Much of the existing word-problem intervention research focuses on children in Grades 3 through 12. However, based on the Common Core standards used in many states across the U.S., children are expected to solve word problems beginning in kindergarten (CCSSM; National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010). Importantly, a number of studies have indicated that kindergarteners are capable of solving word problems (Carpenter et al., 1993; Croset et al., 2024; Elia, 2020). At this level, based on the CCSSM (2010), children solve word problems requiring addition and subtraction within 10. Children are taught to conceptualize addition scenarios as putting together and adding to, and subtraction scenarios as taking apart and taking from. As children learn to read in kindergarten, word problems may be orally presented.

In Grade 1, word problems increase in their computational demands and complexity (CCSSM, 2010). Grade 1 word problems require addition and subtraction within 20. Children must write corresponding equations, including a symbol for the unknown number, which can be in any position (e.g., 8 + ? = 11, 5 = ? – 3, 6 + 6 = ?). Additionally, word problems conceptualized as putting together or adding to can include three addends. Children learn of a third word-problem type, comparing, in Grade 1. Children build algebraic reasoning while solving these word problems (e.g., the communicative property and the inverse relation of addition and subtraction).

Subsequently, in Grade 2, children are expected to solve one- and two-step word problems involving addition and subtraction within 100 (CCSSM, 2010). Children continue to solve word problems conceptualized as putting together or adding to, taking apart or taking from, and comparing. However, at this level, children must also solve word problems involving length and money, as well as word problems with information presented in bar graphs (i.e., graphical displays of data). With the focus on word problems in the standards across kindergarten through Grade 2, it is crucial to understand how children in the early grades may experience difficulties with these tasks.

Many researchers have investigated the knowledge and skills required during word-problem solving. First, the linguistic and literacy demands of word problems are vast. Xu et al. (2022) determined that receptive vocabulary (i.e., children's ability to intake, process, and understand spoken vocabulary) predicted word-problem proficiency. Vilenius‐Tuohimaa et al. (2008) examined the relation between reading skills and word-problem outcomes and determined that decoding skills and reading fluency influenced comprehension, and comprehension influenced word-problem outcomes. Moreover, a large body of research supports the critical relation between mathematics vocabulary knowledge and word-problem proficiency (e.g., Cartwright et al., 2022; Fuchs et al., 2015; Stevens et al., 2023).

Additionally, solving word problems involves computation. Children benefit from both a conceptual knowledge of operations and procedural fluency (Chan & Kwan, 2021; Pongsakdi et al., 2020). That is, along with having a conceptual understanding of addition as putting together or adding to and subtraction as taking away or comparing, children should have procedural fluency that supports efficient and accurate computation.

Beyond the knowledge and skills mentioned above, word-problem solving relies heavily on working memory and reasoning abilities (Passolunghi et al., 2022). Consider the word problem: “Maelia is taking three classes. She has 17 pages to read for a class. So far, she has read 13 pages. How many more pages does Maelia need to read?” To solve this word problem, children must focus on which value is missing (i.e., how many pages Maelia has left to read). Children must disregard the extraneous information that Maelia is taking three classes. Although this problem includes the word more, children must find the difference between the target number of pages and how many have been read. This process requires the child to disregard extraneous information and retain the critical information in their working memory until they determine the solution (i.e., the word problem’s answer). Without engaging in reasoning, the child might focus on the word more and add 17 and 13.

Early childhood teachers face a unique challenge. At this stage, children must simultaneously learn how to decode words, understand text, add, and subtract. When solving word problems, children must implement multiple skills. Considering the complexity, range of difficulty, and numerous processes related to solving word problems, researchers must determine effective evidence-based practices for word problems in the early grades. In the next section, we describe one such evidence-based practice.

