The increasing role of metacognitive skills in math: a cross-sectional study from a developmental perspective

Abstract

Both intelligence and metacognitive skillfulness have been regarded as important predictors of math performance. The role that metacognitive skills play in math, however, seems to be subjected to change over the early years of secondary education. Metacognitive skills seem to become more general (i.e., less domain-specific) by nature (Veenman and Spaans in Learn Individ Differ 15: [159][160][161][162][163][164][165][166][167][168][169][170][171][172][173][174][175][176] 2005). Moreover, according to the monotonic development hypothesis (Alexander et al. in Dev Rev 15:1-37, 1995), metacognitive skills increase with age, independent of intellectual development. This hypothesis was tested in a study with 29 second-year students (13-14 years) and 30 third-year students (14-15 years) in secondary education. A standardized intelligence test was administered to all students. Participants solved math word problems with a difficulty level adapted to their age group. Thinking-aloud protocols were collected and analyzed on the frequency and quality of metacognitive activities. Another series of math word problems served as post-test. Results show that the frequency of metacognitive activity, especially those of planning and evaluation, increased with age. Intelligence was a strong predictor of math performance in 13-to 14-year-olds, but it was less prominent in 14-to 15-year-olds. Although the quality of metacognitive skills appeared to predict math performance in both age groups, its predictive power was stronger in 14-to 15-yearolds, even on top of intelligence. It bears relevance to math education, as it shows the increasing relevance of metacognitive skills to math learning with age.

Using Writing Strategies in Math to Increase Metacognitive Skills for the Gifted Learner

“…Writing can be used to reflect on problem solving through exploring the meaning of problems, writing self-reflecting reports about one's thinking during the problem-solving process, and providing an overall written reflection of the problem, the process, and the solution (Kuzle, 2013). For example, students can use writing strategies, such as designing a plan to solve a problem or paraphrasing a problem, to help incorporate writing into math while increasing metacognition (Van der Stel, Veenman, Deelen, & Haenen, 2010). The written explanations can show what the student did during the solution process and why it worked (McCormick, 2010).…”

Exploring the relationship between metacognitive and collaborative talk during group mathematical problem-solving – what do we mean bycollaborativemetacognition?

“…Metacognitive beliefs and monitoring are also associated with mathematical problem-solving performance in primary school students (Cornoldi, Carretti, Drusi, & Tencati, 2015). Similarly, metacognitive ability has been shown to predict mathematical achievement in high school (Van der Stel, Veenman, Deelen, & Haenen, 2010;Veenman, Kok, & Blote, 2005).…”

The effect of surprising events in a serious game on learning mathematics

“…Four other lines of research can also be interesting. First, there is some evidence that (meta)cognitive skills in math improve with small differences in age (van der Stel, Veenman, Deelen, & Haenen, ). The students in the current study came from the 2nd‐year class (mean age of 13.9–14.1 years) and the (meta)cognitive skills of some students may have been insufficiently developed.…”