Habit and Mindsets are Difficult to Change

In March, after attending a workshop by Gary Stager at ASB Unplugged I posted The Future of Math Education and two recent articles on math education have me thinking about this topic again. The New York Time article, Why do Americans Stink at Math, by Elizabeth Green and Jessica Lahey’s article, Teaching Math to People Who Think They Hate it from The Atlantic should be the sources for a professional learning community (PLC) study. The purpose of this post is not to fully analyze these two articles. The purpose is to share a few of the main ideas in hopes that they will stimulate thinking and a dialogue.

The main idea behind Green’s article is that:

“The new math of the ’60s, the new, new math of the ’80s and today’s Common Core math all stem from the idea that the traditional way of teaching math simply does not work.”

And even though these curricular initiatives were designed to transform math education, little has actually changed. Green presents one major reason for this inertia.

“Consequently, the most powerful influence on teachers is the one most beyond our control. The sociologist Dan Lortie calls the phenomenon the apprenticeship of observation. Teachers learn to teach primarily by recalling their memories of having been taught, an average of 13,000 hours of instruction over a typical childhood. The apprenticeship of observation exacerbates what the education scholar Suzanne Wilson calls education reform’s double bind. The very people who embody the problem — teachers — are also the ones charged with solving it.”

The “apprenticeship of observation phenomenon” is something that all educators face when it comes to changing practices in their subject matter. We’ve seen over the years that educators have a difficult time changing their mindsets. To add to the problem, parents have a view of how education should be based on their experiences. When educators actually do change practices, parents can be critical because the changes don’t match their vision (frustrated parent’s rant on Common Core math practices).

Lahey profiles the work of Steve Strogatz from Cornell University. Strogatz is teaching an introductory math course for non-math majors. “The curriculum he teaches is called Discovering the Art of Mathematics: Mathematical Inquiry in the Liberal Arts (DAoM); it was developed at Westfield State University byJulian Fleron and three colleagues and funded by a grant by the National Science Foundation.” The learning focuses on using “student-led investigations into problems, experiments, and prompts.” The curriculum looks promising and they are already sharing the results through student quotes, videos, other data.

I’d love to dive deeper into these ideas even though I’m one of those individuals who thinks he hates math.

Best Practices Just Aren’t Enough These Days

Best Practices – Aren’t. Mike Myatt. Forbes Magazine. 15 Aug. 2012. http://www.forbes.com/sites/mikemyatt/2012/08/15/best-practices-arent/

Just over a year ago I read George Couros’s post, Ignoring the Status Quo and after this I have been campaigning against best practices. I was in search of alternatives to looking at “best practices”. Unfortunately I’ve been doing a poor job of communicating the concept that best practices keep up the status quo without taking us to a new level. Thanks to Brett Jacobsen at Mount Vernon Presbyterian School I started reading Decisive by Chip and Dan Heath. They clearly explain the benefits of best practices mixed with “bright spots”.

“They’ve long since learned to “benchmark” competitors and absorb industry “best practices.” While these habits are useful, they are rarely transformative. Good ideas are often adopted quickly.”

In Decisive, they give the example of how Sam Walton replicated practice that Ben Franklin was using where customers paid for their items at one location at the front of the store. In the past customers would pay separately in the respective departments. As more stores starting adopting this strategy it became common practice. Walton would frequently ask, “Who else is struggling with a similar problem, and what can I learn from them?” I find that we do this all the time in schools. In the international school community, The Principal’s Training Center listserv is buzzing with colleagues who are gathering information on what others are doing (“best practices”). This type of sharing is necessary and very helpful. For example, about a year ago we asked schools (see The Best Time – Design Thinking Part 2) how they were organizing their classroom without walls trips. We received some excellent ideas and ended up piloting trips based on the best models that we found.

The Heath Brothers present a case for a combination of best practices and “bright spots.” The bright spots are solutions that come from alternative thinking within the organization. Thinking that is tailored to meet your needs and takes the solution to the next level. This type of thinking can lead to mash-ups or innovative practices.

