In many ways, the classroom is a laboratory of study on multiple levels. Students are studying the content posed while teachers are studying the students as well as how to effectively teach.
With that in mind, I've been digging in deep this year with regard to helping lots of individual students as well as groups of students during and after the school day. As I work with the students, I learn more and more about how to teach each concept with depth. I see how students puzzle through problems, make connections, and learn. As I do this, I wonder if a prerequisite to teaching whole groups should be teaching individual students, and coaching them to mastery since there is so much to learn when you work with a child one-to-one.
I remember a colleague of mine who retired once commenting how much more she could teach in a one-to-one tutoring session than in a whole class setting. Yet there's good synergy that occurs when students are working together to solve problems, explore, and learn too.
As I explore student learning with greater depth, I am recognizing the following.
Model to Abstract
Teachers know it's important for students to work with all kinds of hands-on, online, and paper models to learn about mathematical concepts. These models provide students with a rich understanding of concepts and relationships. When we work too fast and forgo the models, we often forgo the depth and richness of math. Manipulating models in multiple ways helps students to gain fluidity with math thinking and learning, and then later translate that fluency into their more abstract number work and problem solving.
Personalized Tech
The quick feedback, often engaging, and multi-modal online math tech venues can really help students practice and learn-to-learn math. The key here is to personalize a child's math tech use in ways that truly help them to build greater capacity for math learning and thinking. It's also important to teach children how to use the tech venues so that they are able to access hints, use helpful videos, enlarge the screen, and utilize other assistive attributes of the specific tech venue for better learning.
Asking Questions and Leading Their Learning
As much as possible we have to encourage students to ask lots of questions and lead their learning. A simple practice of having students use That Quiz to practice skills, and then to ask for a reset if they get lower than 75 on the quizzes, puts children in the driver's seat. That simple practice helps them to identify when they understand a concept well and when they need more help. Students need to understand that learning is a step-by-step journey and we all move at different paces/ways, so there's no need to worry about where you are, but instead worry about if you're moving ahead in positive ways.
Packets and Worksheets
I know that many recoil when they hear the words "packet" or "worksheet," but it remains true that with large classes of children, the packet or worksheet often serves as an independent guide, resource, or road map to concept, skill, or knowledge proficiency. When used in tandem with many other learning vehicles such as online games and tools, manipulatives, games, videos, problems, and projects, these workbook/packet guides offer a child some independence with regard to speed and order of completion as well a tool to see what they know and what they need to ask about. To gain a math concept with depth does take practice, and while games and projects are great ways to offer that practice in meaningful ways, sometimes classroom numbers and time point in the direction of using worksheets and packets as practice vehicles and guides.
Projects and Problems
Good, deep, meaningful math projects and problems open the doors to learning in terrific ways. This is where we need to reach as math teachers today. Boaler supports this with her research and outreach. The more we can do this, the better the learning will be.
Tutoring
In-school tutoring which means giving individuals and small groups the support they need can bring about rich teaching/learning relationships and progress. Looking for ways that we can offer this is another way to deepen the teaching we do.
Model/Problem Making
Asking students to make models and design problems related to mathematical concepts, and then to use those models and problems to teach others is another way to deepen the teaching and learning.
Team with Families
To foster optimal math learning, we have to team with families. This is integral to a child's math success.
As I continually look for ways to focus the teaching on learning more than behavior or expected routines, I am looking at the pedagogy that results in rich, deep, satisfying teaching and learning, the kind of pedagogy that inspires students' independent drive and personal responsibility with regard to mastering the standards (and more) in ways that matter.
