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Abstract

Problem posing has always been elusive in the Philippines, especially now that there is no articulation of it either as a teaching strategy or as a learning competency in the new national mathematics curriculum rolled out during the 2024–2025 school year for Grades 1, 4, and 7. This poses a dilemma because school mathematics teachers will have no motivation to incorporate problem posing in the classroom; without its explicit mention in the curriculum, they will not think about it for their own classes regardless of its importance in mathematics. However, efforts have been underway in recent years to promulgate the practice of and research on problem posing. This article capitalizes on a renewed interest in problem posing among mathematics educators and mathematicians in the country. In this article, we present opportunities for problem posing that we have found in the new national mathematics curriculum. We discuss potential tensions and struggles related to these curriculum opportunities for problem posing and briefly conclude with our thoughts for the future.

Keywords

curriculum opportunities mathematics curriculum problem posing

1. Introduction

In preparing for a future full of increasing uncertainty, pupils need to learn not only skills to secure jobs but also certain strengths such as curiosity, resilience, and imagination (Taguma, 2018). In mathematics classrooms, students have traditionally been positioned as receivers of knowledge. Problem posing, which is part of critical thinking, involves curiosity and is seen as a skill that leads to competences applicable to nondomain-specific situations. Further, it can be used as a tool to transition students from being mere receivers to active participants. Silber and Cai (2021) noted that problem posing helps students who have previously struggled with math anxiety, whereas Oxman et al. (2018) found that it helps pupils attain a sense of participation in the learning process. Pedagogically, problem posing encourages knowledge sharing as it allows for teachers to relinquish mathematical authority and encourages collaboration and active participation in class between and among students and the teacher (Cai & Hwang, 2021; National Council of Teachers of Mathematics [NCTM], 2020; Singer et al., 2015; as cited in Cai, 2022).

Problem posing is defined as the act of generating new problems based on given situations or the reformulation of previously existing problems (Cai & Rott, 2023). Brown and Walter (2005) encouraged the shift of the locus of control to the students themselves; they asserted that by posing new problems after solving a problem, new meaning is made by generating and analyzing a new set of problems. Whereas textbooks would make it seem that problem-solving techniques are the chief skills to learn, problem posing may enable the acquisition of deeper understanding of problems by helping students see a topic in a different light. It encourages the creation of new ideas that may be derived from multiple perspectives.

Problem posing, however, is as elusive as it has always been for our country, the Philippines. Feedback from school mathematics teachers indicates that whereas problem solving has been accepted as part and parcel of school mathematics goals, problem posing is almost unheard of. Bongco and David (2020) noted that teachers are caught in the middle of implementing a national curriculum that needs to be balanced with their own classroom context. The curriculum handed down from the Philippine Department of Education (DepEd) to schools often causes teachers plenty of confusion in implementation due to a mismatch between curriculum goals with local realities and short and abrupt training to address a constantly revised curriculum. Teachers, thus, end up becoming passive implementers of the curriculum (Bongco & David, 2020; Vilches, 2018) to simply comply with the DepEd directives (Vistro-Yu & Verzosa, 2024). Nonetheless, efforts have recently been underway to spur renewed interest in problem posing as more and more educators recognize its value in the teaching and learning of mathematics. An example is the first author's plenary presentation at a national conference of the Mathematical Society of the Philippines in 2023. She strongly called for more attention to be given to problem posing in the mathematics classroom (Vistro-Yu, 2023a). Moreover, a Special Interest Group on problem solving and problem posing was formed at the 2023 Biennial and International Conference of the Philippine Council of Mathematics Teacher Educators (MATHTED), Inc. It aimed to engage its members in promoting problem solving and problem posing through research and practice (Vistro-Yu, 2023b). Another notable initiative that has been undertaken by the Department of Mathematics of the Ateneo de Manila University is the Problem-Solving Enrichment and Training Program (ProbSET), which featured a workshop on problem posing for its teacher-participants during its 5-day in-campus intensive training program in January 2024 (Punzal et al., 2024).