Schema instruction has been identified as an evidence-based practice for improving word-problem proficiency (Jitendra et al., 2015; Peltier et al., 2018; Root et al., 2021). Schema instruction is a method in which children learn to identify the underlying structure (i.e., concept) of various word-problem types and is grounded in cognitive load theory (Marshall, 1995; Sweller, 1994). In the early grades, children primarily solve additive word problems, meaning word problems that require addition or subtraction. Researchers have identified three reliable categories (i.e., schemas) for additive word problems, which we discuss in the next section (Nesher et al., 1982).

Word-problem interventions have been the focus of reviews for over two decades (e.g., Jitendra & Xin, 1997). Many of these reviews have focused on a broad range of word-problem interventions (e.g., Kong et al., 2021; Lein et al., 2020; Zheng et al., 2013). To date, authors of at least half a dozen reviews focused exclusively on schema instruction (e.g., Clausen et al., 2021; Cook et al., 2020; Jitendra et al., 2015; Peltier & Vannest, 2017; Peltier et al., 2018; Powell, 2011). However, among these reviews, most included studies involved children in the late elementary grades and beyond. In this section, we summarize a selection of these reviews that, to an extent, included studies that focused on the word-problem outcomes of young children.

Peng et al. (2025) conducted a systematic review and network meta-analysis focused on group-design studies that implemented word-problem interventions with elementary children (Grades 1–5) with mathematics difficulty (MD). The authors analyzed and compared 53 studies to identify which combinations of instructional strategies were the most effective. However, of the 53 studies, only three (6%) implemented schema instruction with children in the early grades (Fuchs et al., 2021, 2022; Powell et al., 2015). Ultimately, the authors determined that interventions combining schema instruction with the concrete-semi-concrete-abstract framework were most effective. Moreover, the addition of metacognitive strategies (e.g., an attack strategy) and graphic organizers increased efficacy.

Myers et al. (2022) conducted another comprehensive meta-analysis on word-problem interventions. Their meta-analysis included 52 experimental group-design studies that implemented word-problem interventions for elementary children (Grades 1–5) with mathematics difficulties. Of the 52 studies, only four (8%) implemented schema instruction with children in the early grades (Fuchs et al., 2021; Huang et al., 2012; Jitendra et al., 1998; Powell et al., 2015). Myers et al. (2022) demonstrated a significant positive effect across all 52 word-problem interventions (g = 1.01 with outliers, g = 0.81 without outliers); however, their meta-analysis did not focus exclusively on schema instruction and included only a handful of studies from the early grades.

Conversely, Peltier and Vannest (2017) conducted a meta-analysis of 21 studies that implemented schema instruction as the primary intervention component. Their meta-analysis included group-design studies that measured the word-problem performance of elementary children (K–6) with or without disabilities. Only two (10%) of the studies implemented schema instruction with children in the early grades (Fuchs et al., 2010; Jitendra et al., 1998). Peltier and Vannest (2017) reported overall positive effects of schema instruction (g = 1.57 for proximal measures; g = 1.09 for distal measures). However, the authors noted a wide distribution of effect sizes across the 21 studies, and their moderator analyses did not include participant grade level(s). Therefore, conclusions about the efficacy of schema instruction within the early grades could not be made.

In 2018, Peltier et al. conducted a meta-analysis of 16 single-case design studies that implemented schema instruction with children identified with disabilities. Among the 16 studies, only three (19%) involved children in the early grades (Peltier & Vannest, 2018; Root et al., 2017; Saunders, 2014). The authors identified schema instruction as an evidence-based practice with strong effects on the mathematics performance of children with learning disabilities (Tau U = 88.29%). Participants were categorized into elementary (K–5) or middle/high school (6–12) to investigate whether grade level was a moderator, but participants in the early grades (K–2) and the upper elementary grades (3–5) were not differentiated. Peltier et al. (2018) provided compelling evidence of the effectiveness of schema instruction for children with disabilities across grade levels. However, conclusions could not be made about participants with and without identified disabilities, particularly in the early grades.

