Reinventing Math

Most students when asked what they think their role is in math classrooms say: it is to answer correctly. They don’t think they are in math classrooms to appreciate the beauty of mathematics, to approach the rich set of connections that make up the subject, or even to learn about the applicability of the subject. They think they are in the math classroom to perform. – Jo Boaler, What’s Math Got to Do With It?

At our Learning Lunches this month, teachers and administrators at the Willows began our time together pondering two questions:

Why do so many students loathe math?

Why do many teachers feel uncomfortable teaching math?

The initial discussion that followed focused on a few recurrent themes:

  • Math is different from other more open-ended subjects – there is just one correct answer, and you’re either right or you’re wrong
  • When students struggle with math problems, teachers feel they only have a limited amount of strategies to help students get to the correct answer
  • Teachers feel less comfortable with teaching math in different ways than they learned it as students

One teacher even spoke about math as being its own language, separate from the usual language we use to engage with language arts, history or even science.

All of this set the stage for us to watch a provocative TED talk from renowned physicist, mathematician and technologist Conrad Wolfram, who will be one the keynote speakers at the upcoming Reinventing Mathematics Education Symposium being held here at the Willows on January 4th.wolfram ted

In a recent Financial Times article, “Stop teaching kids to add up – maths is more important,” he states:

At its core, maths is a problem-solving process. You specify a real-world problem, develop an abstract representation of it, calculate an answer for the abstraction and then translate back into the real-world language you started with. Before computers, almost all human energy was focused on the third stage: calculating. Now it is usually focused on the other steps instead.

Throughout the video we watched, Wolfram essentially sidesteps much of the traditional debate about how to teach mathematics, in favor of a discussion about why we teach math – and, more crucially, what math is actually taught in schools.

Wolfram’s idea for reinventing math education: use computers. Not just for calculation, but also to build conceptual understanding beyond mere calculation. He maintains that the primary way that people understand processes and procedures that drive most of our modern world is through programming; a great way to check if someone understands math, he claims, is have them write a program to do it!

Implications

Looking at our classrooms at the Willows, we can see some applications of Wolfram’s ideas, mainly in the programming that students have been doing at our school for many years now. Even our youngest students begin wrestling early on with the basics of programming as they work with Bee Bots, working later with more formal programming in Turtle Art, Scratch and Microworlds.

beebots

Beyond providing opportunities for programming (year round, not just for the Hour of Code), Willows teachers have also begun to take steps this year to reinvent math in other ways. Inspired by our school-wide theme of action, teachers in the P.E. department have started to incorporate the concepts of estimation and averages into the weekly activities happening in the gym. Utilizing pedometers for precise data collection, K-5 students were asked to estimate and then discover how many steps it took to complete a lap around the gym. Real-world results enabled rich discussions, as students saw that different student factors (pace, stride, height) influenced the findings. Further conceptual understanding of variance was explored as they worked to estimate and find the average number of steps per grade level.pe data

Further data collection and analysis has taken place in Middle School classrooms, centered around the question: What does a typical middle school student do for all four of his/her P.E. physical fitness tests?  Students estimated mean, median, mode and range for the tests, used Excel to work with the data collected by the P.E. teachers, and created graphs to make conclusions about the data. Best of all, student engagement in real-world math in action was clearly evident throughout both of these projects.

Next Steps

With our Math Symposium right around the corner, mathematics is on everyone’s mind at the Willows. Look for future posts on the subject after the Symposium in January!

Reinventing_Math_Flyer

Unplug and Just Talk!

Technology has changed our world and our lives. The benefits are endless. It even assists with revolutions and, of course, in any crisis.  Just witness the recent terrorist attacks in Paris where Parisians launched the hashtag on Twitter, #PorteOuvert (DoorOpen) to offer shelter to those in need, who could simply follow the tweets on their cell phones to find refuge. Smart phones, laptops, iPads, all these devices and the always present, turned-on, mobile connectivity unite us and isolate us presenting social challenges–especially for our younger children, who are growing up with the ever-present, ever-tempting cellphone connection.

Informate, a mobile measurement firm, in March 2015 reported that during January 2015, Americans spent 4.9 hours per day on their smartphones and sent an average of 32 texts per day. Teens are thought to spend more than the average time. The 2015 Pew Research Center Study said that, “89 percent of cellphone owners said they had used their phones during the last social gathering they attended.”

