Designing a lesson around a hard problem: physics education research
Lead. A short lesson around one anchor problem should run in this order: commit to an answer on a conceptual question that exposes the likely error, compare two contrasting cases that differ in the one feature that matters, then get a short explicit explanation and a worked step, then solve small steps with feedback on each, then re-solve the anchor and a changed version alone. Each element has support, but mostly from university lecture halls and from short school experiments, not from Indian Grade 12 students. Attempting before being told helps conceptual understanding and transfer and leaves procedural skill about the same (Schwartz et al. 2011; Kapur and Roll 2023), but only when the attempt is followed by explicit instruction (Schwartz and Bransford 1998; Alfieri et al. 2011), and for tasks with many interacting steps the evidence leans toward telling first (Chen, Kalyuga and Sweller 2016). Conceptual and procedural knowledge feed each other (Rittle-Johnson, Siegler and Alibali 2001), and a conceptual floor seems to be needed before problem solving works (Hestenes, Wells and Swackhamer 1992), which supports a mastery check that tests both, unassisted. Students will feel they learned less from this kind of lesson than from a clear explanation, even when they learned more (Deslauriers et al. 2019), so the coach must never use a student’s feeling of understanding as a mastery signal.
Scope note. Every row below was opened and read in a downloaded copy on 2026-10-30. Most of this evidence comes from group classroom teaching (lecture halls, tutorial sections, school classes) where peer discussion and a live instructor are part of the treatment. The Avanti coach is one student and one AI. Elements that depend on peers transfer to the teacher’s class time, not to the coach. Kalyuga’s expertise reversal, worked examples, retrieval and feedback are covered in learning_science.md and AI tutor trials (including Kestin et al. 2025) in ai_tutors.md; they are not repeated here.
Evidence table
Section titled “Evidence table”| Study | Design and population | n | Effect (unit) | What it means for the coach |
|---|---|---|---|---|
| Hake 1998 | Survey of pre/post concept-test data, 62 intro mechanics courses in US high schools, colleges and universities; self-submitted data | 6,542 students; 14 high-school courses (1,113 students) | Average normalised gain 0.23 (SD 0.04) in 14 traditional courses vs 0.48 (SD 0.14) in 48 interactive-engagement courses; high-school interactive courses 0.55 (SD 0.11) | Interactive engagement raises conceptual gains, in schools as well as universities. The sample favours good courses, so treat the size as an upper bound |
| Crouch and Mazur 2001 | Ten years of course data, Harvard intro physics for non-majors; Peer Instruction vs traditional years; no randomisation | 117 to 246 per year | Calculus-based course: normalised FCI gain 0.25 (traditional 1990) vs 0.49 to 0.74 (Peer Instruction 1991-1997). Algebra-based: 0.40 traditional vs 0.65 and 0.63 with Peer Instruction. Mechanics Baseline problem test 66% (1990) vs 71-79% | Concept questions with a commit step did not cost problem-solving scores. Discussion helps most when 35-70% answer a question right at first |
| Deslauriers, Schelew and Wieman 2011 | Quasi-experiment, two sections of first-year calculus-based physics for engineers, University of British Columbia, one week | 267 and 271 | End-of-week test 74% vs 41% (guessing 23%); effect size 2.5 SD; attendance 75% vs 53%; engagement 85% vs 45% | Pre-class reading, concept questions, group tasks and immediate instructor feedback beat lecture on a short topic test. The test was author-written and the instructors differed, so the 2.5 SD is not a planning number |
| Deslauriers et al. 2019 | Randomised crossover, Harvard intro physics, two class meetings; active class solved problems in groups first, then got the same full solution the lecture class saw | 149 | Test of learning +0.46 SD for active; feeling of learning -0.56 SD for active | Attempt-then-solution beats solution-only, and students rate it worse. Self-reported understanding cannot gate mastery |
| Freeman et al. 2014 | Meta-analysis of active learning vs lecture, undergraduate STEM | 225 studies (158 on scores, 67 on failure) | Exam and concept-inventory scores +0.47 SD; odds ratio of failing under lecture 1.95; failure 21.8% vs 33.8%; larger on concept inventories than instructor exams; largest in classes of 50 or fewer | The broad case that doing beats listening. Undergraduate only; the “active learning” treatments vary widely |
