quot; (application requiring fluent knowledge). ### Step 3: secure deficient prerequisites before proceeding **The decision point**: When assessment reveals deficient prior knowledge, teach it before continuing with planned content. **This requires difficult choices**: - **Accept curriculum delays**: Teaching prerequisites takes time. Running out of curriculum time is preferable to teaching content students cannot learn. - **Prioritise ruthlessly**: If time is limited, focus on most essential prerequisites. Some content might need omitting entirely. - **Resist the temptation to continue**: "We'll pick this up as we go" rarely works. If students lack prerequisites, they will learn nothing from new instruction, wasting all the time spent on it. **How to teach prerequisites effectively**: - Teach explicitly-students have already failed to learn this through discovery - Focus on fluency, not just accuracy-prerequisites must automate - Address misconceptions properly through cognitive conflict - Practice until retrieval becomes effortless - Check retention before resuming original content **Common resistance**: "But they should already know this!" Whether they should is irrelevant-if they don't, new learning cannot occur. Focus on what is, not what should be. ### Step 4: monitor prerequisite retention throughout **The ongoing task**: Ensure prerequisites remain accessible as new learning builds on them. **Why monitoring matters**: Knowledge that isn't retrieved regularly becomes less accessible (Cepeda et al., 2006). Students might have had fluent prerequisites at unit start but lost fluency by unit end if they haven't continued practicing. **Monitoring strategies**: - Include prerequisite questions in all assessments - Use warm-ups reviewing prior content (distributed practice) - Observe during practice for prerequisite errors - Reteach promptly when gaps emerge - Build systematic review into curriculum design (Rohrer & Taylor, 2007) **Addressing knowledge decay**: When prerequisite fluency degrades, pause new content to rebuild it. The lost time will be recovered through more efficient learning once foundations are secure. ## Special cases: common prerequisite challenges ### Challenge 1: wide variation in prior knowledge **The situation**: Some students possess strong prerequisites whilst others have significant gaps. **Why it's difficult**: Proceeding assumes readiness that some students lack. Reviewing extensively bores students who are ready whilst possibly still rushing students who need substantial foundational work. **Approaches**: - **Pre-teaching for struggling students**: Provide prerequisite instruction before the unit to groups needing it - **Parallel foundation building**: Some students work on prerequisites whilst others extend current understanding - **Careful task design**: Use [[Low-Floor High-Ceiling]] tasks accessible to students at different prerequisite levels - **Accept differentiation reality**: Students with vastly different prior knowledge need different instruction, not just faster/slower pacing of identical content **The equity imperative**: Students from disadvantaged backgrounds disproportionately lack the specific academic prior knowledge schools assume (Dochy et al., 1999), making systematic prerequisite teaching essential for equity. ### Challenge 2: misconceptions masquerading as knowledge **The situation**: Students confidently believe they understand when they actually possess systematic misconceptions. **Why it's dangerous**: Misconceptions actively interfere with new learning worse than missing knowledge. Students resist correction because their understanding feels correct. **Approaches**: - Use diagnostic questions with distractors representing common misconceptions - Create cognitive conflict demonstrating impossible results from faulty reasoning - Explicitly teach correct understanding, don't assume it emerges from exposing errors - Provide extensive corrective practice - Monitor for misconception reoccurrence under pressure **Example**: Students believing "multiplication makes bigger" will struggle with fraction multiplication until this misconception is explicitly corrected-simply showing examples won't overcome the defective schema. ### Challenge 3: the prerequisite chain **The situation**: Prerequisites themselves have prerequisites in long chains. Students missing early links cannot learn subsequent ones. **Why it compounds**: Missing one element makes the next impossible to learn, creating cascading failure where gaps widen over time. **Approaches**: - **Work backward systematically**: When students lack a prerequisite, check whether they have its prerequisites - **Identify the actual starting point**: Begin instruction where students actually are, not where the curriculum assumes - **Build systematically forward**: Ensure each prerequisite is fluent before adding the next - **Accept the time investment**: Filling fundamental gaps takes time but enables all subsequent learning **The difficult reality**: Students with major prerequisite gaps might need returning to content from years earlier. ## Implications for curriculum design Understanding prior knowledge transforms how curricula should be designed and sequenced. ### Explicit prerequisite mapping **The need**: Every curriculum unit should explicitly identify what students must know before beginning. **Implementation**: - Document prerequisites for all major concepts - Map prerequisite relationships showing what builds on what - Make this visible to teachers so they know what to check - Include guidance on assessing and building identified prerequisites **Benefit**: Transforms prerequisite assessment from teacher intuition to systematic process. ### Spiralling vs. mastery approaches **The tension**: Spiralling curricula revisit content repeatedly at increasing