3. Construct viable arguments and critique the reasoning of others.
How are fourth and fifth grade teachers helping their students construct viable arguments and critique the reasoning of others?
How can students be helped to:
- understand and use stated assumptions, definitions, and previously established results in constructing arguments
- make conjectures and build a logical progression of statements to explore the truth of their conjectures
- analyze situations by breaking them into cases
- recognize and use counterexamples
- justify their conclusions, communicate them to others, and respond to the arguments of others
- reason inductively about data
- make plausible arguments that take into account the context from which the data arose
- compare the effectiveness of two plausible arguments
- distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is
The CCSS states:
Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
What are you doing to help students develop this practice? What makes it hard? What challenges are you encountering?
First, it is important to create a classroom climate where students feel comfortable sharing their thinking and strategies even if they are incorrect. Students also learn how to respectfully disagree and then share their thinking. They construct viable arguments and critique others reasoning through pair share and whole class sharing. During these conversations, students lead whole class discussions with friendly debate. Therefore, they are learning from one another and coming to conclusions as a community.
First is to create the expectation that all students will defend their learning- math thinking. In my practice, the students spend a great deal of the year establishing the culture by getting used to the ELMO, developing norms, my systems, ( think-pair-share, call sticks, exit tickets, etc.)and the acceptance of making mistakes- we take the plunge. Through this practice the kids are able to take math risks and gain the confidence that they need to be successful learners. In our opinion, the Overarching Habit of Mind is really number 3; construct viable arguments and critique the reasoning of others.
I think it is very important to first make sure that students have the skills to discuss and argue appropriately and precisely. This is something that needs to modeled and fostered in a collaborative and safe classroom environment. I believe it is difficult to help students develop this practice because many students have not had the opportunity to have open discussions with their peers. They are used to a teacher-lead class in which the teacher asks a question and chooses one student to answer.
As a classroom teacher, I think it is very important to start having class discussions (at the very beginning of the year) around all subjects/topics to give the students different chances to practice constructing arguments that are clear and precise. I think that as the teacher you need to model what you’d like your students to be doing. I think that this practice will be difficult for many teachers to embrace because they are so used to leading all discussions in the classroom.
To name something is know it, that’s the name of the game. Communication and discussion are key elements; and vocabulary, vocabulary, vocabulary, vocabulary, vocabulary. Ultimately we need to facilitate discussions and provide time to students to explore and let them make mistakes.
I agree with Alison and Sarah that it is key to establish the culture of learning/sharing/risk-taking in our classroom. Students need to be expected to show and explain their work. I often have students share with a partner and then have a few share their work on the Smartboard or Elmo. We often ask if someone did it a different way. We also have students who are willing to share the mistakes they made along the way and allow discussion about the errors. The conversations students learn to have with their partners and as a whole class, lead to a deeper understanding of the strategies they use and the other possible strategies that are available. It all requires students to know how to defend their answers and be able to explain why they did what.
The first step for students to be able to construct viable arguments and critique the reasoning of others, is to create a respectful, safe place for students to take that risk. Students need to have a variety of opportunities to talk, and write about their understandings, as well as practice actively listening to others. In our classrooms we use Kagan structures that allow different students to work together throughout each school day. They may work with their shoulder partner, face partner, or whole team of 4 depending on the activity. So, discussions about learning are going on daily during partner, small group, and whole class discussion. We start these structures day 1 of school and build from there. The challenges are reinforcing and practing active listening during discussions, so that students can build upon other ideas instead of just their own. We also have some students that still are not willing to take the risk of being incorrect in front of others, and therefore have to be prompted to share their thinking! I have these students for another year, so I’m excited to work on these challenges.