| McDermott 2001 (Oersted lecture), with the University of Washington tutorial data reprinted there | Pre/post data from Tutorials in Introductory Physics, US undergraduates; graduate TAs as a comparison group; no control group | About 560 pretest, 405 post-test, 55 TAs on the example shown | Multi-slit interference item: correct with correct reasoning under 5% before vs 40% after the tutorial; graduate TAs 25% before any tutorial | Elicit, confront, resolve. Break reasoning into steps “of just the right size”. Telling students not to make an error does not work |
| Etkina and Van Heuvelen 2007 | Description and authors’ outcome reports for ISLE (observe, explain, predict and test, apply), US university courses | Several courses | FCI normalised gains 0.60 and 0.64 in two ISLE courses; electricity concept survey 63-74% vs a 47% average for calculus-based courses; 73% vs 58% on 8 reused final-exam MCQs | A predict-then-test cycle is a usable lesson skeleton. The evidence is the developers’ own uncontrolled comparisons |
| Schwartz and Bransford 1998 | Three classroom experiments, US college students, psychology concepts; outcome a prediction task about 1 week later | 24, 18 and 36 | Experiment 3: analyse contrasting cases then lecture, 43.8% of possible predictions; analyse cases twice with no lecture, 16.7%; summarise a text then lecture, 14.6% | Contrasting cases prepare students to learn from an explanation. Discovery alone and telling alone both did worse than the two together |
| Schwartz, Chase, Oppezzo and Chin 2011 | Two experiments, US 8th-grade physics (density, speed), invent-with-contrasting-cases vs tell-and-practice, same cases | 128 and 120 | Transfer to spring constant 53.5% vs 23.0% (Exp. 1) and 50.9% vs 23.3% (Exp. 2); word-problem accuracy 70.1% vs 75.2% and 64.8% vs 66.4% (not significant); worksheet accuracy during lessons 84.7% vs 91.8% | Inventing first, telling after, improved transfer and kept procedures equal. Students looked worse during the lesson. It cost about 10 extra minutes over 4 days |
| Kapur and Roll 2023 (chapter reporting Kapur 2012 and Sinha and Kapur 2021) | Kapur 2012: quasi-experiment, Singapore Grade 9 maths (standard deviation), four 50-minute periods. Sinha and Kapur 2021: meta-analysis, as summarised by its author | 133 (Kapur 2012); over 12,000 in 166 comparisons (meta-analysis) | Kapur 2012: productive-failure students better on conceptual and transfer items, equal on procedural; no group generated the correct formula. Meta-analysis as reported: d = 0.36 [0.20, 0.51] on conceptual and transfer, up to 0.58 with high fidelity, procedural not compromised | Struggle first helps only if followed by consolidation that compares the student’s attempt with the correct method. The meta-analysis was not opened; these figures are its author’s summary |
| Kirschner, Sweller and Clark 2006 | Narrative review and argument from cognitive load theory | Review | No pooled effect; argues minimal guidance is less effective for novices and that worked examples beat unguided problem solving until learners become expert | The case for explicit instruction and worked examples. It attacks unguided discovery, which none of the designs above use |
| Alfieri, Brooks, Aldrich and Tenenbaum 2011 | Two meta-analyses, discovery learning vs other instruction, children to adults | 164 studies (580 and 360 comparisons) | Unassisted discovery vs explicit instruction d = -0.38; enhanced discovery vs other d = +0.30; for adolescents unassisted discovery d = -0.53; enhanced subtypes: elicited explanation +0.36, guided discovery +0.50, generation alone -0.15; vs worked examples +0.06 (not significant) | Never leave a student to discover alone. Asking for explanations and guiding discovery help; bare generation does not |
| Chen, Kalyuga and Sweller 2016 | Randomised experiment, Year 6 geometry, Chengdu, China; guidance level crossed with element interactivity | 50 | Low-interactivity task: generating beat being shown, d = 0.57. High-interactivity task: worked example ahead of problem solving, d = 0.46, p = .06 one-tailed (not significant). Interaction p = .028 | For a multi-step procedure with many interacting parts, show a worked step before asking for one. Small sample, young students |