“The search for options might lead the manager to search first for best practices. In a world with thousands of other organizations, someone has surely faced this problem before. Next, she might look for bright spots within her own organization, …”

Using the classroom without walls trip example. We’re basically at a point now where we need to develop brights spots that will improve our school trips. Based on the feedback that we received from teachers and students, the pilot trips were excellent, but they weren’t innovative and we didn’t quite accomplish our objectives. We’re now in the process of developing a new iteration for next year’s learning experiences and we plan to take them to another level. A level that better meets are needs and will hopefully be seen as a “next practice”. Notice that I said “learning experiences”. We’re realizing that the activities for the week don’t have to be trips.

I’m changing my campaign in support of best practices and bright spots.

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The Future of Math Education

Lately I have been asking the question, “What is  math education going to look like in the future?” As of right now, I don’t have a clear picture and I’m fairly optimistic that significant changes will not take place in the near future. While I frequently hear from teachers (not all) that math requires students to practice learning the steps to solving problems that will lead them to being able to apply their learning afterwards. It seems to me that they are saying that the traditional lecture, in class practice, and homework practice is the way that it has to be.

“If we taught dancing like we teach math we’d never let people dance until they drew out all steps on paper.” Seymour Papert (From Gary Stager’s TEDxASB talk)

On the other hand I’m hearing from others that math education has to change. Forget the flipped classroom and Khan Academy, they’re talking about substantial changes. What are they?

Dan Meyer’s 2010 TED Talk, “Math class needs a makeover”, certainly got people thinking about this topic back in 2010.

Since then I’ve been on a quest to search for the future of mathematics. I had a small epiphany at the recent ASB Unplugged Conference when I attended Gary Stager’s workshop, Electrifying Children’s Mathematics. Now I’ve seen Gary speak many times but this was the first time that I participated in one of his hands on workshops. By actually being able to work through the exercises in a constructivist way I was able to make just a little bit of sense out of the possibilities in the math classroom.

Gary started the presentation by showing us that,

“The NCTM Standards state that fifty percent of all mathematics has been invented since World War II. (National Council of Teachers of Mathematics, 1989) Few if any of these branches of mathematical inquiry have found their way into the K-12 curriculum. This is most unfortunate since topics such as number theory, chaos, topology, cellular automata and fractal geometry may appeal to students unsuccessful in traditional math classes. These new mathematical topics tend to be more contextual, visual, playful and fascinating than adding columns of numbers or factoring quadratic equations. ” (Stager and Cannings, 1998)

We then watched a video of math instruction in an elementary class where the teacher uses Piaget’s theory to help students construct knowledge on concepts. The videos are the work of Constance Kami, Professor of Early Childhood at The University of Alabama at Birmingham. My take-aways from this video are that…

  • students don’t need to know all of the ways to solve a problem. Whatever works for them is sufficient.
  • the refrains from telling the student whether or not their answer is right or wrong. teacher should let the students talk through their methods and to let them work through the problems together. The less teacher involvement, the better.
  • doing endless numbers of problems that you already understand does not do you any good.

We then moved into the hands on portion of the workshop and in a very short amount of time I realized the value of playing with tools and ideas to learn mathematical concepts.

We played with Turtle Art. We were given a simple exercise to get started and then were left to play on our own. The connections to mathematical thinking were easy to make and the results were definitely visual.

We used MicroWorlds to try to figure out a problem that we later learned was unsolvable. Something that is referred to as the 3N + 1 Conjecture, Collatz Conjecture, Ulam Conjecture, and many others. It was amazing how much math we were having to use to struggle through this problem. It was a good learning experience and it’s probably better that we didn’t know that it was unsolvable.

But, my favorite activity had to do with determining values for iTunes radio users’ actions. The work had us tackle computational thinking. Gary was very clear about his views on teaching computational thinking skills.

Computational thinking is useful when modeling a system or complex problem is possible, but the programming is too difficult.

The activity involved assigning values to the following actions.

Photo from About.com from Sam Costello
We also considered when the person just let the song play.

This was a room full of math teachers and I’m pretty sure that none of them had the programming skills to code the algorithms behind these choices. We did struggle with equating a value while thinking about the users’ thinking and how the numbers would be used behind the scenes. Many of our students have no idea of what is taking place behind the scenes when users click on a button. While very few actually have to know how to do the programming, there is definite value to understanding the computational thinking.

So, after the workshop I asked a couple of math teachers if they felt that they learned skills and/or knowledge that they could take back to their classrooms and, the general consensus was, “most definitely”. These were primarily teachers in international schools.

