Effects of Calculation and Reading Fluency Interventions Focusing on Awareness and Adaptive Use of Strategies: Supporting Children With Comorbid Fluency Problems

Abstract

This quasi-experimental study examined the benefit of intervention focusing on awareness and flexible use of strategies in arithmetic and reading among Finnish children with comorbid arithmetic and reading fluency problems (Grades 2–4). Children participated either in a calculation intervention (n = 45) or a reading intervention (n = 51) or received business-as-usual support at school (n = 47). Both domain-specific and cross-domain effects were investigated. The calculation group improved in single- and multi-digit addition fluency significantly more than the other two groups, while the progress in sentence and text reading fluency was not different in the reading intervention group compared with the other two groups. Also, neither intervention showed cross-domain effects. The results of this study add to the existing knowledge of pedagogical practices to support arithmetic and reading fluency in children with comorbid difficulties and lead us to consider the developmental and instructional differentiations between the skills.

Keywords

calculation fluency reading fluency comorbidity intervention elementary school

Introduction

Fluency is an essential component in the development of complex academic skills such as reading comprehension (Klauda & Guthrie, 2008) and mathematical problem-solving (Nunes et al., 2012). Accordingly, slow and laborious decoding (Ziegler et al., 2003) or calculation skills (Cirino et al., 2015; Jordan et al., 2003) are common characteristics of difficulties in these academic domains. Also, the co-occurrence of these difficulties is common (Landerl & Moll, 2010) and more stable compared with single fluency problems (Koponen, Aro, et al., 2018) highlighting the need for effective pedagogical practices. Many interventions aiming at enhancing fluency focus on training arithmetic facts (Dowker, 2019) and through repeated reading training (Stevens et al., 2017) or with practices aiming at increasing overall volume of reading (Zimmermann et al., 2021). However, traditional repetitive training alone may not sufficiently promote skill development in children with comorbid math and reading difficulties (Powell et al., 2020). Although knowledge about comorbidity is increasing, the number of interventions targeting to this subgroup has been extremely limited thus far (Fuchs et al., 2013; Powell et al., 2020). This study aims to partly fill in this gap by investigating whether domain-specific support focusing on awareness of different calculation and sublexical strategies can improve calculation and reading fluency in Finnish children with comorbid fluency problems.

From One-by-One Coding Toward Fluency: Role of Metacognitive Knowledge

Arithmetic and reading activities can be approached differently depending on the task’s features and one’s knowledge of how to complete it. Awareness of different strategies and their appropriate use depending on the task’s characteristics are essential elements of metacognitive knowledge that develop with practice and learning experiences (Schraw, 2001). For example, calculation fluency develops gradually from counting-based calculation strategies to more efficient retrieval-based strategies (Butterworth, 2005). Children initially count all addends from the start of the number sequence, then from the first addend, and eventually use the commutative property to count from the larger addend (Siegler, 1987). Over time, through repetition, children develop more advanced ways to solve arithmetic problems, like retrieving answers from memory or deriving them using known arithmetic facts (e.g., 6 + 9 = 6 + 6 + 3 = 12 + 3 = 15). Calculation fluency also requires adaptively selecting the most appropriate strategy based on task characteristics and the individual’s preference (Verschaffel et al., 2009).

In orthographically transparent languages like Finnish, learning to read starts with decoding words letter-by-letter due to the one-to-one correspondence between letters and sounds before recognizing larger units more efficiently (M. Aro, 2017). Wood et al. (2001) propose that text reading fluency consists of two central elements: automaticity and anticipatory processes. Recognition of units like syllables, morphemes, and familiar words becomes faster as they become increasingly more familiar with practice and repetitions (Share, 1995). However, reading connected text requires more than accurate and fast word decoding, as it aims at understanding the meaning. Thus, anticipation of the upcoming text is another important component of fluent reading (Wood et al., 2001). Activating knowledge of word meanings (semantics), sublexical units (i.e., morphemes and syllables) and sentence structure (syntax) is needed to support fluent reading (Carlisle & Kearns, 2017).

Acknowledging the importance of these linguistic elements is particularly crucial in languages that have consistent orthography but complex morphology like the Finnish language (M. Aro, 2017; Borleffs et al., 2019). Finnish has a complex inflectional morphology, where for example nouns (root koulu [school]) can have multiple inflectional suffixes indicating case and number or clitics (e.g., koulussa, kouluissa, and kouluissammekaan [at school, in schools, and not even in our schools]). Furthermore, the Finnish word-formation system is productive, meaning that the root can occur in many compound words (koulupäivä [school day]) or derivations (koululainen [schoolchild]), which are further inflected following similar rules (koululaisissammekaan [not even in our schoolchildren]). The syllable is another relevant linguistic unit in the orthographically transparent Finnish language, as the words usually consist of multiple syllables with relatively stable pronunciation (M. Aro, 2017). Due to that, early reading instruction quickly proceeds from practicing single letter-sound correspondences to combining them into syllables and words. Frequent encounters with syllables through reading activities likely foster their quick recognition (Huemer et al., 2010), highlighting their role in supporting reading fluency.

Children struggling with arithmetic and reading fluency often have difficulty moving beyond the one-by-one decoding strategy, especially if not emphasized in school instruction. Thus, instruction should incorporate a conceptual understanding of calculation principles and awareness of sublexical units to enable their conscious utilization. Self-monitoring one’s thinking processes during a task is a key component of metacognitive regulation (Schraw, 2001), which is an important aspect of applying a suitable strategy to solve a particular arithmetic problem (Verschaffel et al., 2009) and comprehending the meaning of a text (Duke et al., 2021). From this perspective, incorporating a metacognitive perspective that highlights awareness of calculation strategies in arithmetic problems and relevant linguistic units within reading activities could be a potential component to consider in interventions targeting children with difficulties in these domains.

