## Key Ideas > [!abstract] Core Concepts > > - New knowledge integrates with existing schemas. Missing or incorrect prior knowledge prevents learning > - Teachers must identify, assess, and ensure fluency in prerequisite knowledge before teaching new concepts > - The Curse of Knowledge blinds teachers to prerequisite networks that novices must build ## Definition **Prior Knowledge**: Existing knowledge, skills, and schemas that students bring to new learning, which forms the foundation for integrating and understanding new information. ## Overview Prior knowledge affects learning outcomes (Dochy, Segers, & Buehl, 1999). When students lack necessary prerequisite knowledge, new learning is difficult regardless of instruction quality. New knowledge must integrate with existing understanding stored in long-term memory as schemas (Anderson, 1977; Bartlett, 1932). When prerequisite schemas are missing, defective, or inaccessible, learning is impeded. Prior knowledge assessment involves identifying what students need, assessing what they possess, and addressing deficiencies. ## Connected To [[Schema]] | [[Cognitive Load Theory]] | [[Constructivism]] | [[Chunking]] | [[Misconceptions]] | [[Fluency]] | [[Part-whole approach]] | [[Experts and Novices Think Differently]] | [[Curse of Knowledge]] | [[Memory]] --- ## Why prior knowledge determines learning possibility Prior knowledge is the foundation without which new learning cannot occur. ### The constructivist reality: knowledge builds on knowledge Learning differs from direct transmission models. Instead, learning follows constructivist principles (Anderson, 1977): **New knowledge must attach to existing knowledge**: Students integrate new information with existing [[Schema|schemas]] in long-term memory. They use vocabulary, concepts, and relationships they already understand to make sense of new content. When teaching algebraic equations, you build on students' understanding of arithmetic operations, equality concepts, and number properties. Without these foundations, the instruction literally makes no sense-students lack the conceptual framework needed to interpret what you're teaching. **Missing foundations prevent integration**: If existing schemas are deficient or absent, new information has nowhere to attach. It might enter [[Memory|working memory]] temporarily, creating the illusion of understanding during the lesson, but fails to transfer into long-term memory because the integration cannot occur. The student processes isolated symbols or words without constructing coherent meaning. Teaching advanced content to students lacking prerequisites overwhelms them. The content exceeds their capacity to process not because they lack ability but because they lack the foundational knowledge required to make sense of it. ### Prior knowledge determines cognitive load [[Cognitive Load Theory]] illuminates precisely how prior knowledge affects learning capacity (Sweller, van Merriënboer, & Paas, 2019): **Strong prior knowledge reduces intrinsic load**: When students possess automated prerequisite knowledge, they can retrieve it effortlessly from long-term memory, treating complex information as chunked units (Miller, 1956). Solving $4a = 12$ imposes minimal cognitive load on a student with automated schemas for equality, algebraic notation, and inverse operations. **Missing prior knowledge multiplies intrinsic load**: The same problem overwhelms a student lacking these prerequisites. They must consciously process: What does the equals sign mean? What does 'a' represent? Is '4a' one thing or two? How does division work here? Why does dividing both sides maintain equality? Each element demands working memory resources, rapidly exceeding the 4-item capacity and making learning impossible (Cowan, 2001). With roughly 4 slots in working memory (Cowan, 2001), content requiring conscious processing of more than 4 novel elements cannot be learnt. Prior knowledge determines how many elements are novel versus automated, directly determining whether learning is possible within working memory constraints. ### Prior knowledge creates cumulative effects Prior knowledge enables learning and makes it progressively easier: **Existing knowledge attracts new knowledge**: Well-developed schemas facilitate related new learning (Dochy et al., 1999). Students with strong foundational knowledge find new related learning relatively easy because information connects readily to existing understanding, patterns become visible quickly, and integration occurs naturally. **Weak knowledge creates learning difficulties**: Conversely, students with weak or missing prior knowledge find learning progressively harder. New content seems disconnected and arbitrary, patterns remain invisible, and understanding develops