| Rittle-Johnson, Siegler and Alibali 2001 | Two experiments, US grades 5-6, decimal fractions on number lines | 74 and 117 | Initial conceptual knowledge predicted procedural gains, and procedural gains predicted later conceptual gains; supporting a correct problem representation improved procedural knowledge (Exp. 2) | Concept and procedure build each other in a loop. A lesson should move between “why” and “how” questions, not finish one before starting the other |
| Hestenes, Wells and Swackhamer 1992 | Development and administration of the Force Concept Inventory; US high-school and university students | Over 1,500 high-school and over 500 university students | Authors propose 80% as the threshold for Newtonian thinking and report a conceptual threshold near 60% below which problem solving was ineffective; distractors are built from common-sense beliefs | Wrong options should name a specific belief. A conceptual floor is needed before procedure practice pays off |
What the evidence says
Section titled “What the evidence says”Interactive engagement beats listening, in schools and universities
Section titled “Interactive engagement beats listening, in schools and universities”Hake (1998) collected pre/post scores on the Force Concept Inventory (FCI) and its predecessor for 62 mechanics courses and 6,542 students. Fourteen traditional courses averaged a normalised gain of 0.23. Forty-eight courses using interactive engagement averaged 0.48. The pattern held in the 14 high-school courses, where interactive courses averaged 0.55. Hake says himself that the data were volunteered and so lean toward good courses. Freeman et al. (2014) pooled 225 undergraduate studies and found +0.47 SD on exams and concept inventories and a failure rate of 21.8% against 33.8%. The effect was larger on concept inventories than on instructor-written exams. Freeman et al. cover undergraduates only.
These numbers come from whole courses, not single lessons. They say that a lesson where the student must answer, predict or explain will teach more than one where the student reads a clear explanation. They do not say which order of activities is best.
Commit, then compare, then hear the answer
Section titled “Commit, then compare, then hear the answer”Peer Instruction (Crouch and Mazur 2001) gives a conceptual question, one to two minutes to answer alone, two to four minutes of discussion, then a revote and explanation. At Harvard the normalised FCI gain rose from 0.25 under traditional teaching to between 0.49 and 0.74 under Peer Instruction, and scores on the problem-solving Mechanics Baseline test also rose, from 66% to 71-79%. Discussion helped most when 35% to 70% of students got a question right at first, with the largest gain near 50%. Pre-class free-response questions on the reading replaced reading quizzes.
Deslauriers, Schelew and Wieman (2011) ran one week of an electromagnetic waves unit for first-year engineers at the University of British Columbia. A section taught with pre-class reading, clicker questions, group tasks and immediate instructor feedback scored 74% on the end-of-week test against 41% for a lecture section (2.5 SD). The test was written by the first author, the instructors differed and the comparison lasted one week, so this is evidence for the format, not a size to plan around.
Deslauriers et al. (2019) is the cleaner test of order. Students at Harvard were randomly assigned, in a crossover, to a lecture or to a class where they first worked the same problems in small groups and then saw the identical full solution. The active class scored 0.46 SD higher on a test of learning and rated its feeling of learning 0.56 SD lower. Interviews named frustration, interruptions and worry that errors would not be corrected. A 20-minute talk early in the semester explaining this effect led over 65% of students to report that their view of active learning improved.
Elicit, confront, resolve
Section titled “Elicit, confront, resolve”McDermott’s group (McDermott 2001) builds each tutorial from research on specific student errors. A pretest elicits the error. A worksheet, done in groups of three or four, guides students to notice an inconsistency and reason through it in steps “of just the right size”: too small and no thinking is needed, too large and students get lost. Tutors ask questions rather than give answers. Homework and an exam question follow. On one interference item, correct answers with correct reasoning rose from under 5% before the tutorial to 40% after, against 25% for graduate teaching assistants before any tutorial. McDermott (2001) also reports that warning students not to make a particular error is ineffective, and that a single encounter is seldom enough. The evidence is pre/post without a control group.
