Doing Math
Jun. 28th, 2009 09:02 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
velvetpageI haven't been posting all my discussion posts here, but here's another one for those who care.
To do math is to construct new knowledge from several building blocks: prior knowledge, understandings reached through kinesthetic and visual observation, innate and built number sense, and connections made with the world around us. Doing math requires building understanding; unlike doing pencil-and-paper computations, it's impossible to do math without understanding how it works either before you start or as you continue.
For learning to occur in any subject, students need to feel safe; they need to know that attempts will be valued and supported. They need to have their new learning approached from a perspective that activates their prior knowledge and validates it, and the new learning has to be just slightly beyond the level of their prior knowledge so that they can understand what they're being asked to learn. They need to be encouraged to make connections with their hands, their head, and their heart - because only when their motivations, their intelligence, and their movements are all engaged will learning be deep and lasting. And they need opportunities to talk through what they are learning and what they have learned, and to assess for themselves when they've learned it.
A classroom environment that will support these needs in mathematics must therefore be based in pre-assessment of every task, to know exactly where students are starting and tailor the current expectations to moving them one step from where they are to start with. The learning environment needs to be a supportive place, where insults and teasing are unacceptable and kindness and support are the norm. Students need to be supported in working with concrete materials, drawing or otherwise creating visual representations of their understanding, representing with numbers, and communicating their understanding in a variety of ways. Manipulatives need to be easy to access and encouraged. Accountable talk around math concepts, before, during, and after learning, is essential. Lessons need to be embedded in a problem-solving approach that helps students form connections between math concepts and their world, and encourages creativity and curiosity. Different solutions need to be celebrated and shared so that students can learn from each other.
A math classroom should have a purposeful hum to it. It should involve students moving around purposefully as they model concepts and check their understanding with each other and with the teacher. It should involve group work, and it should have expectations for learning and supports to go with the expectations, posted clearly and reviewed so students know what they're aiming for.
To do math is to construct new knowledge from several building blocks: prior knowledge, understandings reached through kinesthetic and visual observation, innate and built number sense, and connections made with the world around us. Doing math requires building understanding; unlike doing pencil-and-paper computations, it's impossible to do math without understanding how it works either before you start or as you continue.
For learning to occur in any subject, students need to feel safe; they need to know that attempts will be valued and supported. They need to have their new learning approached from a perspective that activates their prior knowledge and validates it, and the new learning has to be just slightly beyond the level of their prior knowledge so that they can understand what they're being asked to learn. They need to be encouraged to make connections with their hands, their head, and their heart - because only when their motivations, their intelligence, and their movements are all engaged will learning be deep and lasting. And they need opportunities to talk through what they are learning and what they have learned, and to assess for themselves when they've learned it.
A classroom environment that will support these needs in mathematics must therefore be based in pre-assessment of every task, to know exactly where students are starting and tailor the current expectations to moving them one step from where they are to start with. The learning environment needs to be a supportive place, where insults and teasing are unacceptable and kindness and support are the norm. Students need to be supported in working with concrete materials, drawing or otherwise creating visual representations of their understanding, representing with numbers, and communicating their understanding in a variety of ways. Manipulatives need to be easy to access and encouraged. Accountable talk around math concepts, before, during, and after learning, is essential. Lessons need to be embedded in a problem-solving approach that helps students form connections between math concepts and their world, and encourages creativity and curiosity. Different solutions need to be celebrated and shared so that students can learn from each other.
A math classroom should have a purposeful hum to it. It should involve students moving around purposefully as they model concepts and check their understanding with each other and with the teacher. It should involve group work, and it should have expectations for learning and supports to go with the expectations, posted clearly and reviewed so students know what they're aiming for.