slowly if at all. Students attempting to build new knowledge without the necessary foundations face ongoing difficulties. This creates cumulative advantage and disadvantage. Strong students accelerate whilst struggling students fall further behind (Stanovich, 1986). Strong students learn more easily not because they're inherently smarter but because their accumulated prior knowledge makes new learning easier. Meanwhile, weak students struggle more not because they're less capable but because missing prior knowledge makes learning harder. ## The hidden complexity problem: the Curse of Knowledge A major challenge in addressing prior knowledge stems from the systematic way expertise blinds teachers to prerequisite complexity. ### How the Curse of Knowledge operates The [[Curse of Knowledge]] creates a profound blind spot for expert teachers (Hinds, 1999): **Experts cannot experience novice thinking**: When you possess automated schemas for content, you literally cannot experience the cognitive load novices face (Chi, Feltovich, & Glaser, 1981). Your chunked knowledge makes the content feel simple-you retrieve vast prerequisite networks effortlessly, process multiple elements as single chunks, and see patterns invisible to novices. **"Simple" problems hide vast prerequisites**: What experts perceive as straightforward often rests on extensive prior knowledge they've forgotten acquiring. Consider solving $4a = 12$: **Expert perception**: "Trivially simple-divide both sides by 4." **Novice reality requires fluent understanding of**: - Equality symbol meaning and properties - Algebraic notation conventions (letters represent numbers) - Implicit multiplication representation (4a means 4 × a) - Inverse operation relationships (multiplication/division) - Maintaining equality principle (same operation to both sides) - Algebraic division procedures - Basic arithmetic facts (12 ÷ 4 = 3) - Simplification recognition (when the solution is complete) Each element demands conscious processing if not automated. What feels like 1-2 elements to the expert represents 7-8 to the novice-nearly double working memory capacity. ### Systematic underestimation of prerequisites The Curse of Knowledge causes teachers to systematically underestimate what students need: **Planning becomes dangerously optimistic**: When listing prerequisites, teachers typically identify only the most obvious ones, missing the numerous sub-skills and foundational concepts that students must have automated for learning to succeed. **Pacing becomes unrealistic**: Underestimating prerequisite complexity leads to unrealistic expectations about how quickly students should learn. "They should be able to do this-it's simple!" reflects expert perception, not novice reality. **Explanations skip essential steps**: Teachers often omit explanation steps that feel "too obvious to mention"-precisely the steps novices most need because they haven't automated those schemas. **Student struggles seem mysterious**: When students fail to learn despite "clear" instruction, teachers puzzle over what's wrong. The issue often isn't the current instruction but missing prerequisites that remain invisible to expert teachers. ## Four types of problematic prior knowledge Prior knowledge problems take distinct forms, each requiring different instructional responses. ### Type 1: missing knowledge **Characteristics**: Students lack essential prerequisites entirely-they've never encountered the concept or skill. **How it appears**: Blank stares, inability to begin tasks, guessing randomly, complete confusion about what's being asked. **Why it's problematic**: New content cannot integrate with non-existent foundations. Attempting to teach without these prerequisites wastes time-students process incomprehensible symbols or words. **Instructional response**: - Stop the planned lesson - Teach the missing prerequisite explicitly - Build to fluency before returning to original content - Accept that this takes time that cannot be rushed **Example**: Teaching division of fractions to students who don't understand fraction representation-they lack the foundational concept needed to make sense of the operation. ### Type 2: incorrect knowledge **Characteristics**: Students possess [[Misconceptions|misconceptions]]-what they "know" is wrong and actively interferes with learning (Vosniadou & Brewer, 1992). **How it appears**: Systematic errors following predictable patterns, confident incorrect answers, resistance to correction (because their understanding feels intuitively correct). Incorrect prior knowledge is worse than missing knowledge because students must unlearn faulty schemas before constructing correct ones (Chi, 2008). The defective schema feels correct to them, making it resistant to superficial