PED 3151 Enacting Collaborative Inquiry in Professional Practice:

Professional Inquiry and Action Research

Elizabeth Cowan (7896636)

Professor Sarah Parke-Erochko

University of Ottawa

March 23, 2017

1. Overview

As our 21st century students are seeking learning experiences that hold relevance for them outside the classroom walls, a major focus of educational reform involves the establishment of thinking as the foundation for teaching and learning (Gini-Newman & Case, 2015). While it seems like common sense, many components of traditional classrooms have “non-thinking” qualities. For example, the teacher plans lessons based on the assumption that students can’t or won’t think, and there is a pervasive lack of thinking occurring within the walls of the classroom. Through his research, Peter Liljedahl (2017) found that most classrooms look the same regardless of their geographic location, socio-economic setting, the curriculum, the textbook used, available technology, etc. In short, he notes that classrooms around the world look more alike than different.

With this focus in mind, my inquiry project explores Peter Liljedahl’s idea of a thinking classroom and the conditions necessary to build and maintain such an environment. Liljedahl (2017) argues that teachers need to start playing with the “non-negotiable” elements of classrooms; in other words, teachers need to experiment with the things that we have not changed in classrooms in any significant way in the recent past. According to Liljedahl (2016), these “non-negotiables” include: type of problems, how we give the problem, how we answer questions, room organization, how groups are formed, student work space, autonomy, how we give notes, hints and extensions, how we level (e.g. bringing the class together to share out the answer), and assessment.

For instance, in a traditional classroom, students would usually be found sitting at their desks and writing in notebooks (Liljedahl, 2016). But what if we, as teachers, challenged this assumption? Liljedahl (2016) identifies vertical non-permanent surfaces as one of the easiest and most effective ways (along with using good problems and visibly random groupings) to teach thinking and problem-solving in mathematics classrooms (Figure 2). Thus, for this research, I investigated the element of student work space and how it can be leveraged for teaching problem solving and thinking skills. More specifically, I sought to answer the following inquiry question:

How can the use of vertical non-permanent learning surfaces help to build and maintain a thinking classroom?

My observations during practicum were in line with Liljedahl’s (2016) main findings, resulting in four key ways that vertical non-permanent learning surfaces help to build a thinking classroom.

2. Links to Practicum

For my Year 2 practicum, I was placed in a grade 8 math and science class at St. Joseph High School in Barrhaven. I had the same class for homeroom and Period 1 math each day, and this class included a mixture of core and immersion students working at a wide range of math levels (from very weak to very strong). My AT had the space set up with ten whiteboards (i.e. vertical non-permanent learning surfaces) mounted and spaced around the walls of the classroom. Each whiteboard had an associated playing card with a value of 1-10 posted next to it, which was used in conjunction with a deck of playing

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cards to form visibly random groupings for tasks (3-4 students/group). Whiteboard markers and erasing cloths were located on the side counter of the classroom (and students were expected to return these to their home after use). When working in groups, each group knew to take one marker to use on their whiteboard. The questions that students worked on were sometimes printed and taped directly adjacent to the whiteboards, or projected on the SMART Board at the front of the room. Small whiteboards were also available for use at student desks during quick lessons to check for understanding. These small whiteboards had one blank side and one grid side.

Figure 1: Vertical non-permanent learning surfaces in a Grade 8 math classroom at St. Joseph High School, Ottawa.

