The Learning Environment
First create an environment that lends itself to positive math teaching and learning. It's often difficult to anticipate the environmental needs prior to knowing your students, schedule, and expectations, but for starters, the environment should have the following elements:
- Well organized, labeled space for manipulatives
- Well organized, labeled spaces for learning tools such as notebooks, pencils, colored pencils, rulers and more.
- Space for the word wall.
- Word wall vocabulary cards that are easy to see and access from the learning spaces.
- Tech tools that are readily accessible and easy to update when new tools are discovered and/or needed.
- A place to listen, present, and view lessons.
- Well organized spaces for paperwork.
- Multiple spaces for small group and one-to-one work.
It takes lots of time to set up a terrific learning/teaching space. I still have work to do in my classroom to make the space more user friendly. In an ideal world, teachers would get about a week's worth of time before the students arrive to set up their teaching/learning space and the time and money before that to order the supplies necessary to support that kind of empowering environment. Fortunately our shared teaching/learning model at the grade-level provides more time and space for setting up environments focused on specific areas of study which helps.
Know Your Students
The first lessons of the year should be focused on getting to know your students well. In some kind of mathematical way students should have a chance to introduce themselves to you and classmates. This is a good time to begin the important student-teacher relationship building that's critical to teaching math or any other subject well. In the past students have written letters about their math autobiographies. This year students created a Math Team bulletin board.
Know the Standards
The best math teachers understand the standards they are expected to teach with depth. These teachers also understand the learning progressions related to each standard which means they understand the foundation skills, concepts, and knowledge for the standard as well as the related standards at the grade-levels ahead of the current focus. One good way to learn the standards is to complete the Khan Academy exercises related to that standard prior to teaching it. Khan Academy has good videos and exercises that make use of the math vocabulary, apt explanations, models, numbers, and more to well explain each standards. Also taking a look at the CCSS learning progressions related to each standard will help you understand how to teach each child with regard to what they know now and what you want them to achieve.
Multimodal, Differentiated Program
A good math program is a multi-sensory program that involves a myriad of differentiated lessons and learning experiences that appeal to the many ways that students learn as well as students' need for proactive learning-to-learn mindsets and behaviors.. These learning experiences will include online practice sites, problem solving, project work, paper pencil practice, whole class lessons, videos, homework, and more. Good planning will ensure that one day's learning will build on another day's effort. Coordination of the teaching team's efforts matter here as well since special educators, assistant teachers, classroom teachers, coaches, and others need to coordinate their efforts and time to teach all the students well. There are countless resources on the Internet and elsewhere to support this kind of teaching, and if a teacher has and makes times for this, his/her lessons and student learning will benefit.
Feedback and Goals
It's vital to provide feedback. There are multiple ways to do this from one-to-one sessions, student conferences, online reports, comments on student work, assessment scores, and more. The more students explicitly understand the goals and expectations as well as where they stand with regard to current understanding and what they need to do to gain greater knowledge, concept, and skill, the better they'll do.
Informal and formal formative and summative assessments will help teachers to respond to current program needs and plan for deeper, more targeted student learning and development.
To teach math well you need to be a lifelong learner who has a steady diet of professional learning via books, online threads, periodicals, association membership, courses, and more. I recommend that all math teachers join NCTM and regularly read the literature from that association. I also recommend joining the online organization youcubed.org. There's countless other online and offline associations that share terrific math information that leads to better teaching and learning so make some time to investigate what's out there.
We learn better if we work with others. It's important to work with colleagues to create dynamic systems of idea share and learning to support positive teaching and student development. How can you and your colleagues revise current systems and programs for professional learning and share so that you're all working together to support a dynamic math teaching/learning program? How do you make use of online share threads, collegial share, professional learning time, and outside venues to support this work? What districts and schools do this well, and how do they do it? Research and development in this area will support the good work possible. Having a strong professional learning network (PLN) related to math will help you as well in this regard.
Tomorrow night the university students and I will revisit these categories and perhaps add more detail and other categories. What else do you think is integral to teaching math well? What would you add, revise, or perhaps take away to enrich this list?