Introduction

Arithmetic word-problem solving involves problem translation and integration, planning, and ultimate solution execution (Hegarty et al., 1992). From cognitive and linguistic perspectives, word-problem solving differs from pure mathematic calculation given that the decomposition of word-problem questions requires text comprehension skills (Harlaar et al., 2012; Fuchs et al., 2006). It has been found that reading subskills correlate with word-problem-solving skills among elementary-age students (Fuchs et al., 2006; Spencer et al., 2020; Vilenius-Tuohimaa et al., 2008). Reading subskills such as morphological awareness can serve as a critical component in helping learners construct their reading comprehension abilities. Once these reading subskills are honed, students can overcome text comprehension difficulties, facilitating the transformation of word-based arithmetic problems into pure mathematical calculations by integrating their mathematical understanding (Purpura et al., 2011; Fuchs et al., 2006). The current study aimed to extend beyond the current literature in two ways. First, we integrated and refined the reading subskill (morphological awareness) into the model of arithmetic word-problem solving, thus testing the potential linguistic demand underlying word-problem solving. Second, we emphasized late elementary students to test whether the relationship between reading subskills and word-problem solving diminished with age (Aunola et al., 2004; Kyttälä and Björn, 2014).

Chinese morphological awareness as a reading requisite

Morphological awareness, as an essential reading subskill, is considered as prior knowledge in reinforcing reading comprehension that is also a foundation in reading comprehension. Specifically, morphological awareness refers to the ability to manipulate and reflect upon morphological structures (Carlisle, 1995; Zhang and Koda, 2013). Morphological awareness has been studied extensively in reading research. Considering the interconnected characteristics of phonology, semantics, and orthography interwine in morphological awareness (Kuo and Anderson, 2006; Kirby and Bowers, 2017), it entails the ability to decompose words, analyze morphemic structures, and retrieve partial-word meaning for general comprehension. Prior studies have endorsed the facilitative effect of morphological awareness on Chinese children’s language and reading development (e.g., Ku and Anderson, 2003; McBride-Chang et al., 2003; Tong et al., 2017; Zhang, 2015; Zhao et al., 2019). Compounding morphology is the most productive word-formation rule in Chinese (Ceccagno and Basciano, 2007) given that 75–80% of Chinese words are comprised of more than two characters/morphemes, notably, lexical compounding and derivation of bound roots play a dominant role in forming and identifying Chinese words (Packard, 2000). For example, 汽车 (car), 火车 (train), 公交车 (bus), 自行车 (bike) all reveal the same regularity, that those nouns share the same right-handed bound roots ‘车’ (morpheme), which indicate that they belong to wheel-driven land traffic tools, while the left-hand word represents the difference between those traffic tools. While the term 搭车 (Hitchhiking) also shares the same ‘车‘ morpheme, it is distinguished by the morpheme ‘搭‘, which denotes the verb ‘to hitch a ride’. This differentiation, known as morpheme discrimination, requires the reader to identify not just the meaning but also the grammatical role of ‘搭‘ in this context. As morphological awareness is crucial for readers to speculate and understand words, research emphasizes its importance in developing Chinese compound awareness among early adoles (Chen et al., 2009; Wang et al., 2006; Zhang, 2016; Zhang and Koda, 2013).