Although the aforementioned efforts ideally paved the initial steps toward heightened awareness of and improved practices related to problem posing, it is a fact that unless a content topic or its corresponding strategy is explicitly mentioned in the intended curriculum or alluded to in any pertinent document from the DepEd, it will never become part of the pedagogical arsenal of mathematics teachers. We face this reality in the new curriculum introduced by DepEd and rolled out during the 2024–2025 school year for Grades 1, 4, and 7 (DepEd, 2023). In the new mathematics curriculum document released by DepEd (2023), problem posing or any semblance of it is noticeably absent. This contrasts with the previous national mathematics curriculum which featured learning competencies in a few topics that pertained to problem posing (DepEd, 2013). For example, in Grade 4, students were expected to “create problems with reasonable answers involving GCF (greatest common factor) and LCM (least common multiple) of 2 given numbers” (DepEd, 2013, p. 110).

Given the resurging interest in problem posing and the gradual implementation of the revised national mathematics curriculum, we searched for curriculum opportunities that teachers could exploit to incorporate or introduce problem posing in their mathematics classes. These curriculum opportunities must appeal to teachers’ basic instincts as progressive educators to be useful. For our discussion, we present these identified curriculum opportunities in the new mathematics curriculum where problem posing may be strategically implemented for teaching and learning mathematics. We hope that even if problem posing is not explicitly cited in the revised curriculum, this article might be able to provide ideas and the necessary motivation for our mathematics teachers to incorporate problem posing in the teaching and learning of mathematics. We also hope that this article will provide the needed support and references for policy makers to introduce problem posing in future versions of the Philippine school mathematics curriculum.

2. Curriculum opportunities for problem posing

An analysis of the new curriculum document for Grades 1, 4, and 7 Mathematics reveals potential for problem posing in Philippine mathematics classrooms. Despite the absence of direct mentions in the document, problem posing may strategically manifest in several curriculum opportunities that we identified. These opportunities are inter-related in such a way that we frame our discussion from a general aspect to specific aspects of the curriculum. We begin our discussion with theoretical principles that not only underpin the curriculum but also serve as a basis for problem-posing opportunities. The discussion then progresses to identifying problem-posing opportunities in learning standards across key stages, which then moves toward a finer aspect of the curriculum—the performance standards. We offer hypothetical teacher–student dialogs in some of the performance standards to help teachers begin problem-posing episodes in their classes.

2.1 Curriculum opportunity 1: Theoretical principles

The new mathematics curriculum document mentions several theoretical principles related to pedagogy, assessment, and resources that are vital in achieving the curriculum goal of developing a Filipino learner who is a “mathematically proficient and critical problem solver” (DepEd, 2023, p. 5). Theoretical principles based on constructivist perspectives that include Piaget's (1977) theory of cognitive development, Vygotsky's (1978) social constructivism, and von Glasersfeld's (1987) radical constructivism open up curriculum opportunities for problem posing. These theories all support the idea that conceptual learning begins with active engagement. Moreover, the curriculum document points out that these theories are manifested through the incorporation of manipulatives, models, and contextual problems together with the teaching of underlying concepts instead of rote memorization as well as the use of both concrete and abstract representations to interpret physical and social phenomena (DepEd, 2023, p. 4). Teachers who take this seriously will realize that allowing students to engage in problem-posing activities enhances their active engagement with lessons.

Problem posing is thus integrated in the pedagogical process, utilizing it as a means of delivering the teaching and learning of mathematics in class. Cai (2022) noted that teaching through problem posing theoretically and empirically supports students’ learning. The Problem-Posing-Based-Learning instructional model (Cai, 2022) is a culmination of years of research that allows teachers and students to interact with students, dialog with them, and understand their mathematical comprehension based on the types of problems posed.

Problem-posing skills are linked to creativity, flexibility, and originality (Bonotto & Santo, 2015). The act of problem-posing is identified as an opportunity to interpret and to critically analyze reality because students need to discern important data, identify relations between data, decide if enough information is present, and investigate if their problems are coherent (Bonotto & Santo, 2015). A popular problem-posing strategy is the What If Not (WIN) strategy. The WIN strategy was defined by Brown and Walter (2005) as examining each component of a problem and manipulating it through the process of asking “What if not?” A study by Oxman et al. (2018) utilized the WIN strategy and expanded it to three substrategies: What If More (WIM), What If Less (WIL), and What If Instead (WII). These three substrategies explore adding features to the original problem configuration (WIM), removing features from the original configuration (WIL), and adding other possible features to the configuration (WII).

