I'm always on the look out for new science of learning research, hunting for new studies that help move the field forward. Research summaries of the extant research are particularly helpful. They can offer insights into the state of the field more broadly—and help give a sense of the weight of evidence in a particular area or practice.
So I was excited to come across the recently published "Evidence for Cognitive Science Principles that Impact Learning in Mathematics.” Julie Booth at Temple lead the study, and it provides a fantastic summation of the latest science of learning research in math.
The key principles that Booth outlines are here:
The paper was part of a new book titled "Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts,” and I've shared a copy here.
The paper brings to light some of the new and growing research in particular areas. For instance the paper emphasizes “error reflection” in math, and it argues that that “thinking about errors improves problem representation and conceptual understanding.”
The paper also underscores the value of video feedback, noting that it may be even better than "traditional textual feedback as it was found to slow down the pace of the learner, suggestively allowing more time for the student to internalize the concept.”
If you’re trying to better understand the science of learning in math—or need a solid overview—this is very helpful document.