This section begins by outlining the language of mathematics, a primary aspect contributing to the challenges in word problem-solving. While teaching and learning should be viewed as reciprocal processes in mathematics word problem-solving instruction, it is vital to scaffold teachers’ and learners’ understanding of mathematics vocabulary. Next, the role of critical and creative thinking is explored as a foundational component for scaffolding instruction in word problem-solving. Thereafter, the focus shifts to the role of asking leading questions in scaffolding learners’ thinking from lower-order thinking to higher-order thinking. Lastly, the literature explores Bloom’s Revised Taxonomy and the role it plays in structuring cognitive growth.

Solving word problems is only possible once teachers and learners are able to think mathematically (Machaba, Sipholi & Motseki 2024; Setati, Molefe & Langa 2008). The use of the language of mathematics creates tension between learners’ interaction with the mathematical meaning of word problems and the mathematical processes required to solve them (Machaba et al. 2024). Without understanding the language of mathematics, solving word problems would become very challenging (Machaba et al. 2024). What makes word problem-solving challenging is that the language used in word problems needs to be understood to such an extent that the problem solver is able to apply critical thinking. The language of teaching, learning and assessment is critical for acquiring mathematical comprehension and successfully interpreting word problems (Graven & Sibanda 2018). This perspective sheds light on the importance of accessing the language of teaching and learning so that learners’ thought processes do not ‘switch off’ when they encounter a word problem (Machaba et al. 2024). Pimm (2019) explains the similarities between learning mathematics and learning a language ‘since mathematics has particular ways of speaking, reading and writing’ and that mathematics is a way of communicating (Pimm 2019; Wilkinson 2019; Zevenbergen 2001). The language of mathematics is also referred to as the mathematical register (Pimm 2019; Swanepoel 2022; Wilkinson 2018, 2019). Word problems are challenging: the answer needs to align with the original question and correspond to the context of the word problem. The biggest challenges that deter both teachers and learners from solving word problems are the unfamiliar context of the word problem, which is often different from that of the teachers’ and learners’ life-worlds; the specialised mathematics vocabulary, which differs from the everyday register used; and the language barrier where the language of learning and teaching (LoLT) is also different from the learners’ home languages. Swanepoel (2022) notes that solving word problems is embedded in critical and creative thinking, an element that neither teachers nor learners are accustomed to applying as a means to understand the context of the word problem and answer it effectively. The intricate relationship between language and mathematics is highlighted by Essien (2018) and Essien and Moleko (2025). It is even more pronounced between multilingualism and the LoLT (Essien & Moleko 2025).

Learners use strategies to solve word problems that emanate from textbook instruction (Kirkland & McNeil 2021:2). Instead, learners should be encouraged to face the word problem from a perspective where they use their knowledge of everyday events and occurrences. Solving word problems from this perspective allows learners to engage in critical thinking (Kirkland & McNeil 2021). Instead of ‘activating and using their knowledge of the world’, learners do not think ‘outside the box’ (Wallis & Steptoe 2006) to delve into their natural problem-solving abilities; they make use of a strategy such as looking at keywords to determine what the word problem requires of them. When learners see words, such as ‘take away’ or ‘in total’, they perform a calculation based on what they presume the keywords are telling them to do (Greer 1993; Kirkland & McNeil 2021). Although there is a specific place for a strategy, such as isolating keywords and solving a word problem accordingly, this limits learners’ critical thinking and prevents them from thinking about the context of the word problem realistically. Fitzpatrick et al. (2019) argue that the use of matching keywords to the operations and numbers in a word problem ends up as a game where the objective is to find an answer to the problem, by using all the numbers, operations and keywords. However, Kirkland and McNeil (2021) point out that this ‘game of word problems’ may likely indicate a lack of reading comprehension. This furthermore indicates that without intentionally comprehending the meaning of the keywords, critical thinking cannot be applied. Thus, for critical thinking to be applied in solving word problems, learners need to have adequate knowledge of the keywords, which is reflected in sound reading comprehension. Examining the integration of critical and creative thinking within the framework, critical thinking and creative thinking are not opposite sides of the spectrum; instead, they complement each other.

Creativity is an essential component in developing innovative ideas aimed at supporting society and bringing about change (Amabile, Burnside & Gryskiewicz 1999). Creativity is linked to ‘thinking outside the box’ (Wallis & Steptoe 2006), an essential ingredient in implementing innovation across various spheres of society (Puccio et al. 2023). Puccio, Murdock and Mance (2007:29) defined creative problem-solving (CPS) as a ‘comprehensive cognitive and affective system built on our natural creative processes that deliberately ignites creative thinking and, as a result, generates creative solutions and change’. The first step in solving a problem is to engage in creative thinking (Raz, Reiter-Palmon & Kenett 2023). This process often begins with asking thoughtful questions that clarify the nature of the problem. Sasson Lazovsky, Raz and Kenett (2025) explain that ‘when developing questions, the asker must articulate and express the problem or perplexity they encounter and transition from perplexity to the formulation of the problem and expression of a question’.