Calculation and Reading Fluency Problems and Their Comorbidity

Children with poor arithmetic skills often employ immature and error-prone counting strategies instead of retrieval, decomposition or deriving strategies to solve even single-digit problems (Dowker, 2009; Geary, 2011). Reliance on counting strategies is also related to weaker performance in more complex calculation problems (Hopkins et al., 2022). In reading, difficulties usually manifest as slow and laborious word decoding (Ziegler et al., 2003) emphasized by a reading strategy that relies on letter-by-letter reading instead of recognizing larger units like syllables or morphemes (Di Filippo et al., 2006; Loberg et al., 2019). As described above, morphological complexity hinders quick word recognition (M. Aro, 2017), and places demands particularly on children with reading difficulties (Borleffs et al., 2019). On the contrary, it has been suggested that readers with poor reading skills may compensate for their slow reading by relying on morphological cues (Elbro & Arnbak, 1996; Giazitzidou & Padeliadu, 2022). However, focusing heavily on letter-by-letter decoding can strain reading comprehension (LaBerge & Samuels, 1974), especially with long polysyllabic and inflected words. Efficiency requires knowledge of sublexical units and practice, which helps establish orthographic representations of words and frequent sublexical units (Share, 1995; Verhoeven et al., 2022) leading to more fluent decoding and text context utilization while reading. Likewise, successful experiences in solving arithmetic problems strengthen the formation and retrieval of problem-answer mappings.

In addition to similarities in the development of arithmetic and reading fluency, difficulties in these domains often co-occur more than expected. When defined as fluency problems, comorbidity rates range from 22% to 44%, with the likelihood of co-occurrence increasing with the severity of difficulties (Koponen, Aro, et al., 2018; Landerl & Moll, 2010; Moll et al., 2014). As already discussed, fluency problems in arithmetic and reading are characterized by the tendency to use immature strategies to solve arithmetic problems or printed texts, but both sub-domains also build up on language requirements (Moll et al., 2019). This interconnectedness highlights the need to increase knowledge on potential ways to support skills within but also across domains. Comorbid difficulties have been associated with higher stability during school years compared with single-deficits (Koponen, Aro, et al., 2018), lower math- and reading-related motivation and self-beliefs (Pulkkinen et al., 2022) and risks for disrupted educational trajectories and reduced well-being in adulthood (T. Aro et al., 2019). Therefore, knowledge of efficient pedagogical practices to support children with co-occurring problems in reading and calculation skills is needed already in elementary grades.

Fluency Interventions: Increasing Children’s Awareness of Strategies

Few intervention studies have addressed the high prevalence of comorbid difficulties. Powell and colleagues (2020) concluded that only a handful of math intervention studies examined in their synthesis (10 out of 65) provided information on children’s reading performance that accounted for comorbid reading problems. The findings of very few existing studies indicate that children with comorbid difficulties benefit less from pure drilling-type training compared with those without concurrent reading problems (Powell et al., 2009, 2020), suggesting that this subgroup might need different support to develop their calculation skills (Fuchs et al., 2013). Koponen, Sorvo, et al. (2018) suggest that strategy-based instruction that combines conceptual and procedural understanding with factual knowledge increases the use of more efficient calculation strategies and improves addition fluency in children with calculation fluency problems, although they did not account for co-occurring reading problems. Fuchs et al. (2009) in turn examined a subgroup of children with comorbid difficulties (although their screening measures consisted not only an arithmetic fluency measure but also an orally presented word problem-solving task with a time limit and a non-timed word-decoding task) and found that teaching number combinations (n + 1, n − 1, doubles, n + 2, n − 2) and encouraging counting from the larger addend improved both single-digit arithmetic fluency and procedural skills with double-digit problems. Thus, supporting knowledge of calculation strategies appears to be effective for children with math problems, with and without comorbid reading difficulties.

Considering the analogical elements in (dys)fluent reading and calculation skills and promising results on strategic instruction, further research on reading interventions should consider comorbid arithmetic difficulties. Many reading intervention studies have examined the efficacy of repeated reading (i.e., reading a particular text multiple times) suggesting that it could improve the automaticity of word recognition (Huemer et al., 2010; Stevens et al., 2017), while other fluency interventions have emphasized increasing the number of various reading activities to promote general reading fluency (Huemer et al., 2010). However, repeated reading training alone does not appear to significantly improve the reading fluency of learners with reading difficulties (Galuschka et al., 2014) perhaps due to the persistent nature of reading fluency problems. Also, the training effects seem to restrict on practiced materials (Huemer et al., 2010; Wexler et al., 2008). Training that aims to automate the representation of a whole word (e.g., school) does not necessarily fit in languages where a single word can have even 2000 different inflected forms (see M. Aro, 2017). Furthermore, the effects of alternative methods for enhancing reading fluency have been studied primarily in the context of the English language (e.g., Zimmermann et al., 2021), limiting the knowledge of evidence-based reading fluency interventions (R-Is) other than repeated reading in more transparent languages. For example, explicit morphology training has been shown to have clear effects on children’s morphological awareness (Martinez et al., 2024; Mendes & Kirby, 2024) but the results on reading fluency outcomes have been mixed. Some studies have demonstrated its potential benefits for improving reading outcomes, including reading fluency (Reed, 2008). In contrast, other studies have found the lack of transfer effect (Mendes & Kirby, 2024). The contradicting findings highlight the need to further examine the effects of activating awareness of sublexical units on reading fluency.

In summary, repetition alone may not sufficiently support skill development in children with co-occurring difficulties. While focusing on calculation strategies shows promise for arithmetic skills, the effectiveness of activating knowledge of sublexical cues for reading fluency remains unclear. Both domains require metacognitive skills, including assessing task difficulty, selecting appropriate strategies, and monitoring performance. Mastering these skills necessitates awareness and conscious practice. Thus, there is a need for pedagogical tools that account specifically for the persistent nature of comorbid problems and include other components besides repeated training practices. Increasing children’s awareness of various strategies and their adaptive use could be a beneficial component of fluency interventions in both academic areas. In addition to similarities between fluency problems and their reliance on language, it is worth examining whether targeted support on metacognitive skills within one domain would have reflections on the other, as they are needed in arithmetic and reading activities.