Morphological awareness as a mediator promoting arithmetic skills

Reading subskills, which naturally develop and mature as children grow and engage more with language and literacy activities, could serve as a potential mediator in improving learners’ mathematical abilities, especially arithmetic word problems. Morphological awareness, as a key indicator of reading proficiency, enables learners to construct the interface between number naming and compounding morphology in Chinese at an early stage of mathematic learning (Ng and Rao, 2010; Liu et al., 2016), which facilitates arithmetic and mathematic development. More specifically, Zhang and Lin (2015) examined the longitudinal relations between general cognitive abilities (visual-spatial skills), language and reading subskills (phonological awareness, morphological awareness, orthographic knowledge), and arithmetic skills among Chinese kindergarteners. The results highlighted the linguistic contributions to arithmetic skills. Notably, morphological awareness was found to uniquely predict arithmetic word-problem solving. Subsequently, Liu et al. (2016) specifically examined the longitudinal effect of morphological awareness on kindergarten children’s counting abilities. After the effects of age, non-verbal IQ, visual-spatial skills, and phonological awareness were accounted for, morphological awareness made significant contributions to concurrent and longitudinal counting skills. Additionally, Liu et al. (2020) tested the relative contributions of executive functioning, phonological awareness, morphological awareness, and receptive vocabulary to kindergarten children’s arithmetic skills, which they defined to include both number fact recall and arithmetic word-problem-solving skills. Therefore, word-problem solving constitutes a subset of arithmetic skills, requiring the understanding and application of numerical operations within a textual framework. Drawing on a path analysis that covariates all variables, Liu et al. (2020) found morphological awareness to be the sole factor impacting both aspects of arithmetic skills. For instance, Chinese morphological awareness is predominantly based on compounding. Similarly, the numbering system in Chinese is based on the compounding of base-10 lexical morphemes. For example, multi-digit numbers 11 to 19 are decoded as 十一(ten-one), 十二(ten-two), 十三(ten-three), …十九(ten-nine) with the compounding of two lexical morphemes “十(ten)” and “X-number”. Morphological awareness is thus considered an important constructing block in the identification of mathematical vocabulary, and the acquisition of mathematical vocabulary also plays a significant role in facilitating the development of subsequent mathematical skills.

Morphological awareness is crucial for beginners not only in learning Chinese words and grasping basic mathematics but also to mediate meaning in arithmetic word problems. By grade 4, learners are expected to transition from learning to read to reading to learn that able to combine their reading comprehension abilities with other fields, such as arithmetic word problems. More specifically, reading comprehension, which is the application and integration of various reading subskills, is thought to facilitate comprehension of mathematical applications. By mastering these reading subskills, learners can achieve effective reading comprehension, which in turn makes it easier for mathematics learners to incorporate context as well as prior knowledge to support and plan the solution of mathematical components, such as the process of converting words into equations (Vilenius-Tuohimaa et al., 2008; De Smedt et al., 2009). Vilenius-Tuohimaa et al., (2008) demonstrated that the extent of reading subskill using, such as morphological awareness, not only predicted learners’ reading ability, but was also a potent mediator in relation to arithmetic word-problem solving, helping the readers to maximize their prior knowledge of the topic at hand, yet readers with undeveloped reading subskills often struggle with the text, hindering their problem-solving abilities.

In summary, reading subskills, such as morphological awareness, not only enhance readers’ reading comprehension but also aid in recognizing initial mathematical terminology, hence constructing a foundation for future mathematical learning. Subsequently, arithmetic word problems that learners encounter later could potentially be influenced by the extent to which reading subskills are used and the reading comprehension abilities driven by the development of reading subskills. Therefore, compounding morphology embedded in the Chinese numbering system facilitates number word learning (Ng and Rao, 2010), which can subsequently enhance arithmetic competencies. The aforementioned studies unpacked the relationship between morphological awareness and arithmetic skills in preschool children. Recently, Ng et al. (2021) tested the relationship between reading subskills and arithmetic word-problem-solving abilities among elementary-age students. Reading subskills included morphological awareness, syntactic knowledge, inferencing making, and comprehension monitoring. Word-problem solving was coded based on equation formation and computation. A mediated path model was proposed to delineate the relationship between reading subskills and arithmetic word-problem solving. Morphological awareness was found to predict arithmetic word-problem solving directly and indirectly through inference-making and comprehension monitoring. Morphological decomposition and extraction in Chinese enhance basic counting ability given the compounding numbering system. Additionally, it helps to construct the meaning at the initial stage of word-problem solving by translating mathematic texts into arithmetic equations.

The present study

Morphological awareness could be an inevitable factor that initially enhances learners’ reading abilities and recognize Chinese mathematical words, constructing the foundation while setting the stages of further mathematic learning, especially in arithmetic word problems. Nevertheless, previous work focused more on emphasizing learning in early elementary or preschool years among Chinese children. To date, few studies have examined language-specific reading subskills in shaping arithmetic competence among early adolescent students. As discussed above, the strength of the correlation between reading and word-problem solving varies as a function of age (Aunola et al., 2004). Notably, Chinese early adolescents around grade 5 are considered to a relatively mature readers transiting from learning to read to reading to learn, with high-frequency exposure to arithmetic word problems in mathematics learning. Therefore, the question of whether older children’s word-problem-solving skills can be improved by reading subskills is worth empirical investigation. Given the interface between Chinese compounding morphology and arithmetic competencies (Ng and Rao, 2010; Liu et al., 2016), the aim of the current study was to explore the effect of Chinese morphological awareness facets on arithmetic word-problem solving among early adolescents. We hypothesized that Chinese morphological awareness would uniquely predict arithmetic word-problem-solving abilities among early adolescent students.

