Using Student Clinical Interviews About Fractions and Decimals as a Diagnostic to Determine Student Misconceptions and Plan Instructional Next Steps

Area(s) of Focus: math
Division(s): Intermediate, Junior
Level(s): Grade 4, Grade 5, Grade 6, Grade 7, Grade 8

Research into junior/intermediate student misconceptions in fractions and decimals through conducting student clinical interviews in math. Lessons and number talks designed to address misconceptions for gap closing.

An understanding of both fractions and decimals is foundational and related. Teachers at this inner-city Toronto school have noticed profound gaps in students’ conceptual knowledge by the time they arrive in intermediate grades. This points to the importance of early intervention at the Grade 4 level and up to ensure that fraction and decimal misconceptions do not persevere. Gaps of this sort, when not addressed, may lead to students being unfairly pushed into special education classes and later into applied math in secondary. As an intervention, junior and intermediate teachers at Portage Trail will be trained on how to design and administer student clinical interviews as a diagnostic to determine misconceptions in students’ conceptual understanding of fractions and decimals. They will base their structured interviews on the Fractions Learning Pathway. Teachers will use the results of their student interviews to design targeted instruction to both address misconceptions and close gaps through their inclusive special education model. Ongoing fraction and decimal number talks will also be designed to allow repeated practise and concept reinforcement throughout the year. Student interviews will be repeated to determine the impact of instructional interventions to ensure increased achievement and equitable outcomes for all students.

Team Members

  • Jennifer Fannin

    Toronto District School Board

  • Nicole Brown

    Toronto District School Board

  • Paul Kerins

    Toronto District School Board

  • Christine Haladay

    Toronto District School Board

  • Veronica Broomfield

    Toronto District School Board

  • Michelle Bailey

    Toronto District School Board

Professional Learning Goals

Teachers learned how to design and use student clinical interviews as a diagnostic tool. These are structured interviews designed by teachers to determine student strengths and misconceptions in a certain strand or topic. These interviews were conducted with four students from each class, targeting both struggling learners and students in the middle. Results helped teachers design focused instruction to clarify misconceptions and build on student strengths. Teachers learned more about the Fractions Learning Pathway and different fractional models presented in Cathy Bruce’s Ministry monograph “Paying Attention To Fractions.” This helped teachers acquire a deeper understanding of why misconceptions arise and how they can be addressed. Teachers researched and created number talks to use on an ongoing basis to reinforce the relationship between fractions and decimals. Number talks made the links between fractions and decimals more explicit.

Activities and Resources

Our work was broken into the following sequence: literature review, analyzing samples and designing student clinical interviews, conducting interviews with students, analyzing results and structuring lessons/number talks to address misconceptions, and reviewing results of final interviews. The literature review focused on bringing staff together to read and discuss current research on fractions/decimals and number talks. The second session involved looking at how student clinical interviews are a form of pedagogical documentation that can give information about student learning and based on examples staff will design their own interview. The learning coach for the school and staff conducted the interviews with students. Teachers analyzed these videotaped interviews together to have multiple staff perspectives included. After structured lessons/number talks were designed and implemented, interviews will be repeated to determine effectiveness.

Unexpected Challenges

The interviews themselves took much longer than expected. After dedicating several days to conducting the interviews by herself, it was determined by the learning coach and the staff involved that staff would also have to be a part of the interview process. As such, one of the days originally set aside for analyzing interviews was split between conducting the interviews and analyzing them. This turned out to be beneficial since staff found that they learned a lot more by actually conducting the interviews themselves. They also required less time to analyze the interviews since they had been there in person to conduct them and were already familiar with student responses.

Enhancing Student Learning and Development

We saw student misconceptions addressed through targeted instruction. This was evident in the change demonstrated from our first student clinical interviews to our end-of-year interviews. Teachers analyzed both of these at the end of our work to see the impact and movement in student thinking. Anecdotally, students demonstrated greater mastery and increased achievement in the strand of Number Sense and Numeration throughout the year. Given the cross-grade nature of this project, we are hoping that similar instructional strategies can be implemented the following year to ensure that concepts are reinforced and that students retain mastery of these skills. Cathy Bruce’s research on fractions recommends delivering instruction in fractions in small chunks throughout the year to ensure mastery, so we are hoping that by embedding this into regular number talks, this criterion will be met and greater mastery achieved.


Outside of the school, we shared our findings at the 2017 OAME Conference. This included samples of videotaped interviews and their scripts. We also plan to propose and present our findings at the TEAMS conference during this coming November. Within the school, we will share our work at a school-wide staff meeting in June so that this work will be generalized to other grade levels and teams. Our research findings were also incorporated into a Math AQ Part 1 facilitated by our learning coach, which was hosted at the school and involved 19 members of staff.

Project Evaluation

We based our effect by looking at the change in learning demonstrated from the diagnostic student clinical interviews to the final interviews conducted towards the end of the year. Teachers also checked-in with each other during release days to ensure that they felt supported throughout the inquiry and to determine if greater support or research was needed to help staff feel effective. If we were to repeat this research, we would allocate more time for the interviews themselves and embed this release into our requested funds. This would put less pressure on staff to conduct interviews quickly and allow more time for intentional analysis.

Resources Used

“Fraction Learning Pathway” from EduGains describes a developmental trajectory for learning about fractions concepts

“Paying Attention To Fractions” describes different fractional models and provides suggestions for their implementation in the math classroom

Making Number Talks Matter. C. Humphreys and R. Parker, Stenhouse Publishers, 2015

Number Talks: Fractions, Decimals & Percentages. S. Parrish and A. Dominick, Math Solutions Publishers, 2016