Oxman et al. (2018) combined these strategies with technology applets from GeoGebra and peer-sharing activities to successfully expand student knowledge, interest, and understanding of quadrilaterals.

Because problem posing is a pedagogical strategy, it also becomes part of classroom assessment. Problem posing as a method of evaluation and assessment may be employed to gauge how students demonstrate critical thinking and creativity as they generate problems that exhibit their understanding of the learning content. Cai (2022) noted that problem posing has long been part of numerous scientific discoveries. Problem posing is cognitively demanding but easily adaptable to students’ abilities and allows students with different levels of understanding to participate and pose good problems based on their level (Cai, 2022). This characteristic of problem posing makes it a low-floor and high-ceiling activity for students of all levels. In addition, Papadopoulos et al. (2022) found that problem posing can be used as an assessment tool for teachers to uncover the deficits in and obstacles to knowledge acquisition while also being used as an educational tool that prompts students to use more sophisticated mathematical thinking. The new Philippine curriculum describes assessment as a supporting component along with pedagogy in achieving the curriculum goals and explicitly states that it “should not only record learners’ level of achievement in understanding concepts, reasoning, and the solution of mathematics problems, but should also result in the development of appropriate feedback for improving instruction” (DepEd, 2023, p. 7). This definition of assessment offers mathematics teachers opportunities to incorporate problem posing in their class activities, particularly assessments, to give better feedback to students on the knowledge gained and to properly gauge students’ understanding of concepts presented in class.

The curriculum document likewise cites resources as a supporting component. It asserts that learning mathematics must be supported by a variety of resources (DepEd, 2023). This statement gives a hint to teachers that students asking questions and posing problems are learning resources. Students learn a great deal from one another and teachers must recognize this. Problem posing is an opportunity to harness background knowledge and learning materials, among other possible resources, to support pedagogy and assessment. By carrying out problem-posing tasks in the classroom, students are allowed access to their different lived experiences and backgrounds as they pose different types of problems (Cai & Leikin, 2020). In recent years, studies have shown significant effects of problem posing on the cognitive and noncognitive measures of learning (Akben, 2020; Bevan & Capraro, 2021; Cai & Hwang, 2021; Yang & Xin, 2021). Yang and Xin (2021) implemented a problem-posing course for students with learning disabilities, and, after the intervention, the students were observed to have begun identifying relationships in mathematical equations despite their initial difficulties with interpreting mathematical language. The studies of Akben (2020) and Cai and Hwang (2021) showed significant improvement in student metacognitive awareness and cognitive and noncognitive measures after problem-posing interventions were implemented.

Theories related to pedagogy, assessment, and resources that have been adopted for the new curriculum are hidden opportunities for teachers to engage students in problem-posing activities. As Filipino teachers always try to conform to DepEd's directives, we expect that by taking the theories cited in the curriculum document seriously they will find it in their hearts and minds to think out of the box and take initiatives to include problem-posing activities in their classes. In particular, teachers need to understand the pertinent aspects of the theories that relate specifically to initiating problem-posing activities in the classroom.

2.2 Curriculum opportunity 2: Key stages and learning standards

The Philippine mathematics curriculum features three key stages that outline the desired learning outcomes of learners at the end of Grades 3, 6, and 10. Key Stage 1 (KS1) covers the first three grade levels, whereas Key Stage 2 (KS2) focuses on the last 3 years of grade school. Meanwhile, Key Stage 3 (KS3) is for junior high school, which spans Grades 7 to 10. Each key stage has five learning standards, some of which are linked vertically to one another. These key stages and their respective learning standards are another set of curriculum opportunities, as problem posing is already implied in them. We also emphasize viewing these key stage learning standards through a vertical progression across the three stages. This set of curriculum opportunities is divided into four subsections in which we elucidate how problem posing manifests across key stages and learning standards: (a) conceptual and procedural fluency; (b) communicating and reasoning mathematically; (c) problem solving and critical thinking; and (d) values, attitudes, and dispositions toward mathematics.

2.2.1 Conceptual and procedural fluency

The first set of learning standards advocates a good grasp of mathematical content and applying such in solving problems.