The Present Study

This quasi-experimental study examined the effectiveness of two domain-specific intervention programs aimed at enhancing children’s awareness of various calculation or reading strategies and instructing them to apply them flexibly, depending on the task. Calculation strategies focused on applying knowledge of calculation principles and arithmetic facts to solve addition tasks while reading strategies emphasized the use of sublexical and contextual cues during reading. The overall aim was to support children in moving from slow serial processing to more efficient and adaptive strategy use. The study also explored whether focusing on strategies in one domain (calculation or reading) could improve fluency in the other. Accordingly, the study included three intervention conditions: calculation fluency intervention (C-I), reading fluency intervention (R-I) and a control group receiving business-as-usual (BAU) instruction in school. The groups from each school were assigned into one of the treatment conditions randomly considering, however, that only one condition could be carried out at each school and by each teacher to prevent leaking of intervention content. To ensure ecological validity, teachers conducted the interventions during school days. The following research questions were formed:

Research Question 1 (RQ1): Does intervention on calculation strategies targeted for children with comorbid fluency problems improve their calculation fluency (domain-specific effect) and reading fluency (cross-domain effect)?

Research Question 2 (RQ2): Does intervention on reading strategies targeted for children with comorbid fluency problems improve their reading fluency (domain-specific effect) and calculation fluency (cross-domain effect)?

Materials and Method

Participants

This study is part of a longitudinal research project (Reading and arithmetic dysfluency in children, 2014–2018) presenting findings on two domain-specific interventions targeted for children with comorbid fluency problems. Volunteering teachers (mostly special education teachers) carried out the intervention and the assessments on school days. The children’s guardians provided written consent for their children’s participation, and the children were informed that participation was voluntary. The university’s Ethical Committee evaluated and approved the research plan which was modified based on the committee’s comments and suggestions.

Screening Procedure

The study adopted a two-phase screening procedure. First, to limit the number of children attending to the second phase with individual assessments, the voluntary teachers administered two computerized arithmetic and reading fluency tasks for whole class groups of children with permission to participate to the study. Overall, 3306 children from Grades 2 (n = 1,226), 3 (n = 1,066), and 4 (n = 1,014) from 93 schools across Finland participated in the first screening phase in October 2017. Of them, 363 children scoring in the lowest quintile in both computerized tasks proceeded to the next phase, where 337 of them completed individually administered arithmetic and reading fluency tasks. The inclusion criteria for the intervention were scoring below the 25th percentile in the individual assessment tasks. In addition, teachers were requested to evaluate, based on their knowledge, whether the child had or did not have adequate language and group working skills to participate in the intervention. Eventually, 215 children met the inclusion criteria.

After the initial assessments, 18 children dropped out due to a lack of teacher resources for participation. The remaining 197 children were assigned to three intervention conditions: C-I (n = 65), R-I (n = 65), and BAU control (n = 67) groups. After that, 20 children dropped out before or during pre-assessment due to the teacher’s re-evaluation of their resources. Regrouping was not possible in this phase as some teachers had already familiarized themselves with the manuals. Three teachers left their positions during the intervention, reducing sample size by 12 children. Three children decided to withdraw from the study, and two children changed schools during the study. Furthermore, 17 children were unavailable for the post-assessment due to a lack of teacher resources or for unknown reasons. The flowchart (see Figure 1) in Supplemental Materials presents the screening, group assignment and intervention phases visually.

Our analyses included 143 children from 48 schools who participated in the pre- and post-assessments. Independent samples t-test showed no significant differences between the attrition group (n = 54) and the final sample in two reading fluency measures (Luksu, t(195) = 1.71, p = .090; text reading, t(195) = 1.20, p = .230) or in the other calculation fluency measure (Matsu, t(195) = 1.80, p = .074). The attrition group had a significantly better average performance on the other arithmetic fluency task (addition fluency, t(195) = 2.03, p = .044, M = 18.96 (SD 6.22) vs. M = 17.02 (SD 5.89) for the attrition vs. the final sample, respectively). To ensure all three groups had equal initial levels in arithmetic and reading fluency, we compared their mean standardized scores in the four screening tasks. Standardization was based on grade-level means and standard deviations from the current screening sample (Matsu and Luksu) and a comparable population-based sample (addition fluency and text reading). Mean scores ranged from −1.2 to −1.4 in addition fluency tasks and from −1.3 to −1.6 in reading fluency tasks, with no statistically significant group differences.

Intervention Programs

Each intervention group, consisting of maximum of four children, started the 6-week program after completing the pre-assessment. Post-assessments were conducted after all sessions were completed. The BAU group participated in all assessments and received BAU instruction and support. The intervention groups followed either a calculation or a reading intervention program. Both programs aimed to activate students’ awareness of various calculation and reading strategies as well as their efficient use. The instruction language was Finnish. Programs began with an orientation session to familiarize participants with the content, schedule and each other. Groups met twice a week for 45 minutes, with 15-minute recap paper–pencil task sessions on the following day. The recap tasks aimed at increasing the intensity of training and strengthening the learning process. They included already practiced content and were meant to be completed in the child’s own classroom independently or with the help of their own teacher or teaching assistant. Session-by-session content of both interventions is summarized in Supplemental Table 1. Both programs followed a similar structure. The teacher introduced the session structure and presented the specific session topic with an example or a problem that was discussed and solved together, followed by one or two tasks that were done either in a group or individually. Each session was concluded with either a classification task or a timed minute-task. Teachers were instructed to allocate time for this recurring task. Children had personal notebooks to attach progress monitoring sheets of repeated tasks during the intervention and a picture of a train with wagons that they colored after each completed session. At the end of the intervention, children received diplomas with teacher feedback on their progress.

