Finding Math in Nature’s Patterns

Succulent spiral
Succulent spiral

As I recently wrote in Don’t Teach Them Facts – Let Student Discover Patterns 

It’s unfortunate that student don’t get to use their innate perceptual skills more often in the classroom. Instead of discovering patterns on their own, students are “taught” to memorize patterns developed by someone else. Rather than do the messy work of having to figure out what’s going on, students are saddled with graphic organizers which take all the thinking out of the exercise. 

“Doodling in Math Class: Spirals, Fibonacci, and Being a Plant” captures the fascination of patterns in nature. Discover more patterns from Vi Hart – Mathemusician

Image credit: flickr/Duff Axsom

Solve the Problem

Solve the problem
Solve the problem

This problem was inspired by an advertisement I saw in Wired Magazine. (Modified for this blog post). When I first saw the page, I realized I was looking at a puzzle, but I wasn’t sure what I was supposed to do. Then I “got” what was going on and I figured it out.

The key to solving a problem often lies with finding a pattern. That’s a very human skill. Even newborns can soon recognize faces. As Jon Medina has said “We…are terrific pattern matchers, constantly assessing our environment for similarities, and we tend to remember things if we think we have seen them before.”

It’s a pity we don’t do a better job of teaching pattern recognition in school. Uncovering an underlying pattern is essential to constructing meaning. In school we typically “teach” patterns to students as “facts,” rather than ask students to discover the pattern for themselves. Of course this strips the activity of its real value as a learning strategy, and turns into just another thing to memorize. Asking students to file some pre-selected information into a graphic organizer isn’t analysis – it’s just moving stuff around. True analysis involves doing the challenging work of trying to make sense of information. Powerful learning occurs when students have to answer questions like - Is this a sequence? Is it cause and effect? How would I organize this material into categories? Could I explain my system to someone else?   Exactly the type of skills that are demanded by the new Common Core standards.

Enough commentary, have you solved the problem yet?

Credit: Inspired by CenturyLink ad in Wired Magazine, October 2011 p. 148

Teachers, Have the Courage to be Less Helpful

I’ve been thinking about the educational implications of passage in Tom Friedman’s recent editorial The Start Up of You. Here Friedman quotes a comment made to him by LinkedIn’s founder, Reid Hoffman.

“The old paradigm of climb up a stable career ladder is dead and gone,” he [Hoffman] said to me. “No career is a sure thing anymore. The uncertain, rapidly changing conditions in which entrepreneurs start companies is what it’s now like for all of us fashioning a career. Therefore you should approach career strategy the same way an entrepreneur approaches starting a business.”

So does that mean we’re supposed to prepare our students to become hi-tech startup entrepreneurs? I don’t think that’s realistic, or wise. But I do think that it should remind us that we need to craft learning environments that ask students to increasingly take responsibility for their learning – products, process and evaluation – and the type of deeper thinking and reflection called for in the Common Core standards.

“I want kids behaving like a journalist, like a scientist… not just studying it, but being like it.” ~ Larry Rosenstock, High Tech High

Unfortunately, most of our students get a steady diet of force-fed information and test taking strategies. We’re giving a generation of kids practice for predictable, routine procedures – and that happens across the “bell curve” from AP test prep to meeting minimal proficiency on NCLB-mandated tests.

If LinkedIn’s Hoffman is correct, it makes you wonder how our students are getting prepared for “uncertain, rapidly changing conditions?” School mission statements claim to foster “life-long learning,” but walk in most classrooms and you’ll see students hard at work on a task that’s been scripted by their teacher. Most likely they’re working to replicate a final product that’s already been prescribed (with rubrics) by their teacher.

If students are going to be productive in a dynamic society and workplace they will need to be agile, fluid learners. Students that are encouraged to explore their own approaches and reflect on their progress. Students who can work collaboratively with their peers to plan, implement and evaluate projects of their own design. As Larry Rosenstock of High Tech High put it, “I want kids behaving like a journalist, like a scientist… not just studying it, but being like it.”

Every summer, teachers get to re-invent themselves – to rethink their instructional approach. Here’s your essential question for the coming school year – “How can I stop scaffolding every task for students, and have the courage to be less helpful?” Does this seem like a crazy idea? Asking student to “figure it out themselves,” when every time you’ve given an assignment, you’ve been bombarded with trivial questions like, “… How long does it have to be? … What’s it supposed to look like?”

I think students have been taught that they work for the teacher and the grade. I’ll bet the most “what it supposed to look like” questions come from the “best” students who have learned that their averages are based on faithfully executing assigned work.

For a more on the benefits of “figuring it out for themselves” see my posts Don’t Teach Them Facts – Let Student Discover Patterns or The Four Negotiables of Student Centered Learning

So be courageous – remember, the same students who seem to be unable to function independently in school are highly motivated by the uncertainty of video game. You can retrain them to “figure it out” at school, as well.

