Inquiry-Based Learning in Math: What the Research Says About Guided Inquiry With Data
Inquiry-based learning in math is linked to larger conceptual gains, and the best-supported versions give students real guidance along the way. A 2025 meta-analysis in the International Journal of Education in Mathematics, Science and Technology found an overall effect of g = 0.91 on conceptual understanding in science and math, with guided inquiry averaging g = 0.79.
That headline needs context before it goes in a slide deck. The analysis pooled only 12 studies and 786 students, and its authors' own prediction interval runs from -0.25 to 2.07. Older and larger reviews report smaller, messier results, and the work on how much guidance students need points in one direction.
Live prices as a dataset, a teacher as the guide
The Rapunzl simulator gives each student a simulated $10,000 portfolio priced on live Nasdaq data, so students choose companies and then watch prices that move unpredictably and match no textbook example. A student can make a prediction about a holding and check it against what the market did.
The guidance comes from the teacher. The curriculum is standards-aligned with project-based learning throughout, which gives a teacher a framework to build questions around, and it includes a financial math course.
The studies below find that guided inquiry does better than unguided discovery. None of them tested market data, and the limits section says so.
What does the research say about inquiry-based learning in math and science?
| Study | Design and size | Learners | Main result |
|---|---|---|---|
| Mediana, Funa & Dio (2025) | Meta-analysis: 12 studies, 14 effect sizes | 786 students in science and math, across countries and levels | Overall g = 0.913 (prediction interval -0.25 to 2.07); senior high school g = 1.176 (3 effect sizes); math g = 1.191 (4); guided inquiry g = 0.786 (11); open inquiry g = 1.530 (1) |
| Minner, Levy & Century (2010) | Research synthesis of 138 studies from 1984 to 2002, tallying outcomes | K-12 science | 51% of studies positive, 33% mixed, 14% no impact, 2% negative |
| Furtak et al. (2012) | Meta-analysis of 37 experimental and quasi-experimental studies from 1996 to 2006 | Science students | Mean effect size .50; teacher-led activities about .40 larger than student-led |
| Lee, Linn, Varma & Liu (2010) | Quasi-experiment: delayed cohort comparison | Middle and high school science students of 27 teachers who moved from typical instruction to online inquiry units | Significant main effect of inquiry instruction on knowledge integration; the effect differed by course and teaching context (the abstract gives no size) |
| Alfieri et al. (2011) | Two meta-analyses of 164 studies | Learners of several age groups, with math one of six task domains | Unassisted discovery d = -0.38 against explicit instruction; enhanced discovery d = 0.30 against other methods |
| Lazonder & Harmsen (2016) | Meta-analysis of 72 studies | Learners of several age groups | Guidance improved learning outcomes, d = 0.50 |
The 2025 meta-analysis is the newest source and the thinnest. Its overall g = 0.913 puts the average inquiry student near the 82nd percentile of the comparison group. The subgroups that make the best headlines are small: math (g = 1.191) rests on four effect sizes, senior high school (g = 1.176) on three, and open inquiry (g = 1.530) on one. Math and science did not differ significantly (science g = 0.727; p = 0.197), and the studies disagree widely (I² = 81%).
Minner and colleagues give a more cautious picture. Their own summary calls it "not overwhelmingly positive" while still describing a clear, positive trend. Instruction that asked students to think actively and to draw conclusions from data was the pattern linked to better conceptual learning, though the data-conclusions link was only marginally significant (p = 0.070). Among the 101 studies they modeled for conceptual understanding, the overall amount of inquiry was not significantly linked to gains.
Furtak's 0.50 is about the 69th percentile. Lee and colleagues did not report an effect size in the abstract, so there is no percentile to give. Their design is still useful: the same 27 teachers taught the same topics one year with typical methods and the next with online inquiry units, and inquiry instruction had a significant effect on knowledge integration that varied by course and context.
Does it matter how much guidance students get?
Yes, and the larger syntheses agree on it.
Alfieri and colleagues pooled 164 studies in two analyses. Students left to discover material without help did worse than students taught explicitly (d = -0.38, roughly the 35th percentile of the explicit group). The penalty was steeper for adolescents (d = -0.53) than for adults (d = -0.26). Enhanced discovery, where students explore with support, beat other methods (d = 0.30, roughly the 62nd percentile). The authors name what the support looked like: feedback, worked examples, scaffolding and prompts that make students explain their reasoning. Their studies span many tasks and ages, with math one of six domains, so they speak to inquiry in general rather than math classrooms alone.
