Worked Examples vs Practice Problems: Why Examples That Fade Work Better

Short answer: when a skill is new, studying worked-out solutions teaches more than solving problems cold. A meta-analysis of math studies, from elementary school through college, found the worked-example effect at g = 0.48 (Barbieri et al., 2023). But the help has to go away as you improve: once you know the steps, worked examples stop helping and can slow you down. The best plan is examples first, then fade them out.

Why cold practice is slow at first

Solving a new kind of problem from scratch uses up working memory on searching for a way in, leaving little room to notice the method that worked (Sweller, 1988). In an early algebra study, students who studied worked examples spent less time studying, then solved similar problems faster and with fewer errors than students who practiced solving (Sweller & Cooper, 1985). The gain was mostly on problems with the same structure, which is exactly what a dosage exam is full of.

See it: one worked example

Order: 20 mg/kg/day, divided every 12 hours. Child: 44 lb. Available: 250 mg per 5 mL. How many mL per dose?

1. Weight in kg: 44 ÷ 2.2 = 20 kg.
2. Dose per day: 20 mg/kg × 20 kg = 400 mg/day.
3. Every 12 hours is 2 doses a day: 400 ÷ 2 = 200 mg per dose.
4. Volume: 200 mg ÷ 250 mg × 5 mL = 4 mL.

Fading: hand the steps over one at a time

The next step is not a cold problem. It’s the same kind of problem with the last step left for you. Renkl and colleagues (2002) found that fading the steps out worked better than pairing each example with a practice problem, and that removing the last steps first (backward fading) worked better than removing the first ones.

Order: 30 mg/kg/day, divided every 8 hours. Child: 33 lb. Available: 125 mg per 5 mL.

1. Weight in kg: 33 ÷ 2.2 = 15 kg.
2. Dose per day: 30 × 15 = 450 mg/day.
3. Every 8 hours is 3 doses a day: 450 ÷ 3 = 150 mg per dose.
4. Volume: your turn.

Now on your own: order 10 mg/kg per dose, child 55 lb, available 100 mg per 5 mL.

Why the help has to go away

Support that helps a beginner can stop helping, or even get in the way, once you know the material. Researchers call this the expertise reversal effect (Kalyuga et al., 2003). If you already know the steps, reading them again is extra work, not help. That’s why a good study plan doesn’t keep giving you the full solution forever.

Fading that follows you

Fixed fading takes the steps away on a schedule. Adaptive fading takes them away when you show you’ve learned them. In a computer tutor, adaptive fading beat fixed fading, and both beat plain problem solving, in a lab study and a classroom study (Salden et al., 2010).

That’s the model for Smart practice in the Dosage Calc Coach. Each problem type has its own help level: the full walk-through while it’s new or shaky, then the tutor sets the problem up and hands you the rest, then you work it alone. The cut-offs between those levels are our design choice; no study sets them.

Feedback on each step, not just the answer

Worked examples pair well with practice that gives feedback at each step. In VanLehn’s 2011 review, intelligent tutoring systems, which give feedback step by step, came out nearly as effective as human tutors (d = 0.76 vs. 0.79, each compared with no tutoring). What the feedback says matters too: in computer-based learning, an explanation of the error helped far more (0.49) than being told right or wrong (0.05) (Van der Kleij et al., 2015).

Try one with the walk-through, then one alone

Open a weight-based problem and tap “Walk me through it” for the full worked version. Then press Next and try the next one straight into the answer box.

Try weight-based doses with TalaA fresh problem in place. Answer it, or tap “Walk me through it” for one small step at a time. Free, no account.Start

Studying for the TEAS? The same idea works for two-step equations. Example: a gym charges a $25 sign-up fee plus $15 a month, and you’ve paid $100. Take away the fee: $100 − $25 = $75. Divide by the monthly price: $75 ÷ $15 = 5 months. Try one below in the TEAS Math Coach; it can draw the equation as a balance.

Try a two-step equation with FurahaA fresh problem in place. Answer it, or tap “Walk me through it” for one small step at a time. Free, no account.Start

Honest limits

• Mostly near transfer. Fading helps most on problems like the ones you practiced (Renkl et al., 2002; Atkinson, Renkl & Merrill, 2003). It is not a shortcut to problems you’ve never seen.
• “Explain it to yourself” prompts are mixed. One study found prompts to explain the principle helped (Atkinson et al., 2003), but across math studies, adding prompts weakened the worked-example effect (Barbieri et al., 2023).
• Mostly school students. Most of these studies were in school classrooms or lab experiments, not nursing programs. Applying them to dosage calculation is a reasonable step, not a proven one.

For how the rest of the coach is built, see how the NurseSavvy math coach teaches. For the research on spacing and retrieval across all your nursing courses, see the learning science inside NurseSavvy.

Sources

• Barbieri, C. A., Miller-Cotto, D., Clerjuste, S. N., & Chawla, K. (2023). A meta-analysis of the worked examples effect on mathematics performance. Educational Psychology Review, 35(1).
• Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. Cognitive Science, 12(2), 257–285.
• Sweller, J., & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59–89.
• Renkl, A., Atkinson, R. K., Maier, U. H., & Staley, R. (2002). From example study to problem solving: Smooth transitions help learning. Journal of Experimental Education, 70(4), 293–315.
• Kalyuga, S., Ayres, P., Chandler, P., & Sweller, J. (2003). The expertise reversal effect. Educational Psychologist, 38(1), 23–31.
• Salden, R. J. C. M., Aleven, V., Schwonke, R., & Renkl, A. (2010). The expertise reversal effect and worked examples in tutored problem solving. Instructional Science, 38(3), 289–307.
• VanLehn, K. (2011). The relative effectiveness of human tutoring, intelligent tutoring systems, and other tutoring systems. Educational Psychologist, 46(4), 197–221.
• Van der Kleij, F. M., Feskens, R. C. W., & Eggen, T. J. H. M. (2015). Effects of feedback in a computer-based learning environment on students’ learning outcomes: A meta-analysis. Review of Educational Research, 85(4), 475–511.
• Atkinson, R. K., Renkl, A., & Merrill, M. M. (2003). Transitioning from studying examples to solving problems: Effects of self-explanation prompts and fading worked-out steps. Journal of Educational Psychology, 95(4), 774–783.