Quantitative modelling demonstrates format‐invariant representations of mathematical problems in the brain

Abstract

Mathematical problems can be described in either symbolic form or natural language. Previous studies have reported that activation overlaps exist for these two types of mathematical problems, but it is unclear whether they are based on similar brain representations. Furthermore, quantitative modelling of mathematical problem solving has yet to be attempted. In the present study, subjects underwent 3 h of functional magnetic resonance experiments involving math word and math expression problems, and a read word condition without any calculations was used as a control. To evaluate the brain representations of mathematical problems quantitatively, we constructed voxel‐wise encoding models. Both intra‐ and cross‐format encoding modelling significantly predicted brain activity predominantly in the left intraparietal sulcus (IPS), even after subtraction of the control condition. Representational similarity analysis and principal component analysis revealed that mathematical problems with different formats had similar cortical organization in the IPS. These findings support the idea that mathematical problems are represented in the brain in a format‐invariant manner.

Cortical representational geometry of diverse tasks reveals subject-specific and subject-invariant cognitive structures

“…Encoding models quantitatively predict brain activity based on a combination of features from presented stimuli. This approach has been applied to model brain response patterns in visual (Kay, Naselaris, et al 2008; Nishimoto et al 2011; Çukur et al 2013), auditory (Norman-Haignere, Kanwisher, and McDermott 2015; Nakai, Koide-Majima, and Nishimoto 2021), emotion (Horikawa et al 2020; Koide-Majima, Nakai, and Nishimoto 2020), language (Huth et al 2016; Nishida and Nishimoto 2018; Nakai, Yamaguchi, and Nishimoto 2021), and mathematical domains (Nakai and Nishimoto 2023a, 2023b). The weight matrices obtained during the encoding model construction reflect how target features are represented in the brain (Nakai and Nishimoto 2020; Koide-Majima, Nakai, and Nishimoto 2020), facilitating subsequent RSA and ISC analyses based on the model weights.…”