No One-Size-Fits-All: Participation in the Mathematics Classroom
By Megumi Asada and Pamela E. Harris
How many of us continue to use participation as a percentage of final course grades? How much do we weigh the value of participation in the learning process as grades are assigned? In this process of assigning participation grades, what equity issues arise that we are not aware of and therefore not addressing?
These are just some of the questions that come to mind as we think about the concept of “participation” in mathematics classes and who benefits from the current grading schemes we have implemented.
Of course as educators, we are trying to follow best practices in asking students to participate in class discussions and activities, often citing the education literature which supports that participation promotes higher learning [3]. For example, in Assessment: Class Participation, Dr. Volker Ecke states that by encouraging in-class student participation, professors are working to support the following student goals:
Students will strengthen their reasoning skills and become better problem solvers.
Students will strengthen their skills in reading, writing, argumentation, and speaking.
Students will become more self-monitoring, reflective learners, and take greater personal responsibility for their learning.
Students will approach mathematics more positively and gain a balanced perspective of mathematics.
Students will improve their mathematical confidence [2].
Dr. Volkmer Ecke also gives a description of grading scheme in which participation accounts for 30-40% of a student’s final course grade. In the grading description they state “If you attend class regularly and you participate in your group, but if you, for instance, don’t share your thinking regularly with the whole class, you can only attain a B” [2].
At first glance, this may seem like an adequate and appropriate grading scheme, especially as Dr. Volker Ecke mentions that they have a mid-semester check-in with students in which they discuss a student’s current participation grade. If the student agrees, they can improve their participation grade during the second half of the semester, and their final participation grade will be based on their improved performance. This gives a student the ability to increase their participation and thereby earn a higher participation grade.
Yet this does not address one big challenge: How can educators balance potential inequities that may arise from encouraging and requiring student participation?
One thing we must acknowledge is that there are gendered and racial trends about who tends to speak and feel empowered to participate within a mathematics class [1,4,5]. This empowerment could be potentially due to stereotype threat and/or peer intimidation, and these challenges affect certain students more than others [3]. Moreover, working to build safe classroom environments does not always work and could further alienate students who already feel like they do not belong within mathematics spaces. Of course, working to build community within our classroom is a powerful and important step towards addressing some of these challenges and we all do this in different ways. Some of us introduce community agreements (here is a sample), which detail the type of behavior that is expected when participating in small group collaborative learning activities and how building a positive community environment is the responsibility of all involved. For example, Dr. Federico Ardila details building community and welcoming the humanity of those in the space through his first day activities.
Even with the best intentions and most detailed planning, there will be times when we fail at building the right community within the classroom. The success of such activities is absolutely dependent on the personalities and people within the course and it is very difficult to pinpoint exactly what might go wrong and how it could be prevented. Moreover, interactive participation can be synchronous or asynchronous, both are valuable and provide ways in which students can be engaged, while they may also introduce new sets of challenges. Regardless, it often takes time and distance to be able to reflect on how we might have been able to adapt in order to make the environment better. Cue in growth mindset for professors!
But let us suppose we are in the middle of a course in which the environment somehow prevents all students from feeling empowered by the requirement of interactive participation. What do we do then? Or better yet, how do we recognize that things are not going as planned?
Sometimes recognizing that students are not participating can be difficult. Especially if you hear ample speech/sound and what appears to be communication between all in the room. Yet, there may be a few students who have not shared their thoughts or solutions, and no matter how many times the professor says “I’d like to hear from someone new” or whether the role of “reporter” is assigned to a student who is often quiet, they might still not want to share. In light of these challenges, it is worth asking ourselves frankly whether our perceived values of participation and engagement are more important than a student's comfort.
Let us ask this again: At what point do we as educators think that the value of having students share their mathematical process or thinking outweighs whatever anxiety and discomfort they are experiencing in the moment? Do we honestly think it acceptable to push students who are clearly uncomfortable by citing the development of certain skills, such as those delineated above by Dr. Volker Ecke, as more important than accommodating the current stress they are feeling?
Of course, a skill-building exercise is not more important than a student's comfort. Sure, we agree that some discomfort is needed to actually learn. The issue here is not that. It is that we as educators cannot possibly know whether what we are asking of students will merely result in mild discomfort or whether it will actually cause damage, for instance, by triggering the memory of past traumatic experiences.
