Putting the Problem First Can Create the Knowledge

Dan-meyer-math As I blogged in my Apollo 13 video post,  Watch Problem Based Learning in Action  ”While our students have been conditioned to ‘learn the basics – then solve the problem,’ that’s not how life always works.” 

Here’s a great 4-minute video by Dan Meyer that gives three examples of how to bring real-life problem scenarios into the math classroom.  To paraphrase Dan, “In these examples student have to first ask the question – what information do I need to solve this problem? The textbook usually gives you that information. But here students build the problem and decide what matters. The question that’s usually buried at the bottom – it’s the last thing in the textbook problem – now becomes the first thing in the student’s mind. I want to make that question “irresistible” to the student, so they have to know the answer.”  For more great ideas on how “math makes sense of the world” – go to Dan’s blog dy/dan

What Would Schools Look Like, If Students Designed the Schools?

Independent 4 As you watch this video, think about what could happen in schools, if adults got out of the way. 

You’ll hear students say things like,  ”A subject comes up that I don’t know about, and instead of glossing over it,  I truly find myself thinking was is that about? I could learn about it! I’m finding questions in everything.” And “We learned how to learn, we learned how to teach, we learned how to work.”

Of course, it’s easy to discount these kids as atypical. Marginalizing them is far easier than wondering why other high school students are stuck doing worksheets.

For more information on the project and associated lesson plans for students see:  ”Independence Day: Developing Self-Directed Learning Projects

 

Student Personal Tech Devices in the Classroom? A Cartoon Parable

“The Cameraman” – From Cartoonist Chris Ware, animator John Kuramoto and Ira Glass of This American Life. First grade teacher, Jeff Potter tells Ira about an art project and the impact of  personal “technology” in the classroom. 

“The camera really changed the way we behaved…. We lost our humanity.”

Were the cameras really responsible for the student insensitively to the fight? Was banning the cameras the only alternative the teachers had? I don’t know. I wasn’t there. 

But it does strike me that the cameras were also a catalyst to creativity, collaboration, and powerful student engagement. Is this a parable about balancing the benefits and liabilities of cell phones and other student personal technology in the classroom?

Hat tip to David Kwasigroh

The Four Negotiables of Student Centered Learning

I spent most of last week guiding teachers on classroom walkthroughs. (Here’s links to my protocol and some recent participant responses.) It’s an effective approach to professional development – one that focuses on the students, not the teacher. Think of it as a roving Socratic seminar that provokes reflections on teaching and learning.

One of the subjects that often comes up during walk throughs is how to recognize a student-centered approach. I tell participants to watch the students and try to decide the extent to which they are being asked to manage the four central elements of any lesson – content, process, product and assessment. Any or all can be decided by the teacher, by the students, or some of both. As I often said to my own students when introducing a lesson – “Which elements do you want to be in charge of? Which do you want me to decide? Remember you don’t  all have to take the same approach.”

You can’t simply “throw students in the deep end” and expect them to take responsibility for all their learning decisions. But with scaffolding and support, students will increasingly take more responsibility for their learning. The reward is the increase in student motivation that comes with greater student choice. And as students take more ownership of the learning process, they are better able to monitor their own progress and reflect on themselves as learners. See my Taxonomy of Reflection for useful prompts.

Stop Worrying About Shanghai, What PISA Test Really Tells Us About American Students

Sputnik replica
Sputnik replica

The latest results from the Program for International Student Assessment (PISA) are public, and already some pundits are declaring it “a Sputnik wake-up.” Others shout back that international comparisons aren’t valid. Rather than wade into that debate, I’d rather look more closely at the questions in the PISA test and what student responses tell us about American education. You can put international comparisons aside for that analysis. 

Are American students able to analyze, reason and communicate their ideas effectively? [Think Common Core standards] Do they have the capacity to continue learning throughout life? Have schools been forced to sacrifice creative problem solving for “adequate yearly progress” on state tests? For more on that last question see my post “As NCLB Narrows the Curriculum, Creativity Declines.” 

PISA provides some answers to those questions and offers an insight into the type of problem solving that rarely turns up American state testing. FYI: PISA is an assessment (begun in 2000) that focuses on 15-year-olds’ capabilities in reading literacy, mathematics literacy, and science literacy. PISA assesses how well prepared students are for life beyond the classroom by focusing on the application of knowledge and skills to problems with a real-life context. For more examples of PISA questions and data click here. 

Do American students learn how to sequence or simply memorize sequences

Here’s one insight into what American students can (and cannot) do that can be gleaned from the 2003 PISA test results. We spend a lot of time in school getting students to learn sequential information – timelines, progressions, life cycle of a moth, steps for how to. Typically the teacher teaches the student the sequence and the student correctly identifies the sequence for teacher on the test. Thus we treat a sequence as a ordered collection of facts to be learned, not as a thinking process for students to use.  This memorization reduces the student’s “mastery” of the chronology to lower order thinking. I was guilty of this when I first started teaching history “Can someone give me two causes and three results of WWII?” 

Sample sequencing problem from PISA

The Hobson High School library has a simple system for lending books: for staff members the loan period is 28 days, and for students the loan period is 7 days. The following is a decision tree diagram showing this simple system:

Pisa-1

The Greenwood High School has a similar, but more complex library lending system:
All publications classified as “Reserved” have a loan period of 2 days.
For books (not including magazines) that are not on the reserved list, the loan period is 28 days for staff, and 14 days for students. For magazines that are not on the reserved list, the loan period is 7 days for everyone.
Persons with any overdue items are not allowed to borrow anything. 

Task

Develop a decision tree diagram for the Greenwood High School Library system so that an automated checking system can be designed to deal with book and magazine loans at the library.  Your checking system should be as efficient as possible (i.e. it should have the least number of checking steps). Note that each checking step should have only two outcomes and the outcomes should be labeled appropriately (e.g. “Yes” and “No”).

Student Results

Only 13.5% of US students were able correctly answered the question. Does it really matter if students in Shanghai did any better? (The student results were rated on a rubric scale.) 

When students are asked to observe a process and develop a sequence they have an opportunity to use a full spectrum of higher-order thinking skills – they must recognize patterns (analyze), determine causality (evaluate) and then decide how they would communicate what they’ve learned to others (create). Sequencing can be taught across the curriculum at a variety of grade levels – we simply have to ask the students to observe and do the thinking.

In case you’re wondering,  correct response should look like this.
Click image to enlarge.

pisa answer
pisa answer 
 

Image credit/ NASA