When taking a closer look at the FCTMV, first the teacher and later on the learner are encouraged to ignite their own creativity and critical thinking by asking leading questions that lead them to understand the context of the word problem, the meaning of the mathematics vocabulary and what the word problem is asking them to do. This new approach to solving word problems is supported by the integration of critical and creative thinking (Puccio et al. 2023). It is vital to understand that the framework is not about reinventing the metaphorical wheel. Instead, this is about strengthening and accommodating problem solvers’ existing problem-solving strategies within a new perspective by asking leading questions, activating critical thinking and critically examining the meaning of the words in a word problem while giving the problem solver some leverage to think ‘outside the box’ (Wallis & Steptoe 2006).

Within the FCTMV, creativity is not treated as an ‘additional’; instead, creativity is embedded across the framework as a progression of increasingly flexible sensemaking and strategy generation (Table 1, Figure 1). At the lower-order levels (remember and understand), learners demonstrate creativity by rephrasing the word problem, clarifying mathematics vocabulary and constructing a coherent understanding of the problem context. At apply, creativity is evident when learners connect the problem to real-life experiences, model it using drawings or manipulatives and test whether the chosen operation fits the context. At analyse, learners engage creatively by breaking down multi-step problems, separating linguistic from numerical information and exploring alternative solution pathways. At evaluate, creativity is enacted through justification and revision as learners verify the realism of their answers, identify errors and propose corrections. Finally, at create, learners generate their own word problems using similar contexts and operations. In this way, creativity is enacted through rewording, re-representing, strategy flexibility and problem generation across the FCTMV, rather than being confined to the final level.

The FCTMV makes the asking of leading questions applicable to both the teacher and the learners. The physical act of asking questions serves as a catalyst for the problem solver to think critically about the questions and their answers while allowing for an element of creative thinking. Sasson Lazovsky et al. (2025) support this notion by stating that ‘In everyday life, people constantly ask questions to interact with others, make informed decisions, and navigate the world around them. It is through questioning that we can solve problems and adapt to new situations, making it an essential skill for personal and professional development’.

Through the composition of the FCTMV, attention was given to the act of asking leading questions as a means to unlock the meaning of word problems. Question-asking is a fundamental tool for gaining information, requesting clarification or understanding a particular topic or subject (Sasson Lazovsky et al. 2025). Questions range from simple to complex, encouraging both basic understanding and deeper exploration. Questions can be open ended, allowing for broad exploration and discussion, or they can be closed ended, seeking specific answers (Ortlieb et al. 2012; Sasson Lazovsky et al. 2025).

The process of asking leading questions enables learners to connect their background knowledge to the context of the word problem while integrating the mathematical register creatively, with the thinking being scaffolded from lower order to higher order (Sasson Lazovsky et al. 2025). Wiranata, Widiana and Bayu (2021) explain that the process of thinking in word problem-solving is an important element that teachers should continually pay attention to.

Verbal skills are presumed to be the cornerstone of mathematics word problem-solving, continually interacting with mathematical processes during word problem-solving (Strohmaier et al. 2022). Verbal skills, such as discussing word problems and asking questions, were found to be the most consistent predictor of successful word problem-solving strategies (Strohmaier et al. 2022). In a similar study, Peng et al. (2020) categorised ‘verbal skills’ needed in word problem-solving as skills required from phonological processing to oral comprehension. It was ascertained that reading comprehension has a more substantial effect than phonological processing on problem solvers’ abilities to solve word problems.

The FCTMV contains different question types. As the level of knowledge increases, so do the questions, ranging from basic information retrieval questions to higher levels of synthesis and integration (Sasson Lazovsky et al. 2025). This is evident in the scaffolding of knowledge dimensions ranging from quadrant one to quadrant four in Figure 1. Bloom’s Revised Taxonomy is the vehicle used to facilitate critical and creative thinking through the use of leading questions.