Looking for a few practical ways to start? Here’s four ideas from “Student-Directed Learning Comes of Age: Teachers Adopt Classroom Strategies to Help Students Monitor Their Own Learning” by Dave Saltman in Harvard Education Letter, July/August 2011 [Summary courtesy of The Marshall Memo – a valuable weekly round-up of important ideas and research in K-12 education]

Moving Students Toward Directing Their Own Learning
“An insistent drumbeat of research findings, as well as newly adopted curriculum standards, continues to sound out a message to educators that the work of learning must be shifted from teachers to the ones doing the learning,” says teacher/writer Dave Saltman in this Harvard Education Letter article. “That’s because research and anecdotal evidence suggest that when students manage their own learning, they become more invested in their own academic success.” Saltman describes four approaches that develop self-direction:

Continue reading “Teachers, Have the Courage to be Less Helpful”

Jerry Seinfeld: History Teacher – Observations in the SNL Classroom

Seinfeld-history-teacherCurrently this link works. (9/15/15)

 Last week I used this classic Jerry Seinfeld piece from Saturday Night Live as part of an administrators’ workshop. We had lots of fun. Here’s your chance to borrow the idea.

Goal: I was working with a team of principals and district administrators who wanted to provide more consistency in their teacher observations and look for strategies for using observations to assist teachers in reflecting on their instructional approaches. We first met at district office before going out to observe a few classrooms and share our impressions. I thought it would be useful (and fun) to warm up with Seinfeld’s disastrous history lesson.  

Seinfeld-class
Here’s the process I used:

  1. We watched the video.
  2. A volunteer agreed to take the role of an administrator who just observed Seinfeld teaching. I played the role of Mr. Seinfeld as we both met for a post-observation conference.
  3. I set up a “Fishbowl” discussion group among the remaining participants. Half would pay attention to the administrator conferencing with Seinfeld. They were asked to record two types of admin questions or comments on a T-Chart – either ones that caused Seinfeld (me) to reflect on myself as a teacher or judgmental questions / comments that caused me to get defensive. The second half of the fishbowl group focused on me (Seinfeld). They were asked to record two types of comments I made – either comments where I was reflective on my lesson / teaching or comments where I got defensive / argumentative.
  4. I asked each of the fishbowl groups to compare within their two groups.  We then we shared in a full group discussion.

While there was little positives to find in the Seinfeld lesson – the activity got us thinking about ways in which an administrator can give teachers feedback that is less judgmental and more likely to cause teachers to reflect on their lesson and instructional approaches. 

Sample judgmental admin question: “You say that you want the students to ‘think about history’ and forget about the details, so why did you start asking a series of content questions on material they had already failed on the test?”
Similar theme explored in a non-judgmental, reflective tone:  “What are some of  the methods you like to use to gather feedback on student mastery of content? How do you use the information to design a lesson?”

It was a great icebreaker and loads of fun for everyone. Later in the day we observed some actual classrooms taught by teachers who had volunteered to host us. We came back together as a group and compared our impressions using the district evaluation instrument. We compared our results to calibrate the observation tool. Our final activity was to develop some feedback to give the teachers who hosted our visits. We crafted comments that were more reflective than judgmental. The volunteer teachers’ principal later delivered the feedback to the teachers. 

Everyone thought it was valuable session. I hope you can find some use or ways to modify. 

How to set up a Fishbowl discussion group  Download Fishbowl-discussion 58kb pdf


Historypin – Make DBQs with a Digital Time Machine That Layers Image, Story and Location

While planning for my next document based question (DBQ) workshop, I discovered Historypin. It’s a great mashup of digital photos with stories layered over Google maps. Users can search images by geography / time and post historic photos with stories to maps. It’s fascinating to view historic photographs set against the backdrop of current Google map street view.

Historypin

Here’s a circa 1894 photo I uploaded to Historypin showing a bridge crossing the Erie Canal in downtown Rochester NY. It’s layered over a functioning “street view” in Google maps.

In Historypin’s story section, I provide a brief history of the canal’s impact on the growth of the city.

Then I pose a question. “I wonder if the people in the old photograph still appreciated the canal’s role in creating the city of Rochester, or if they had come to see it as outmoded nuisance which divided the city in half?”

For more ideas for classroom see:  image guide | story guide | teachers’ notes

What I like most about Historypin is that it adds a new dimension to the DBQ approach to instruction – students don’t simply learn from historic documents – they get to document their world for future generations.

More from Historypin:

Historypin was created as part of our current campaign to get people from different generations spending more time together. From a lot testing, we found old photos are a great way of getting people talking about how their street used to look, what their grandparents were like and what’s changed (or not) over time. 

We decided to create a website where people everywhere could share their old photos and the stories behind them, pinning them to a map of the world. We also thought it would be neat if you could compare these old photos with how the world looks today, making the site a bit like a digital time machine. So we asked Google if they’d help. They let us use their map and Street View functionality and helped us build the site. 

The great thing about Historypin is that when they’re using the site, loads of people are spending time with someone from a different generation. Older people have attics full of old photos, younger people know when to click and when to double click.