Reading is the primary means by which human beings acquire information and knowledge, which is an integral part of their productive lives. In the international mathematics education community, the importance of mathematics reading has received widespread attention from researchers and educators. For example, the UK National Curriculum (Mathematics), implemented in September 2014, not only emphasized mathematical reasoning, mathematical language, and problem solving, but also integrated “reading and writing literacy” into the stage goals, which are Key Stage 1, Lower Key Stage 2, and Upper Key Stage 2 [1]. China’s mathematics curriculum standard for compulsory education (2011) [2] emphasized that diverse learning styles such as reading for self-study should be promoted, and teachers should guide students in reading for self-study.

In terms of the relationships between reading and academic achievement, some studies have explored the correlation between mathematics reading ability and mathematics achievement and found that these two share basic cognitive abilities to some extent, including memory, visualization, and language skills ^[3][4][3,4]. Most of these studies, however, have tended to explore their relationship among students with dyslexia ^[5][6][5,6]. Additionally, the educational assessment was outcome evaluation, which focuses only on test scores. This has been criticized for ignoring the students’ individual development and constraining teachers’ personalized teaching. The emerging value-added assessment makes up for the shortcomings of this result-oriented approach by focusing on the students’ longitudinal growth data and providing a basis for the students’ sustainable development, pursuing not only “attainment” but also “growth”.

2. Mathematics Reading Ability and Value-Added Mathematics Achievements

2.1. Mathematical Reading Ability and Achievements

According to existing research, scholars agree that reading is a complex cognitive psychological process that involves acquiring meaning from linguistic symbols. In order to acquire meaning, one needs to have the appropriate mental lexicon and be able to integrate the meaning of linguistic symbols [7]. Mathematics reading is different from general reading in that it has its own unique abstraction in terms of vocabulary and grammar. Mathematics reading is a psychological process of acquiring mathematical knowledge and skills, mathematical ideas, mathematical methods, mathematical abilities, and other mathematical achievements from mathematical materials through mental activities such as perceptual recognition, comprehension, memorization, evaluation, and the auxiliary participation of hypothesizing, proving, inducting, generalizing, judging, and reasoning. At the secondary school level, the content of mathematical reading includes the development processes of mathematical conclusions in mathematical textbooks, textbook examples, and test questions. In particular, when reading to understand the mathematical conclusions presented in textbooks, the core of reading at this time does not only lie in comprehension, but also in thinking in relation to the unfolding process of the conclusions that already existed in the past. Young children develop reading and Mathematics skills at different rates. Some children’s numeracy skills develop rapidly until they are faced with word problems. This is because the verbal and formulaic information in mathematics can be difficult for children. When the learning task involves calculating sums, products, or quotients and the information is presented in numerical terms with the symbols ordered conventionally, students who understand algorithms can solve these problems and learn easily. When the learning task requires the student to decide whether to calculate the sum, product, or quotient and the information is hidden in sentences, the student needs to understand the language in the text before he or she can apply the appropriate algorithm. To solve these types of mathematics problems (which are a common part of school curricula), children need to learn to read mathematically [8]. Mathematics reading ability is an important factor affecting student learning in mathematics. Adams [9] stated that students read mathematics not only simply by reading words, but also by reading numbers and symbols for comprehension. However, students who have difficulty reading “mathematical language” are mostly weak in mathematics. The National Council of Teachers of Mathematics stated that to know mathematics is to do mathematics (1989). Alternatively, if students know mathematics, they know how to apply mathematics. Yu and Yang [10] have found that middle school students with mathematics dyslexia have more difficulties in learning. This difficulty can affect the students’ enthusiasm, self-confidence, and their mathematics achievements. Using 314 pairs of twins as their experimental sample, Hart et al. [11] found that the students’ performance in mathematics was not entirely determined by their general cognitive abilities. Their mathematics reading and problem-solving abilities, among others, were more significantly influenced by their genetics and environment. Vilenius-Tuohimaa et al. [12] found that mathematics reading and ability remained significantly correlated when controlling for two influential factors, gender and parental education. Vista [13] explored the role of students’ language background in their mathematics achievement growth and found that their language background did not affect the mediating effects of mathematical reading abilities between problem-solving skills and mathematics achievement growth. This study’s focus was on the role of reading skills in mediating the relationship between mathematical problem-solving skills and mathematics achievement, but it did not explore the value-added issue in mathematics achievement. Based on the literature, it was easy to conclude that there exists a relationship between mathematics reading ability and mathematics achievement; however, limitations still exist. First, most previous research was cross-sectional, and there has been a lack of studies investigating the relationship between mathematics reading ability and mathematics achievement from a longitudinal perspective [14]. Moreover, most studies have explored the relationship between general reading and mathematics achievement in a broader sense, but not in any specific discipline. Additionally, most studies have focused only on words or vocabulary and not on comprehension in reading. Lastly, most research on reading has only studied students with dyslexia, which has limited the sample to a particular small group of participants ^[15][16][15,16].

