Common Core Learning Community – A Vision Emerges pt 2

In my last post, I spent some time outlining a vision that colleague Jon Wray and I have began to develop regarding collaborative resource development. In a nutshell, we believe that the solution to America’s mathematics crisis lies within the collective passion and expertise of the entire mathematics community.  If every student, teacher, mathematician, teacher leader, STEM professional…everyone submitted one great idea, and that idea were aligned to a Common Core standard, and those collective ideas could be rate by teachers and improved upon by the community at large, then we would have achieved something we have never been able to achieve.  We will have provided students, teachers, and stakeholder with all of the resources necessary to effectively design lessons that build a deep relational understanding of mathematics.

In this post, I’d like to explore some of the categories of resources that we would challenge the community to build.   We have spent a great deal of time meeting with teachers and students to ask them to define exactly what they would need to successfully balance conceptual understanding and procedural knowledge.  But we are sure that we are leaving out critical ideas.  This is where we will need your help.  Please follow up in the discussion area to add your ideas for supports.

Learning Object Category #1:  “Y-Casts” (Still looking to coin a name for this object)

These professional development resources will be submitted as short videos, Livescribe pencasts, recordings from document cameras, or podcasts.  These resources are designed to demonstrate (in 10 minutes or less) how to develop conceptual understanding for a given standard.  Think Khan Academy but with a focus on conceptual understanding.  (or “Khan”-ceptual understanding)  We have been working with groups of teachers to develop these resources as a professional development experience.  This category represents a non-negotiable for our vision.  There are loads of resources to support procedural fluency, particularly at the secondary level, but resources of this nature are virtually non-existent.  (Those that exist are scattered among websites)  An example of a pencast can be found here. The draft rubric that we have designed to provide guideline for submission can be found below this post.

Learning Object Category #2:  Worthwhile Mathematical Tasks

Peg Smith, et. al. have literally written the book on the critical component of effective mathematics instruction.  When I do a search for these exemplary items, there are very few samples to choose from.  We are aware of the Illustrative Mathematics Project being spearheaded by Bill McCallum, but those will represent just the first 400 tasks that we will need to support instruction.  Peg Smith has illuminated the difficulties with developing truly worthwhile tasks and have explained how teachers tend to leach the rigor from the task upon implementation.  We believe in the power of the development of tasks and endeavor to create the repository for such tasks.  A link to a primitive rubric, refined from NCTM Teaching Standards  and Problem Solving Brief can be found here.  We believe that teachers and students can begin lending their best ideas immediately.  We’d like to perpetuate the challenge set forth by folks like Dan Meyer and capture the true creativity of the entire community.  We want to take it one step further…we’d like to use aforementioned technologies to annotate the task with samples of student work, anticipated student misconceptions, and higher-order thinking questions that could be used to enhance classroom discourse. 

Learning Object Category #3:  Annotated Lesson Plans or Lesson Seeds

Sample lesson plans or lesson seeds are certainly not a new idea.  One can find tens of thousands of such lessons on the Internet right now.  What we would like to create is a repository of annotated lesson plans created with tablets, Livescribe Pens, or other recording devices.  Imagine watching and listening to a Presidential Award winning math teacher develop an exemplary lesson plan.  Think about the potential of this resource to be used to train educators, capturing the metacognition featured in the before, during, and after sates of lesson development.    Further, think about issues of equity if every student, teacher, and district has access to world-class instruction.  Video cases of these lesson activities feel like a natural extension of this resource but could be unwieldy given FERPA.

That’s plenty to chew on for now.  In the next set of posts, I will provide some additional ideas.  What is really needed is to begin putting experts sets of eyes on the project to make sure that we can be comprehensive and strategic in our approach. 

Until next time, dream big!

Bill

(William_barnes@hcpss.org, Follow me on Twitter @billjbarnes) 

Resource to Review…

“Y-Cast” Rubric

To what degree does your contribution…

• Help teachers understand mathematical concepts using abstract reasoning, concrete and pictorial representations, paying careful attention to the use of appropriate mathematical language, vocabulary, and notation.  (Help teachers understand the meaning behind the mathematics, balancing procedures with conceptual understanding.)
• Demonstrate how various representations connect with each other, are similar/different, and are useful for different purposes.  When appropriate, make teachers aware that each representation only partially captures the essence of a definition most of the time.  (Help teachers understand that there are multiple ways to represent concepts and the connection among those methods are critical for deepening understanding.)
• Help teachers develop an understanding of alternative approaches and diverse strategies for doing mathematics and solving problems.  Provide examples that serve to clarify common student understandings as well as identifying potential student errors with suggestions for addressing misunderstandings.  (Help teachers understand how to take advantage of teachable moments when alternative approaches and/or common misunderstandings present themselves.)
• Help teachers promote student thinking about mathematical ideas by providing sample questions such as:  Why?  How do you know? What does this mean? Who uses these concepts and for what situations?