correction. **Instructional response**: - Identify the specific misconception - Create cognitive conflict showing why it produces impossible results (Limón, 2001) - Explicitly teach the correct understanding - Provide extensive practice to replace the faulty schema - Monitor for reoccurrence under pressure **Example**: Students believing "multiplication always makes bigger" struggle with fraction multiplication because their prior knowledge actively predicts wrong answers. ### Type 3: incomplete knowledge **Characteristics**: Partial understanding that appears sufficient but breaks under pressure-gaps emerge when complexity increases. **How it appears**: Success with simple examples but failure with slight variations, correct procedures with supportive context but errors independently, inability to explain why methods work. **Why it's insidious**: Incomplete knowledge masquerades as adequate understanding during initial teaching. Students and teachers both believe learning has occurred, only discovering gaps later when building on this foundation. **Instructional response**: - Deepen understanding through varied examples - Require explanation to reveal gaps - Practice in diverse contexts to build robustness - Test transfer to ensure knowledge is truly usable **Example**: Students can add fractions when denominators are given but cannot find common denominators independently-their fraction understanding is incomplete, missing essential components. ### Type 4: inaccessible knowledge **Characteristics**: Students possess knowledge but cannot retrieve it fluently when needed-they recognise concepts but cannot recall or apply them (Tulving & Thomson, 1973). **How it appears**: "I learnt this before but can't remember," recognition when prompted but no independent retrieval, success when given hints but failure without support. **Why it's problematic**: Inaccessible knowledge creates the illusion of readiness. Students did learn the content previously, but without sufficient practice to automate retrieval, it remains unavailable when needed (Ericsson & Kintsch, 1995). During new instruction, working memory gets consumed retrieving prerequisites that should be automatic. **Instructional response**: - Provide extensive retrieval practice (Roediger & Karpicke, 2006) - Build fluency through distributed practice (Cepeda et al., 2006) - Reduce complexity until retrieval becomes automatic - Accept that knowing and automated knowing differ (Ericsson & Kintsch, 1995) **Example**: Students who "learnt" multiplication facts but must still consciously calculate them-the knowledge exists but isn't fluent enough to free working memory for new learning. ## Systematic prerequisite assessment: a four-step process Addressing prior knowledge requires systematic process, not assumptions about what students should know. ### Step 1: identify prerequisites during planning **The task**: List all knowledge, skills, and concepts students must have fluent before new learning can occur. **How to combat Curse of Knowledge**: - Perform the task yourself, noting every piece of knowledge you use - Assume students need explicit instruction in everything that isn't automated - Consult curriculum progressions to see what's been taught previously - Consider what errors would indicate if specific prerequisites are missing - Err toward over-identifying rather than under-identifying **Document comprehensively**: Create explicit prerequisite lists for all units and major lessons. This protects against forgetting to check knowledge that seems "too basic to mention." **Common mistake**: Listing only major concepts whilst ignoring foundational sub-skills and conceptual understanding. Remember that what feels like one element to an expert often represents numerous elements for novices. ### Step 2: assess fluency, not just familiarity **The task**: Determine whether students can retrieve and apply prerequisites automatically, not just whether they've encountered them. **Critical distinction**: Recognition differs from fluent recall and application (Tulving & Thomson, 1973). Students might nod when you mention a concept (recognition) yet be unable to use it independently (fluent recall). **Diagnostic question principles**: - Test application, not vocabulary recognition - Require speed appropriate for automated knowledge - Include varied contexts to assess flexibility (Chi et al., 1982) - Use wrong answers to reveal specific gaps or misconceptions - Assess whole class, not volunteers who likely have strongest knowledge **Example**: Instead of "Who remembers what equivalent fractions are?" (recognition), use: "Show me three fractions equivalent to $\frac{2}{3}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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