Problem-Based Learning and the Common Core

This post is broken into a reflection and set of Resources (click here to skip to them).  I hope both are useful!

Reflection:

Problem-Based Learning in mathematics is really blossoming and reaching a much larger audience.  Why it is blossoming now, I am uncertain, but some of my initial thoughts are listed below:

1. attempt to address possible lack of student engagement in the classroom
2.  attempt to infuse math curricula with more authentic, “real-world” scenarios
3.  attempt to leverage the new ease of creating and interacting with content through technology and integrate it into the classroom experience
4.  attempt to find a middle road in the “math wars”   by creating problems  that integrate procedural skills with conceptual understanding in rich contexts (mathematical or “real-world”)
5.  attempt to link mathematics to broader set of skills around critical thinking and conversations on 21st Century Learning
6.  attempt to meet some of the demands associated with or articulated within the Common Core State Standards for Mathematics both in the content and practice standards

If these are true or not, I’m not sure.  It could just be math teachers find them more interesting or that content creation has grown beyond publishers and the “math” diet has broadened.   Whatever the reason, the “problem-based learning” thing is  producing some really great stuff AND it is  aligning it to common core.   I think that fact is important in the ongoing debate about common core.  Here is another list of why this is important:

1. Illustrates that common standards do NOT stifle creativity.
2. Demonstrates that common standards do NOT dictate any particular curriculum (see 1 above for another version of this).  Problem-based learning is just one of many translations of common standards into the classroom.
3. Provides a common ground for teachers to learn from, interact with, and build upon a variety of different content creators across state lines.
4. Promotes conversation about great instructional practices out of a shared commitment to comment standards.
5. Stimulates a deep conversation on the mathematical practices, particular “Model with Mathematics.”

There are many more, I’m sure and I welcome comments and insights in the comments below.  Please add your additions or criticism to improve the post!

Resources

Geoff Krall

One of the best,  clear, and reflective posts on problem-based learning comes from Geoff’s blog.  His post, “Things that are Good: A Problem Based Learning Approach in Mathematics” helps frame the discussion on problem-based learning from the perspective of a teacher who is always looking to improve his practice, engage students, and encourage a love for and the ability to do mathematics.  He is cobbled together from across the web a variety of quality problems into common core aligned  curriculum maps ranging from 6th grade up to Algebra 2.

Problem-Based Learning Curriculum Maps:

http://emergentmath.com/my-problem-based-curriculum-maps/

Robert Kaplinsky

There is so much to learn from Robert Kaplinsky!  Where to begin?  First, if you have the time, read his excellent description of problem-based learning, entitled “Problem-Based Learning for All: The Four C’s.”  The Four C’s that he develops are: communication, curiosity, critical thinking and content knowledge.  A concise statement about why problem-based learning is a powerful modality for the math classroom.

Second, the lessons!  Find a superbly organized and well developed set of lessons spanning the common core standards.  I recently did Dr. Evil in class and it was a great way to get the conversation on exponential growth, inflation, and time value of money going!

Last, but certainly not least is the “how to” guide.  While the lessons are detailed and full of the “how” of implementation he has also articulated an excellent set of personal, department, or school-wide professional development tools on questioning.  Really amazing and the kind of instructional reflection and support that anybody needs to do this type of instruction.

Three-Acts Math

Dan Meyer’s has put a frame around problem-based learning that is rooted in engagement, questioning, curiosity, and the revelatory power of mathematics.  His “3Act Math” has taught me a great deal about learning and the role of narrative in the math classroom.  He explains the overall “lesson design” of  3Acts on this post, “The Three Acts of a Mathematical Story“and has recently started a journey into “how” to teach the acts.  His narrative of how to teach Act 1 is entitled, “Teaching with Three Act Tasks: Act One.”  Dan has also done great work exploring questioning and its role in learning mathematics with his site, 101 Questions.  The well known work of Dan Meyer has spawned other three act task developers, including Andrew Stadel.  I have included his spreadsheet of links as well.

Dan Meyer: https://docs.google.com/spreadsheet/pub?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE&gid=0

Andrew Stadel: https://docs.google.com/spreadsheet/ccc?key=0AkLk45wwjYBudG9LeXRad0lHM0E0VFRyOEtRckVvM1E#gid=0

Fawn Nguyen

Fawn Nguyen is an engaged educator who loves mathematics and thrives on developing, encouraging, and harnessing students as problem-solvers.  She has a couple of websites and a very detailed blog about how problem-solving happens within her classroom.  Her home blog is simply http://fawnnguyen.com/, and it holds detailed descriptions of questioning sequences with students around problems, reflections on practice, and other ideas around teaching mathematics–there is so much to learn there (at least there is for me).  She also does an excellent job practicing what she preaches around questioning.  She has a brief post on questioning in the math classroom here.  Lastly, she narrates her classroom experiences or 180 days on a blog entitled, “180 Days of Math at Mesa.”

Mathematics Vision Project  (MVP)

Is a project  funded by the Utah State Office of Education to create a common-core aligned  integrated mathematics curriculum for high school.  Many things are unique about this project and really require a second look, but for the purposed of this post MVP  represents an entire curriculum built around meaningful problems and classroom experiences engaging those problems.  It is also a dynamic curriculum in that as you use it (as you see fit) you can provide feedback on specific aspects of it.  The team at MVP actually wants input!  The philosophy around problem-based learning embedded in the project can be found in a few presentations and files that they have generously posted.

Secondary One Mathematics

Secondary Two Mathematics

Georgia Task Sets

The state of Georgia has re;eased sets of problems for classroom use k-12 on their Common Core GPS Mathematics site.  The curriculum guides, as they are called, are a series of tasks that vary between purely mathematical and “real-world” contexts and really push on the conceptual development of ideas.  The guides range k-12 with some really solid work spread throughout, including some robust problems through which students investigate the major work of the grade (guides also include collaborative activities, hands-on activities, sorts, etc.)  The two pictures below will show you how to navigate to them!

Math Mistakes

Another side of problem based learning is examining completed problems and analyzing what they reveal both in terms of approach and misconceptions.  A great crowd-sourced website of math mistakes is found at Math Mistakes.  As the site suggests each of the posted problems are “more or less” common core aligned and are nicely organized according to standard.  The Mathematics Assessment Project also does a great job of investigating “math mistakes” through their problem-solving lessons.  They are also a great tool in this vein of problem based learning and provide a particular instructional approach to examining student responses to problems as a way of learning.

Graphing Stories

Is a joint project between Dan Meyer (mentioned above) and Buzz Math and is another look at problem-based learning that begins with experience and pushes the translation of that experience into mathematical modeling.  It is really beautiful work and situates math as a practice or modality that teases out variables and their relationship graphically.  Definitely a place to inflect problem-based learning in a new direction.  I am currently thinking through this site toward classroom experiences involving “writing stories,” “acting stories,” and “creating stories.”

There are so many more places like The Math Forum, Yummy Math (awesome!),  Inside Mathematics, Park School of Baltimore, Phillips Exeter Academy,…  Let me know others that you like and add them to the comments!

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