Calculation Intervention

The calculation intervention aimed to improve children’s calculation fluency by focusing on their awareness of various calculation strategies, identifying the most efficient strategies for them, and using them adaptively in different arithmetic problems. The basic principles of the current intervention were based on the SELKIS program (Koponen et al., 2011; Koponen, Sorvo, et al., 2018). The intervention included frequent game activities with addition cards or 1–10 dice sent to the teachers. Addition classification was a recurring task held every other session, starting from the first meeting. It aimed to increase children’s awareness of their calculation strategies and help them identify and use efficient ways to solve addition problems. Children sorted 20 cards into two piles: known answers and unknown problems. Subsequently, each child showed the cards they had classified into the pile of known additions and gave the answer. If the child did not know the answer, the card was moved to the other pile. They then formed two other piles from the unknown problems: additions solvable by deriving from known facts and those requiring counting. Children chose one card from the first pile and presented their strategy. If someone had the same card, strategies were discussed. The group continued for at least two rounds and then moved to the last pile of additions classified as solvable by counting. Problems were solved together, starting from the larger addend. The same set of cards was used for two consecutive weeks before switching to a parallel version (three parallel sets in total). Minute-calculation took place every other session, starting from the second meeting. This task aimed to utilize different strategies and visualize individual progress in addition fluency. Children had one minute to solve as many of 30 single- and two-digit additions as possible. The answers were checked together. Children tracked their progress by coloring a sheet consisting of six towers (six repetitions during the intervention) with blocks representing the number of correct responses. The same version of the task was used throughout the intervention.

Reading Intervention

To detach from slow and laborious ways of reading, children were introduced to more efficient reading strategies and their flexible use. The intervention focused on the anticipation component of reading fluency, supporting children to actively monitor their reading, consciously anticipate the upcoming text, and use knowledge of sublexical units and text context to read more fluently. Word classification followed similar principles as the addition classification task. Each child had a sheet of 21 words, and their task was to underline words they could read quickly without decoding, and circle words that include familiar words (i.e., kahvi pannu [coffee pot]) or syllables (i.e., man sikkahillo [strawberry jam]) they could recognize quickly. Two versions alternated each session. The teacher recorded the number of underlined words for each child, and the group’s total score was followed during the intervention. Minute reading followed the same principles as the minute calculation. The teacher chose a text from three options. Each child read the text for one minute while the teacher recorded errors. Feedback was given after each turn, focusing on fluent reading or overall speed improvement. Errors were re-read together, and children colored the blocks of the tower representing the number of correctly read words. The reading order varied from session to session to avoid familiarity with specific text parts.

Assessment and Measures

Teachers carried out screening and pre- and post-assessments based on the research group’s instructions. Tasks including children’s oral performance were individually administered and recorded with a web-based application developed for this study. The recordings were used to verify and, if needed, correct the initial teacher scoring. After completing each set of assessments, the teacher entered the scores into an electronic survey and mailed the hard copies of the scoring sheets to the research group via the postal service. Correlations between the screening and pre-test outcome measures are presented in Table 1.

Table 1.

Pearson’s Correlations for Screening and Pre-Assessment Measures.

Measure	1	2	3	4	5	6	7	8
1. Matsu, screening 1	—
2. Addition, screening 2	.61***	—
3. Addition, pre-assessment	.61***	.71***	—
4. Calculation task, pre-assessment	.60***	.70***	.73***	—
5. Luksu, screening 1	.53***	.55***	.43***	.44***	—
6. Text reading, screening 2	.49***	.55***	.42***	.51***	.80***	—
7. Text reading, pre-assessment	.39***	.48***	.39***	.44***	.77***	.76***	—
8. Sentence reading, pre-assessment	.38***	.48***	.30***	.42***	.78***	.88***	.90***	—

***

p < .001.

Calculation Fluency Measures

A computerized addition task, Matsu (Heikkilä & Koponen, 2017), consisting of 81 single-digit additions, was used to assess children’s arithmetic fluency in the screening phase. In the task, the children were instructed to indicate whether an addition statement (e.g., 5 + 7 = 11) was correct or not. The score was the number of correct responses within the time limit of 120 seconds. In another population-based sample, the correlations of Matsu and a paper–pencil addition fluency task were .71–.82 in Grade Levels 2–4 (Heikkilä et al., 2023). Addition fluency task (Koponen & Mononen, 2010), a paper–pencil task consisting of single-digit addition problems, was used to verify screening results as well as an outcome measure in pre- and post-assessments. The child was instructed to solve as many problems as quickly and accurately as possible within the 120-second time limit. The score was the number of correct responses within the time limit. Calculation fluency task was designed for this study. The paper–pencil task consisted of 20 single- and two-digit addition problems, that required utilization of commutative property (e.g., 2 + 9 = 9 + 2), derived fact strategies (e.g., 8 + 3 = 8 + 2 + 1 = 11), and recognition of familiar arithmetic facts (e.g., doubles: 3 + 6 + 6 = 12 + 3 = 15, 10 pairs: 7 + 5 + 3 = 10 + 5 = 15). The child was instructed to solve all 20 calculation problems as fast as possible. The time was recorded and the number of correct answers within 60 seconds was used as a score for the task. Test–retest intraclass correlation coefficient (ICC, two-way mixed model with consistency) scores for addition and calculation fluency tasks were calculated based on the pre- and post-assessments within the BAU group, the scores being .78 and .77, respectively.