Etkina and Van Heuvelen (2007) describe ISLE, in which students observe, propose explanations, predict the outcome of a testing experiment, and then apply the idea. They report FCI gains of 0.60 and 0.64 in two courses and 73% against 58% on eight reused final-exam questions. These are the developers’ own comparisons.
Struggle first, then be told: when it works
Section titled “Struggle first, then be told: when it works”Schwartz and Bransford (1998) gave college students contrasting cases to analyse, then a lecture. A week later, students who analysed cases and then heard the lecture made 43.8% of possible predictions, against 16.7% for those who analysed the cases twice with no lecture and 14.6% for those who summarised a text and then heard the lecture. Contrasting cases and the explanation worked together; neither worked alone.
Schwartz et al. (2011) tested order directly with US 8th-graders learning density and speed from the same contrasting cases. One group invented a formula from the cases and was told the standard formula afterwards; the other was told first and then practised. On word problems that used the formulas the groups were level (70.1% vs 75.2%, not significant). On transfer to an untaught ratio concept the invent-first group did far better (53.5% vs 23.0%; replicated at 50.9% vs 23.3%). Invent-first students were less accurate during the lessons (84.7% vs 91.8%), and lower-achieving invent-first students beat higher-achieving tell-first students at transfer (40.9% vs 32.9%).
Kapur’s productive failure has the same shape. In Kapur (2012), as described in Kapur and Roll (2023), 133 Grade 9 students in Singapore spent 40 minutes trying to invent a measure of consistency before being taught standard deviation. No group found the correct formula. They still beat a direct-instruction group on conceptual and transfer items and matched it on procedural items, and the number of methods a student generated predicted learning. Kapur and Roll (2023) report that the Sinha and Kapur (2021) meta-analysis, 166 comparisons and over 12,000 participants, found d = 0.36 on conceptual knowledge and transfer, up to 0.58 when the design followed productive-failure principles closely, with procedural knowledge not compromised. That meta-analysis was not opened for this review. The design principles are specific: the problem must allow several approaches, include contrasts the student can judge without being told, and be followed by consolidation that compares student attempts with the correct method. Tasks take two to three iterations to get right.
Where telling first wins
Section titled “Where telling first wins”Alfieri et al. (2011) pooled 164 studies. Unassisted discovery lost to explicit instruction (d = -0.38), and more so for adolescents (d = -0.53). Enhanced discovery, with guidance, feedback or a request to explain, beat other methods (d = +0.30). Within enhanced discovery, asking learners to explain helped (d = +0.36) and guided discovery helped (d = +0.50), but asking learners only to generate answers did not (d = -0.15). Against worked examples, enhanced discovery made no difference (d = +0.06).
Kirschner, Sweller and Clark (2006) argue from working-memory limits that novices learn more from worked examples than from searching for a solution, and that guidance should fade only as expertise grows. Chen, Kalyuga and Sweller (2016) tested the boundary in 50 Year 6 students in China. On a low-interactivity geometry task, generating beat being shown (d = 0.57). On a high-interactivity task, the worked example scored higher (d = 0.46), though that difference alone was not significant. The interaction between guidance and task complexity was significant.
A JEE problem such as the non-uniform charged sphere has many interacting elements (Gauss’s law, shell decomposition, an integral, the 4π bookkeeping). The direct reading is: struggle first on the conceptual question (what does flux depend on, what changes when density varies), and show a worked step first on the long procedure.
Mastery means concept and procedure, measured separately
Section titled “Mastery means concept and procedure, measured separately”Rittle-Johnson, Siegler and Alibali (2001) followed grade 5 and 6 students learning decimals. Initial conceptual knowledge predicted gains in procedure, and those procedural gains predicted later conceptual gains. When the experimenters made a correct problem representation easier to form, procedural knowledge improved. Neither kind of knowledge was complete at the start or end. Hestenes, Wells and Swackhamer (1992) built the FCI so that each wrong option is a common-sense belief, and report a conceptual threshold near 60% on the inventory below which students could not use Newtonian ideas to solve problems. Hake (1998) and Crouch and Mazur (2001) both found that courses which raised conceptual scores also raised problem-solving scores. McDermott (2001) reports that solving standard quantitative problems is not an adequate test of understanding.