So, what are your thoughts on the future of mathematics?

Jumping on the Innovation in Education Bandwagon

Our school’s leadership team is reading Tony Wagner’s book “Creating Innovators: The Making of Young People Who Will Change the World” as we grapple with what innovation looks like in schools. (You can follow our discussion on Twitter – #gradedllt) I highly recommend Wagner’s book along with Suzie Boss’s book “Bringing Innovation to School: Empowering Students to Thrive in a Changing World”. It’s extremely easy to find definitions on innovation that we can all agree on. The really difficult step is to change practices to become innovative. I recently attended a conference where the word, “Innovation” was overused and mis-used. I went to one presentation where the presenter was convinced that his school had been innovative by adopting a program that has been around for 40 years. The new program changed their culture but it certainly wasn’t something that was innovative to the world of education.

“Innovation may then be defined as the process of having original ideas and insights that have value, and then implementing them so that they are accepted and used by significant numbers of people. By this definition, a major innovation is one that is so successful that soon after its introduction few people can even remember what life was like before the innovation was introduced.” Rick Miller, President Olin College

“creative problem solving.” She said, “Problem solving without the creative element is not truly innovative.” And creativity that is not applied to real world problems cannot be considered innovation either. Innovation is our lifeblood at P&G—but not just innovation for its own sake. It’s about taking real needs and creating a bridge to a solution.” Ellen Bowman

Our question is, “What is innovation at Graded?”  My thinking has gone in two different directions lately.

  1. What are we doing at Graded that is innovative?
  2. How are we cultivating innovators?

Since our Core Values state, “Learners at Graded strive to be Innovative: They engage in creative and imaginative thinking that enables them to extend their learning in original and insightful ways.”  I’ve been focusing on #2.

Montessori schools have been cultivating innovators for over 100 years.

When you ask someone to list the schools that they consider innovative, how often do Montessori schools make the list?

What do you suppose the founders of Google, Larry Page and Sergey Brin; Amazon’s founder and CEO, Jeff Bezos; Wikipedia founder Jimmy Wales; Julia Child; and rapper Sean “P. Diddy” Combs all have in common? Gregersen’s research, cited earlier, uncovered an extraordinary commonality among some of the most innovative individuals: they all went to Montessori schools, where they learned through play. (Wagner, pp27-28)

If you consider Wagner’s characteristics of a learning culture that cultivates innovators, you can see why Montessori schools most definitely should be on your list.

  • collaboration
  • multidisciplinary learning
  • thoughtful risk-taking, trial and error
  • creating
  • intrinsic motivation: play, passion, and purpose (Wagner p. 200)

I’m currently a participant in the Deeper Learning MOOC (#DLMOOC) which is organized by High Tech High and supported by a number of organizations. One of which is Expeditionary Learning Schools. I don’t know much about EL Schools other than I have worked with several educators who once were involved in the organization. I’ve frequently heard from them that, “The EL schools organization, and their schools, aren’t what I would call innovative.” If you look at their website you find no mention of innovation in the “Our Approach”section,  yet, it’s easy to argue that EL schools provide students with the type of environment that Wagner has defined.

Maybe a truly innovative school focuses on answering both questions.

“What are we doing that is innovative and how are we cultivating innovators?

How is your school handling Google Glass?

Last week we started our second semester and one of our students created a bit of a stir when he came sporting his Google Glass. Go figure…, there are only 10,000 in the world and he landed one. Several e-mails from teachers were flying back and forth asking if we needed a new policy for Google Glass. Obviously, people are worried about privacy issues and wondering if he is secretly videotaping or photographing them.

Graded Student Sporting Google Glass

Turn the clock back three years ago when our leadership team was discussing whether or not to allow cell phones in the classroom. After months of discussion we came up with the following:

Cellular phones may be used as educational tools with the permission of a classroom teacher. Otherwise, the use of cellular phones on campus is prohibited except for in the student center, cafeteria and hallways during breaks. Unauthorized use of cellular phones will result in the confiscation of the phone and the phone will be delivered to the Assistant Principal.

By the time we went 1 to 1 we realized that a cell phone was just another mobile device for students to use (this is just one example). We’ve all become comfortable with them and they are a regular tool used in our classrooms. So now all of a sudden we’re faced with an alien object that we’re not sure how to handle. We have to take a step back and assess the situation.