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My observations while teaching in this classroom closely resembled the results of Liljedahl’s (2016) research. Namely, I found that vertical non-permanent surfaces (VNPSs) help to build and maintain a thinking classroom through (Table 1):

1) Decreased time to first notation: similar to Liljedahl’s (2016) findings, I noticed that in comparison to more traditional chart paper or even notebooks, allowing students to use VNPSs resulted in a shorter time span between giving the task and each group making the first mathematical notation on the surface. In the words of Liljedahl (2017), “[w]hen students have the ability to erase, they are more likely to risk something.” I observed that in their small groups of 3-4, students were more willing to make that first notation on the VNPS because they knew they could erase. They didn’t feel tied to the results of their first attempt at solving a problem, and were therefore more comfortable with trying. Even the use of a small whiteboard on a desk showed decreased time to first notation in comparison with putting pencil to paper. However, the standing aspect was important for the following point…

2) Increased eagerness, participation, discussion and persistence: I was lucky enough to observe this class during the first two weeks of September when routines were being established, and I paid close attention to how students adapted to the use of VNPSs and small group tasks for math learning. While they took some time to adjust to the expectations for such an environment (e.g. not wandering around the class aimlessly, collaborating with peers, teacher not there to give the answer directly), the class got on board with this strategy pretty quickly. Students loved that they didn’t have to sit in their desks for the duration of the period; they were more engaged by standing and solving challenging problems; and the different groups motivated each other to keep trying if they hadn’t come up with a solution yet. The whiteboard problems often sparked lively discussions and prompted students to share strategies that worked and strategies that didn’t work. Students who would never have participated in a more traditional lesson were highly engaged, and looked forward to working at the VNPSs.

3) Increased non-linearity of work: while the ability to erase helped students feel more comfortable with starting a problem, they actually didn’t erase that often. Instead, they used the VNPS space to write, cross out, add, expand and explain their strategies. So, their work space more accurately represented the non-linearity of problem solving by showing the different strategies and attempts that they used to get to an answer that made sense (Liljedahl, 2016).

4) Increased mobility of knowledge: In line with Liljedahl’s (2016) results, I observed that students learned to engage with other groups close by while working at VNPSs. There was always lots of interaction among groups, especially those that were trying different strategies. This helped to break down social barriers within the classroom and decreased the students’ reliance on the teacher. The teacher’s role was more as a guide, asking prompting questions and providing guidance when groups were stuck or going too far down the wrong track.

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Table 2: Average times and scores of 8 proxies for engagement to measure the effectiveness of different surfaces during collaborative problem solving (Liljedahl, 2017).

3. Strategies for professional practice

Through his research, Liljedahl (2017) identified clusters of strategies in terms of their effect and how easy they are for teachers to implement in the classroom (Figure 2). For example, beginning with good questions, vertical non-permanent surfaces and visibly random groups are the easiest and most effective strategies for teachers to start with to implement change in their classrooms. When considering how to build and maintain a thinking classroom, vertical non-permanent learning surfaces are thus an excellent starting point.

These non-permanent surfaces are more freeing for the students. In order to use VNPSs in the classroom:

Make sure the surface is vertical and erasable; VNPSs can be in the form of a whiteboard, chalkboard or window (with

appropriate markers); Ensure that there is only one marker or piece of chalk per group, in order to

promote collaboration among students;

The vertical component forces students to stand, which increases their engagement as they have fewer ways to disengage (Liljedahl, 2017). As Liljedahl (2017) comments, students are “[q]uicker to make notations, quicker to try, and more engaged in every measure if the surface is non-permanent.”

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As a side note, it is worth considering how you could use VNPSs in conjunction with visibly random groupings to enhance the thinking culture in the classroom. This means that small groups (2-3 students) for tasks would be randomly assigned (e.g. with playing cards) in front of the students. The groups would then stand and work together at a whiteboard. Liljedahl (2014) found that this grouping strategy was better than any strategic effort that teachers could come up with, eliminated social barriers within the classroom, and further increased mobility of knowledge between students. The students are more willing to work in any group they are placed in and they are more excited to attend math class, even if their attitudes for the subject itself haven’t changed (Liljedahl, 2014).

However, it is important to emphasize that the tools in the first cluster (e.g. first circle in Figure 1) are just a starting point for fostering and sustaining a thinking classroom. See Table 3 for a summary of strategies that had a positive effect according to Liljedahl’s (2016) research. For a more thorough explanation of each of the positive effects below, refer to Liljedahl’s (2016) paper Building Thinking Classrooms: Conditions for Problem Solving.