Reading Fluency Measures

A computerized version of the Sentence verification task (Luksu; Salmi et al., 2011), was used as a screening measure to assess children’s reading fluency. The task had a time limit of 120 seconds and included 70 short and semantically simple sentences (e.g., Birds fly better than snakes). The children were instructed to read the sentences silently one by one and use a keyboard to indicate whether they were correct or incorrect. The score was the number of correct responses within the time limit. In another population-based sample, the correlations of Luksu and a text reading fluency task were .65–.86 in Grades 2–4 (Heikkilä et al., 2023). Individually administered text reading task (Salmi et al., 2011) was used to verify the screening result as well as an intervention outcome measure in pre- and post-assessments. Three parallel versions were used. The child was asked to read aloud an informational text as fast and accurately as possible within 90 seconds. The score was the number of correctly read words within the time limit. Sentence reading task was created for this study. The individually administered task included 20 unrelated simple sentences varying in length from three to four words in length. The child was instructed to read the sentences as fast and accurately as possible, while the reading time was recorded. The final variable was constructed based on tape recordings, and when the tape was unavailable, the coding was supplemented with teacher notes. The correlations between tape review and teacher recording were .94 and .95 for pre- and post-tests, respectively. The final score was the number of correct words read within 60 seconds. Test–retest ICC scores for pre- and post-tests in the BAU group for the text and sentence reading fluency tasks were .87 and .91, respectively.

Background Measures

Non-verbal reasoning was measured using Colored Progressive Matrices (Raven, 1956) at pre-assessment phase. For each test item, the child’s task was to choose from six presented visual stimuli the one that matched to a missing piece of a target picture. As the test was carried out in a small group, the teacher ensured that the children had responded before the next item was presented. The score for non-verbal intelligence was the number of correct answers. Parental educational level was measured as the parental highest degree using a parental questionnaire with a 5-point scale: 0 = no further degree after compulsory education; 1 = upper secondary education (vocational or high school); 2 = bachelor’s degree or equivalent; 3 = master’s degree or equivalent; and 4 = licentiate or doctorate.

Teacher Training and Fidelity

Before starting the assessments, teachers were instructed to watch two video lessons on the study aims and structure and familiarize themselves with the assessment instructions and forms. All materials, including instructional videos and materials for assessments and intervention programs, were shared with teachers via a university’s online platform which required personal login credentials. To avoid contamination bias, the intervention materials were made available only to teachers tutoring the specific program, while the control group teachers had no access to the materials during the intervention. Teachers guiding intervention groups watched an instructional video on the program’s aims, structure and practical principles. They followed a detailed intervention manual for each lesson and recap session. Teachers had the opportunity to contact the research group via email or phone if needed. After each session, teachers recorded the session date, attendance, and completed activities and provided additional comments in an intervention diary. In case of absence, they noted the date when the lesson was compensated with an individual session. Only one diary was not returned. Teachers reported 60 missed sessions (4.8% of all sessions), mostly single missed sessions by individual participants. Three children (one in C-I and two in R-I) missed three sessions each, with no make-up sessions for two of them. Missed and make-up sessions were evenly distributed between the two groups. Teachers reported 17 make-up sessions (28% of all the missed sessions), indicating difficulties in scheduling individual sessions during school days. Based on teachers’ diary reports, the overall average proportion of completed tasks within all sessions was 96% (mean scores per session varied 93%–100%) and 95% (86%–100%) for calculation and reading interventions, respectively. At post-assessment, children in the R-I and C-I groups completed a survey on the intervention activities (the questionnaire and the results are presented in Supplemental Table 2). The rate of agreement to statements defining the presence of central elements of intervention was high, being on average 90% for both interventions.

Data Analysis

First, preliminary analyses confirmed that the three groups were similar in terms of arithmetic and reading fluency as well as background measures. A one-way analysis of variance (ANOVA) was used for comparisons in arithmetic and reading fluency, parental educational level, and non-verbal reasoning. Group differences in gender and grade-level distributions were examined with a chi-squared test. Another preliminary aim was to investigate whether grade level significantly affected the interventions’ effectiveness. Accordingly, a repeated-measures ANOVA was used with a time × grade design for each intervention group separately. As none of the associations were statistically significant (see Supplemental Table 3), the main analyses were conducted with whole intervention groups. Furthermore, as there was usually only one teacher from each school and nearly half of the schools had only one or two participating children, it would have been difficult to reliably separate teacher- or school-level variation from individual-level variation. Therefore, the analysis was conducted at a single level.

To examine the domain-specific intervention effects, a repeated-measures ANOVA with a time × group design was used. In case of a significant interaction effect, pairwise post hoc comparisons of gain scores were analyzed with a one-way ANOVA to determine which groups differed. The Bonferroni or Dunnett’s T3 tests were used for equal or unequal variances, respectively. In case of missing responses (see Tables 2 and 3), a pairwise deletion was applied allowing the use of data as complete as possible. Due to rather small group sizes and partly non-normally distributed data (Shapiro–Wilk’s test p < .05 in 8 of 24 distributions; four measures at two time-points for three groups), the nonparametric Kruskall–Wallis test was also used to examine the group differences in gain scores. In case of significant group differences, a Mann–Whitney U test with Bonferroni-corrected p-level interpretation (p_adjusted = .05/12 = .004) was employed to identify groups that differed. The results of the repeated-measures ANOVA are reported, as nonparametric analyses yielded similar results, except for a difference between C-I and BAU groups in calculation fluency for which the p value slightly exceeded the Bonferroni-corrected p-level (Z = −2.630, p = .008). Cross-domain investigations were also conducted utilizing a repeated-measures ANOVA. To examine whether the C-I had cross-domain effects on reading fluency, we compared the C-I and BAU groups in reading measures. Similarly, the R-I and the BAU groups were compared to examine reading intervention’s effect on arithmetic.

Table 2.

Descriptive Statistics for the Three Groups.

