Pedagogy
The New Media LiteraciesThe New Media Literacies are the skills people need today to fully engage with our new participatory culture. Generally, students know a lot about this already, though they probably didn’t learn it during class.
The New Media Literacies project identifies a list of 11 needed skills:
- Play
- Performance
- Simulation
- Appropriation
- Multitasking
- Distributed cognition
- Collective intelligence
- Judgment
- Transmedia navigation
- Networking
- Negotiation
- Imagine
- Create
- Play
- Share
- Reflect
These skills are the survival skills of the future. Students generally sense this and are eager to learn them. In this course, we have woven them together with the learning of algebra. Every day, in class and through assignments, we teach these skills as well as math skills.
There are several related issues that you need to watch out for.
- Not all students have had the same access to technology. Your class is an opportunity to help close this participation gap by helping students who are not tech-savvy to learn to be so.
- Any time students do research on the internet, there is no telling what they might find. Additionally, collaborative spaces provide new opportunities for bullying, theft, and all sorts of problematic behaviors. We think school is a fantastic place to unpack these issues, whenever they arise, but you need to be ready to meet this ethics challenge.
Discovery, Invention, and Appropriation
While there is no formula for teaching, we envision a general pattern.
Encouraging Emerging Thinking
There is a strong connection between emerging mathematical thinking and the emerging language that students use to articulate these new, half-formed ideas. As we anchor each new concept in a real-world problem situation, students trying to find a solution must also invent a vocabulary to communicate their ideas.
Meaningful, Guided Inquiry
Our strategy is not to begin with formulas and traditional formalized mathematics vocabulary. Rather, we allow students, as they share their developing ideas with us and with their peers through group discussions, to invent ways of communicating, repurposing the words they know. We also encourage gestures and drawings to articulate their emerging understandings. We encourage efforts within the group to further articulate and develop these ideas. Subtly and gently, at the right moment, we slip in a conventional word or the articulation of a mathematical strategy that helps move the students’ discussion forward. Our goal is to arrive at the proper formal language of mathematics, but the pacing of this arrival must be guided by the teacher’s intuition.
Discovery
Our goal is that a student arrives at the algebraic formula for a line not as a passive recipient of this knowledge but as an active and critical thinker. This model of learning as discovery, invention, and appropriation is, in a sense, an illusion. We are not waiting for students to discover everything on their own, nor are we handing them ready-made solutions. We are guiding them through a process of discovery so that they arrive at knowledge as critical and engaged thinkers.
Situated Practice
Our strategy here is to ground our classroom work in real-world situations. This involves presenting realistic, real-world problems and framing problems in relation to a real-world community that deals with these kinds of practical problems.
Pure and applied mathematicians are one of these real-world communities. But the world of professional mathematicians generally requires a level of abstract thinking that is quite distant from the world of 9th graders. So, in addition to mathematics, we are linking our activities to the world of:
This list can expand and contract to suit the interests of your students. Our approach is virtual, peripheral participation. By developing realistic knowledge of and familiarity with the concerns and interests of people in these communities, students will have taken a significant step towards participation.
Storytelling, Critical Framing, and Meta-Cognition
In addition to leading an evolving, goal-oriented, problem-based, inquiry-based group discussion in our classroom, there is a need to regularly step off to the side of this road in order to reflect about what we are doing, where we are going, and why. As on any journey, there are opportunities for storytelling, which, along with experiential learning, is one of the oldest human methods of teaching.
The stories we want to tell in math class are many. We want to talk about the world of mathematicians, the history and evolution of mathematics, the disciplines within the world of math, always in loose relation to the classroom activities. We also want to situate our journey within the other related more-concrete-world disciplines, such as commerce, sports, or carpentry. A storytelling session does not have to be one way. Students should be invited to share ideas and stories in a constructive manner. We want to encourage students to actively relate their classroom activities to what they know of the outside world and history. This larger sense-making is essential for meaningful learning.