Bloom’s Revised Taxonomy provides a structured teaching approach that fosters metacognition and supports the development of critical and creative thinking. This framework is the backbone of the FCTMV. Learning activities were implemented using Bloom’s Revised Taxonomy. Implementing the FCTMV has shown to be effective in enhancing learners’ knowledge acquisition (Gunawan & Palupi 2016). The taxonomy comprises two key dimensions: (1) the cognitive process dimension, which includes remembering, understanding, applying, analysing, evaluating and creating and (2) the knowledge dimension, which encompasses factual, conceptual, procedural and metacognitive knowledge (Adijaya et al. 2023; Gunawan & Palupi 2016). Learning activities aligned with the revised taxonomy are designed to be innovative and varied, explicitly targeting the development of learners’ metacognitive abilities (Sudirtha et al. 2022).

Competent teachers can transform ordinary teaching experiences into engaging, meaningful interactions that promote learner enjoyment, active participation and improved learning outcomes (Andini & Supardi 2018; Sudirtha et al. 2022). Learner performance is closely linked to teacher competence (Sudirtha et al. 2022). One of the key aims of teaching is to involve learners in meaningful learning experiences that foster metacognition. This requires teachers to attend to how learners think, reason and engage with problems (Lestari, Selvia & Layliyyah 2019; Putri & Dirgantoro 2018; Sudirtha et al. 2022).

What distinguishes this taxonomy is its emphasis on reflection and metacognitive awareness. Learners are guided to reflect on what they know and do not know by engaging with leading questions, which fosters honesty about their understanding. This reflective process encourages learners to identify and correct their errors, thereby deepening their understanding and knowledge. Bloom’s Revised Taxonomy not only serves as a framework for teacher development but also supports learners’ learning. The higher-order cognitive processes (applying, analysing, evaluating and creating) form a foundation for critical and creative thinking. During these activities, the use of mathematics vocabulary becomes essential, as it enables learners to articulate their understanding of factual, conceptual, procedural and metacognitive knowledge found within mathematical word problems.

Ultimately, the FCTMV serves as a scaffolding structure. It begins with lower-order thinking (factual and conceptual knowledge). It progressively builds towards higher-order thinking (procedural and metacognitive knowledge), enabling learners to reason more deeply and to communicate more effectively (Sudirtha et al. 2022; see Figure 1).

The word sum-wheel (Swanepoel 2022; Swanepoel & Luneta 2024) served as the driving force behind the study and refers to six steps taken to support teachers in teaching mathematics word problems: (1) read with understanding, (2) communicate and ask questions for clarity, (3) play and interactive strategies to understand the word problems, (4) match the operations to the context and vocabulary of the word problem, (5) calculate the answers of the word problem and (6) double-check the answers. For this study, steps one to three will be examined in detail, as these three steps led to the development of the FCTMV.

Step one of the word sum-wheel requires the problem solver to read the word problem as they would a comprehension passage: by looking for clues, checking meaning and considering its context. Step two encourages the problem solver to ask questions to stimulate critical and creative thinking, including leading questions that explore the meaning behind the words in word problems and encourage thinking ‘outside the box’ (Wallis & Steptoe 2006). Step three requires the problem solver to be actively involved in creating new knowledge through play and being interactive. While the word sum-wheel is a teacher training and development tool in itself, it elevates the FCTMV as another valuable tool for teacher training and development.

The FCTMV was developed based on research conducted by Swanepoel (2022) and serves as a framework to bring together a multitude of aspects that impact the teaching and understanding of mathematics word problems. Recognising that understanding mathematics word problems relies on the same foundational skills as reading comprehension, this framework guides teachers in integrating critical and creative thinking while developing learners’ mathematics vocabulary. Referencing Table 1, the first column refers to the dimensions of cognitive processes. These questions start with lower-order thinking questions (remember, understand) and gradually build to higher-order thinking questions (apply, analyse, evaluate and create). The second column lists examples of leading questions that illustrate to teachers what types of leading questions can be asked under each level of thinking and reasoning. The third column provides the teacher with examples of keywords and actions to be incorporated with the corresponding level of thinking and reasoning. As the levels of knowledge increase in thinking order, so do the complexity of the keywords and actions related to it. The last column connects the knowledge dimensions to the levels of thinking and reasoning. This suggests that metacognition is involved in higher-order thinking and reasoning, which requires metacognitive knowledge. This resonates with questions that require the problem solver to think beyond standard guidelines and function at a level that creates new knowledge. The FCTMV is a platform that teachers can use to systematically and creatively expose learners to mathematics vocabulary. This framework outlines the keywords and actions that learners must be able to achieve, providing teachers with the desired outcomes that learners are expected to attain. Teachers’ instruction of mathematics vocabulary is guided by providing examples of leading questions that learners can ask to activate their knowledge of mathematics vocabulary (Ferlazzo & Sypnieski 2018).