Methodology

Participants

The sample was from a large dataset that emphasized literacy and academic development among early adolescent students. A total of 668 Chinese students (330 fifth graders and 338 sixth graders, 379 boys and 289 girls, mean age = 11.3 years) participated in this study. They were from two public schools in two coastal cities in southeast China. The students began their formal literacy and math instruction from first grade and they received instruction in Mandarin Chinese. All participants were typically developing children without diagnosed cognitive and learning disabilities. Ethical approval was obtained from the ethics committee of the authors’ institution. The procedures used in this study adhere to the tenets of the Declaration of Helsinki. Informed consent was obtained from all participants prior to data collection.

Measures

Receptive vocabulary

Given all measurements were print tasks, reading receptive vocabulary was assessed as a control. A checklist task modeled based on Anderson and Freebody (1983) was to assess students’ receptive vocabulary knowledge. 80 two-character compound words (64 real words and 16 nonwords) were presented to the participants, and they were asked to select the words that they had known. The nonwords were comprised of two real characters but the semantic meanings of the compounds do not exist. In data coding, real words circled as known were labeled as “real hits” and nonwords circled as known were labeled as “false alarms”. Based on the Signal Detection Theory, an equation true \(h = \frac{{h - f}}{{1 - f}}\) (h: real hits; f: false alarm) was used to calculate their performance.

Morphological awareness

Morpheme recognition

The recognition task (adapted from Ku and Anderson, 2003) measured the participants’ ability to understand the morphemic relationship between two presented words. For example, one compound word小心 (small+heart→careful) and its component character/word小(small) were shown and the participants were asked to judge whether the component word was related to the compound. There were 20 items in this task. The reliability was α = 0.725.

Morpheme discrimination

The discrimination task (adapted from Ku and Anderson, 2003) was to assess the ability to discriminate homographic morphemes in two-character compounds. For example, three compound words—白米(white rice), 小米(millet), 厘米(centimeter) were presented, all of which share the morpheme 米(rice/husk/seed), but 厘米(centimeter) carries a different morphemic meaning from the other two. Participants needed to choose the odd word out. There were 20 items in this task. The reliability was α = 0.734.

Compound structure awareness

The compound structure task which was adapted from Liu and McBride-Chang (2010) measured children’s ability to understand the compounding structures of novel words. The task asked the participants to choose the legitimate compound based on each provided description or prompt. In line with Liu and McBride-Chang’s (2010) categorization, the current study focused on four different Chinese compounding structures, namely subject-predicate, verb-object, subordinate, and coordinate. For example, a description, 青蛙在跳跃叫做什么? (How would you say “frog is jumping”), was presented, and the participants needed to choose whether the compound was 蛙跳(frog jumping) or 跳蛙(jumping frog). There was a total of 20 items. The reliability of this task was α = 0.749.

Arithmetic word-problem solving

This researcher-designed task measured students’ ability to form an indicator and generate the solution. Given the participating fifth and sixth graders had learned all types of arithmetic operations, the operation included addition, subtraction, multiplication, division as well as fractions. There were 12 arithmetic word problems of varying types of arithmetic operations and levels of complexity in the calculation. All word problems were controlled for linguistic and numerical complexity. The text length of the word problems ranged from 37 Chinese characters to 57 characters (mean = 44 characters). The linguistic complexity of the word problems was measured by the Chinese Readability Index Explorer (CRIE) (Sung et al., 2016). The indices including the number of words, number of Chinese characters, frequency of difficult words, number of words per sentence, frequency of content words, and logarithmic mean of content word frequency corresponding to external corpora were analyzed to control the linguistic complexity (c.f. Table 1). Regarding the arithmetic complexity, all word problems involved two-digit operations because Grade 5 and 6 students have mastered carry and borrow operations. The arithmetic complexity depends on the difficulty of mathematical operations and the solving steps required to solve the problem (Kingsdorf and Krawec, 2014; Pongsakdi et al., 2020). Problems involving multiple solving steps and operations are more challenging.