Variables	C-I group	R-I group	BAU group	F^a/χ²	p
Girls/boys (%)	48.9/51.1	60.8/39.2	61.7/38.3	1.927^b	.382
Grade 2/3/4 (n)	18/21/6	20/14/17	17/17/13	6.498^b	.165
	M (SD)	M (SD)	M (SD)
Highest parental educational level	1.70 (0.85)	1.60 (0.81)	1.45 (0.80)	1.142	.322
Non-verbal reasoning	27.40 (5.33)	28.16 (5.48)	28.32 (4.55)	0.418	.659
Matsu	13.82 (3.25)	14.06 (4.40)	14.49 (4.16)	0.332	.718
Luksu	15.47 (4.97)	15.00 (5.19)	15.66 (4.90)	0.233	.793
Addition^c	16.69 (4.86)	17.04 (6.07)	17.32 (6.66)	0.130	.878
Text reading^c	47.53 (19.12)	46.12 (20.81)	48.30 (18.47)	0.158	.854

Note. C-I = calculation intervention; R-I = reading intervention; BAU = business-as-usual.

Degrees of freedom were (2, 140) except for parental education level being (2, 138) due to missing data. ^bGroup differences were analyzed using chi-square test. ^c Screening assessment.

Table 3.

Pre- and Post-Test Scores by Group and Effect Sizes.

Measure		Test occasion			Effect sizes
		Pre-test	Post-test	Gain score	Within the group	C-I vs. BAU	R-I vs. BAU	C-I vs. R-I
	Group	M (SD)	M (SD)	M (SD)	Within the group	C-I vs. BAU	R-I vs. BAU	C-I vs. R-I
Addition fluencyn = 45/51/47^a	C-I	16.84 (5.38)	21.31 (7.44)	4.47 (5.89)	0.69	0.49	0.00	0.47
	R-I	19.55 (7.29)	20.96 (8.00)	1.41 (4.42)	0.18
	BAU	19.85 (6.90)	21.28 (6.63)	1.43 (4.49)	0.21
Calculation fluencyn = 44/51/45^a	C-I	3.77 (2.38)	7.08 (3.46)	3.31 (2.50)	1.13	0.56	−0.21	0.74
	R-I	4.53 (2.90)	5.86 (3.02)	1.32 (1.32)	0.45
	BAU	3.94 (2.56)	5.86 (3.06)	1.92 (1.90)	0.69
Text readingn = 41/51/47^a	C-I	48.41 (25.04)	56.37 (27.06)	7.95 (10.81)	0.30	−0.02	−0.10	0.07
	R-I	46.96 (28.25)	53.00 (26.53)	6.04 (12.66)	0.22
	BAU	47.06 (19.95)	55.51 (22.11)	8.45 (10.61)	0.40
Sentence readingn = 40/51/47^a	C-I	34.21 (17.25)	37.80 (17.81)	3.59 (6.09)	0.16	−0.20	−0.08	−0.13
	R-I	29.88 (14.70)	35.50 (18.80)	5.62 (7.52)	0.33
	BAU	32.47 (15.06)	39.23 (18.58)	6.76 (7.31)	0.40

Note. Positive between-group effect sizes indicate improvement favoring the first group mentioned.

Number of participants in calculation intervention (C-I)/reading intervention (R-I)/business-as-usual control (BAU) groups.

The between-group effect size was calculated as the difference in mean pre–post changes between the two groups, divided by the pooled pre-test standard deviation (see Morris, 2008). Cohen’s d was calculated to examine within-group effect sizes by subtracting the pre- and post-test means and dividing the result by the pooled standard deviation. Effect sizes were interpreted as follows: 0.20 = small, 0.50 = moderate, and 0.80 = large (Cohen, 1992).

Results

Descriptive information and comparisons between the groups in fluency and background measures are presented in Table 2. The groups did not differ in any of the arithmetic, reading fluency or background measures, indicating that the distributions of each measure were similar across groups. The results regarding the time × grade effect within each three intervention groups indicated that the improvement between pre and post-tests was independent of grade level (see Supplemental Materials).

Effects of Calculation Fluency Intervention on Arithmetic and Reading Fluency

First, we analyzed whether the calculation fluency intervention showed domain-specific effects on the two arithmetic fluency tasks. The results indicated a significant interaction effect between time and group on addition fluency (F(2, 140) = 5.85, p = .004) and on calculation fluency (F(2, 137) = 13.03, p < .001). Post hoc tests for addition fluency showed that the gain score was higher in the C-I group than in the BAU (p = .011) and R-I (p = .009) groups, and effect sizes were close to moderate. The within-group effect size was moderate in the C-I group and small in the other two groups. As the pre- and post-test means in Table 3 show, the C-I group solved approximately three addition problems less in the pre-test than the other two groups (although the difference was not significant; F(2, 140) = 2.90, p = .059), but the gap was narrowed by the post-test. For calculation fluency, the gain in the C-I group was higher than in the BAU (p = .012) and R-I (p < .001) groups. Effect sizes between the groups were moderate or close to large, while effect size within the C-I was large and in the other two groups moderate or close to it. Cross-domain analyses showed that there was a significant interaction effect between time and group for sentence reading (F(1, 85) = 4.73, p = .032) but not for text reading (F(1, 86) = 0.05, p = .829). Exploring the means on sentence reading gain score revealed that the BAU group improved more than the C-I, although the effect size was small.

Effects of Reading Fluency Intervention on Reading and Arithmetic Fluency

The reading fluency intervention did not affect reading fluency outcomes. Time × group effect was not significant for text reading fluency (F(2, 136) = 0.60, p = .549) or Sentence reading fluency (F(2, 135) = 2.21, p = .114). Between- and within-group effects were small. Analyses of the effect of reading intervention on calculation fluency outcomes showed that the intervention did not have a cross-domain effect either on addition (F(1, 96) = 0.00, p = .988) or on calculation fluency (F(1, 94) = 3.28, p = .074). The effect size between R-I and BAU was zero, but within-group effects were small. For calculation fluency, the between-group effect size was small, favoring the BAU group, for which the within-group effect size was moderate, while in the R-I group, the effect was close to moderate.

