"Can you please tell me if this is right?"When a student emails me this I sometimes feel like I’m being tested by the ‘good teaching’ gods. Of course, I do want to be helpful – and it’s not so hard to let the student know that, yes, they’re on the right track, or, no, they seem to have missed something. I want to say (and sometimes I do), “you should be resourceful enough to evaluate this yourself.” However, this is the mathematics-cultural mindset our students have been taught to think with – that there’s a right answer, and that the teacher knows what it is. My hope when facilitating peer feedback between students is that we can tap into behaviours and attitudes that steer away from this. When a student evaluates another’s work, they may intuitively become aware of the need to understand the content more deeply. When they evaluate a number of students’ approaches to a similar problem, they can become aware of how one question might allow for a wide variety of solution approaches and explanations. Then in receiving peer feedback as part of an assessment cycle, there’s the potential for richer and more detailed feedback than is possible when the task is the sole responsibility of a time-poor academic or by-the-hour sessional marker. And when the quality of a solution is judged by peers, explanation, justification and presentation become more important than an answer just being ‘right’ and it becomes a meaningful exercise to think through your solution as it would be read by someone else. Having said all this, like any learning exercise, peer feedback has plenty of potential to be pointless or detrimental for student learning. Implementing it effectively requires careful consideration and planning toward your learning objectives. Here is a brief overview of three different peer review models I’ve tried or considered, along with the intended benefits and potential ways they might go wrong. You can either read the full blog post or watch my video below that summarises the three models. Submission in PairsThis is essentially the same setup as a group assignment. The teacher sets assignment problems, which students attempt individually before then meeting up with each other to cross check and perhaps discuss any differences. Alternatively, they may split the problems between themselves, but they’d still want to check the other’s solutions before submitting by the due date. The teacher then marks the assignments as normal (and one upside here is that there should be half as many assignments to mark) and students would usually need meet up to see their results and feedback. There are two key opportunities here, before submission and afterward, for students to engage in discussion and higher level thinking that might not usually occur if completing assessments individually. Of course, the main danger with this model is that some students might freeload off their partner, which means those discussions won’t occur and one of the students might not engage with the assignment at all. Although it’s possible, some students might copy each other anyway, and so at least here you can promote a culture that encourages peer interaction. Peer Assisted ReviewRather than just hoping those fruitful discussions will occur, here the strategy is to schedule peer review activities during class-time. After attempting problems themselves, students engage in a structured critique of each other’s work. Such in-class activities can then be the basis for a graded assignment where students can demonstrate their new-found explanation skills. The key challenge here, as with any peer review, is that students might not really know how to provide useful feedback or feel confident to judge the work of another. Having a checklist or guidance on what to focus on might help, but even more effective is to dedicate class time to the giving of feedback. For example, you can discuss, as a class, not only what could be done to improve a sample solution, but how you would approach giving that advice constructively. See the work of, e.g. Reinholz, for case studies. L. Reinholz (2016) Improving calculus explanations through peer review, The Journal of Mathematical Behavior 44, 34—49. Formative Peer ReviewThe final model allows students to review drafts of each other’s work. After setting an assignment, students submit a draft solution, and then an online system allocates a number of peers to review and be reviewed by. This can be done anonymously if that’ll help facilitate more honest feedback, and random allocation can ensure that students receive feedback from a number of students with varying ability. Students then have the opportunity to address any suggestions or respond to the feedback with a reflection before submitting a final draft to be graded by the teacher. In writing their assignments with the peer review process in mind, students may come to appreciate the importance of communication, while the drafting process can de-emphasise the notion of answers being right or wrong. Students might still need guidance on how to provide useful feedback, however a key advantage is being able to have a higher number of peer reviewers – students get to see a wider variety of solution approaches and receive feedback from multiple perspectives. The main downside is that the feedback is one-way rather than being a dialogue, and after final submission the feedback the teacher provides may still end up in the feedback graveyard. So that’s three simple models, all of which could be adapted depending on the class or assignment – it’s just a matter of planning what you want to get out of the feedback process and which behaviours you’re hoping to encourage in your students.
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February 2023
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Recordings of sessions
Thursday - welcome
We are pleased to announce that the theme of this year's FYiM workshop to be held in Brisbane is
Celebrating 10 years of First Year in Maths!
Our first forum was in 2013 at The University of Melbourne. Let's look back on 10 years of talking about teaching maths and statistics at the first-year level. What is still relevant? What has changed? What new challenges lie ahead?
Here is the programme.
Details of the workshop are:
When: Thursday 6 July and Friday 7 July - 10 am to 5 pm
Where: The University of Queensland, St Lucia campus and via Zoom
Cost: FREE! Morning tea, lunch and afternoon tea will be provided thanks to UQ's School of Maths and Physics. You are welcome to join us for dinner (at own cost) on Thursday night at a local/CBD restaurant.
We look forward to seeing you in sunny Brisbane!
Deb, Don and Michael
FYiMaths National Steering Committee
Thursday - welcome
We are pleased to announce that the theme of this year's FYiM workshop to be held in Brisbane is
Celebrating 10 years of First Year in Maths!
Our first forum was in 2013 at The University of Melbourne. Let's look back on 10 years of talking about teaching maths and statistics at the first-year level. What is still relevant? What has changed? What new challenges lie ahead?
Here is the programme.
Details of the workshop are:
When: Thursday 6 July and Friday 7 July - 10 am to 5 pm
Where: The University of Queensland, St Lucia campus and via Zoom
Cost: FREE! Morning tea, lunch and afternoon tea will be provided thanks to UQ's School of Maths and Physics. You are welcome to join us for dinner (at own cost) on Thursday night at a local/CBD restaurant.
We look forward to seeing you in sunny Brisbane!
Deb, Don and Michael
FYiMaths National Steering Committee
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