depth. Mastery approaches teach to fluency before advancing. **Prior knowledge implications**: - Spiralling can work if initial exposure builds sufficient foundation for subsequent spirals - Spiralling fails when initial exposure leaves knowledge too weak to build on-each spiral finds students unready - Mastery approach ensures prerequisites are secure before building on them - Mixed approaches work: mastery of foundations, then spiralling for deepening **The key principle**: Don't advance to content requiring prerequisites until those prerequisites are automated, regardless of curriculum structure. ### Building time for assessment and remediation **The reality**: If curricula assume all students possess prerequisites, no time exists for teaching students who don't. **Design requirement**: - Build prerequisite assessment into unit timing - Allocate time for teaching identified gaps - Accept this might mean less total content covered - Recognise that teaching without prerequisites wastes all the allocated time anyway **The trade-off**: Better to teach less content that students actually learn than rush through more content that students cannot access due to missing prerequisites. ## Practical strategies for everyday teaching Understanding prior knowledge changes daily instructional decisions. ### Before each lesson **Quick prerequisite checks**: - "Show me on mini-whiteboards..." for immediate whole-class assessment - Quick application tasks testing prerequisite fluency - Observation during starter activities revealing gaps - Asking students to explain prerequisites, not just acknowledge them **Responsive planning**: - Prepare contingency plans for common prerequisite gaps - Know how you'll adjust if assessment reveals deficiencies - Have materials ready for reteaching common prerequisites ### During instruction **Monitor continuously for prerequisite failures**: - Errors suggesting specific prerequisite gaps - Widespread confusion indicating missing foundations - Success with support but failure independently suggesting weak prior knowledge **Respond promptly**: - Stop and address identified gaps before continuing - Reteach prerequisites explicitly - Provide immediate practice to build fluency - Check understanding before resuming ### After assessment **Analyse errors for prerequisite indicators**: - Systematic patterns revealing specific gaps - Random errors suggesting unstable understanding - Context-dependent success/failure indicating weak prior knowledge **Plan remediation systematically**: - Group students by prerequisite needs - Provide targeted instruction in identified gaps - Ensure fluency before reteaching dependent content - Monitor to confirm prerequisites are now secure ## Conclusion: prior knowledge as the foundation for learning Prior knowledge determines learning possibility in ways that make it a critical factor teachers can influence (Dochy et al., 1999). New learning doesn't occur in a vacuum, it must integrate with existing schemas in long-term memory (Anderson, 1977). When those schemas are missing, defective, or inaccessible, learning becomes impossible regardless of how clearly teachers explain or how hard students try. The Curse of Knowledge makes addressing prior knowledge challenging (Hinds, 1999). Expert teachers literally cannot experience the cognitive load novices face because their automated schemas make content feel simple (Chi et al., 1981). This systematic blind spot causes underestimation of prerequisite complexity and unrealistic expectations about student readiness. The solution requires systematic process: explicitly identify prerequisites during planning, assess student fluency rather than assumed knowledge, teach identified gaps before proceeding with new content, and monitor prerequisite retention throughout learning (Cepeda et al., 2006). This approach demands accepting curriculum delays, prioritising ruthlessly, resisting the temptation to continue when students aren't ready. The equity implications are substantial. Students from disadvantaged backgrounds disproportionately lack the specific academic prior knowledge schools assume, making systematic prerequisite teaching essential for educational equity. Curricula that assume rather than build prior knowledge advantage those who arrive with extensive background knowledge whilst leaving others further behind (Stanovich, 1986). For teachers committed to ensuring all students learn successfully, understanding prior knowledge changes practice. It shifts focus from covering content to building foundations, from assuming readiness to systematically ensuring it, from hoping students can keep up to making certain they're prepared for each new challenge. This foundation makes everything else possible, or its absence makes everything else futile. > [!tip] Implications for Teaching > > - **Identify prerequisites explicitly** when planning units and major lessons-don't rely on intuition about what students need > - **Assess prerequisite fluency** through application tasks, not recognition questions-students must retrieve knowledge automatically, not just remember learning it > - **Teach identified gaps before proceeding** even if it delays curriculum-students will learn nothing from content they lack prerequisites for > - **Combat Curse of Knowledge** by systematically analysing task complexity from novice perspective, not expert perception > - **Build to fluency, not just accuracy**-prerequisites must be automated to free working memory for new learning > - **Monitor prerequisite retention** throughout units-knowledge that isn't retrieved regularly becomes inaccessible > - **Accept that prerequisite teaching takes time** that cannot be rushed-the investment enables all subsequent learning ## References Anderson, R. 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