Lazonder and Harmsen reached a compatible conclusion from 72 studies. They open with the view that inquiry can beat expository teaching as long as students are supported adequately, and they found guidance improved learning outcomes (d = 0.50). Furtak's teacher-led versus student-led gap, about .40 in favor of teacher-led activities, points the same way.
The 2025 meta-analysis also sorted its studies by how open the inquiry was. Open inquiry rests on a single effect size, so we do not weight it. The 11 guided-inquiry effect sizes averaged g = 0.786, about the 78th percentile, and guided inquiry is the version this post recommends.
What does the research not show about inquiry in math?
Start with the subject mix. Minner, Furtak and Lee all studied science. The 2025 meta-analysis is the one source here that breaks out math, and the math estimate comes from four effect sizes. The authors' publication-bias check came out borderline (Begg and Mazumdar p = 0.062), and they note it has little power with so few studies.
Minner's 138-study synthesis tallies whether each study found a positive impact, a cruder measure than an effect size. Only the finer cuts (active thinking, drawing conclusions from data) predicted gains in some of the models.
Unguided discovery also has a direct critic. Evans and Dietrich (2022), writing in STEM Education, reviewed cognitive science and educational psychology research on inquiry-based mathematics education at the tertiary level and concluded that the claim that students learn better when not taught is not supported by evidence. Their paper is a scoping review and critical commentary, aimed at tertiary math and at advocates of reform, so it speaks most directly to unguided versions. It is consistent with Alfieri's finding that unassisted discovery lags explicit teaching.
No study above used financial content. The case for market data rests on the general finding about drawing conclusions from data, plus a design argument that live prices are a rich, realistic dataset. A finance-specific experiment would be a better test, and the studies we reviewed include none.
The abstracts also report conceptual understanding. They do not tell us whether the gains persist for a year or carry over to state test scores.
How do you run guided inquiry with data in a math or science class?
Borrow the pieces the research names as helpful, and keep the teacher in the loop.
- Start with a question that numbers can answer. "Which of these two stocks moved more last month, and how would we know?" beats "Explore stock prices."
- Ask for a written prediction first. A one-line hypothesis gives students something to test and revise, which is the cycle inquiry depends on.
- Show one worked example, then release. Walk a single case end to end (pull the data, compute the measure, state the conclusion), then let students repeat it on their own holdings. This is the scaffolding and worked-example support Alfieri's team found helpful.
- Ask students to explain each result. Why did it come out that way, and what else could explain it? Elicited explanations are on the same list.
- Give fast feedback. Compare predictions with outcomes the same day, as a class, so wrong hypotheses get corrected while they still matter.
- Name the concept after students have worked with the data. This is practical judgment, prompted by the Evans and Dietrich critique; none of the studies above tested the sequence.
- Start with a tidy dataset, then move to live data. This is also our judgment, not a finding from these studies.
For ready-made links between money questions and the math standards you already teach, see personal finance in middle school math. For the case for building a unit around driving questions and student products, see the value of project-based learning.
Frequently Asked
Questions
Probably, with caveats. A 2025 meta-analysis found g = 1.19 across four math effect sizes (g = 0.91 across all 14), but the base is small and the math and science results did not differ significantly. Most of the older evidence comes from science, and the strongest support is for guided versions of inquiry.
Guided inquiry gives students a question and real support, such as worked examples, feedback and prompts to explain. Unassisted discovery leaves them to figure it out alone. Across 164 studies, Alfieri and colleagues found the first helped and the second hurt on average.
It depends on the version. Unassisted discovery did worse than explicit instruction in the largest comparison, while enhanced discovery did better than other methods. A classroom that teaches a concept directly after students have worked with data uses both.
Nothing in the studies above tested financial data directly, so the claim rests on the general finding that drawing conclusions from data supports conceptual learning. Live prices make a workable dataset because they are real and change daily, and the teacher's questions and feedback supply the guidance.
To see how guided inquiry with live market data could run in your math or science classroom, request a free Rapunzl demo.
By Clarissa Collins, Curriculum Designer at Rapunzl.
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