Here is a practical demonstration of how the framework for critical thinking and mathematics vocabulary can be used: the framework supports both lower- and higher-order thinking by guiding teachers to scaffold learners’ reasoning through the purposeful use of leading questions, keywords and action words. At the lower-order ‘Understand’ level, for example, a teacher may use the word problem: ‘Thandi has five apples. She gives her friend two apples. How many apples does she have left?’ The teacher poses the question, ‘What does the word gives tell us?’, scaffolding learners’ understanding by prompting them to explain the action in their own words and to identify the keyword gives as a signal to subtract. The action word explain helps learners interpret the context, clarify meaning and summarise the problem in a meaningful way. At the higher-order analyse level, a more complex problem might be: ‘Sipho bought three packs of crayons. Each pack has eight crayons. He gave four crayons to his sister. How many crayons does Sipho have now?’ The teacher scaffolds critical thinking by asking, ‘What steps do you think we need to follow and why?’ prompting learners to break the problem into parts, identify the keywords each and gave and differentiate between operations (multiplication and subtraction). The related action words organise and attribute support learners in analysing the structure of the problem, making logical decisions and justifying their reasoning. In both cases, the framework helps the teacher align questioning strategies with the learners’ developmental level, building progressively from understanding to deep analysis. Table 1 illustrates the FCTMV.

The integration of Bloom’s Revised Taxonomy and the word sum-wheel highlights the process of scaffolding, as shown in Figure 1. The two concentric circles illustrate the relationship between these two key features of the FCTMV. The smaller circle houses the six steps from the word sum-wheel, while the larger circle houses the levels of dimensions of cognitive processes. Quadrants 1 and 2 represent lower-order thinking prompts and keywords, along with lower-order levels of knowledge. Quadrants 3 and 4 represent higher-order thinking prompts and keywords, along with the higher-order levels of knowledge. There is a progression from Quadrant 1 through Quadrant 4 in a clockwise direction, as indicated by the arrows. Figure 1 and Table 1 should be viewed as complementary to each other rather than as two distinct frameworks.

Ethical clearance to conduct this study was obtained from the University of Johannesburg, Faculty of Education Research Ethics Committee (No. Sem 2-2019-030). Informed consent was provided by participants.

Through the guidance of the FCTMV aligned with the first step of the word sum-wheel (Swanepoel & Luneta 2024), teachers introduced a systematic linguistic approach to analyse and understand mathematics word problems, starting with breaking the word problem into smaller sections, activating background knowledge and defining the meaning of mathematics vocabulary to understand the language of mathematics. Co-researcher explained:

Teachers found that when they broke a mathematics word problem into short sentences and condensed the information, learners were able to read with understanding. This correlates with the lower-order thinking questions found under ‘remember’ and ‘understand’ according to Bloom’s Revised Taxonomy, which takes hands with creating factual and conceptual knowledge (Sudirtha et al. 2022). Including this strategy proved successful in guiding teachers’ instruction on mathematics word problems while also helping learners understand what they read (Orton & Frobisher 2002; Swanepoel 2016). Along with keeping sentences short, it was found that when teachers activate learners’ prior knowledge and explicitly teach the meaning of mathematics vocabulary to learners, they are able to understand mathematics word problems (Ahmadi et al. 2013; Khoshaim 2020). Both teachers and learners had to become fluent in the ‘language of mathematics’ by making time to explicitly use the mathematics register (Xu et al. 2022). It was also found that, in many cases, teachers had to become familiar with the mathematical register before teaching it to learners. This is evident from co-research:

Constant communication and asking leading questions for clarification, as seen in the word sum-wheel (Swanepoel & Luneta 2024), served as a key area of development in unlocking word problem-solving instruction through the FCTMV. Throughout the research, teachers utilised constant communication to create opportunities for learners to continually ask questions about mathematics word problems (Swanepoel 2022). Learners were encouraged to ask as many questions as possible. The co-researcher explained the main role of asking questions to learners:

The purpose of learners asking questions throughout the completion of the mathematics word problem was for teachers to ascertain learners’ comprehension of the word problem (Swanepoel 2016; Vance & Smith 2021). Similarly, teachers asked leading questions throughout the instruction of mathematics word problems to guide learners’ thinking and assess whether they comprehended what the mathematics word problem was asking them to do. Linking back to the FCTMV, this relates to the lower-order thinking questions found under ‘remember’ and ‘understand’ and gradually transitions to higher-order thinking questions, such as ‘apply’ and ‘analyse’, according to Bloom’s Revised Taxonomy. This involves creating factual and conceptual knowledge, as well as procedural and metacognitive knowledge (Sudirtha et al. 2022).