2.2. Value-Added Assessment

In recent years, a new type of assessment called “value-added assessment” (VAA) has emerged in the field of educational assessment, with the aim of providing a scientific and objective evaluation of students’ academic progress. In the value-added assessment, a student’s achievement is not a single test score or an average of scores, but rather the amount of progress a student makes over a period [17]. The novelty of value-added evaluation is that it does not take into account initial student differences, instead using the degree to which the school is effective in helping students grow as a basis for evaluating school effectiveness and teacher effectiveness [18]. There have been some studies on teacher effectiveness since the introduction of value-added assessment. For instance, in one educational study of value-added assessment in Tennessee, Sanders et al. [19] found that students’ socioeconomic status did not have a significant effect on their achievement gains, and that teachers and schools had a far more dominant influence on the students than socioeconomic or family background factors ^[20][21][20,21]. This provided a reference for solving the problem of educational fairness and guided a new direction for educational research. Using this comprehensive model of school effectiveness, Jong et al. [22] empirically investigated Dutch schools. The study showed that in terms of school improvement, the time that teachers spent on students and the learning opportunities given to students were more effective for student achievement growth. For value-added student achievement, what needs to be considered is no longer the school choice, but rather more practical factors such as school internal management and teaching. In 2011, building on Sanders’s (1997) study, the Tennessee Department of Education (TDOE) developed the Tennessee Educator Acceleration Model (TEAM). TEAM conducts teacher effectiveness assessments based on combined information on student achievement and classroom observations. They found that the quality of teacher instruction in U.S. elementary and secondary schools still varied dramatically, even between classes in the same school [23], further affirming the importance of classroom instruction on student academic growth. During this same time, the Measurement of Effective Teaching (MET) project, supported by the Bill and Melinda Gates Foundation, used improvements in student achievement to estimate the value added by teachers. Specifically, based on classroom observations of teaching quality through the process dimensions, the MET project used improvements in student achievement as a measure of teacher quality. They found that teacher quality was unrelated to advanced degrees or certificates and instead more closely associated with the teachers’ experience [24]. Over the past half century, VAA has evolved in the direction of studying more specific objects, and research has shifted closer to teaching, learning, and student-focused investigations. VAA was initially used to explore educational equity at the national level, then to improve school effectiveness and teacher accountability. Gradually, it has moved to research on the student level, focusing on the impact of student factors on growth.

2.3. Effects of Mathematics Reading Ability on Value-Added Mathematics Achievements 

First, mathematics reading skills had a significant positive impact on value-added mathematics achievement, with higher mathematics reading scores associated with higher value-added levels. This positive result was consistent with previous research on similar mathematical reading and academic achievement, which involved conducting longitudinal studies on the relationship between early mathematical skills, reading comprehension, and mathematical problem-solving skills to explore the complex relationship between reading and mathematical abilities and illustrate the role of these abilities in promoting and influencing each other ^[25][26][27][37,38,39]. However, scholras found also a positive impact of mathematics reading on value-added mathematics achievement through a residual model from a value-added perspective. Although both contributed to mathematics achievement, the value-added levels differed from growth. Value-added refers to the extent to which a student’s actual academic achievement improves over a time period relative to the student’s own expected academic level. Achievement growth, on the other hand, refers to the current change in achievement relative to performance on a previous measurement or test. This suggests that in the future, more consideration could be given to these differences when improving the net effect of teachers’ influence on students’ academic achievement in mathematics, and that measures could be tailored to these characteristics. Second, mathematics reading ability was more conducive to high value-added performances for students with high initial scores than for students with low initial scores. “Progress and Growth”, the scatter density of high math reading level codes was higher in the high-basic high-value-added group than in the other groups in theis study, and the difference in math reading scores across the four quadrants also shows that the overall mean value of math reading was higher in the high-basic high-value-added group than in the high-basic low-value-added group with the same initial math scores. That is, more attention can be given to the top students in strengthening the instruction of mathematical reading skills instead of unilaterally taking the improvement of mathematical reading skills as a strategy to improve the mathematical performance of all students, which can accommodate the diversity of students and make teaching more efficient. Vigdor ^[28][40] and Kenan et al. ^[29][41] have also suggested that egalitarian shock improves the skills of underperforming students to some extent, but sharply dilutes the curriculum standards, negatively affecting top-performing students. Therefore, supporting differentiation by adapting the curriculum to meet the diverse instructional needs of students is the best way to promote higher achievement for all students. While mathematics reading does promote value-added performance, as seen in the exploration of differences in mathematics reading among students at different value-added levels, the difference between the mean values of mathematics reading performance in the low-base high-value-added group and the low-base low-value-added group was not significant. These values were close to or below the average overall, suggesting that there was indeed a positive relationship between mathematics reading and value-added scores. However, in the group of students with low initial achievement, this relationship does not seem to be significant. This may be explained by the floor effect: most studies have demonstrated that poor math reading skills may lead to a failure to improve math scores ^[30][31][42,43], and students at the lower end of the achievement scale may be dyslexic or lack math reading learning methods and strategies. For these students, the main factor affecting their performance improvement may not be math reading, but rather other mathematical skills ^[32][33][44,45]. This aspect warrants further investigation.