Even in less damaging cases, there may be moments of tension between a student and an instructor who may not share the same value of class participation. Though challenging, these moments become learning experiences for all involved. For example, some of our students may be questioning the value of a math major, especially now during a time when the world is dealing with the COVID-19 pandemic and the racial violence within the US. Or they may have been raised under a more practical mindset in which the value of education was to find a life of comfort. Under these circumstances, asking students to participate in the mathematics classroom, particularly in courses where the material may be/seem rather removed from the practical or dealing with solving societal issues, can be additionally challenging.
So how do we deal with this?
First, we should have conversations with students that share why we believe participation supports higher learning, and detail the goals for that work as shown above. These conversations must happen often. Through them we should place value in encouraging the right amount of discomfort for students to practice doing difficult things that they will need to do later in life (learn more about “productive struggle” here). Yet, knowing the value of participating and that a classroom provides a place to practice might not be enough because one could ask: why participate in this space at this time in this way? This brings us to the second point.
We have a responsibility to make sure students can participate in ways that feel most safe to them, with the agreement that we will all experience some level of discomfort in the learning process. We can provide options and opportunities. Above all else we must value being kind with each other and ourselves, recognizing that levels of comfort depend on our past lived experience - things we don't often talk about within the mathematics classroom. Hence, we must agree that if someone identifies too high a level of discomfort we will not push a student to participate simply for the sake of participating. Such an agreement foregrounds respect for individual safety, which could help those who feel hesitant to participate in feeling more comfortable communicating their concerns with the instructor. We must have conversations with students about how they can let us know when they have reached too high a threshold of discomfort and that in such instances we will listen and support each other through that experience.
In light of the need of more conversations and to build a safer environment, and in order to support the goals of participation, we recommend that we start classes by having discussions/reflections (either oral or written) based on the following guiding questions:
How will you demonstrate that you have strengthened your reasoning skills to become a better problem solver?
How will you demonstrate that you have strengthened your skills in reading, writing, argumentation and speaking?
How will you demonstrate that you have become a more self-monitoring, reflective learner who takes greater personal responsibility for your own learning?
How will you demonstrate that you now approach mathematics more positively and that you have gained a balanced perspective of mathematics?
How will you demonstrate that you have improved your mathematical confidence?
We could then ask each student to provide a self-assessment of where they are currently at in each of these categories. From this self-assessment, students could write a plan for how they will demonstrate growth in these areas. By selecting a percentage of the participation grade tailored to their own desires for areas of improvement students can grow individually in the way that might best suit their future career plans. For example, some students might prefer to work on public speaking while others might want to improve their mathematical confidence, and a tailored participation grade would be more beneficial to each individually rather than as a whole class. A mid-semester check in could ask the students to reflect on how they have advanced in these categories, and in which there is room for growth. Additionally, it would give space for students to highlight what they are doing well. Final participation grades could then be reported based on the improvement in each of the categories of personal focus.
By implementing such a participation scheme we allow for a more personalized process in which students take an active role in designing what participation best suits them individually. Moreover, we also believe that this new process of assigning participation grades can help address issues of equity that arise in traditional one-size-fits-all participation grading schemes. Lastly, no participation grading scheme will ever be perfect, but by allowing students to make choices in how they are graded we can learn more about the directions in which students want to further develop their skills while allowing each to highlight their strengths. This could be the starting point for new conversations which we hope will help make the classroom environment more conducive to participation by all.
References:
[1] Balau, I., Barak, A. (2010). How do personality, synchronous media, and discussion topic affect participation? Journal of Educational Technology and Society, 15(2), 12-24.
[2] Volker, E. (2014). ‘Assessment: Class Participation’, Discovering the Art of Mathematics, 9 April. Available at: https://www.artofmathematics.org/blogs/vecke/assessment-class-participation (Accessed: 25 August 2020)
[3] Freeman, S., Eddy, S. L., McDonough, M., Smith, M. K., Okoroafor, N., Jordt, H., & Wenderoth, M. P. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the National Academy of Sciences, 111, 8410–8415.
[4] Keller, J. (2007), Stereotype threat in classroom settings: The interactive effect of domain identification, task difficulty and stereotype threat on female students' maths performance. British Journal of Educational Psychology, 77, 323-338. doi:10.1348/000709906X113662
[5] Mudore, C.F. (2012). Are you an introvert? Current Health, 2(29), 17-19.