Clausen et al. (2021) conducted a systematic review of studies that implemented modified schema-based instruction with children with moderate or severe disabilities. Modified schema-based instruction (MSBI) incorporates color-coded graphic organizers, think-alouds, and scaffolds to increase responses and self-monitoring skills. The authors reviewed 12 studies, two of which (17%) included children in the early grades (Root et al., 2017; Saunders, 2014), and reported a large effect size for MSBI (1.0 Tau). This review provided implications for teaching children with moderate to severe disabilities, which cannot be generalized to other populations.

The participants of the studies included in these previous reviews ranged from Grade 1 to 23 years old. The overwhelming majority of studies investigated word-problem performance in the late elementary grades or beyond. Within these reviews, only a handful of studies included children in the early grades. As such, conclusions about the efficacy of schema instruction for young children are limited, restricting both recommendations for future research and implications for classroom practice. With the depth and complexity of word problems in the early elementary grades, evidence-based word-problem interventions must be researched and implemented before deficits widen in the later grades.

Although many syntheses have been conducted related to word-problem interventions, some specific to schema instruction, we believe this may be the first effort to specifically synthesize schema instruction in the early grades. First, we identified experimental studies that implemented schema instruction in kindergarten, Grade 1, or Grade 2. We focused on these three grade levels because word problems are introduced in kindergarten, and these grades are often grouped together due to standardized testing beginning in the U.S. in Grade 3. Then, we synthesized the overall effects of schema instruction on the word-problem performance of children in the early grades and described common features and components of the specific interventions. The research questions guiding this systematic review included: (a) How has schema instruction for word problems been applied in the early grades? (b) What is the overall efficacy of schema instruction on the word-problem performance of children in the early grades?

In May of 2023, the first author searched databases to identify studies that implemented schema instruction in the early grades. Studies of interest measured the effects of schema instruction on the word-problem performance of children in kindergarten, Grade 1, or Grade 2. There was no restriction based on the year of publication. Databases included APA PsycINFO, Education Source, and ERIC. We used the following Boolean Logic to search the full text of records in each database: (total OR group OR combine OR part OR whole OR change OR difference OR compare OR schema OR intervention) AND (“word problem*” OR “story problem*” OR “word-based mathematical question*”) AND (kindergarten OR “first grade*” OR “grade 1” OR “1st grade*” OR “second grade*” OR “grade 2” OR “2nd grade*” OR primary OR elementary). This initial search yielded 1,825 records; after removing duplicates, 1,455 records remained.

After reviewing titles and abstracts, the first author excluded 1,265 records. Many of these exclusions did not use an experimental design, did not implement schema instruction, or only included children in Grades 3 through 12. To assess the reliability of the title and abstract screening, the third author independently reviewed 10% of the 1,455 records. Reliability between the first and third authors was 92%. Among the 12 discrepancies, the third author excluded 10 of the records, whereas the first author included them in the full-text screening. The first author reviewed the full text of the other two records and determined that they did not meet the inclusion criteria. Next, the first author conducted a full-text screening of the remaining 190 records. Overall, 13 studies met the inclusion criteria. The first author conducted a forward search, a backward (i.e., ancestral) search, and a hand search of two prominent journals: the Journal of Educational Psychology and Exceptional Children. These alternative search methods yielded no additional results. In sum, 13 studies met the inclusion criteria (see Figure 2).

We included peer-reviewed studies and dissertations. Studies had to be experimental (i.e., randomized-controlled trial, quasi-experiment, or single-case design). Studies had to measure the effects of schema instruction on the word-problem performance of children in kindergarten, Grade 1, or Grade 2. If the grade level was not reported, we included studies with participants between the ages of 5 and 8. If a study included participants in Grade 3 or beyond, data must have been disaggregated for participants in the early grades. Finally, studies had to be available in English.