Discussion

This quasi-experimental study aimed to enhance understanding of how to support arithmetic and reading fluency in children with comorbid fluency problems. Few intervention studies have focused on children with both math and reading difficulties, limiting conclusions about intervention outcomes for this group. The few existing studies have indicated that children with comorbid problems are not likely to benefit from solely repetitive training, which is frequently used to support automatization processes of learning arithmetic problems (Powell et al., 2020). In languages with complex morphological structure and multisyllabic words, additional methods are needed to promote fluent decoding. Interventions supporting arithmetic fluency through calculation strategies have shown promising results (Fuchs et al., 2009; Koponen, Sorvo, et al., 2018), whereas activating knowledge of sublexical units during reading might help anticipate the text (Borleffs et al., 2019). In this study, we examined the effects of calculation and reading interventions focusing on activating awareness of various strategies and learning to use them flexibly during arithmetic and reading activities. Special education teachers conducted the assessments and interventions during school days, enhancing the ecological validity of the findings. Pre- and post-assessment results showed greater improvement in arithmetic fluency in the C-I group compared with the reading intervention and control groups. However, the reading intervention group showed no improvement on reading fluency compared with the control group. In addition, we explored whether reading fluency intervention would improve arithmetic fluency and vice versa. Our results indicated that focusing on metacognitive elements in both interventions did not produce cross-domain effects.

In terms of the calculation intervention results, the effect size between the pre- and post-tests within the C-I group was moderate for the single-digit addition task and large for the calculation fluency task. The latter likely captured the use of various calculation strategies, such as applying the commutative property and deriving answers from known facts. The moderate effects between the C-I contrasted with R-I and BAU groups reflect the usefulness of the strategic calculation approach combined with timed and repetitive training of arithmetic facts. The finding supports previous suggestions that explicit teaching of calculation strategies benefits children with insufficient basic calculation skills (Fuchs et al., 2009; Koponen, Sorvo, et al., 2018) especially those with comorbid difficulties. The fact that the mean of solved arithmetic problems within a minute was tripled in the group of children participating in the C-I could plausibly reflect the shift from counting-based strategies to more efficient and flexible strategies.

Although the baseline between the groups was comparable in the screening phase, the C-I group had lower pre-test scores in single-digit addition fluency, allowing the participants in this group to catch up with the other groups during the intervention. However, no baseline difference was observed in the calculation fluency task, which had relatively demanding addition problems compared to single-digit additions with only two addends. This may be due to the higher attrition of fourth graders in the C-I group, who presumably perform better in simple single-digit additions than their younger peers. The calculation fluency task, consisting of problems with more addends and two-digit numbers, may highlight the immature calculation strategies used to solve such problems. Overall, the improvement in both arithmetic fluency tasks that became visible already after 13 small-group sessions and short recap tasks highlights the effectiveness of the intervention. According to Fuchs et al. (2013), children with comorbid problems need more frequent support to establish arithmetic fact retrieval, as children without comorbid reading difficulties showed more improvement within a shorter period. The ecological validity of the study is significant, as most math interventions are conducted by external research teams (Powell et al., 2020), limiting their applicability. This intervention, carried out by teachers in a school context, suggests that calculation fluency training with metacognitive elements could be effectively integrated into regular school routines.

In contrast to findings on calculation fluency intervention, focusing on metacognitive awareness of sublexical units, semantic cues and monitoring reading did not improve children’s reading fluency after 13 small-group sessions. The result can be viewed from several perspectives. First, Finnish early reading instruction relies on the systematic teaching of grapheme–phoneme correspondences, which supports accurate reading but not fluent recognition of often long, inflected, compounded, or derived words. Thus, activation of sublexical knowledge, that is, explicit awareness of syllables and morphemes, could help shift from a letter-by-letter reading strategy to more fluent, anticipatory reading. Aro and Björn (2016) examined pre- and inservice teachers’ expertise at various linguistic levels, revealing that their explicit understanding of sublexical constructs, especially morphology, was very weak, emphasizing that this aspect is not strongly present in teacher education curricula. Furthermore, the morphological level of words is not typically present in literacy instruction for children, apart from compound words. Although early reading instruction explicates syllables and materials are typically hyphenated by syllables, their role is limited to the early stages of learning to decode. The syllable is instructed as a substage of letter-by-letter decoding of long words rather than a unit of recognition. Therefore, this approach to reading skills may not be intuitive for teachers or children, and an intervention based on the use of syllables, morphology, semantics, and syntax would probably need more extensive teacher training.

Another possible interpretation is that children in Grades 2–4 may not have sufficient reading skills to benefit from instruction focusing on sublexical, semantic, and syntactic cues to speed up reading through anticipatory processing. For example, Burani et al. (2008) found that sixth-grade Italian children with reading difficulties and younger peers with similar decoding skills benefited from morphological cues when reading pseudowords with familiar roots and suffixes, but struggled with non-existing morphemes. Therefore, before emphasizing metacognitive awareness of sublexical constructs, it is important to ensure that children can adequately identify syllables and morphemes. Conversely, fluent readers may not need to distinguish smaller word units, as their decoding is fluent enough to allow processing of the meaning.

A third possible explanation for the lack of intervention effect on reading fluency relates to developmental and instructional differences between arithmetic and language learning. Formal arithmetic teaching, including the introduction of calculation strategies, begins in the early school years (Opetushallitus, 2014). In contrast, language learning, such as inflecting words according to grammatical rules, typically develops in early childhood through implicit exposure in everyday interactions (Maynard et al., 2018). By preschool, the level at which Finnish children can inflect spoken words is already close to that of adults (Lyytinen & Lyytinen, 2004). Thus, language use does not require an explicit understanding of grammatical constructs, which may also explain why they are not emphasized in formal literacy instruction in the phase when the instructional focus is in supporting reading fluency.