Table 1 Analysis of linguistic complexity based on CRIE.

Two sample problems that have different levels of difficulty are shown below.

One basic problem of Grade 6 is 饲养组有黑兔60只, 白兔比黑兔多1/5, 白兔有多少只? “In the breeding group, there are 60 black rabbits, and the number of white rabbits is 1/5 more than the number of black rabbits. How many white rabbits are there?” The problem can be solved by one solving step and simple operations:

$${{{\mathrm{Number}}}}\,{{{\mathrm{of}}}}\,{{{\mathrm{white}}}}\,{{{\mathrm{rabbits}}}} = 60 \times \left( {1 + 1/5} \right) = 72$$

One challenging problem of Grade 6 is 汽车的速度是火车速度的四分之七。两车同时从两地相向而行, 在离中点十五千米处相遇, 这时火车行了多少千米? “The speed of a car is seven-fourths of the speed of a train. Two cars traveling in opposite directions from two places at the same time meet at a distance of fifteen kilometers from the midpoint, how many kilometers has the train traveled at this point?” This problem needs to be solved by multiple solving steps and operations.

$${{{\mathrm{Total}}}}\,{{{\mathrm{distance}}}} = 15 \div \left( {7/11 - 1/2} \right) = 110\,{{{\mathrm{kilometers}}}}$$
$${{{\mathrm{Travel}}}}\,{{{\mathrm{distance}}}}\,{{{\mathrm{of}}}}\,{{{\mathrm{train}}}} = 110 \times 7/11 = 70\,{{{\mathrm{kilometers}}}}$$

Based on the two-step requirement (equation formation and computation), the participants needed to first translate each problem text into operations and then conduct mathematical computation. Equation formation involves translating the given information into mathematical equations or expressions. It ensures that the problem is properly represented mathematically, capturing the relationships and operations involved. Once the equations are formed, the calculations involved in solving the problem must be performed accurately. Evaluating the calculation step helps identify any computational errors, such as mistakes in arithmetic operations or errors in manipulating fractions, decimals, or percentages. Therefore, two subscales (equation formation and arithmetic computation) were coded for the word problems.

Equation

Two points were awarded for each accurate generation of equation/operation and no point was given if the equation was incorrectly formulated. If the participants can form the equation accurately, they can get full credit for this subscale. No partial scoring was given. The total score of equation formation was 24. The reliability of this task was α = 0.820.

Computation

Two points were given to each correct answer with accurate arithmetic computation. If the participants can get an accurate answer, they can get two points for this subscale. No partial scoring was given. The total score of equation formation was 24. The reliability of this task was α = 0.822.

Data collection precodure

In order to ensure internal validity, separate tasks were administered to rule out carry-over effects from previous tasks. All tasks were paper-and-pencil ones and administered to the participants in multiple regular classrooms at school. Tasks were counterbalanced in multiple regular classrooms. The time allotment was 60 min for all five tasks. Data collection was completed in 8 weeks.

Results

Descriptive statistics and correlations

Table 2 presents the descriptive results of the measured variables. Based on the standard deviations, all measurements showed adequate spread. Vocabulary generated a wide dispersion because scores were converted to percentages. A correlational matrix (Table 3) shows the relational patterns among variables. word-problem-solving was coded based on equation formation and mathematical computation and the two coded variables had very high correlations (r = 0.987, p < 0.001). All tested variables were intercorrelated with each other. Receptive vocabulary had significant correlations with arithmetic word-problem-solving indicators (r = 0.367, p < 0.001; r = 0.366, p < 0.001). Morphological awareness facets also had significant correlations with arithmetic word-problem-solving indicators (r = 0.164, p < 0.001 to r = 0.320, p < 0.001).

Table 2 Descriptive statistics of receptive vocabulary, morphological awareness, and arithmetic word-problem solving.
Table 3 Bivariate correlations among receptive vocabulary, morphological awareness, and arithmetic word-problem solving.

