The Benefits of a Metacognitive Lesson on Children's Understanding of Mathematical Equivalence, Arithmetic, and Place Value

Metacognition is theorized to play a central role in children's mathematics learning. The primary goal of the current study was to provide experimental evidence in support of this role with elementary school students learning about mathematical equivalence. The final sample included 135 children (59 first graders and 76 second graders) who participated in the study across three sessions in their classrooms. They completed a pretest during Session 1, a lesson and posttest during Session 2, and a 2-week delayed retention test during Session 3. For Session 2, children were randomly assigned to receive a lesson on mathematical equivalence with or without integrated metacognitive questions. Relative to the control lesson, children who received the metacognitive lesson demonstrated higher accuracy and higher metacognitive monitoring scores on the posttest and retention test. Further, these benefits sometimes extended to uninstructed items targeting arithmetic and place value. No condition effects were observed for children's metacognitive control skills within any of the topics. These findings suggest a brief metacognitive lesson can improve children's mathematics understanding. Educational Impact and Implications Statement The current study provides novel insights into children's learning of mathematical equivalence (e.g., 3 + 4 = 5 + _ _) and their metacognitive skills, including their ability to evaluate their own knowledge (e.g., did I get that right?). Our results suggest that these skills can be improved after a brief classroom lesson for first and second grade children. Key components of the lesson included (a) a correct strategy for making both sides of the problem the same amount, and (b) a set of reflective questions (e.g., How can I check that my solution is correct?). Importantly, the lesson often resulted in better performance and metacognitive skills on arithmetic and place value items, which were not included in the lesson. These findings have implications for the development of classroom lessons focused on mathematics and metacognition.