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Rich and Robust

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Coffee beansI recently had the pleasure of learning from Tim Kanold of Stevenson High School fame. I heard him speak on several occasions last fall, and he kept saying that we need to involve students in “rich and robust tasks.” He was addressing the Common Core‘s call to the Standards of Practice. These practices can be summarized by saying that the Common Core is demanding students to think and to communicate their thinking. This can’t get done by taking notes from an overhead and doing the odd problems in the textbook. It gets done by purposefully deciding that students are going to solve rich and robust problems rather than simply watch their teacher complete examples of algorithms.

There is still a time and place for direct instruction and guided practice; but that should not be the complete experience for students, which is what we unfortunately find in the vast majority of American classroom instruction. For quite sometime, MPJ has been producing what we hope to be rich and robust tasks. Due to the growth of the internet, the availability of such rich and robust tasks has expanded tremendously. There are many exotic islands of innovation among the seas of tradition, but the blogosphere has made these islands less remote. Below I have listed a few, alongside my paraphrasing of the some of the Common Core Practices. This is not a comprehensive list by any means, however, I encourage you to take a few minutes and peruse these lessons in order to get a quick taste of what I think Kanold means by Rich and Robust.

Listed here are some additional sites that offer rich and robust tasks. {Note: I will be happy to update this list with any reader-submitted links, subject to review.}

The activities listed above obviously are not your typical math lessons. For good or for bad, the mathematical frontier created by the experiences highlighted here would make for a far different academic education than the gauntlet of lectures that most of us remember from school.

Now, I am going to assume that while the thought of introducing these large-scale examples into one’s repertoire is exhilarating for many, it may be terrifying for some. Let me ease those hearts by saying that rich and robust can be done on a much smaller scale. For example, we could simply ask the students: “Is x times x equal to two x or x squared. In other words, which of the following statements do you think is always true, if either: x·x = 2x  or x·x = x2?”

The CC Practices call for students to construct viable arguments and critique the reasoning of others. If your students stare back at you in silence with this question, then you will know why the Common Core Practices are so needed. If you answer the question for them, then they will watch you participate in a rich and robust activity, while they again participate in mundane note taking. For those that believe that this prompt is too elementary for any course above Algebra, let me assure you that it is not. I posed this very question to my International Baccalaureate students. A handful chose incorrectly, while several “could not remember.” When I asked the rest of the class, which was comprised of some of the brightest seniors on campus, no one could justify their correct answer. The best I got was that they “remember someone teaching us that once.” A simple question turned out to be far more rich and robust than it should have been, but it was a worthwhile day. {Try this one and get back to me.}

I must say here that I am grateful for my math education; it was far better than not having one at all. However, admittedly it was not rich and robust. The question is: Will we make it so for our students? It will take a conscious decision on our part to give our students a different educational experience than most of us had. So ask yourselves: When was the last time that you immersed your students in a rich and robust task? When is the next one planned? Has the time between those two dates been far too long? Are we up to the rich and robust task of offering rich and robust tasks?

Blog, Common Core

7 Lessons Learned about the Common Core

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Here is my list of lessons learned at The California Math Council’s South Conference, in Palm Springs. The overall theme of the conference was implementing the Common Core State Standards.

1) The new standards are truly world-class. I wish my own children went through school in the common core era. The expectations of the next generation of students are far higher than anything the state expected of my son and daughter. If our nation can rise to this new bar, we will finally be on par with the top performing countries around the world.
Message for teachers: If we only meet a small fraction of these expectations, the students of the future will still receive a better education than those sitting in our classrooms now.

2) Leaders are optimistic about the train wreck that is about to happen. There is no way that teachers will get students ready in time for the first wave of common core assessments. The change is too great, too quickly. The initial results promise to be abysmal. The question is from that point whether we will rise from the wreckage and move forward, or back pedal towards the old ways. Dr. Bill Schmidt and Tim Kanold are both optimistic that states, schools and teachers will continue to train, learn and eventually meet expectations.
Message for teachers: Brace for impact, then take advantage of the special opportunity that is being presented to us.

3) “We have been doing the common core long before there was a common core.” I heard this phrase from Brad Fulton and several of the reform leaders and innovators at the conference. The Math Projects Journal could make the same claim. For the 14 years of our publication, we have pushed for limited topics, conceptual understanding, higher order thinking and holding students accountable to all the above (4.5 Principles). This is not because anyone of us had unique ideas on education. We were just following the international research studies. I have heard that education is always 20 years behind the research. Any coincidence that California with conduct its first Common Core assessment 18 years after the publication of the TIMSS report?
Message for teachers: Educate yourself; what seems new really is old school.

4) The answers are out there. There was plenty of information on instruction, assessment and professional development. There are no secrets on how to implement the new standards. The only real question is how quickly and pervasively will that information find its way into classrooms. Tim Kanold claims, with evidence, that the best vehicle to deliver the information and practices is teacher collaboration.
Message for teachers: Have your school adopt a PLC model.

5) The Common Core emphasizes teaching practices as much as content. I was aware of the practices listed in the Common Core documentation, and though I regularly implement most (but admittedly not all), they always seemed more like guidelines than rules. (Problem-Solving, Reasoning, Modeling, Arguing, Tools, Precision, Structure, Patterning) In all the featured presentations, there was the consistent message that students learn as much from how we teach as from what we teach. Dr. William Schmidt of the University of Michigan claims that our current practices lack the logic and structure that is inherent in our subject matter.
Message to teachers: You will not only change what you teach, you will change how you teach.

6) One-third of the content of most textbooks can be thrown out. Dr. Schmidt led a study in which teachers corresponded their lessons and accompanying textbook pages to the Common Core standards. The study discovered that on average, one-third of the textbook content was avoided. There really will be time to slow down and to teach problem-solving.
Question for teachers: How well are you going to use the extra three months?

7) “Technology needs to mean more than paper on an iPad.” Dan Meyer gave a compelling presentation on the use of technology to push students to higher levels of thinking. He said that currently many teachers and companies are simply moving textbooks and lesson plans over to electronic devices as scanned material. Much of Mr. Meyer’s presentation was on the unique ways in which videos and photos can be used to perplex students.
Message for teachers: Times are a changin’. It’s time to catch up.

For the alarming number of those who had not heard much of the Common Core, it was a terrifying weekend. For those of us who have embraced its values over the last two decades, it was an exhilarating, yet still disconcerting, conference. Big kudos to the committee for putting on such a hugely successful event. Thank you for helping point us all in the right direction.

P.S. Catch ’em 2012 from Chris Shore’s presentation at CMC.