Fourth, within the Finnish educational context being in the BAU group doesn’t mean not receiving extra support for learning problems. Close to one-fourth of all students in Grades 1–9 receive part-time special education at some point in the school year (Statistics Finland, 2024). Typically, the children who are considered to be in need of extra support for their learning receive part-time special education (as a pull-out service) once a week in a small group instructed by a special education teacher. Furthermore, remedial teaching resources are readily available, especially in the early grades. Thus, one can conclude that our BAU control group comparison was rather conservative, increasing the significance of the observed group differences.

Although research on the effects of instructional support in one domain on outcomes in another domain is limited, arithmetic and reading skills are known to be interconnected (Korpipää et al., 2017). This highlights the relevance of exploring potential interventions that facilitate cross-domain transfer between these skills, particularly in children with comorbid difficulties. In this study, supporting children’s metacognitive skills, that is, being aware of various strategies, self-monitoring one’s learning during activities and choosing an appropriate strategy according to task characteristics, was present in both interventions. The focus was on moving from one-by-one counting or reading strategies to more efficient calculation and anticipatory reading strategies. From this perspective, we aimed to examine whether strategy-based training in one domain would show cross-domain effects in the untrained domain. However, neither intervention group showed improvement in the untrained domain. It is important to note here that neither intervention explicitly guided children to apply metacognitive awareness across domains. Thus, strategy-based training without explicit domain-specific instruction does not seem to generalize, even if fluency problems often co-occur. The cross-domain transfer effect may be worth investigating, not only in the context of fluency but also in higher-level skills, such as reading comprehension and problem-solving, which may share similar demands for language and metacognitive skills. A recent study (Fuchs et al., 2024) found support for the bidirectional transfer effects between reading comprehension and problem-solving interventions. Both interventions targeted the domain-specific text structures, while the intervention had sessions that highlighted children’s awareness of transfer effects between the two domains but without teaching domain-specific text structure strategies.

This study has certain limitations that should be considered. First, while understanding intervention responsiveness in children with comorbid learning problems is important, comparative studies between comorbid and single learning difficulties are needed. The current findings, therefore, do not provide information on whether this type of metacognitive support would be differentially beneficial depending on the combination of learning problems. Second, assessing whether the improvement in calculation fluency is maintained would require a follow-up assessment. However, a study that used similar components of procedural and conceptual arithmetic knowledge to promote calculation fluency (Koponen, Sorvo, et al., 2018) showed that children with low calculation fluency maintained the post-assessment level 5 months later. Third, it was difficult to statistically separate the individual- or group-/classroom-/school-level variation in the current sample, as there were only one or two participating children in nearly half of the 48 schools. On the contrary, viewing the results in light of responsiveness on the individual level in addition to group level is another limitation. Although the current sample included participants with fluency problems in both arithmetic and reading, the sample size did not allow a more fine-grained analysis. Furthermore, as the interventions were carried out across the country, we were not able to monitor the implementation fidelity of the intervention sessions. However, we applied several means to ensure that the interventions were implemented according to the program, including teacher training videos, a session-by-session manual, a teacher diary, and the student survey after the intervention period. Finally, this study did not allow making inferences about whether the interventions influenced the development of children’s awareness of various strategies. Thus, future studies should consider this when examining the effects of this type of support to enhance arithmetic and reading fluency through calculation and sublexical strategies.

Conclusion

Fluency problems are a central bottleneck problem in both arithmetic and reading difficulties, and their co-occurrence is known to be highly probable. A need to prevent further accumulation of comorbid difficulties and their negative consequences calls for evidence-based means to support these skills in school settings. As previous studies have indicated that pure drilling-type training does not appear to be effective alone when the difficulties overlap, this study took a step forward to examine potential additional ways to support fluency in these domains. Both arithmetic and reading interventions included metacognitive elements to help children detach from time-consuming one-by-one decoding strategies toward more efficient ones. The findings showed that a rather short teacher-led small-group tutoring period focusing on awareness and flexible use of various calculation strategies improved arithmetic fluency in children with co-occurring fluency problems in both domains. However, intervention where instruction was based on activating knowledge of sublexical components, that is, syllables and morphemes, and actively utilizing contextual cues while reading, did not influence children’s reading fluency. Despite the interconnectedness between arithmetic and reading fluency and the similarity of the two interventions, neither of them showed cross-domain effects. Future studies should continue investigating instructional methods to efficiently support reading fluency in this subgroup of children.

Supplemental Material

sj-docx-1-ldx-10.1177_00222194261441290 – Supplemental material for Effects of Calculation and Reading Fluency Interventions Focusing on Awareness and Adaptive Use of Strategies: Supporting Children With Comorbid Fluency Problems

Supplemental material, sj-docx-1-ldx-10.1177_00222194261441290 for Effects of Calculation and Reading Fluency Interventions Focusing on Awareness and Adaptive Use of Strategies: Supporting Children With Comorbid Fluency Problems by Jenni M. Pulkkinen, Riikka T. Heikkilä, Kenneth M. Eklund, Tuire K. Koponen and Mikko T. Aro in Journal of Learning Disabilities

Footnotes

Acknowledgements

The authors would like to thank professors Lynn Fuchs and Douglas Fuchs for their valuable support in the planning of the intervention. They thank all the children and teachers for participating in this study.

ORCID iDs

Jenni M. Pulkkinen

Tuire K. Koponen

Funding

This study was financed by the Academy of Finland (Grant number 277340). The Centre of Excellence for Learning Dynamics and Intervention Research (InterLearn CoE) is funded by the Academy of Finland’s CoE Program (2022–2029; grant numbers: 346120, 346119, 346121, 364196, 364197, 364198).

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Supplemental Material

Supplementary material for this article is available at

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