KS1.1: Accurately understand and apply concepts, operations, procedures, and relationships in solving routine and nonroutine problems related to their day-to-day lives

KS1.2: Acquire high-level skills and fluency in the procedures and processes of mathematics through varied frequent practice and meaningful learning experiences

KS2.1: Use efficient mental and written mathematical concepts, operations, procedures, relationships, and tools to solve routine and nonroutine real-world problems

KS3.1: Apply mathematical concepts, operations, procedures, facts, relationships, and tools to describe, explain, investigate, model, and predict phenomena.

KS2.1 opens opportunities for students to not only solve routine and nonroutine problems using mathematical knowledge but also pose these related problems as guided by the teacher. KS3.1 also opens doors for students to generate questions as they learn to investigate various phenomena of interest within their respective contexts. Priest (2009) found that problem posing has been associated with developmental learning changes such as self-regulation, increased integration of prior and current knowledge, and increased socialization. To illustrate, Oxman et al. (2018) showed that introducing problem posing using geometry software allowed students to develop interest and understanding of geometry while also increasing their sense of participation in the learning process. Singer et al. (2013), Kontorovich et al. (2011), and Van Harpen and Sriraraman (2013) emphasized that in the process of posing mathematical problems, students gradually develop their fluency and creativity towards generating highly elaborate and original problems.

2.2.2 Communicating and reasoning mathematically

The second set of learning standards deals with communicating and reasoning mathematically.

KS1.3: Communicate and represent mathematical concepts and understanding using developmentally appropriate language

KS2.2: Reason and communicate using precise mathematical language to discuss ideas, investigate problems, and justify solutions

KS3.2: Reason mathematically, construct plausible arguments, evaluate the reasoning of others, and ask useful questions to clarify or improve arguments

KS3.3: Access, use, interpret, and communicate mathematical information and ideas to engage in and manage the mathematical demands in various 21st-century contexts.

Problem-posing activities rely on language skills and development. Drawing from Zwiers et al. (2017), co-crafting problems allows students to better understand the language of mathematics problems and develop a meta-awareness of the language used in these problems. It is also pointed out that mathematical reasoning must be the focus in posing problems to focus on the mathematical meaning created by the learners (Zwiers et al., 2017). We highlight KS1.3 and KS2.2 in this part of the discussion.

KS1.3 is a curriculum opportunity because problem-posing activities rely on and can facilitate language skills and development in mathematics and general communication. By focusing on communicating and representing concepts, this learning standard paves the way for teachers to encourage students to ask questions and begin posing problems. At this level, students could be encouraged to pose problems similar to what they are exposed to using familiar exercise items and problem structures as resources to give them ideas on the kinds of questions or problems to pose. KS2.2 deals with developing precise mathematical language to discuss ideas, investigate problems, and justify solutions. Students at this level could be encouraged to generate questions when investigating problems, such as posing a simpler problem to shed light on the bigger problem at hand. The same goes for KS3.2, in which students not only ask useful questions but may also pose different problems to aid their argumentation. By allowing students to interact with each other in the problem-posing process, Arikan and Unal (2014) pointed out that the act of problem posing nurtures critical and creative thinking through students’ making attempts regardless of their mathematical ability.

2.2.3 Problem solving and critical thinking

The third set of learning standards caters to the acquisition and utilization of problem-solving and critical thinking skills.

KS1.4, KS2.4: Acquire problem-solving and critical thinking skills through real, situated, or purely mathematical problems

KS2.3: Exhibit willingness and confidence to explore alternative solutions, and to take risks necessary to solve real-world problems

KS3.4: Utilize mathematical thinking in decision making and acquire problem-solving and critical thinking skills through real, situated, or purely mathematical problems.

As could be seen in KS2.3, allowing students to explore alternative solutions and be confident risk takers opens the opportunity for them to pose problems that may be similar to or different from those encountered in class without fear. S. K. Leung (1996) and Kwek and Lye (2008) were among the first researchers to employ problem posing as a tool for assessment among elementary level students. Their studies revolved around the quantity, complexity, and originality of the problems posed by students, and their findings concluded that problem posing as an assessment tool encouraged students to take risks, be open to constructive feedback, and enhance their mathematical understanding. Regarding KS1.4, KS2.4, and KS3.4, the acquisition of problem-solving and critical thinking skills may also be derived from the use of student-posed problems, thereby demonstrating problem posing both as a pedagogical activity and as a resource for learning. As KS3.4 is the culminating learning standard for this set, we hope that by this time students would have acquired good problem-posing skills as well since this equips them with the necessary tools in pursuing higher levels of learning.

