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The Mathematics routines that cultivate learner agency

Samia Henaine, Makassed – Houssam Eddine Hariri High School, Lebanon

This article shares examples of how classroom routines could be one of the effective tools to foster learners’ agency and raise their voice and choice while learning mathematics.

During the last months, the concept of “agency” has dominated the discussion between educators since it is one of new terminologies that appeared in PYP: From principles into practice. Although it is not “new” in the programme because PYP educators were aware of student-centered learning, supporting learners too have voice, choice, and ownership is a challenging journey.

Being responsible for assisting and supporting teachers to implement the Mathematics curriculum effectively and for sustaining the growth of the programme, we started to experiment with practices in mathematics that build student agency. We chose one tool for teaching Math: classroom routines.

 Mathematical proficiency and routines

The National Council Teachers of Mathematics (NCTM, 2001) defines five strands that are interwoven and interdependent in the development of proficiency in mathematics: conceptual understanding, strategic competence, adaptive reasoning, productive disposition, and procedural fluency. One of the known tools or activities that help learners develop procedural fluency and conceptual understanding, as well as reasoning and problem-solving skills, is mathematics routines, where learners work together on a strategy or skill to develop specialized knowledge and language needed for conceptual understanding and applying mathematical concepts.

Dynamic Routines

Supporting learners to guide their learning required making a shift in the way routines are delivered and instructional practices that foster sense-making in Mathematics. Accordingly, I transferred the traditional routines into dynamic ones and put the needed criteria or the key elements that guide us toward planning meaningful experiences that support the learner’s voice and choice.

To apply dynamic routines, teachers create a safe learning environment where learners are provided with opportunities for metacognition, are confident and motivated, contribute to a positive attitude toward Mathematics, are encouraged to use mathematical language and test others’ strategies to assess their validity.

Examples of Dynamic Routines

We have started implementing the dynamic routine this year with fourth grade students. We chose the learning outcome: describe mental and written strategies for adding and subtracting two-digit numbers- Strand Number (Phase 2), and we extended it to teach adding and subtracting three-digit numbers.

Learners were asked to find one or more strategies and justify their answers. They shared their ideas with peers and then in groups using appropriate mathematical language. We used posters in classroom as samples to encourage them communicate and explain their thinking.

Figure 1: Sample of Class Poster

The following are samples of learners’ thinking:

Figure 2: Vertical and horizontal Calculations

Figure 3: Decomposing and Skip Counting

Figure 4: Use of Soroban

Figure 5: Same Change Method

Research suggests that once students have memorized and practiced procedures that they do not understand, they have less motivation to understand their meaning or the reasoning behind them (Hiebert, 1999). Therefore, we aim to develop our understanding of how to create opportunities for students to develop agency in the mathematics classrooms by encouraging them to participate as creative agents, who think and reason for themselves in mathematics, rather than being passive recipients of knowledge. Our routines reflect our beliefs, so all what we need to do is to choose the best way to apply these routines, reflect on their effectiveness in the sense of raising agent learners, and then act to go beyond and deeper.


National Research Council. 2001. Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press.

Hiebert, J. (1999). Relationships between research and the NCTM standards. Journal for Research in Mathematics Education, 30(1), 3–19.



Samia Henaine is a PYP Math coordinator who assists and trains teachers to implement the curriculum effectively, deepens their understanding of how teaching and learning are viewed from the perspective of new educational approaches, and support them to adapt teaching methods and materials to meet students’ varying needs and interests. You can follow her on Twitter @HenaineSamia.


6 Responses to The Mathematics routines that cultivate learner agency

  1. Leonie 25 June 2019 at 10:04 pm #

    Thanks for sharing this. It is really interesting.

  2. CATRIONA TUIMAKA 26 June 2019 at 4:05 am #

    Great article. Very practical. Supports student agency, motivates thinking, develops conceptual understanding and ownership and application of learning.

  3. Simon Gregg 26 June 2019 at 8:53 am #

    Yes! I like the name dynamic routines. All this increases the opportunities for ‘students as decision makers’!

  4. Samia 1 July 2019 at 8:23 am #

    Thank Simon! I created the idea of “Dynamic” as an answer on teachers’ famous question when we introduce a new approach: “How can we implement this with students?” The routines are powerful tools, yet using them in the traditional way will not develop students reasoning and thinking skills. Moreover, I believe that what it really matters is the approach of the practice and not the practice itself; for example, the “number of the day” can be used as a traditional routine where learners complete a worksheet about the number, or simply we can apply the dynamic routines process to develop number sense and number relationships, for example, we ask students: “In how many ways can you decompose the given number?”

  5. Alu 3 July 2019 at 8:19 pm #

    Great Samia

  6. Cecilia 10 August 2019 at 11:48 am #

    Well laid out and easy to engage with. Thanks for publishing this. I would like to adapt some of this for my class.

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