285. https://doi.org/10.1207/s15516709cog1202_4 Sweller, J., van Merriënboer, J. J. G., & Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. *Educational Psychology Review*, 31(2), 261-292. https://doi.org/10.1007/s10648-019-09465-5 Tronick, E., Als, H., Adamson, L., Wise, S., & Brazelton, T. B. (1978). The infant's response to entrapment between contradictory messages in face-to-face interaction. *Journal of the American Academy of Child Psychiatry*, 17(1), 1-13. https://doi.org/10.1016/S0002-7138(09)62273-1 Willingham, D. T. (2007). Critical thinking: Why is it so hard to teach? *American Educator*, 31(2), 8-19. Wynn, K. (1992). Addition and subtraction by human infants. *Nature*, 358(6389), 749-750. https://doi.org/10.1038/358749a0 ---