2.2.4 Values, attitudes, and disposition toward mathematics

The last set of learning standards pertains to the development of the appropriate attitudes and disposition toward mathematics.

KS1.5: Develop appreciation, curiosity, interest, creativity, and other desirable values, attitudes and dispositions in mathematics

KS2.5: Enhance appreciation, curiosity, interest, creativity, and other desirable values, attitudes and dispositions in mathematics

KS3.5: Strengthen appreciation, curiosity, interest, creativity, and other desirable values, attitudes, and disposition in mathematics.

We believe that problem posing can greatly contribute to achieving this set of learning standards. A construct of mathematics education that is heavily related to problem posing is creative mathematical thinking (Papadopoulos et al., 2022). Problem posing is a distinctive and creative act that may even be more valuable than finding solutions (Bonotto & Santo, 2015; Joklitschke et al., 2019; Kontorovich et al., 2011). Meanwhile, Arikan and Unal (2014) asserted that problem posing allows students to feel less pressured to find the right answers while simultaneously believing more in their mathematical capabilities. This internal motivation is noted to significantly decrease the occurrence of mathematics anxiety among students (Hlalele, 2012). Through the act of problem posing, students become motivated to work harder and attain a desirable attitude and state of mind (Pólya, 1981), leading to more cognitive freedom and ownership of their learning. Kopparla et al. (2019) also stated that letting students pose problems allows them to engage in the real world, thus developing an appreciation for and curiosity about mathematics and its applications in real life. In this light, mathematical authority in the classroom is shared through the act of problem posing as it allows students to transition from their traditional role of receivers of knowledge in the classroom into a new role as positive mathematical creators and seekers (Cai, 2022).

2.3 Curriculum opportunity 3: Performance standards

The first two curriculum opportunities pertain to overarching, general components of the new curriculum. Zeroing in on the specific learning content and competencies stated in the new mathematics curriculum, we identify several performance standards in each of Grades 1, 4, and 7 that may be creatively tapped to allow for problem-posing activities to ensue. Although we acknowledge that problem posing is a viable and worthwhile means of teaching and assessment, it should not be the only mode of instruction or evaluation to be used. We discuss these suggestions using the three content strands presented in the new curriculum: (a) Number and Algebra, (b) Measurement and Geometry, and (c) Data and Probability.

2.3.1 Number and algebra

For this content strand, three subsections comprise the discussion: numbers, patterns, and finance.

Numbers. In Grade 1, students are expected to order and decompose (into tens and ones) numbers up to 100. We propose that Grade 1 students be given prompts that center around providing alternate decompositions of a given number. For example: Teacher (T): In pairs, take turns asking each other how to obtain any number from 1 to 100 using other numbers. For example, how can 3s and 2s together form 10?

Student 1 (S1): I want to try! Give me numbers that add up to 79!

Student 2 (S2): Hmmm. 78 and 1!

Student 3 (S3): In how many ways can you have a sum of 5?

Student 4 (S4): Let's see. 0 and 5, 1 and 4, and 2 and 3. Are there only 3, maybe I’m missing something?

Student 3 (S3): It looks complete! But I think you can do it with three numbers! 2, 1, and 2!

Such tasks may allow teachers to gauge the extent of their students’ number sense development while also stimulating student thinking and creativity.

When students reach Grade 4, they should be able to compare and order dissimilar fractions. Teachers may give students the task of coming up with their own dissimilar fractions to compare and use different representations to further check if the comparison is correct or not. For instance, a student may come up with comparing 3/11 and 5/13 and use both computational and graphical methods to justify their comparison.

T: Class, which fraction is bigger: ⅔ or ⅖?

S1: ⅖! Because the lower number (denominator) is bigger!

T: Let's try that again. S1, can you try drawing ⅔ and ⅖ on the board to show that ⅖ is bigger?

[S1 draws it on the board and realizes that ⅖ is smaller than ⅔.]

T: I’m glad you drew the fractions correctly and realized your mistake. Similar to what I did, give your seatmate a pair of fractions. What question will you ask your seatmate?