Together these support defining mastery as two separate unassisted checks: a conceptual item that cannot be answered by recall of a formula, and a procedural item that needs the full calculation. Passing one says little about the other.
Where it is weak or contested
Section titled “Where it is weak or contested”- Population. Hake’s high-school courses, Schwartz et al. (2011), Kapur (2012), Chen et al. (2016) and Rittle-Johnson et al. (2001) are school students, but in the US, Singapore and China and mostly below Grade 10. The physics lesson studies (Crouch and Mazur, Deslauriers, McDermott, ISLE) are university students in the US and Canada. None is from India, from tribal students, or from students preparing for a competitive entrance exam.
- Group vs individual. Peer discussion is part of Peer Instruction, McDermott tutorials and the Deslauriers classes. A one-to-one coach cannot reproduce it. Whether the commit-and-explain parts work without peers is not tested here.
- Short horizons and own tests. Deslauriers 2011 is one week with an author-written test. Schwartz and Bransford tested a week later. Most productive-failure studies test the next day. The large effects are on narrow, aligned tests.
- Uncontrolled and self-reported data. Hake’s sample is volunteered. Crouch and Mazur compare years. ISLE reports are the developers’ own. McDermott’s tutorials are compared pre to post.
- Productive failure vs explicit instruction is a live dispute. The pro side is mainly Kapur’s own work and a meta-analysis by Kapur’s group (not opened here). The contra side (Kirschner et al. 2006; Chen et al. 2016) leans on cognitive load theory and small samples, and the high-interactivity result in Chen et al. was not significant on its own. Ashman, Kalyuga and Sweller (2020) reportedly found instruction-first better when element interactivity was high; it was not opened (see Leads). The disagreement narrows to task complexity and to what is being measured: transfer favours struggle first, procedure is often equal.
- The anchor problem is not new material. These studies teach a concept for the first time. A JEE student who got the anchor wrong has usually been taught it in class already. The lesson is remediation, closer to McDermott’s tutorials, which follow lecture, than to first-exposure productive failure.
- Lesson quality is the treatment. McDermott’s tutorials took years of research per topic. Kapur and Roll say a productive-failure task takes two to three iterations. Freeman’s “active learning” covers very different activities. A badly built lesson in the same order is not the same intervention. This matters for the long-term goal of AI-written lessons: the evidence is for researched lessons, not for any lesson in this shape.
Design rules for an Avanti lesson
Section titled “Design rules for an Avanti lesson”A 20-40 minute lesson triggered by a wrong answer on one anchor problem.
- Open with a commit-and-explain question on the suspected misconception, before any explanation (2-4 minutes). One conceptual MCQ, chosen so the student’s earlier wrong option predicts the wrong answer here, plus a one-line “why”. Basis: elicit step (McDermott 2001); commit before discussion (Crouch and Mazur 2001); elicited explanation d = +0.36 (Alfieri et al. 2011).
- Build every wrong option from a named belief and record which one the student picks. The option chosen decides the next step. Basis: FCI distractors as common-sense beliefs (Hestenes et al. 1992). This is what the existing ladder already does.
- Show a contrasting pair before telling (3-5 minutes). Two cases that differ only in the feature that matters (charge inside vs outside the surface; uniform vs varying density), and ask the student to say what differs and predict the result. Basis: contrasting cases then explanation beat either alone (Schwartz and Bransford 1998); invent-with-contrasting-cases improved transfer (Schwartz et al. 2011); contrasts and variant-invariant features are core productive-failure design (Kapur and Roll 2023).
- Then tell, briefly and explicitly, and connect the explanation to the student’s own wrong choice (2-4 minutes). Never leave the student to discover the principle unaided. Basis: discovery alone lost, d = -0.38 overall and -0.53 for adolescents (Alfieri et al. 2011); analysing cases twice without a lecture did poorly (Schwartz and Bransford 1998); productive failure works only with consolidation (Kapur and Roll 2023). Do not open with “remember not to do X”: warnings do not work (McDermott 2001).