Table 3: Positive effects for 11 different variables in teaching strategies and practices (Liljedahl, 2017).

Variable Positive EffectProblems Begin with good problemsHow we give the problem Oral vs. writtenHow we answer questions 3 types of questionsRoom organization Defront the roomHow groups are formed Visibly random groupsStudent work space Vertical non-permanent surfacesAutonomy Create space and push them into itHow we give notes Use mindful notesHints and extensions Managing flowHow we level Level to the bottomAssessment 4 purposes

Figure 2: Three clusters of strategies for building a thinking classroom.

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4. Further research

The concept of building thinking classrooms (specifically, vertical non-permanent surfaces and visibly random groupings) began to gain traction with Ottawa school boards within the past three years (Wheeler, 2017). However, these strategies seemed to be limited to the math departments, and many teachers in other departments or areas of expertise remained unaware or unconvinced of the applicability of this research for their subjects and classrooms. This was something that I experienced in my Year 2 practicum: as grade 7/8 math teachers were more readily adopting these strategies, teachers in other departments viewed these concepts as a “math thing.” In other words, they did not take the time to become familiar with the research and strategies as they felt that they were not readily applicable to their classrooms (e.g. for English, Religion, Social Studies). This highlights a need for more research on how Liljedahl’s notion of building a thinking classroom could be generalized across subject areas. For example, Liljedahl (2016) identifies nine elements and teaching practices that have the largest influence on fostering and maintaining a thinking classroom, but he explores these elements within the context of mathematics classrooms specifically. There is thus a need to examine if and how these elements work as a framework for promoting problem-solving in all 21st century classrooms.

5. Other resources

To further understand key conditions for problem solving (with a particular focus on mathematics), I would highly recommend that you refer to Peter Liljedahl’s research on building and maintaining thinking classrooms. He has spent over a decade investigating this topic and provides invaluable insight, as well as tools and resources for classroom teachers on his website (Liljedahl, n.d.). Ottawa-based math teacher Laura Wheeler (2017) also summarizes his research and its application in the classroom through her blog posts and associated Sketchnotes, which are an excellent synopsis of Liljedahl’s (2017) main ideas. For a broader look at the challenges and opportunities associated with 21st century learning, consider reading Gini-Newman and Case’s (2015) book Creating Thinking Classrooms, published by The Critical Thinking Consortium (TC²).

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References

Gini-Newman, G., & Case, R. (2015). Creating Thinking Classrooms: Leading educational change for a 21st century world. Vancouver, BC: The Critical Thinking Consortium.

Liljedahl, P. (2014). The affordances of using visually random groups in a mathematics classroom. In Y. Li, E. Silver, & S. Li (eds.) Transforming Mathematics Instruction: Multiple Approaches and Practices. New York, NY: Springer.

Liljedahl, P. (2016). Building thinking classrooms: Conditions for problem solving. In P. Felmer, J. Kilpatrick, & E. Pekhonen (eds.) Posing and Solving Mathematical Problems: Advances and New Perspectives. New York, NY: Springer

Liljedahl, P. (2017, March 14). Building Thinking Classrooms. Global Math Department Webinar. Webinar retrieved from https://www.bigmarker.com/GlobalMathDept/Building-Thinking-Classrooms

Liljedahl, P. (n.d.). Peter Liljedahl: For Teachers. Retrieved from: http://www.peterliljedahl.com/teachers

Overwijk, A. (2014, August 1). Vertical Non-Permanent Surfaces and Visible Random Groupings. (Blog Post). Retrieved from http://slamdunkmath.blogspot.ca/2014/08/vertical-non-permanent-surfaces-and.html

Wheeler, L. (2017, March 15). Building #ThinkingClassrooms. (Blog Post). Retrieved from https://mslwheeler.wordpress.com/2017/03/15/building-thinkingclassrooms/

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