The first author coded studies for essential characteristics (e.g., sample size, participant grade level, and dosage; see Table 1). Next, the first author coded results and effect sizes descriptively and quantitatively (see Table 2 for group-design studies and Table 3 for single-case studies). Moreover, the first author coded for various intervention components and instructional strategies (e.g., systematic instruction, diagrams, and problem-solving heuristics). Finally, the first author coded quality indicators using Cook et al. (2015). For each quality indicator, the first author used dichotomous scoring (i.e., 1 or 0 for meets or does not meet). After the initial round of coding, the second author was randomly assigned five of the 13 included studies. The second author reviewed the information in Tables 1, 2, and 3 and indicated agreement or disagreement with 69 units of information. We calculated reliability by dividing the number of agreements by the total units of information the second author reviewed, resulting in a 94.2% reliability. We identified four discrepancies, with no more than one discrepancy associated with an individual study. The discrepancies related to: (a) whether a particular study was an RCT or quasi-experiment, (b) which grade levels were represented in a study, and (c) the descriptions of two word-problem measures. The four identified discrepancies were discussed and resolved.

We included six group-design and seven single-case design studies. Although there were no date restrictions, these 13 studies were published between 2010 and 2022. The majority of the studies were conducted in the United States. One study (Chadli et al., 2018) was conducted in Algeria, and another (Huang et al., 2012) was conducted in Taiwan. Most participants were in Grade 2, and we located zero studies that included kindergarten participants. Several studies included participants in the upper-elementary grades but disaggregated the data to allow for analyses of participants in the early grades. Participants (n ~ 2,100) included children with and at risk for mathematics difficulties, children with autism, intellectual disabilities, and emotional and behavioral disorders, as well as emergent bilinguals and typically-performing children.

In most studies, the primary researcher or research staff implemented the intervention. Only two of the 13 trained the participants’ teachers to implement the intervention. Moreover, most studies implemented one-on-one intervention. Two studies implemented a combination of one-on-one and small-group intervention, one combined whole-group instruction and small-group intervention, and one implemented whole-group instruction. The frequency and duration of intervention sessions varied tremendously among the 13 studies. Some participants received as few as nine sessions, and others received 45 sessions. The frequency of sessions ranged from 2 to 5 times a week, and the duration ranged from 10 to 90 minutes. Overall duration of treatment ranged from 4 to 17 weeks. Table 1 includes overall dosage minutes.

The interventions incorporated a range of word problems. In most of the studies, participants solved one-step word problems. Four of the 13 studies incorporated multi-step word problems. Nine of the 13 studies included a combination of Total, Difference, and Change schemas, and three included a combination of Total and Change schemas. Root et al. (2017), whose participants were children with autism or moderate intellectual disabilities, focused exclusively on solving word problems with the Difference schema. In eight of the 13 studies, participants solved word problems with unknowns in various positions (i.e., the initial, medial, and final positions; see Figure 1). Five studies included word problems with at least one superficial feature (i.e., irrelevant information, relevant information presented in charts or graphs, or multi-step problems with combined schemas; Fuchs et al., 2010).

Computational demands also varied among the 13 studies. Eight of the 13 studies incorporated two-digit addition and subtraction, with and without regrouping. Two studies (Peltier & Vannest, 2018; Rockwell, 2012) incorporated two-digit addition and subtraction without regrouping. In several studies with participants who had intellectual disabilities (Bowman et al., 2020; Root et al., 2017; Saunders, 2014), calculations were confined to sums and differences within 10, differences within 10, or sums of less than five.

We determined the quality of the 13 studies using the Cook et al. (2015) quality indicators. We assessed the six group-design studies using 24 quality indicators (QIs). Each QI was scored as a 1 (meets) or a 0 (does not meet). The group-design studies met an average of 82% of the QIs with a range of 54 to 96%. (see Table 1). We assessed the seven single-case design studies using 22 QIs (Cook et al., 2015). These studies met an average of 95% of the QIs, with a range of 82 to 100%. Cumulatively, the 13 included studies met 89% of the QIs, suggesting an overall high quality of studies.

