Q1: WHY MIGHT SCHOOLS WANT TO DO DEFENSES OF LEARNING IN MATH? WHAT ARE THE BENEFITS FOR STUDENTS?
Vinci- A1: Defenses put students in charge of what they defend – their own way of understanding something, their own learning.
Jim- A1: One benefit is metacognition. In prepping for defenses, students reflect on what they’ve learned in math and how it fits into everything else they know. They also focus on the processes by which they learned.
@tamyraintech– they also allow students to prioritize and therefore hone their quantitative reasoning skills. Quant skills are key drivers for viability in the ever-changing job market.
@Linked_Learning– Defenses allow students to practice critical thinking skills necessary to thrive in post-secondary. With defenses, students get to practice these skills before they get to college or a career opportunity.
Vinci- Thank you for this point – practice with articulating learning creates opportunities to deepen learning – revising and upgrading understanding so often happens when students communicate what they have learned.
Jim- A1: Defenses in math can also promote coherence for students and educators. Students draw their own connections between math ideas. Educators design for coherence as they work towards a culminating defense event.
Vinci- Learning math for so many students is a long fragmented journey through disconnected topic after topic. What Jim is saying about coherence is especially valuable for bringing coherence to a fragmented journey.
Q2: WHAT KINDS OF MATH ARTIFACTS ARE WORTH DEFENDING?
Jim- A2: Tasks where students had to figure something out, make sense of something in a deep way, something that is already or that becomes meaningful to them. Tasks that are well-scaffolded but not where students are passively following a recipe or prescribed set of steps.
Vinci- Tasks that are open-ended enough set students up to develop and demonstrate agency by choosing tools and representations that are most relevant to the approach that makes most sense to the student. Tasks where students get to flex their mathematical practices (reasoning in and out of contexts, justifying, modeling, etc.)
Vinci- A2: Work that a student is proud of. Work on a problem or project that is connected to a big idea of the math course.
@Linked_Learning– For #LinkedLearning students, they may also defend an artifact connected to their work based learning, internship, or industry pathway, deepening cross-subject connections. Work that a student can identify as a demonstration of their own learning. If a student can name what they learned as they produced the piece of work, it’s a good candidate for defending.
Jim- Yes, and tasks where students can decide on their own questions, how to answer them, what quantities are relevant, and how they are connected.
@tamyraintech– A2: Artifacts that require students to reflect on how key math concepts are applied in relevant and meaningful contexts.
Jim- Yes!! I love how this article talks about possibilities for authenticity in projects: https://www.edutopia.org/blog/authentic-project-based-learning-john-larmer
@Linked_Learning– Love this! We know students work harder and dream bigger when their learning connects with them and connects them to the world.
@DealJT- I’m wondering in what ways you are able to make explicit to students the connection between defense of mathematics and the overall defense of learning.
Jim- Hey thanks for joining and great question! I think about the ways in which students and teachers can make explicit connections between math practice standards and overall critical thinking skills.
@DealJT- Thanks! We are just diving in to defenses of learning , but I’m really excited for the momentum we might build with defenses in math – I’m hoping we can both build capacity to successfully defend learning, and also create rich artifacts to use in the defense.
Vinci- Thanks for your question, Jason. The process of formulating the ingredients of a defense, then rehearsing, then articulating to an audience is the same process across the content areas – and has the same effects: metacognition, coherence, agency.
@DealJT- I love the idea of the math practices as an anchor in that connection.
@DealJT- How do you create buy in with students that that process, specifically in mathematics (but also overall), is a relevant and important process to students’ life-sustaining futures and dreams? –the connectedness between mathematics and defense of learning creates really powerful cohesion, but I want to make sure I’m ready to help students make a strong connection beyond that into their futures.
Jim- I think this speaks to a question of how to help students use math as a tool to read and write their worlds.
Q3: WHAT ARE THE BIGGEST HURDLES TO GETTING DEFENSES OF MATH LEARNING GOING?
Jim- A3: Asking students to defend their use of agentic skills using tasks that didn’t give them enough opportunity to use agency. The urge to design lengthy special artifact-worthy learning events that are disconnected and contradictory to how students are learning math daily.
@DealJT- Would this indicate that the “artifact-worthy” events should change, or that daily learning should change so that students are doing more artifact-worthy things every day? Or somewhere in the middle?
Jim- I think learning should be happening every day so we (Ts and Ss) can find artifacts of it. Still can be special events but only getting to practice something like “justification” once or twice a quarter isn’t enough. What are we doing the rest of the time?
Vinci- Often math teachers feel they must create a separate set of assignments or learning opportunities that are in addition to their regular stream of studying, working and learning together. Ideally, a system gets better — math curriculum gets better and math teachers get better — at creating learning experiences that are worth defending as a regular part of the work that is happening in math class.
Vinci-A3: Another hurdle is the reluctance to put ‘shy’ students in the spotlight – but very often these are the students who benefit most from the experience.
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