First let's stick to the lower grades (under 5th). The evidence isn't as clean for upper grades.

Constructivist teaching favors things like student-centered discovery, inquiry-based, minimal-guidance, "child-led" or "whole-language" approaches.

This is just a plain bad way to teach the basics, like reading, writing and arithmetic. People didn't just magically invent these ideas. Most of human history is pre-literacy. Why are we expecting a 5yo to spontaneously learn to read?

This has been studied extensively. Have a look at Project Follow Through (1968–1977). It's the largest study of its kind.

This U.S. government-funded study involved ~120,000 disadvantaged K–3 students across 20+ instructional models in multiple sites. It directly compared Direct Instruction (Engelmann’s scripted, explicit basic-skills model, e.g., DISTAR) against constructivist-oriented models (e.g., Bank Street child-directed, Open Education/EDC exploratory-discovery, cognitive-conceptual discovery approaches).

Abt Associates did an independent evaluation in (1977). Their findings

DI produced the highest gains in reading, math, language, and spelling—raising performance to near national averages. It was the only model with consistent positive effects across basic skills, cognitive-conceptual skills, and self-esteem/affective outcomes.

See page 311 fig1 for the plot of outcomes. https://andymatuschak.org/files/1988-Engelmann.pdf

For more recent evidence, have a look at the reforms in Mississippi and the UK. Mississippi has striking gains for under privileged students. Mississippi Columbus Municipal School District used the "Reading Mastery Signature Edition" DI program.

Demographics: 92% African American, 100% free/reduced-price lunch, 12% special education.

Results as measured by NWEA MAP and Renaissance STAR assessments:

MAP RIT gains: +15.96 points overall 43–45% of students met or exceeded expected growth; top performers gained ~20–28 points.

Similar results in: Baltimore City Public Schools (1996–2008) Arthur Academies (Portland, Oregon metro, 2007–2013) Rimes Elementary, Florida (2011) Gering Public Schools, Nebraska (2004+)