Among the group-design studies, many lacked sufficient descriptions of the setting, participant demographics, and control conditions. We considered a description of the setting to be sufficient if it included (a) a geographic location, (b) contextual information about the school or district beyond elementary school, and (c) clarity about where the intervention occurred (e.g., in a resource room). For participant demographics, we considered reporting to be sufficient if studies included at least two participant characteristics (e.g., gender and race/ethnicity, or age and socioeconomic status). We considered a description of the control condition to be sufficient if it included any information about how instruction was provided to those students (e.g., the textbook used or the most common instructional strategies). Moreover, some group-design studies lacked specificity in descriptions of word-problem measures or did not report assessment reliability. Another commonly missed QI among the group-design studies related to reporting attrition rates. Finally, among the single-case design studies, the most frequently missed QI related to the timing of outcome measures. Studies received a 1 for this QI if the timings of all measures used in the study were clearly reported.

The included studies measured a range of dependent variables, such as mathematics computation and pre-algebraic reasoning, but this systematic review focused on the effects on word-problem performance. Overall, schema instruction positively affected the word-problem performance of children in the early grades. Table 2 provides an overview of the results and effect sizes of the six included group-design studies. Only treatment conditions that implemented schema instruction were included. We described each study's measure of word-problem performance along with the results.

Fuchs et al. (2022) implemented two variations of schema instruction, one with added working-memory training and one without. Participants in both conditions significantly outperformed the business-as-usual group. However, the participants who received schema instruction without working-memory training outperformed those who did. The authors of Fuchs et al. (2022) suggested that participants benefited from the increased dosage of schema instruction. Fuchs et al. (2021) implemented schema instruction with and without embedded language-comprehension instruction. Both treatment conditions significantly outperformed the control group. However, participants who received the supplemental language comprehension instruction outperformed those who did not.

Fuchs et al. (2014) and Fuchs et al. (2010) implemented a proximal measure of word problems and a distal measure of word problems. In both studies, participants who received schema instruction performed significantly better than the business-as-usual condition on the proximal measure, but results for the distal measure were insignificant. The authors of Fuchs et al. (2010, 2014) suggested that the multiple-choice format and inclusion of multiplication, division, and fraction concepts (outside the intervention’s scope) explained the disconnect.

Chadli et al. (2018) and Huang et al. (2012) implemented computer-assisted interventions. The experimental group in Chadli et al. (2018) significantly outperformed the control group on the posttest. Huang et al. (2012) included Grades 2 and 3 participants. After disaggregating pretest scores, a statistical analysis detected no significant discrepancy between the pre-and posttest scores based on grade level. So, the subsequent analyses were not disaggregated. Overall, participants who received the computer-assisted intervention scored significantly higher on the posttest than the control group.

Table 3 provides an overview of the results of the seven single-case design studies. Each study varied in methods and statistical analyses, so we calculated the percentage of non-overlapping data (PND) for each participant. All single-case design authors reported positive results of schema instruction on participants’ word-problem performance, except for Hughes and Cuevas (2020). Hughes and Cuevas (2020) reported schema instruction as minimally effective in improving the seven participants’ word-problem performance. The authors of Hughes and Cuevas (2020) suggested that these results were due to off-task behavior related to group size, insufficient instruction on computational skills, and inadequate dosage. When using PND as the measure of effectiveness, the intervention in Luevano and Collins (2020) was also minimally effective. Two participants had PNDs of 85 to 100%, but the other two had PNDs of 0 to 9%. However, the authors reported that all four participants demonstrated an increase in drawing accurate schematic diagrams. Overall, most experimental studies that implemented schema instruction in the early grades achieved positive results regarding word-problem performance. In the next section, we summarize the qualities and components of each schema intervention.

Schema instruction was not implemented identically across the 13 studies. Root et al. (2017) only focused on one schema. In the other 12 studies that focused on 2 or 3 schemas, the majority (i.e., 8 of the 12) introduced schemas to participants one at a time. Upon introducing a new schema, participants had consecutive opportunities to practice solving those word problems. After receiving consecutive practice opportunities for each schema, participants engaged in interleaved practice opportunities (i.e., solving word problems with mixed schemas). For example, in Fuchs et al. (2022), nine lessons focused on Total problems, nine lessons focused on Difference problems, and nine lessons focused on Change problems. Then, in the last nine lessons, participants engaged in interleaved practice. Alternatively, in four of the 13 studies, participants engaged in interleaved practice throughout the scope of the interventions.