Cellular phones may be used as educational tools with the permission of a classroom teacher. Otherwise, the use of cellular phones on campus is prohibited except for in the student center, cafeteria and hallways during breaks. Unauthorized use of cellular phones will result in the confiscation of the phone and the phone will be delivered to the Assistant Principal.

Is it sufficient to delete “Cellular phones”and substitute it with “Mobile and Wearable Devices”? Hopefully mobile device implants are far off in the future.

A quick look at our LARK (Legal, Appropriate, Responsible and Kind) guidelines seems to show that we have policy in place to handle this new toy.

Legal

  • Get permission to record and publish images or video of others.

Appropriate

  • Access media that is focused on learning and is fitting for the academic environment.

Responsible

  • Use cell phones for educational purposes when requested by teachers.

Our director of technology was commenting that he imagined a scenario in the future where students and teachers will be using them with their prescription glasses.. Let’s face it, it won’t be long before prescription lenses are inserted into the frame.

So we have decided to engage the perpetrator in a discussion over how we should deal with this new tool. He is beginning to develop ideas for how they can be used in education. He did say that that they should not be allowed during tests and quizzes. In terms of our current policy, he thinks that they will work but that we will need to change the language. By the way, he’s sharing his feedback on Google Glass with users from around the world and knows that he has created a bit of a commotion at school. Just as we had students participate in our discussions around cellphones, we will include them in these new discussions. We look forward to dealing with this situation in a positive way to that our entire community can learn from it.

What are your schools doing to prepare for this new device?

If you’re interested in learning more about Silvia Tolisano‘s (our Middle School Academic Technology Coordinator) experience with Google Glass she  wrote an excellent piece entitled, First Experiences with Google Glass at School. I highly recommend it.

Jumping Right into Design Thinking – Part 1

Jumping in Pool

I have always been someone who likes using defined processes groups. Probably the most useful workshop that I ever attended was David Langford’s Quality Learning seminar. I have used his tools for problem solving as an individually and with groups for years. For several years now I have been wanting to learn more about design thinking because the concept seems sensible and interesting. Instead of solving problems this focuses on finding solutions by learning about the  stakeholders. So, instead of taking the time to attend a workshop I decided to jump right in and learn by doing. Thankfully, IDEO has a free online toolkit to guide me through the process and my colleagues are game for trying something new.

For several years we have struggled with our annual week long trips in the high school. For one week in September the entire high school travels to four different locations in Brazil. The groups are organized by grade level and there have been two objectives.

To gain a deeper appreciation and knowledge of Brazil – The trips provide students with real life experiences within Brazil. Trips may focus on…

  • exploring various cultural aspects of the respective community.
  • environmental issues in the community.
  • sustainable development and the economic environment in the community.
  • fun activities that are representative of the community.

To develop relationships within our community – The trips are an excellent opportunity for students and teachers to start the year off by learning about each other in a non-classroom setting. In doing so, students and teachers can build an appreciation for others and a respect for differences. Relationship building may occur in the following ways: 

  • team building activities
  • discussion groups focused on objective #1
  • group projects
  • informal dialogue throughout the trip

We have also been working, with mixed success, to link the trips to course curricula. Each year we get mixed reviews from students and teachers and we feel like we just haven’t gotten them right yet. The factor that tipped the scale is that for two years in a row we had a large number of seniors decide to not travel with their classmates. So, this seemed like the perfect opportunity to give the design thinking process a chance.

After reviewing the trips from this year and that past we have defined our challenge, set a timeline and gathered the information that we have on hand.

“Redesign the experiences to make them indispensable and unforgettable so that the mission and core values come to to life.”

We’re now in the research phase where we define exactly what we need to learn from our students and teachers and look for inspiration from various sources. With that information we’ll work in teams to develop prototypes of trips for review. There is still much work to do but we all seem to feel that there are plenty of possibilities for making the trips “indispensable and unforgettable”

I’d love to hear ideas and suggestions from design thinking experts that are out there. We’re definitely going to need support throughout the process.

This photo, “8579 S jumps into pool” By WoofBC under CC BY-NC-SA 2.0, modified slightly from original