Three‐component mathematics for students

Abstract

There has been a long-standing debate on situational and symbolic mathematics, which is associated with how to design and execute mathematics education for all students.Brain studies can give some clues for how to deal with the debate. There are situational, verbalized, and visuospatial brain networks and the connectivity among the networks, which suggest the representation of mathematical knowledge should be situational, verbalized, and symbolic. Moreover, the representation should be mapped onto one another. Previous studies have shown the importance of situational and verbalized mathematics, but they are typically treated as preliminary and auxiliary introductions for formal symbolic mathematics. Each of the three mathematics types and their mapping would be the core learning goal in mathematics education.

How are different math knowledge presentations associated with math anxiety?

“…There has been a long‐standing debate on the relationship between symbolic and situational mathematics in mathematical education 30–32 . The outcome of the debate greatly affects the design of mathematical curricula, development of textbooks, class teaching, and assessment of mathematical achievement in students 15 . To prevent math anxiety, educators and teachers should consider how to arrange curricula and teaching by flexibly using different mathematical representations to impart mathematical knowledge.…”

“…According to the three‐component theory, 15 the form of mathematical representation can vary. Unlike symbolic mathematics, situational mathematics emphasizes that students can learn mathematics in real‐life situations.…”

“…Unlike symbolic mathematics, situational mathematics emphasizes that students can learn mathematics in real‐life situations. “Students need to know a variety of situations that embody quantitative information and their relationships.” 15 A typical example illustrates the variety of mathematical representations. For symbolic mathematics, the commutative law of addition can be described as “a + b = b + a”; for verbalized mathematics, it can be described as “In addition, switch the two addends and the sum remains the same”; for situational mathematics, “Switch the two baskets, and the sum of eggs in the baskets remains the same.” As verbalized and situational mathematics are based on natural language descriptions and are more concrete than symbolic mathematics, it is reasonable to expect that symbolic mathematics is more closely associated with math anxiety.…”

Algebra dissociates from arithmetic in the brain semantic network

“…Distinct approaches should be used to learn algebra and arithmetic. A verbalization approach emphasizing semantic comprehension was used to learn algebra, and visualization and phonological approaches were used to learn arithmetic [41]. To test this hypothesis, we compared the fMRI data regarding brain activation for algebra with that for arithmetic, and we conducted a single-trial (item-wise) interindividual correlation analysis and a traditional mean-trial interindividual correlation analysis to examine the brain-behavior correlations [25,42].…”

Assessing gender difference in mathematics achievement

“…Specifically, girls outperformed boys in arithmetic calculations, but this advantage in arithmetic disappeared merely after controlling for differences in reading ability. Reading ability may promote learners’ understanding of mathematical knowledge (e.g., mathematical terminology, principles, and rules), since the acquisition of this knowledge involves semantic processing (e.g., Li et al, 2019; Liu et al, 2019; Zhou & Zeng, 2022). The verbalized mathematical teaching approach helps students acquire mathematical knowledge (OECD, 2015).…”