Background: I have been teaching Geometry for a few years now and LOVE teaching proofs. Students are asked to identify appropriate evidence that supports a claim, use logic and deductive reasoning, construct accurate mathematical representations, use mathematical notation and vocabulary, and…the list goes on! In my first blog post, I describe in detail why this topic is important in mathematics
POP: Unfortunately, students don’t understand the value or creativity that is involved in doing proofs since I’ve never given them the time and space to identify what makes a proof unique to the presenter. This semester, I wanted to allow students to develop their own proof style.
Tasks Attempted: In order to do this, I tried the following:
- I provided two different articles in class where students hear from other mathematicians, including Einstein, about what they value about proofs and how they personally define a proof.
- Students were asked to choose a proof from each project, that they felt comfortable with, to present in front of the class. This allowed students to exhibit their own understanding and their own proof style to their peers so they can learn from one another.
- Lastly, in the final project students were asked to look at several different proof methods (Two-Column, Paragraph, and Flow-Chart and also compare two proofs completed by different students) and identify what was valuable about each proof method and which style they preferred.
Challenges: All the activities listed above helped students identify the different proof methods and why they are valuable, but I don’t think the activities helped them identify their own proof style. They needed more time and space to process what their ‘style’ really is.
Next Steps/Recommendations: To fix this, next year I’m going to ask students to partner with another student that completed a similar proof and ask them list the differences and similarities of each and identify what they appreciate about the differences and similarities. This may help students see that there are several different ways to do the same proof and they can choose the way that makes the most sense to them.
Reflection: The work that our department did this semester around Authenticity has really helped me change my mindset around content. I have always been so focused on teaching as much content as possible but left little room for creativity or self reflection. I will always value the importance of the skills that I teach in Geometry, but I’m also learning how important it is for students to feel personally attached to what they’re doing so that they find meaning in what we’re learning.
Artifact: Please watch an example of a student presenting their own proof and feel free to give me feedback. Thanks!
https://www.dropbox.com/s/mxfg4kw73n6d475/IMG_3328.TRIM.MOV?dl=0
I love your reflection. I really see that shift from teaching content to providing opportunity for connection happening in your class, now that you mention it. In the roundtable for your class I asked “What is a proof?” and different students had different answers, they did not just provide one rote definition. I look forward to seeing their thinking deepen through the next semester!
I love your POP and reflection (and proofs!). I think that creating space for students to be creative, personally identify with a math style, and emphasizing multiple correct ways to be a mathematician is so cool and valuable. It makes me want to be a student in your class.
Your next step also seems great. I also have building in more student reflection time as a next step of mine. I think my natural instinct is to keep pushing content and skills and that it makes me under-value processing and reflection time, both for myself and my students.