S2: [faces S3] What about 3/11 and 5/13?

S3: Could they be equal? How can we draw to find out?

By Grade 7, these problem-posing tasks could be extended to include signed numbers and, likewise, transitions between mathematical symbols and worded statements.

Patterns. Another performance standard in which problem posing is highly applicable is extending existing repeating patterns and creating new ones. Grade 1 students may be tasked with asking their classmates to extend a pattern they designed or collaboratively design a pattern inspired by their surroundings. When they reach Grade 4, they are expected to be able to generate simple patterns and explain the rule(s) behind them. A possible problem-posing task here is for students to design their own patterns and have their classmates examine them and determine the rule(s) behind them. By Grade 7, the students learn the fundamentals of algebra and thus should be able to see the patterns of numbers and arithmetic being generalized. One performance standard in which problem posing could be utilized is in solving literal equations. Students may create their own equations that involve several variables and pose questions on expressing one variable in terms of other variables. This activity can exhibit students’ understanding of the properties of equality.

Meanwhile, Grade 7 students are also exposed to the basics of sets and set operations. A problem-posing dialog that teachers could begin with is the following:

T: Given this Venn diagram consisting of three sets A, B, and C, create a problem with an appropriate situation whose solution requires this Venn diagram.

Another example of how teachers might initiate problem posing is by saying:

T: Draw a Venn Diagram consisting of two or three sets, and shade portions of it. Work in groups and ask one another possible questions that you can think of based on the Venn Diagram you drew.

S1: How do we name this portion of the diagram?

S2: I think that might be the intersection of A and B?

S3: What if we find the intersection of A and B, then intersect it with C? Can we find that on our Venn diagram?

These prompts would require students to engage each other in creating possibly different problems and situations.

Finance. In adding and subtracting money, Grade 1 students may come up with their own buy-and-sell scenarios and use actual bills and coins to simulate transactions. Problem posing comes as an activity between students in handling money during role playing. By Grade 4, students have learned decimals and rounding off decimals and can thus pose problems concerning estimation of money. Lastly, students not only learn percentages and rates but are also expected to come up with a financial plan in Grade 7. These can be integrated in problem-posing tasks that involve students posing scenarios that will require a financial plan, thereby integrating their knowledge of numbers and advanced arithmetic.

2.3.2 Measurement and geometry

For this content strand, we divide the discussion into two subsections: measurement and geometry.

Measurement. The new curriculum aims for Grade 1 students to be able to use nonstandard units, such as body parts or familiar objects (e.g., paper clip), to measure and compare lengths and distances. In this regard, they can be tasked with choosing a nonstandard tool, posing questions concerning measurement, and manipulating the different measurements that arose from this activity. On the other hand, Grade 1 students may also be prompted to generate questions and problems relating time and dates with their personal experiences and circumstances. For example, they may be asked to create a schedule and pose questions concerning the activities they prioritize and the amount of time they intend to devote for each.

Geometry. Students learn symmetry and reflection in Grade 4. Problem posing could be integrated into this performance standard with activities that allow students to creatively work around an image to produce reflections and tessellations. Students may be asked to create artistic designs from a base shape, and they may then ask their peers to recreate their drawings through a series of reflections.

T: We’ve seen how shapes can be reflected over a line. Let's make geometry a little more artistic. I saw this picture on the Internet (shows a tessellation on Manila paper). What questions do you have about this picture?

S1: Can I make this using another shape?

S2: What shape is being repeated?

S3: What does the mirror image look like?

T: Those are good questions.

When students reach Grade 7, they should be able to work their way through tasked with posing their own volume problems as contextualized in real-life situations along with verifying the reasonableness of the units they provided.

2.3.3 Data and probability

Problem-posing opportunities in the realm of data and probability revolve around data collection, presentation, and interpretation. As early as Grade 1, students are expected to be able to represent and interpret data using pictographs without a scale. This can be an avenue for them to pose their own data-driven questions, leading to creative means of representing and interpreting their findings. For instance, they may be given an existing data set and tasked with generating several questions arising from it or creating their own pictograph out of it. Similar tasks may be given to Grade 4 students, with these aiming to check if students can work using different representations (e.g., pictographs and bar graphs). When they reach Grade 7, students may be tasked with designing their own data-informed investigation, thereby exhibiting opportunities for problem posing. This may be as simple as asking which type of data presentation best communicates the data set or as complex as posing how the different variables in the data set potentially relate to each other.