Verbal feedback was a strategy proposed by many teachers, claiming that if learners were able to provide a verbal answer instead of a written one, it meant that learners understood what had been asked. Furthermore, teachers noted that through the inclusion of constant communication, learners made a point of remembering to have two answers: one answer as part of the calculation and a second answer in the sentence answer. This aligns with step five of the word sum-wheel (Swanepoel & Luneta 2024). Lastly, learners also remembered to double-check (step six of the word sum-wheel) their answers by going back to the mathematics word problem and verifying that the mathematics register matches the calculation and the answers generated.

Not only was the FCTMV instrumental in supporting teachers’ ability to solve word problems, but, as noted by teachers, the FCTMV, along with the word sum-wheel, has supported learners’ abilities. Teachers have found that through the use of constant communication, asking leading questions and allowing learners to ask questions freely, learners have begun to revisit the questions and the operation(s) they used and are now starting to double-check their answers.

This is a result of learners understanding the process of mathematics word problem-solving, the word sum-wheel, along with the mathematics register. The practice of learners checking answers has led to the elimination of learners’ instant gratification and their tendency to rush through solving mathematics word problems. Based on learners’ improved performance in mathematics word problem-solving, teachers’ instruction in mathematics word problem-solving has been enhanced.

The third element in the word sum-wheel is ‘play’, which is an umbrella term encompassing the integration of peer and group instruction, the inclusion of practical and real-life experiences in mathematics word problem-solving instruction and the application of the MI theory in mathematics word problem-solving instruction. The ‘play’ element gives rise to the opportunities that are presented by the higher-order questions as proposed by Bloom’s Revised Taxonomy, some of which include questions resulting from ‘apply’, ‘analyse’, ‘evaluate’ and ‘create’. Procedural and metacognitive knowledge is created through participation, such as when opportunities for ‘play’ are implemented. The co-researcher stated:

The inclusion of peer engagement, where teachers allow learners to turn to each other and teach the mathematics word problem to one another, proved to be very successful. Group engagement was also effective in allowing learners to teach and learn in unconventional ways. Learners appreciated the variation in routine. Teachers found that when learners were able to freely discuss the word problem with each other and explain it to one another, they understood the content and context of the problem better. Through the use of peer and group engagement, learners were given the freedom to discover the meaning of the mathematics word problem and to experiment with solutions to the problems while working in their groups. One significant finding was the importance of integration, where mathematics word problem-solving is integrated into practical activities (Ariba & Luneta 2018).

Additionally, the foundation of asking leading questions and maintaining constant communication is integrated into other learning programmes, such as language and life orientation. Teachers have found that as there is little to no time reserved for explicit mathematics word problem-solving instruction, it should be adhered to and attended to in as many informal and integrated ways as possible. In addition, teachers have also noted that practical activities, such as baking and art, as well as physical activities, can be incorporated into mathematics word problem-solving instruction (Khoshaim 2020). This is especially true when learners are asked questions that contain mathematical vocabulary and have to process the question in light of the context, with their comprehension of the question incorporating the mathematics register. Lastly, through the integration of concrete materials and manipulatives, learners are given the opportunity to concretely experience what they are reading in the mathematics word problem. Some learners require the reassurance that concrete manipulatives provide to grasp the essence of a mathematics word problem. There should be time allocated for learners to actively engage with these concrete materials and manipulatives, allowing them to experiment and discover how the mathematics register, number operations and relationships complement each other.

Future research should explore how the FCTMV is implemented across diverse classroom contexts, including multilingual and under-resourced environments. Longitudinal studies could examine how sustained use of the framework in professional development affects teachers’ instructional practices and learners’ progression through different levels of cognitive and metacognitive understanding. In particular, there is a need to investigate how teachers adapt leading questions and vocabulary prompts to suit learners’ varying cognitive readiness and how these scaffolds influence learner outcomes in mathematics word problem-solving. Additionally, future studies could assess the effectiveness of using the FCTMV as a formative assessment tool to track and support learners’ growth from lower- to higher-order thinking. Comparative studies across provinces, languages of learning and teaching and phases of schooling may also provide insights into the framework’s scalability and adaptability in broader educational systems.

This strength of the study include the innovative FCTMV framework, which supports both teacher development and learner cognition, and its participatory design involving teachers as co-researchers. The research is contextually relevant to multilingual classrooms and aligns well with Bloom’s Revised Taxonomy. However, limitations include a small sample size, a short implementation period and a lack of quantitative learner performance data. Additionally, potential researcher bias and limited scalability were noted, along with minimal focus on linguistic diversity beyond English and Afrikaans contexts.