- For the long procedure, show one worked step before asking for the next (worked step, then faded steps). Use struggle-first for the conceptual question, telling-first for multi-step calculation. Basis: Chen et al. 2016 (generation helps on low-interactivity tasks, worked examples lean better on high-interactivity ones); Kirschner et al. 2006. For chapters where the student is strong, skip the worked step (expertise reversal, see
learning_science.md). - Break the procedure into steps of the right size and give feedback on each before moving on (10-20 minutes). Each rung is one new idea; a wrong rung gets feedback that names the error, then a near-identical retry. Basis: tutorial worksheets break reasoning into steps “of just the right size” (McDermott 2001); attempt-then-full-solution beat solution-only by 0.46 SD (Deslauriers et al. 2019).
- Mix “why” and “how” questions inside the ladder, not concept first and procedure after. At least one rung asks the student to predict or check a result qualitatively (for example, the small-r limit of the field must match the uniform sphere). Basis: concept and procedure develop iteratively (Rittle-Johnson et al. 2001); conceptual gains came with problem-solving gains (Hake 1998; Crouch and Mazur 2001).
- Pitch rung difficulty where the student is likely to be right about half the time. Use the cohort’s item statistics. Basis: Peer Instruction gains were largest when 35-70% answered correctly at first, peaking near 50% (Crouch and Mazur 2001). This comes from group discussion; treat it as a starting point for one-to-one use.
- End with two unassisted checks: re-solve the anchor, and solve one conceptual isomorph with new surface features. Both count toward mastery; neither alone does. Basis: equal procedure but different transfer after different lessons (Schwartz et al. 2011); quantitative problem solving is not an adequate test of understanding (McDermott 2001); conceptual threshold before problem solving (Hestenes et al. 1992).
- Repeat the concept on a later day with a new item. One encounter is seldom enough (McDermott 2001). Spacing schedule per
learning_science.md. - Never use the student’s self-rating, or accuracy during the lesson, as a mastery signal. Students learned more and felt they learned less in active classes (Deslauriers et al. 2019), and invent-first students were less accurate during lessons that taught more (Schwartz et al. 2011). Tell students once, early, that the lesson is meant to feel hard (the 2019 intervention).
- Leave peer discussion to class time. Give teachers the class-wide wrong-option counts so they can run a concept-question round on the most-missed rung. Basis: Peer Instruction and tutorials depend on peers (Crouch and Mazur 2001; McDermott 2001).
- Treat each lesson as a researched object that needs iteration and expert review, especially if an AI wrote it. Basis: tutorials rest on research per topic (McDermott 2001); productive-failure tasks need two to three iterations (Kapur and Roll 2023).
References
Section titled “References”Archived copies are in the session scratchpad under sources/lesson_design/ (SHA-256 in SHA256SUMS.txt), to be published to gs://avantifellows-research-sources/ai-coach/lesson_design/.
- Alfieri, L., Brooks, P. J., Aldrich, N. J., and Tenenbaum, H. R. 2011. Does discovery-based instruction enhance learning? Journal of Educational Psychology 103(1), 1-18. https://doi.org/10.1037/a0021017 (copy from https://www.fisme.science.uu.nl/publicaties/literatuur/2011_alfieri_discovery_learning.pdf). Opened 2026-10-30. Archived:
alfieri2011_discovery.pdf. - Chen, O., Kalyuga, S., and Sweller, J. 2016. When instructional guidance is needed. Educational and Developmental Psychologist 33(2), 149-162. https://doi.org/10.1017/edp.2016.16 (accepted manuscript, Loughborough repository, https://hdl.handle.net/2134/12052683.v1). Opened 2026-10-30. Archived:
chen2016_guidance.pdf. - Crouch, C. H., and Mazur, E. 2001. Peer Instruction: Ten years of experience and results. American Journal of Physics 69(9), 970-977. https://doi.org/10.1119/1.1374249 (copy from https://ctne.fct.unl.pt/pluginfile.php/256/mod_data/content/4180/peer_instruction.pdf). Opened 2026-10-30. Archived:
crouch2001_pi.pdf. - Deslauriers, L., Schelew, E., and Wieman, C. 2011. Improved learning in a large-enrollment physics class. Science 332(6031), 862-864. https://doi.org/10.1126/science.1201783 (copy with supporting material from https://cetl.uni.edu/sites/default/files/improved_learning_in_a_large_enrollment_physics_class.pdf). Opened 2026-10-30. Archived:
deslauriers2011_science.pdf. - Deslauriers, L., McCarty, L. S., Miller, K., Callaghan, K., and Kestin, G. 2019. Measuring actual learning versus feeling of learning in response to being actively engaged in the classroom. PNAS 116(39), 19251-19257. https://doi.org/10.1073/pnas.1821936116 (full text XML from Europe PMC, PMC6765278). Opened 2026-10-30. Archived:
deslauriers2019_pnas.xml. - Etkina, E., and Van Heuvelen, A. 2007. Investigative Science Learning Environment: A science process approach to learning physics. In Redish and Cooney (eds), Research-Based Reform of University Physics, PER Reviews vol. 1. https://www.per-central.org/per_reviews/media/volume1/ISLE-2007.pdf. Opened 2026-10-30. Archived:
etkina2007_isle.pdf. - Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., and Wenderoth, M. P. 2014. Active learning increases student performance in science, engineering, and mathematics. PNAS 111(23), 8410-8415. https://doi.org/10.1073/pnas.1319030111 (copy from https://cdn.serc.carleton.edu/files/nagt/profdev/twp/sanbernardino/freeman_et_al._2014.pdf). Opened 2026-10-30. Archived:
freeman2014_pnas.pdf. - Hake, R. R. 1998. Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses. American Journal of Physics 66(1), 64-74. https://doi.org/10.1119/1.18809 (copy from https://web.mit.edu/jrankin/www/Active_Learning/hake_active_phys.pdf). Opened 2026-10-30. Archived:
hake1998_ie.pdf. - Hestenes, D., Wells, M., and Swackhamer, G. 1992. Force Concept Inventory. The Physics Teacher 30, 141-158. https://doi.org/10.1119/1.2343497 (copy from https://gwern.net/doc/science/physics/1992-hestenes.pdf). Opened 2026-10-30. Archived:
hestenes1992_fci.pdf. - Kapur, M., and Roll, I. 2023. Productive failure. In Overson, Hakala, Kordonowy and Benassi (eds), In Their Own Words: What Scholars and Teachers Want You to Know About Why and How to Apply the Science of Learning in Your Academic Setting. APA Division 2. https://www.unh.edu/teaching-learning-resource-hub/sites/default/files/media/2023-06/itow-productive-failure-kapor.pdf. Opened 2026-10-30. Archived:
kapurroll2023_pf_chapter.pdf. (Source for the Kapur 2012 study description and the Sinha and Kapur 2021 summary figures.) - Kirschner, P. A., Sweller, J., and Clark, R. E. 2006. Why minimal guidance during instruction does not work. Educational Psychologist 41(2), 75-86. https://doi.org/10.1207/s15326985ep4102_1 (copy from https://www.davidlewisphd.com/courses/EDD8121/readings/2006-Kirschner_et_al.pdf). Opened 2026-10-30. Archived:
kirschner2006_minimal.pdf. - McDermott, L. C. 2001. Oersted Medal Lecture 2001: Physics education research, the key to student learning. American Journal of Physics 69(11), 1127-1137. https://doi.org/10.1119/1.1389280. Read in the University of Washington Physics Education Group’s selected-readings packet, which also reprints Wosilait, Heron, Shaffer and McDermott 1998 (Am. J. Phys. 66, 906): https://aapt.org/Conferences/newfaculty/upload/PEG-papers-16-6-for-e-distribution.pdf. Opened 2026-10-30. Archived:
mcdermott2001_oersted_packet.pdf. - Rittle-Johnson, B., Siegler, R. S., and Alibali, M. W. 2001. Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology 93(2), 346-362. https://doi.org/10.1037/0022-0663.93.2.346 (scanned copy from https://alibali.psych.wisc.edu/wp-content/uploads/sites/371/2018/02/Rittle-JohnsonSieglerAlibali2001.pdf, text by OCR). Opened 2026-10-30. Archived:
rittlejohnson2001_iterative.pdf. - Schwartz, D. L., and Bransford, J. D. 1998. A time for telling. Cognition and Instruction 16(4), 475-522. https://doi.org/10.1207/s1532690xci1604_4 (copy from https://www.wright.edu/sites/www.wright.edu/files/uploads/2017/Feb/event/Schwartz_Bransford_1998_TimeForTelling.pdf). Opened 2026-10-30. Archived:
schwartz1998_telling.pdf. - Schwartz, D. L., Chase, C. C., Oppezzo, M. A., and Chin, D. B. 2011. Practicing versus inventing with contrasting cases: The effects of telling first on learning and transfer. Journal of Educational Psychology 103(4), 759-775. https://doi.org/10.1037/a0025140 (author’s in-press copy, https://aaalab.stanford.edu/assets/papers/2011/Practicing_versus_inventing.pdf). Opened 2026-10-30. Archived:
schwartz2011_contrasting.pdf.