3. Struggles and tensions

Although we were successful in finding curriculum opportunities for problem posing in the new mathematics curriculum and in implementing further suggestions for practice, we anticipate some struggles and tensions that mathematics teachers and their supervisors will undergo. These are not meant to discourage the utilization of the curriculum opportunities, but being aware of these struggles and tensions could hopefully challenge mathematics teachers to find more curriculum opportunities for problem posing as the new curriculum for the other grades is rolled out over the next 12 years, at most.

Finding curriculum opportunities is not necessarily a struggle; not having these opportunities explicitly presented in the curriculum or teaching guides is the struggle. As initially referenced, strategies or techniques that are not written explicitly in the curriculum guides—in this case, problem-posing strategies and techniques—will not be utilized by most Philippine school mathematics teachers. More importantly, teachers will not be able to recognize these hidden opportunities because they will stick to what is written in the curriculum documents. Thus, unless someone who understands the value of these curriculum opportunities demonstrates how these opportunities can be harnessed, they will never be recognized or used by teachers. Indeed, these issues may not be isolated in the Philippine context. When curriculum opportunities for problem posing do become recognized and integrated into curricula, tensions may arise as more conservative educational leaders insist on maintaining what is explicitly written rather than take risks with new ideas that are not articulated. An expected challenge worldwide is the training of teachers in the art of problem posing. Research has cited that problem posing is a struggle for students and teachers alike (Cai, 2022; Silver & Cai, 1996 as cited by Cai, 2022). With numerous other professional development programs regularly offered to teachers that cater to problem solving, adding one more dedicated to problem posing will certainly be difficult to begin much less sustain.

Outside of the curriculum documents, more struggles exist, as Philippine education is in a flux. The results of international large-scale assessments (Ines, 2023) coupled with learning loss (Chanco, 2022) experienced by our students has led to numerous actions by the government, including holding remedial learning camps (Hernando-Malipot, 2023; Parungao, 2024) and conducting an end-to-end systematic review of the Philippine education system by the Second Congressional Commission on Education [EDCOM] (2023; Hernando-Malipot, 2022). With much of the work of EDCOM 2 focusing on multisectoral factors affecting the state of education (e.g., digitization, early childhood education, bullying, etc.), tensions between DepEd, school leaders, and EDCOM 2 commissioners have arisen. The reexamination of the curriculum has been put on the backburner given the amount of political unrest and teacher dissatisfaction stemming from the release of the newest version of the DepEd's curriculum (Hernando-Malipot, 2024; Magsambol, 2024b; Servallos, 2023). The appointment of a new Education Secretary (Magsambol, 2024a) put the DepEd in transition, making it difficult to solidify its action plans and strategic priorities, which include the uncertainty of a curriculum reexamination. We are cognizant of the fact that the politicization of education systems is a universal problem and political promises by those in power often penetrate the education realm leading to constant curriculum upheaval.

To wit, there is potential for problem posing to be strategically implemented in mathematics classrooms in the Philippines, as can be seen in the different curriculum opportunities identified in this article. The initial piecemeal proposals for the curriculum opportunities of problem posing have proven to be implementable in other countries as well in that they require minimal integration and a targeted professional development program. However, because problem posing is not explicitly stated in the curriculum, there is a need for sustained efforts in conducting professional development programs on problem posing so as to raise stronger awareness of it.

4. What the future holds

Given the volatility of Philippine mathematics education and the exclusion of problem posing from the new mathematics curriculum, the future of problem posing in Philippine mathematics education is uncertain. Curriculum opportunities are helpful to know but will be difficult to sustain.