Hierarchical regression analysis

Before running the inferential statistics, we tested the statistical assumptions underlying regression analysis (Table 4). The Shapiro–Wilk test along with the skewness and kurtosis indices were analyzed to check the normality. The normality of morpheme discrimination was violated and the square root transformation was conducted to adjust the distribution of the variable for the subsequent analysis. The assumption of homoscedasticity was checked and the residuals were equally distributed. In addition, the variance inflation factor (VIF) ranged from 1.08–1.19 and the assumption of collinearity was confirmed. Two sets of regression analyses were then employed to test the relative contributions of morphological awareness facets to arithmetic word-problem solving (Table 4). The results showed that morphological awareness facets explained an additional 4.7 and 4.8% of the total variance in arithmetic word-problem solving (equation and computation) after age and receptive vocabulary were controlled. Among the individual contributions, morpheme recognition and morpheme discrimination had the stronger predicting power (β = 0.18, t = 4.56, p < 0.001; β = 0.10, t = 2.58, p < 0.05 and β = 0.18, t = 4.71, p < 0.001; β = 0.10, t = 2.54, p < 0.05).

Table 4 Hierarchical regressions predicting arithmetic word-problem solving.

Path analysis

A further covariance-based path model (shown in Fig. 1) was to test the individual effects of all the variables on arithmetic word-problem solving. Standardized path estimates of different routes are presented in Fig. 2. The findings (Table 5) showed that receptive vocabulary significantly contributed to both equation formation and computation (β = 0.277, p < 0.001; β = 0.279, p < 0.001). Among the morphological awareness facets, morpheme recognition and morpheme discrimination generated the significant predicting variance (β = 0.196, p < 0.001; β = 0.192, p < 0.001; β = 0.080, p < 0.05; β = 0.2080, p < 0.05) whereas compound structure awareness did not have a significant effect on word-problem solving (β = 0.042, p = 0.272; β = 0.040, p = 0.248).

Fig. 1: Cognitive and Linguistic Pathways to Math Problem Solving.
figure 1

A path model illustrating the influence of age, receptive vocabulary, and morphological awareness on the ability to solve arithmetic word problems.

Fig. 2: Regression Weights in Math Skill Development.
figure 2

Standardized regression weights show the strength of the relationships between age, language skills, and math problem-solving abilities, with direct paths solidly lined and indirect paths dashed.

Table 5 Standardized regression weights for the preferred path model.

Discussion

The current study examined the relationship between morphological awareness facet and arithmetic word-problem solving among early adolescents. The results underscored the significance of Chinese morphological awareness in word-problem solving. In general, the findings were in line with the existing studies showing the positive relationship between reading subskills and word-problem solving (Björn et al., 2016; Fuchs et al., 2006; Spencer et al., 2020; Vilenius-Tuohimaa et al., 2008). More specifically, by emphasizing adolescents’ word-problem solving, the study expanded the literature that tested the relationship between morphological awareness and arithmetic skills among elementary and preschool children (Liu et al., 2016; Zhang and Lin, 2015).

Based on the dual representation model (Kintsch and Greeno, 1985) as well as the construction-integration model (Kintsch, 1988), a textbase is constructed by local linguistic input as well as readers’ knowledge base. In word-problem solving, inferencing and comprehension build surface-level propositions with prior mathematical knowledge thus forming elaborative propositions to solve arithmetic word problems. Ng et al. (2021) proposed a path model tracing the routes from structural language (morphological and syntactic skills) and higher-order comprehension to arithmetic word-problem solving. Morphological awareness, as one foundational structural linguistic competence, shapes initial linguistic comprehension, which in turn fosters the conversion of word-problem text into mathematical solutions.

A few interpretable findings need further explanation. First, one objective of the study was to focus on a different age group to verify if the relationship between structural linguistic input and word-problem solving would be strengthened or diminished. Despite the emerging relationship between text comprehension and word-problem solving, Kyttälä and Björn (2014) found that there was no direct effect of reading subskills on arithmetic word-problem solving among Finnish adolescent students. The current study highlighted the unique contribution of reading subskill (morphological awareness) to arithmetic word-problem solving among Chinese adolescents. In conjunction with prior studies among preschool and early elementary-age children (Liu et al., 2016; Liu et al., 2020; Zhang and Lin, 2015); our findings infer that the relationship between morphological awareness and arithmetic competence persists and remains significant as children progress from preschool to adolescence. More specifically, structural linguistic input constructs meaning from text, which subsequently facilitates arithmetic word-problem-solving abilities.

