The involvement of the semantic neural network in rule identification of mathematical processing

The neural correlates underlying mathematics processing have been examined for years, and brain regions around the parietal lobe, known as a visuospatial network, have previously been observed to play pivotal roles in numerical and arithmetical processing (see review Hawes et al., 2019; Sokolowski et al., 2017). For example, neuropsychological studies have shown that patients with brain lesions in the parietal lobe demonstrate deficits in arithmetical operations and numerical processing (e.g., Ashkenazi et al., 2008; Cipolotti et al., 1991). In addition, functional magnetic resonance imaging (fMRI) studies have found consistently greater activation in bilateral regions of the intraparietal sulcus, as well as inferior and superior parietal lobules, when processing quantity information (e.g., Damarla et al., 2016; Harvey et al., 2017 for review; Holloway et al., 2010; Krueger et al., 2008). Moreover, studies using the event-related potential (ERP) method showed that numerical processing and arithmetical computation processing elicit P2p and late positive potential in parietal lobes (e.g., Hyde & Spelke, 2012; Zhou, 2011), with P2p component relevant to numerical distance (Hyde & Spelke, 2012) and the late positive potential relevant to operation effects during multiplication (Zhou, 2011).

Recently, several studies indicated that the processing of numerical/arithmetical computation and the processing of mathematical conceptual knowledge are dissociated (e.g., Rasmussen et al., 2003; Wei et al., 2012; Zhang et al., 2016). Apart from the visuospatial network that supports the numerical processing in mathematics, a semantic network subserving the processing of mathematical conceptual knowledge may exist (e.g., Cheng et al., 2022; Li et al., 2019; Wang et al., 2022; Zhang et al., 2012; Zhou et al., 2018). It could involve the brain regions that were previously been found to subserve language processing, such as the left middle temporal gyrus, inferior frontal gyrus, dorsomedial prefrontal cortex, and angular gyrus (see review in Binder et al., 2009; Jackson, 2021; Noonan et al., 2013). Studies of patient having lesions in the temporal lobe but not parietal lobes demonstrate impaired conceptual knowledge, or arithmetic facts, but relatively intact numerical abilities (e.g., Cohen & Dehaene, 1994; Delazer et al., 2004; Papagno et al., 2013). For instance, Cohen and Dehaene (1994) reported a patient with a selective deficit in arithmetic facts that cannot retrieve correct answers for multiplication problems (e.g., 4 × 5), but they had intact procedural knowledge for arithmetical problems (e.g., number reading, numerical comparison, and multi-digit computation procedures). In addition, fMRI studies have repeatedly demonstrated that compared with numerical/arithmetical computation, the greater activation of the semantic network when doing tasks that involve the conceptual knowledge of mathematics, such as tasks using mathematical terms, mathematical principles, number series completion, and mathematical problem solving (e.g., Cheng et al., 2022; Li et al., 2019; Wang et al., 2022; Zhang et al., 2012; Zhou et al., 2018).

However, still some studies revealed the disassociation between semantic network and brain networks subserving mathematical processing (e.g., Amalric & Dehaene, 2016, 2019; see review Amalric & Dehaene, 2018). For instance, studies of Amalric and Dehaene (2016, 2019) demonstrated that general semantic knowledge elicited higher brain activation in semantic network (i.e., inferior angular gyrus, middle temporal gyrus, inferior frontal gyrus, and mesial prefrontal cortex) when compared with mathematical statements, whereas mathematical statements elicited higher activation in bilateral intraparietal sulci and inferior temporal regions. The foregoing dissociation may due to that general semantic knowledge relied more on the semantic network than mathematical conceptual knowledge (e.g., Liu et al., 2017; Wang et al., 2022; Zhang et al., 2012). However above studies also found mathematical conceptual knowledge elicited higher brain activation in semantic network when compared with numerical/arithmetical computation, which revealed that mathematical conceptual might also rely on the semantic network.