Discussions, Workshops, and Activities
Group discussions and shared explorations are at the heart of teaching and learning. At the same time, we are hoping to nurture independence and self-reliance among our students. These two goals are not contradictory. A strong community can nurture a strong individual.
Good Questions: We often start a class with a group discussion, perhaps recapping what we have done previously, and then introducing the day’s activities and related concepts, and anchoring these activities to a real-world community .
Class Configurations: It is useful to envision a variety of classroom configurations:
Discovery, Invention, and Appropriation
While there is no formula for teaching, we envision a general pattern.
Encouraging Emerging Thinking
There is a strong connection between emerging mathematical thinking and the emerging language that students use to articulate these new, half-formed ideas. As we anchor each new concept in a real-world problem situation, students trying to find a solution must also invent a vocabulary to communicate their ideas.
Meaningful, Guided Inquiry
Our strategy is not to begin with formulas and traditional formalized mathematics vocabulary. Rather, we allow students, as they share their developing ideas with us and with their peers through group discussions, to invent ways of communicating, repurposing the words they know. We also encourage gestures and drawings to articulate their emerging understandings. We encourage efforts within the group to further articulate and develop these ideas. Subtly and gently, at the right moment, we slip in a conventional word or the articulation of a mathematical strategy that helps move the students’ discussion forward. Our goal is to arrive at the proper formal language of mathematics, but the pacing of this arrival must be guided by the teacher’s intuition.
Discovery
Our goal is that a student arrives at the algebraic formula for a line not as a passive recipient of this knowledge but as an active and critical thinker. This model of learning as discovery, invention, and appropriation is, in a sense, an illusion. We are not waiting for students to discover everything on their own, nor are we handing them ready-made solutions. We are guiding them through a process of discovery so that they arrive at knowledge as critical and engaged thinkers.
Situated Practice
Our strategy here is to ground our classroom work in real-world situations. This involves presenting realistic, real-world problems and framing problems in relation to a real-world community that deals with these kinds of practical problems.
Pure and applied mathematicians are one of these real-world communities. But the world of professional mathematicians generally requires a level of abstract thinking that is quite distant from the world of 9th graders. So, in addition to mathematics, we are linking our activities to the world of:
- sports analytists
- artists
- entrepreneurs
- travel planners
- naturalists
- and First Nations communities
This list can expand and contract to suit the interests of your students. Our approach is virtual, peripheral participation. By developing realistic knowledge of and familiarity with the concerns and interests of people in these communities, students will have taken a significant step towards participation.
Storytelling, Critical Framing, and Meta-Cognition
In addition to leading an evolving, goal-oriented, problem-based, inquiry-based group discussion in our classroom, there is a need to regularly step off to the side of this road in order to reflect about what we are doing, where we are going, and why. As on any journey, there are opportunities for storytelling, which, along with experiential learning, is one of the oldest human methods of teaching.
The stories we want to tell in math class are many. We want to talk about the world of mathematicians, the history and evolution of mathematics, the disciplines within the world of math, always in loose relation to the classroom activities. We also want to situate our journey within the other related more-concrete-world disciplines, such as commerce, sports, or carpentry. A storytelling session does not have to be one way. Students should be invited to share ideas and stories in a constructive manner. We want to encourage students to actively relate their classroom activities to what they know of the outside world and history. This larger sense-making is essential for meaningful learning.
Discussions, Workshops, and Activities
Group discussions and shared explorations are at the heart of teaching and learning. At the same time, we are hoping to nurture independence and self-reliance among our students. These two goals are not contradictory. A strong community can nurture a strong individual.
Good Questions: We often start a class with a group discussion, perhaps recapping what we have done previously, and then introducing the day’s activities and related concepts, and anchoring these activities to a real-world community .
Class Configurations: It is useful to envision a variety of classroom configurations:
- Group Discussions
- Group Discussions using a whiteboard or projector
- Workshop Mode
- Working in small groups
- Student presentations
- Question period (emphasizing feedback and reflection)
- Classroom visitor from a data focused community