The second aim of the study was to verify the role of morphological awareness facets (in the form of Chinese compound awareness) in arithmetic competence. As an example listed in the arithmetic word solving section, basic Chinese mathematic words such as 四分之七 (4/7; seven fourths), 十五 (fifteen/15/ten-five, are considered the most simple ones for learners to identify by using morphological awareness in the early mathematic learning stage, then forming the internalization of the recognition ability later. Also, 汽车(car) and 火车(train) share the same morpheme of ‘车’; this shared morpheme helps learners to first recognize and discriminate those two nouns or two variables in word-problem solving. Subsequently, the quantifier ‘千米’ (1 kilometer/1000 meters/one thousand meters) shares the same logic as before, ‘米’ is a morpheme representing a distance unit, and ‘千’ reveals its quantity. Notably, ‘相遇’ (meet) and ‘相向’ (face-to-face) are left-handed verbs that share ‘相’ (each other), simultaneously right-handed words reveal the movement trajectory of those two traffic tools. According to the morphological elements discussed above, mathematical learners ideally read the text by applying those reading subskills as prior knowledge to understand the text, then ultimately combine their mathematical knowledge to solve the problems. The results showed that the abilities to recognize and discriminate compounds contributed uniquely to arithmetic word-problem solving, even when factors such as age and receptive vocabulary were taken into account. As discussed above, Chinese compound awareness helps to construct local semantic meanings (Chen et al., 2009; Wang et al., 2006). The fundamental linguistic demands involved in morphological awareness are the ability to recognize sublexical elements in multimorphemic words and to map those elements onto orthography (Koda, 2000). Recognition and discrimination abilities can affect the success in arithmetic word-problem solving. Surprisingly, however, compounding structure awareness was not significantly related to arithmetic word-problem solving. Chinese compounding structure awareness may enhance basic arithmetic word-problem solving and computation given the compounding structure in Chinese number naming (Ng and Rao, 2010). However, the essence of adolescents’ word-problem solving requires more than computation skills. Awareness of compounding structures necessitates the understanding of structural regularity and salience in word formation, which is linked with counting ability (Liu et al., 2016). Structural sensitivity may not be directly transferred to the formation of propositions in word-problem texts. In addition, the results showed that equation formation and ultimate computation were very highly correlated at r = 0.987. That is, the participants would get an accurate solution once they formulated the equation correctly. Calculation skills may not be the core of word-problem solving among early adolescent students. Therefore, the interconnection between lexical compounding structure and number naming has a reduced effect on adolescents’ word-problem solving. It is worthy of note that meaning extraction at the lower level aids the construction of a mathematical text base, which ultimately facilitates word-problem translation and equation generation.

Conclusions and limitations

The present study examined the role of morphological awareness facets in early adolescents’ word-problem solving ability. The findings were consistent with the prior findings on younger students that reading subskills are positively related to arithmetic word-problem solving. More importantly, the study highlighted the language-specificity of linguistic input in the construction of word-problem text comprehension. The study infers that reading subskills such as recognizing and discriminating compound words might be associated with the way students understand word-problem texts, which could facilitate problem translation and solution.

More importantly, our research highlights the importance of morphological awareness in arithmetic word-problem solving, particularly among adolescents. These findings suggest potential benefits of incorporating morphological awareness into the curriculum, which could enhance students’ mathematical capabilities. The unique contribution of reading subskills, specifically morphological awareness, to arithmetic word-problem solving underscores the potential benefits of an integrated teaching approach that couples reading subskill development with mathematics instruction.

Due to the exploratory nature of this study, there are a number of limitations that need further examination. First, the current study focused on the concurrent pattern of morphological awareness and word-problem solving. It would be valuable to incorporate additional time points to track the developmental path and assess the robustness of the correlational pattern across time. Second, the number of variables was limited in the current study. Orthographic knowledge, syntactic knowledge, and working memory can be included as covariates. More critically, to further confirm the dual representation model, general text comprehension should be incorporated.