In nine of the 13 studies, participants were explicitly instructed to determine the schema of word problems before solving them. In four of these studies (Fuchs et al., 2010, 2014, 2021, 2022), participants followed the problem-solving heuristic RUN, in which the N stands for “name the problem type.” In Hughes and Cuevas (2020), participants followed FOPS, in which the F stands for “find the problem type.” In other studies, participants were trained to select and use the appropriate schematic diagram (Luevano & Collins, 2020; Peltier & Vannest, 2018; Rockwell, 2012; Saunders, 2014). Of the studies that did not explicitly instruct participants to determine the schema of word problems before solving, two did not include a wide enough range of schemas to require this step. In Bowman et al. (2020), participants learned to solve Total and Change problems limited to sums within five and did not differentiate between the schemas. In Root et al. (2017), participants only solved Difference problems. In Huang et al. (2012), the computerized intervention provided participants with the appropriate schematic diagram depending on the problem type (i.e., Total, Difference, or Change). In the next paragraphs, we describe common instructional components used within the mathematics interventions.

Before concluding, we provide a few limitations to this systematic review. First, we may have missed relevant studies. Word problems have been heavily researched for decades, and grade level was the only participant characteristic required for inclusion. There are many terms for schema instruction, as well as different variations of it. Next, we only coded for and discussed the results of word-problem measures. As previously described, word problems are complex tasks and require various knowledge and skills. Due to the multi-component nature of many of the included studies, examining additional dependent variables (e.g., computation skills) could have obtained a broader understanding of the benefits of schema instruction in the early grades. Further syntheses should include a wider range of dependent variables, such as computation skills, pre-algebraic reasoning, and mathematics vocabulary.

The results of this systematic review implicate a few future directions for research on schema instruction. First, although we had no date restrictions on our systematic search, the earliest study to meet our inclusion criteria was Fuchs et al. (2010). This demonstrates that the experimental research base behind implementing schema instruction in the early grades is relatively new. Second, we were unable to locate any experimental studies that implemented schema instruction with kindergarteners. Word problems are introduced in kindergarten, and previous research has supported schema instruction in Grade 1. Future research should test the efficacy of schema instruction in kindergarten. Third, most included studies implemented schema instruction in a one-on-one setting. Additional studies need to implement whole-group schema instruction. Fourth, only one study (Hughes & Cuevas, 2020) used a natural change agent (e.g., a special educator at the research site) as the intervention agent. Most included studies used primary researchers or trained graduate assistants to implement the interventions. Using natural change agents can better measure the true effects of an intervention and garner credibility among practitioners. Lastly, embedding technology within schema instruction requires additional research. Incorporating technology has the potential to increase engagement and can be a helpful tool amid staffing shortages. For example, technology can facilitate engaging, targeted practice with some children while the teacher provides small-group instruction to others.

This systematic review can be used as a guide for planning and implementing schema instruction in the early grades. In summary, the results support (a) systematic and explicit instruction on word-problem schemas; (b) diagrams, meta-equations, and gesturing; (c) the use of a problem-solving heuristic; (d) inclusion of numberless or intact story problems and isolated practice with identifying schemas; (e) explicit instruction on mathematics and word-problem specific vocabulary; (f) incorporating concrete or virtual manipulatives and a fact fluency component; and (g) the inclusion of a self-monitoring behavior component.

There is a need for continued research on implementing schema instruction in the early grades, particularly in kindergarten. The results of this systematic review highlight common intervention features both researchers and early childhood teachers could implement. Although more research is needed, there is quality evidence suggesting the benefits of schema instruction for young children.