Student Engagement in Math Tasks

Collaborative Inquiry in Math @ Darcel S.P

Open-Ended Questions in Math for Student Engagement


This is a case study facilitated by the Student Work study teacher collaborating with two grade six classroom teachers in the Peel District School Board. This study explores the impact of open-ended questions in mathematics to increase student engagement and conceptual understanding. Open-ended questions provide a platform to stimulate student thinking and drive participation. Students are involved as active, thinking beings through collaboration, metacognition and differentiation, facilitating task completion and therefore fostering student engagement and student success. Collaboration with teachers allowed better teacher efficacy by incorporating high yield strategies and reflective teacher practice of assessment and instruction of student thinking and learning.

Collaborative Inquiry Proposal - Open Ended Questions in Math

Once in the classroom sitting with students that were selected for the study, I realized that my physical presence allowed students to feel safe and comforted that there was help if needed. Some questions I began to ask myself when I observed students diving into an activity were:

· What activities were engaging?

· Where students engaged with the particular activity?

· How do we measure student engagement?

· How might we program to differentiate for all learners to encourage participation?

· How do students accept certain roles in groups to allow for deeper thinking for every member?

Collaborating with host teachers we discussed this and together came up with our inquiry.

Collaborative Inquiry:
To encourage student collaborative inquiry using open ended questions in math.

Theory of Action: If we approach mathematical instruction by encouraging student collaborative inquiry through open ended questions in math then all learners will make their mathematical thinking more visible.

Example of Open-Ended Rich Task in Math Through Pedagogical Documentation

Action! & Consolidation


  1. How might we talk less and let students have the floor?
  2. How do we balance whole class instruction and group work?
  3. How do we begin to extract level 4 answers from students?
  4. How might we differentiate further to meet the needs of all learners?

Making Thinking Visible

  1. Selected a lesson from Marion Small's book Eyes on Math
  2. Students were asked open ended questions on parallelograms
  3. Students shared their thinking with the class

  • students made thinking visible by communicating their ideas to their peers
  • gave valuable information on the assessment and evaluation of student thinking
  • students learned from each other
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Students were given open-ended questions of a parallelogram and asked to answer the questions in groups. They were allowed to approach the screen to visually understand their thought process and collaborate with their peers. Anecdotal notes were taken by the teacher to assess their understanding conceptually of parrallelograms. Students made their thinking visible through accountable talk. They were asked to further check their understanding through a cut and paste activity reinforcing their ideas.

Resources We Used

Open Ended Questions help students learn.

TeIn the article Using Open-Ended Learning Activities to Empower Teachers and Students, Nancy Hertzog writes, “Open-ended activities provide a vehicle for personalizing instruction because they elicit students’ opinions, concerns, values, and knowledge. This becomes building blocks for students of all abilities.” (Hertzog, 1998) She further points out that that this is consistent with a constructivist approach in that teaching is shifted less towards the whole class and driven more towards individualizing instruction through the thoughts of each student. (Hertzog, 1998) In addition, she states, “Successful open-ended activities require a shared responsibility between the teacher and the students.” (Hertzog, 1998) The student and teacher together gain an acceptance of and understanding that learning together by less teacher talk and listening more to student-to-student voice plays a valuable part in conceptual understanding of mathematics and valuable assessment information. Students become aware that their voice matters and at any stage can participate in the activity and gain understanding. In the Capacity Building Series, Student Voice: Transforming Relationships which is produced by the Student Achievement Division to support leadership and instructional effectiveness in Ontario Schools, it states, “Developing reciprocal relationships- with students, parents and colleagues- is critical for sharing ownership for learning. Many observe that as students are made partners in decisions about their learning, motivation and perseverance grow, resulting in new and more in-depth learning”. (Watkins, 2009)

The impact of open ended questions and student engagement

We are asking students to think outside the box, therefore there is a high level of cognitive demand rather than drill and kill activities that provide total reinforcement of procedural understanding with little support for conceptual understanding. (Varygiannes, 2013) What we know about student engagement is that while there is quanitative research to suggest student engagement through graduation rates and test scores, more interest towards qualtitative research is being explored. Students who feel deeply connected to their school through their peers, teachers, extracurricular activities and community involvement have a better sense of belonging and are engaged more in their own learning in school. “While there exists great anticipation in what is possible when we engage students in their own learning, the challenge remains in hearing the voices of all students.” (Fielding, 2007) Open ended questions helps facilitate this. For the purpose of this study, it was our aim to encourage students to collaborate effectively in groups through open-ended questions geared at differentiating for all learners to participate and increase student engagement. This would further their conceptual understanding of mathematics. Working with the host teachers through knowledge sharing, collaboration and communication allowed development of teacher efficacy. “Research shows that teachers working together to support children’s learning is an effective means of teacher professional development. (Edwards, F. 2012, Lieberman, A., & Miller, L. 2011, Rigelman, N., & Ruben, B. 2012) Research suggests by engaging teachers in professional learning communities to collaborate on effective teaching methods such as open ended questions in math, allow students to engage more in school. Teachers who share this learning with the students through reciprocal learning partnerships provide greater freedom for students to uncover their own learning and further metacognition. Allowing students to collaborate with their peers fosters independence and differentiates for all learners through multiple answers, creating student engagement, participation and a shared sense of belonging.



Bandura, A. (1997). Self-efficacy: The exercise of control. New York: W.H Freeman.

Bruce, D. Catherine, Flynn Tara, Ross, John. Assessing the Effects of Collaborative Professoinal Learning: Efficacy Shifts in a Three-Year Mathematics Study. Ministry of Education.

Capacity Building Series. (2013) Student Voice: Transforming Relationships. September 2013.

Fielding, M. (2007). Jean Rudduck (1937-2007). Carving a new order of experience”. A preliminary appreciation of the work of Jean Rudduck in the field of student voice. Education Action Research, 323-336.

Fraser, S., & Gestwicki, C. (2012). Authentic childhood: Experiencing Reggio Emilia in the classroom. Delmar & Thomson Learning.

Goddard, Y. L., Goddard, R. D., & Tschannen-Moran, M. (2007) A theoretical and empirical investigation of eacher collaboration for school impmrovement and student achievement in public elementary schools. Teachers College Record, 109(4), 887-896.

Hertzog, B. Nancy. (1998). Using Open-Ended Learning Activities to Empower Teachers and Students. Teaching Exceptional Children. July/Aug 1998.

Small, Marian. (2012). Good Questions: Great Ways to Differentiatie Mathematics Instruction. New York, Teachers College Press.

Small, Marian. (2013). Eyes on Math: A Visual Approach to Teaching Math Concepts. New York, Teachers College Press.

Student Achievment Division. Research Monograph # 46. (2013). Using a Professional Learning Community to Support Multimodal Literacies. February 2013.

Watkins, C., Carnell, E., & Lodge, C. (2007). Effective learning in classrooms. Thousand Oaks, CA: Sage Publications.

Sheila Sastri

I am a Student Work Study Teacher working with the Peel Board of Education. Teaching and learning is a passion of mine.