Image source: @bryanmmathers |

*Summerhill.*Not very likely in our current reality of testing and grading. But someday maybe a boat like this can float in many bodies of water.

I’ve been listening to David Bodanis’s book Einstein’s Greatest Mistake and was pleasantly surprised that Bodanis told the story of Flatland where 2 dimensional figures such as circles, squares and lines are the inhabitants that could never imagine a 3 dimensional world. Einstein’s genius was recognizing a new dimension that goes beyond the 3 dimensional world we inhabit. He was after a unified theory of the universe when he realized along the way that the universe’s structure could be curved. This realization eventually led to his ground breaking general theory of relativity. It made me think about a statement made about the latest iteration of the NCTM standards

*Principles to Actions*(PTA) which followed the 2000

*Principles and Standards*and the 1989

*Curriculum and Evaluation Standards for School Mathematics*. PTA was almost as good as you can get claims the current president of NCTM and will survive the test of time. Each iteration of the standards has taken a new dimensional look at mathematics education and suggested what teaching and learning math should be. But is there a "dimension" that’s missing? I challenge the following statement in thinking about a new paradigm: "

*Good teaching is a prerequisite for good learning in schools*."

Teaching and learning are going through an identity crisis. There was a time when it was easy to distinguish the teacher from the learner. But times and roles are changing in today’s schools. The main function of teachers is to facilitate learning. The assumption of course is that the students are doing all the learning. That’s not true any more because in the modern classroom teachers and students can switch roles. We’ve known for a long time that a great way to learn something is to teach it. As a result teachers have honed their craft well, but the same can’t be said for students. Especially the ones sitting in the back of the room looking out the window. But those kids can’t look out the window so easily any more since they are busy collaborating with their peers preparing to present to the whole class what they have learned. Teachers in the meantime are coaching, facilitating, and observing students making sure they are on track for their upcoming presentations. Occasionally the teacher will jump on stage and share something very cool that is of interest to everyone. This scene is an example of personalized learning at its best. A win-win for teacher and students. So if PTA is describing a third dimension of “teaching and learning” I’d like to suggest a 4th dimension paradigm shift which turns the 3rd dimension on its head calling it “learning and teaching” or good learning leads to good teaching. It’s a subtle distinction but an important one. It begs the question “when (and how) do students learn?” In schools that's usually the teachers job and the good ones make the students learn. (Not always. See Alan Schoenfeld’s

*When Good Teaching Leads to Bad Results: The Disasters of “Well-Taught” Mathematics Courses.)*

The bottom line is that students learn well when they are interested. (The chief enemy of learning is boredom which is way too prevalent in schools particularly in math classes.) The challenge to good teachers is to adjust their teaching and support a vision where all students are interested. Our curriculums need radical reform for this to happen. (More about this in future blogs.)

When motivated, students try their hardest, reach out for help, and receive supportive help from teachers. This happens best in student-centered learning environments.

Here’s my list of criteria for student-centered, personalized learning environments.

- Math is learned best in a community of learners where students are engaged in authentic activities that illuminate important powerful ideas (intellectual tools) in math.
- The environment can be, for example a school, which is a hub for personalized learning.
- The curriculum is a project based design for a creative, student driven learning path.
- The community is constantly evolving with teachers, students, administrators and parents acting as change agents.
- Choice and voice for student agency are prized.
- Learning styles are respected.
- Commitment to ongoing professional development for teachers so they can be the best coaches/guides for their students.
- School time is flexible designed for anytime/everywhere learning.
- Students learn best when they are interested in the topic being investigated.
- Technology is a tool that is a platform for personal learning.

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