Leads, not opened
Section titled “Leads, not opened”Their findings are not stated as fact above.
- Sinha, T., and Kapur, M. 2021. When problem solving followed by instruction works: Evidence for productive failure. Review of Educational Research 91(5), 761-798. https://doi.org/10.3102/00346543211019105. CC BY. The SAGE PDF returned a bot-check page and the ETH Research Collection copy (https://www.research-collection.ethz.ch/bitstreams/f6c98c41-ec4b-4996-b677-97fa3c997cf9/download) returned “Rate Limited” on four tries. Figures above come from the author’s own chapter (Kapur and Roll 2023). Highest-priority lead: it reports moderators by age and by outcome type.
- Loibl, K., Roll, I., and Rummel, N. 2017. Towards a theory of when and how problem solving followed by instruction supports learning. Educational Psychology Review 29, 693-715. https://doi.org/10.1007/s10648-016-9379-x. Closed access; Springer returned a bot-check page; no repository copy found via Unpaywall, OpenAlex or Semantic Scholar.
- Rittle-Johnson, B., Schneider, M., and Star, J. R. 2015. Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review 27, 587-597. https://doi.org/10.1007/s10648-015-9302-x. The only copy found sits on a login-gated course site; closed access otherwise.
- Ashman, G., Kalyuga, S., and Sweller, J. 2020. Problem-solving or explicit instruction: Which should go first when element interactivity is high? Educational Psychology Review 32, 229-247. https://doi.org/10.1007/s10648-019-09500-5. Closed access; no open copy found. Search summaries describe two RCTs with Year 5 students on light energy efficiency; not verified.
- Kapur, M. 2014. Productive failure in learning math. Cognitive Science 38(5), 1008-1022. https://doi.org/10.1111/cogs.12107. Closed access; no author copy found.
- Hmelo-Silver, C. E., Duncan, R. G., and Chinn, C. A. 2007. Scaffolding and achievement in problem-based and inquiry learning: A response to Kirschner, Sweller, and Clark (2006). Educational Psychologist 42(2), 99-107. https://doi.org/10.1080/00461520701263368. Closed access; no open copy found.
- Smith, M. K., Wood, W. B., Adams, W. K., Wieman, C., Knight, J. K., Guild, N., and Su, T. T. 2009. Why peer discussion improves student performance on in-class concept questions. Science 323(5910), 122-124. https://doi.org/10.1126/science.1165919. Paywalled; not retrieved. Bears on whether Peer Instruction gains come from discussion or from peer copying.
- Etkina, E., Karelina, A., Ruibal-Villasenor, M., Rosengrant, D., Jordan, R., and Hmelo-Silver, C. E. 2010. Design and reflection help students develop scientific abilities: Learning in introductory physics laboratories. Journal of the Learning Sciences 19(1), 54-98. https://doi.org/10.1080/10508400903452876. Paywalled; the ISLE outcome evidence above is from the 2007 chapter instead.
- Shaffer, P. S., and McDermott, L. C. 1992. Research as a guide for curriculum development: An example from introductory electricity. Part II. American Journal of Physics 60(11), 1003-1013. https://doi.org/10.1119/1.16979. Paywalled; the 2001 Oersted lecture was used for the tutorial method and data.