To further explore the involvement of the semantic network in mathematical processing, the current study adopted the ERP method to identify a neural marker that indicated the involvement of the semantic network in mathematical processing. The ERP method can provide high temporal resolution in the millisecond range, and it can also determine a number of characteristics (e.g., peak and latency of the components) that reveal the underlying cognitive processes occurring during tasks. The ERP method can also provide topographical information and lateralized hemisphere information of brain activation, as previous ERP studies have revealed the involvement of left temporal cortex during semantic processing with a left-lateralized scalp distribution of ERP components in temporal areas (e.g., Koppehele-Gossel et al., 2019; Palolahti et al., 2005). The number series completion task with a sequence of four numbers was used as the mathematical task in the current study. The number series completion task was used for the following reasons. First, a recent fMRI study has shown that compared with arithmetic computation, the number series completion task involves more activation of the semantic network (Zhou et al., 2018), which might result from the involvement of the semantic network in processing mathematical knowledge and rules. Second, this task uses digit numbers, and it does not involve any verbal materials compared with the tasks of mathematical terminology and principle, as well as mathematics word problems. Thus, the activation of the semantic network during this task cannot be related to a verbal component. Third, the number series completion task can be divided into four stages, encoding, rule identification, rule extrapolations, and answer production (Girelli et al., 2004; Holzman et al., 1983). Thus, when the numbers are presented in sequence, the specific stages that involve the semantic network can be examined. In a task with four numbers presented in sequence, the four stages could be matched with the presentation of the four numbers, as follows: (1) encoding: when the first number is presented, the perceptual analysis begins; (2) rule identification: when the second number is presented, the relation of the two presented numbers starts to be detected; (3) rule extrapolation: when the third number is presented, whether the rule can be applied to the new number can be examined; and (4) answer production: when the fourth number is presented, whether the rule can be extrapolated to the fourth number is further examined (rule extrapolation), and whether the fourth number is consistent with the identified rule can be judged simultaneously (Girelli et al., 2004; Holzman et al., 1983; Qin et al., 2009).

Prior studies have examined the neural correlates of the number series completion task with the numbers sequentially presented (Lang & Kotchoubey, 2002; Li et al., 2012; Nie et al., 2021; Nunez-Pena & Escera, 2007; Nunez-Pena & Honrubia-Serrano, 2004; Qin et al., 2009; Xiao et al., 2018, 2019); however, none of the studies found the activation of the semantic network. One possible explanation is that no study has focused on the pure rule identification process, because most of them focused on the later rule extrapolation and answer production processes that at and after, respectively, the presentation of the third number in the number series. These studies showed that rule violation during the rule extrapolations/answer production process elicits increased P200 (Li et al., 2012; Qin et al., 2009; Xiao et al., 2019), increased N200 (Li et al., 2012; Nie et al., 2021; Nunez-Pena & Escera, 2007; Qin et al., 2009; Xiao et al., 2018, 2019), decreased P300 (Lang & Kotchoubey, 2002; Nie et al., 2021; Qin et al., 2009; Xiao et al., 2019), and increased late positive component (Li et al., 2012; Molnár et al., 2013; Nunez-Pena & Escera, 2007; Nunez-Pena & Honrubia-Serrano, 2004; Xiao et al., 2019), reflecting attention reallocation, the detection of conflict between the expected and the displayed numbers, rule uncertainty, and the updating working memory caused by the rule violation, respectively.

In addition to the rule extrapolation and answer production that were the main foci of previous studies, rule identification is also a vital process in number series completion. During this period, task performers retrieve their semantic knowledge to determine the relationships between numbers (Diefenderfer et al., 1985; LeFevre & Bisanz, 1986). For instance, Grade 6 students who were asked to describe orally the features they found in a number series perform better in rule identify and inducing compared with those students who were asked to do the task in silence (Diefenderfer et al., 1985). This suggested that there was semantic processing during the rule identification process of the number series completion task. To further examine the involvement of the semantic network in mathematical processing, the current study focused on the rule identification process during the number series completion task. The mean amplitude of the late negative component (LNC) has been associated with the semantic integration and rule identification processes. Larger mean amplitudes of LNC was identified in the left brain hemisphere in ERP studies using conditional (Qiu et al., 2007), syllogistic (Qiu et al., 2009), and analogical (Qiu et al., 2008; Zhao et al., 2011) reasoning. For instance, during a word pair analogical reasoning task, larger mean amplitudes of LNC was found in the left hemisphere during the rule induction stage, in which participants identified the semantic relations of the presented word pair, and coded it as semantic rules (Zhao et al., 2011).

The current study used a number series completion paradigm, as well as the ERP technique, to examine whether the semantic network supports mathematical processing and to find the corresponding spatiotemporal neural marker. Specifically, in each trial of the number series completion task, four-digit numbers were presented in sequence, and we focused on the ERP when the second number was presented, which is the rule identification stage. An arithmetical computation task having a similar procedure was designed as the baseline of the number series completion task. This was similar to the procedure of Zhou et al. (2018). We expected that the rule identification process would involve more semantic processing than the arithmetical computation processes, and it would elicit a higher amplitude of the LNC component in left hemisphere, which is relevant to semantic rule identification.

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