Dr Katrina McChesney, University of Waikato
The first two posts in this three-part series have highlighted two pedagogical approaches that are increasingly popular both in Aotearoa New Zealand and internationally: mathematics teaching that centres on rich tasks and problems, and the “Writing Workshop” approach to teaching writing. This post concludes the series by reflecting on the connections and alignment between these two pedagogies.
We often tend to think about pedagogical approaches separately for different learning areas. However, the impetus for this series came from my reflections on teaching pre-service teachers at the University of Waikato about both problem-based mathematics teaching and Writing Workshop. Teaching across both maths and literacy papers, I was able to see that while these pedagogies each have much to offer in themselves, they also have much in common. Understanding these commonalities can support teacher practice in both literacy and mathematics, and allow us to build classrooms where students experience more consistent teacher expectations and ways of working across the curriculum. This post focuses on highlighting those connections.
Connection 1: The nature of mathematics and writing
A key strength of both Writer’s Workshop and problem-based mathematics teaching is that these approaches engage students in doing real mathematics and real writing – students get to (regularly) do the same things that real writers and real mathematicians do. These authentic experiences contrast with the ways we can sometimes represent the nature of mathematics and writing in our classrooms.
For example, real mathematicians don’t solve collections of similar questions using methods that have just been demonstrated to them by an expert. Instead, real mathematicians tackle challenging problems that they don’t immediately know how to solve; they try different approaches and persevere until they eventually conquer each problem. Real mathematicians don’t turn to an expert to tell them whether their answers are correct or not – they use argumentation and reasoning to convince first themselves and then others that their work is sound. Problem-based mathematics teaching allows students to share these experiences of ‘real mathematics’.
Similarly, real writers don’t just fill exercise books or Google Drives with texts written for artificial scenarios – texts that never get read or used except to judge the skill of the writer. Instead, real writers write with an awareness of purpose and audience, and their texts are published or sent in other ways to their intended audiences. Real writers also don’t just write in order to practice a particular text structure or genre. Instead, they write out of a sense of passion and motivation – they write what they want (or even feel called) to write, growing their toolkit and learning to use different structures and genres over time as a result of considering varying topics, purposes, and audiences. Writing Workshop offers these ‘real writing’ experiences to students.
It’s interesting to reflect that sometimes, we seem to value authentic learning opportunities in other curriculum areas much more readily than we do in literacy or mathematics. For example, in physical education we don’t just teach ball skills – we want students to engage in actual games or sports that use those skills. In science, we don’t just teach isolated concepts or skills – we value opportunities for students to conduct experiments and inquiries, experiencing the Nature of Science. In the Arts or Technology, we want students to actually create and design things, considering the purpose and effectiveness of their creation/design. It’s important for students to have (lots of) these authentic experiences in literacy and mathematics, too.
Connection 2: Responsive, “just-in-time” learning
The NZ Curriculum reminds us that learning is enhanced when students see the relevance of new learning and make connections to prior learning and experiences. In both problem-based mathematics teaching and Writing Workshop, students begin by working on a meaningful task (a worthwhile piece of writing or mathematical problem/task) using their existing knowledge and skills. New learning then comes out of the needs that become evident through their work – for example, a technique or concept that would help them with this particular mathematics problem, or an aspect of their writing that could be enhanced to help them meet their goals for this particular text. Situating new learning in the meaningful context of a task-in-process ensures that students are receptive to the new ideas.
This “just-in-time” learning can happen in several ways:
- Needs-based mini-lessons or workshops, (used in both problem-based mathematics and Writing Workshop), with students opting into – or being identified by the teacher for – specific workshops.
- In problem-based mathematics lessons, opportunities for students to hear how others solved mathematics problems (during the “sharing” or “summary” phase of the lesson), as well as opportunities to make connections to other mathematical ideas (through the “connect” or “consolidate” phase of the lesson).
- In Writing Workshop, one-on-one student-teacher conferencing focused on next steps for a specific piece of writing, as well as student-to-student conversations during both writing and sharing time.
Just-in-time learning can enhance student motivation because students approach the new learning from a position of curiosity, interest, need, and expectancy that all relate to a clear mastery (rather than performance) goal.
Connection 3: The role of dialogic pedagogy
In both problem-based mathematics teaching and Writing Workshop, classrooms become learning communities as students engage in rich, interactive (dialogic) talk among themselves and with their teacher/s. Students discuss possibilities, techniques, strengths, and areas for growth. They ask and answer questions; develop ideas collaboratively; respond to the thinking of others; and “interthink” through the opportunities for shared dialogue.
In problem-based mathematics lessons, students are positioned as mathematical inquiry communities or discourse communities. They use mathematical talk practices such as argumentation, agreement/disagreement, and questioning as they interact around a problem or rich task, first in small groups and then as a class. In Writing Workshop, students are similarly positioned as a community of writers who engage in peer feedback, sharing, and response as well as discussing (conferencing) their writing with the teacher. All this rich talk fuels learning, sense-making, and reflection.
A major goal for teachers implementing either problem-based mathematics teaching or Writing Workshop is to scaffold students’ talk in ways that ensure that all children can engage, have a voice, and be heard and respected within the discourse community of the classroom. This is the heart of dialogic pedagogy.
Connection 4: Benefits of these “powerful pedagogies”
Given that the pedagogies themselves have so much in common, it’s perhaps not surprising that problem-based mathematics and Writing Workshop can also bring many of the same positive outcomes for learners.
Specifically, these pedagogies can enhance student achievement in mathematics (e.g. see here, here, and here) and in writing (e.g. see here and here). They also promote students’ confidence, identity, and self-efficacy as writers and mathematicians, which feed students’ engagement in writing and mathematics and foster growth mindsets. Finally, these pedagogies support cultural responsiveness and success for learners from all cultures and backgrounds (e.g. for mathematics, see here, here, and here; for writing, see here and here).
The above outcomes are things we all want for all of our learners. Enacting problem-based mathematics teaching and Writing Workshop in your classroom can help you and your learners achieve these outcomes. We hope this blog series helps you give these “powerful pedagogies” a go!
Dr Katrina McChesney is a senior lecturer in Initial Teacher Education at the University of Waikato – Tauranga. She teaches across mathematics and literacy education as well as concepts of teaching and learning. Her research focuses on people’s experiences in educational spaces and places, with an underpinning concern for equity, social justice, success, and wellbeing for all.
Cover photo: Krissia Cruz on Unsplash