To put ourselves at ease, we looked at initial results from countries like Australia, China, Singapore, Turkey, and the United States for hints toward future of our curriculum opportunities (Arikan & Unal, 2015; Australian Education Council, 1991; Chinese Ministry of Education, 2011; Divrik, 2023; Ministry of National Education, 2018; NCTM, 2000). As early as 2005, the Turkish Ministry of Education was already including learning competencies of problem posing in fractions within their primary education curriculum (Milli Eğitim Bakanlığı, 2009). A study by Rosli et al. (2014) showed that countries like the United States and Turkey have shown clear improvements in problem-posing skills due to their inclusion in the national curricula. Although there have been successes, studies have also revealed that the struggles surrounding implementing problem posing that have emerged from these countries include, but are not limited to, the following: teacher hesitation to adopt problem posing, differences in performance due to socioeconomic status, inadequate linguistic skills to pose problems, difficulties in implementing a new curriculum, and a need to overhaul the training and assessment framework (Arikan & Unal, 2015; Cheng, 2013; Leung, 2013; McDonald, 2017; McDonald & Smith, 2020; Rosli et al., 2014). These are not vastly different from the struggles we face in the Philippine context; with this paper, we provide suggestions on how teachers can begin the process of incorporating problem posing in different parts of the curriculum.

The task is clear for us; we need to exert more effort to make our education leaders aware of the value of problem posing and thus need to incorporate it explicitly in the new intended mathematics curriculum. We take heart that despite the process being a slow one, we are not alone in the endeavor of incorporating problem posing. We will need the cooperation of all stakeholders as we know fully well that we cannot succeed at it by ourselves alone. Seeing the successes and struggles of other countries in implementing problem posing, we see that we are on the right path. We are also hopeful that teachers in other countries can draw inspiration from the opportunities for problem posing we have outlined in this article. An important implication of this paper is the need to rethink the process of designing curriculum so that it is more responsive to the cognitive demands and explicitly identifies points at which complex skills, such as problem posing, may be introduced.

Footnotes

Contributorship

Catherine P. Vistro-Yu initiated and conceptualized the paper, wrote parts of the paper for coherence and completeness, added references, and did the final editing; Lester Hao wrote and revised several parts of the paper, organized the curriculum opportunities identified by the authors, and added references; Marc Helton Sua wrote several parts of the paper, including curriculum opportunities on assessment and performance standards, conceptualized and wrote most of the sections on the struggles and tensions and what the future holds, and added references.

Declaration of conflicting interests

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

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Informed consent

Obtaining informed consent was not applicable in this paper as there were no human subjects involved.

ORCID iDs

Catherine P. Vistro-Yu

Lester C. Hao

Marc Helton Sua

Author biographies

Catherine P. Vistro-Yu is a professor and program coordinator for mathematics education at the Department of Mathematics, School of Science and Engineering, Ateneo de Manila University. She's a member of the department's Didactics of Mathematics Research Group. Her research interests include curriculum, problem-posing, ethnomathematics, sociocultural aspects of mathematics teaching and learning, and critical mathematics education. She is the president of the Philippine Council of MATHTED, Inc and the Editor-in-Chief of its official journal, Intersection.

Lester C. Hao is an assistant professor at the Department of Mathematics, School of Science and Engineering, Ateneo de Manila University. His research interests in mathematics education include multilingualism, multiculturalism, educational technology, problem-solving, and problem-posing. He is a member of the department's Didactics of Mathematics Research Group and Problem-Solving Enrichment and Training Program. He also serves as a cofacilitator of MATHTED's Special Interest Group on Problem-Solving and Problem-Posing.

Marc Helton Sua is a Master of Science in Mathematics Education candidate at the Department of Mathematics, School of Science and Engineering, Ateneo de Manila University. He is a Senior High School mathematics teacher at Xavier School San Juan, Philippines. His research interests include problem-posing, critical mathematics education, and project-based learning.

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The struggle is real: Finding opportunities for problem posing in the Philippine school mathematics curriculum

Abstract

Keywords

1. Introduction

2. Curriculum opportunities for problem posing

2.1 Curriculum opportunity 1: Theoretical principles

2.2 Curriculum opportunity 2: Key stages and learning standards

2.2.1 Conceptual and procedural fluency

2.2.2 Communicating and reasoning mathematically

2.2.3 Problem solving and critical thinking

2.2.4 Values, attitudes, and disposition toward mathematics

2.3 Curriculum opportunity 3: Performance standards

2.3.1 Number and algebra

2.3.2 Measurement and geometry

2.3.3 Data and probability

3. Struggles and tensions

4. What the future holds

Footnotes

Contributorship

Declaration of conflicting interests

Funding

Informed consent

ORCID iDs

Author biographies

References