In a recent New York Times article entitled Stop Googling, Let’s Talk  by Sherry Turkle, author of  Reclaiming Conversation ReclaimingConversation_3dand Alone Together, Why We Expect More from Technology and Less from Each Other, writes, “What has happened to face-to-face conversation in a world where so many people say they would rather text than talk? . . . Studies of conversation both in the laboratory and in natural settings show that when two people are talking, the mere presence of a phone on a table between them or in the periphery of their vision changes both what they talk about and the degree of connection they feel. People keep the conversation on topics where they won’t mind being interrupted. They don’t feel as invested in each other. Even a silent phone disconnects us.”

Turkle continues with the idea that this disconnection is an assault on empathy, intimacy, and deep conversations, as well as solitude.

Ann Levit, a Willows parent, asked her daughter, Joby Levit, a current eighth grade student, to read Ms. Turkle’s article and write down her reflections regarding it. Joby wrote this thoughtful essay in response:

Joby Levit
Joby Levit

          The report “Stop Googling. Let’s Talk.” written by Sherry Turkle is about how my generation of pre-teens, teenagers, and even some adults’ social skills are stifled by electronics and social media.  I wish I could disagree with that and say it’s not true, but I have to be honest with myself: this writer is 100% correct. I try to tell myself that I shouldn’t be on my phone, but now it’s just a bad habit, like biting your nails or forgetting to brush your teeth.

            In this article, Sherry Turkle talks about the technicalities, logic, and science behind the reason people use their phones while at, for instance, the dinner table. Look, I’m only thirteen, and science has never been my best subject, but the parts of this paper I was able to understand are completely true. The writer mentions that we use our phones at a table full of friends because we’re so obsessed with our mobile devices that we can’t help but check them all the time. That may be true for grown-ups and college students, which was the age group this article focused on, but I know that for me, it’s a bit different. I, personally, am a bit an awkward person. I tried to avoid admitting that, but I think my friends and family can all agree that that’s true. When there are gaps in a conversation, the easiest thing to do to avoid awkwardness is to take out my phone and show my friend(s) something funny on it to create conversation. And I know as I’m writing this that my mom will probably get mad at me when I read that fact to her, but I’m sorry, it’s true! Like Rebel Wilson said in Pitch Perfect, “I guess I’m not really living if I’m not 100% honest.” J

            All right, enough about the article. My essay, my opinion! To the people my mother might send this to, my mother, if you may not know, is the biggest phone police ever. I mean I had to write a persuasive essay to get a Snapchat. And I know she’s just looking out for me, but we can all admit she’s a bit crazy when it comes to this stuff. In the middle of sixth grade, my mom gave me the privilege of creating an Instagram account for myself. If I was on it in the morning, she got mad. If I was on it in the car, she got mad. If I was on it after school, she was totally fine with it! Just kidding, you can guess how she felt about it. After a few years with social media, having recently added Snapchat and Pinterest to my phone, I get her point. She was trying to prevent me from becoming one of the people my generation has become. It’s time to face the facts: we are addicted to our phones. You might not think it’s bad, but trust me, you’re going to grow up and then get to high school and college not knowing how to verbally/physically connect to people. My mom thinks I have it bad, but I know people who have it a lot worse.

So get ready, parents. I can’t believe I’m saying this, but try shutting off all screens at 9:00 tonight. All you really need it for is your alarm in the morning. And what is that alarm set for? Certainly not to check your Instagram feed. That loud, annoying beeping sound that wakes you up in the morning is there to get you up for school, where you can get an education you can’t learn from Facebook or Twitter. Trust me, it’s going to be hard, but I promise you, you can live and thrive without your phone. Unplug! And don’t hesitate to tell your community about it too! We can all join in to help create a better tomorrow.

Some great insights for all of us! What is the answer to all of this connectivity? BALANCE and CONVERSATION. MS_16_Retreat_HR098Balance is a word you hear often around The Willows. We are a balanced, progressive school. Tradition is balanced with innovation. Academics, the arts, athletics, and social emotional development are balanced in our educational program.

Conversation is also extremely important and valued at The Willows, and is also at the very heart of technology and collaboration. Middle SchoolQuestioning, deep critical thinking, and creative inquiry, and sharing this as a group, is accentuated in all our classrooms. Walk through our hallways and glance in any classroom and you will see that conversation is thriving and technology is integrated effectively and appropriately.

The balance of technology and personal interaction is a key to the issue of connectivity. As our eighth grade student Joby so beautifully put it: Unplug! And don’t hesitate to tell your community about it too! We can all join in to help create a better tomorrow.

The Company We Keep

Personalized learning is all the rage these days. Scan the latest headlines of major publications covering education, and you’ll inevitably come across lots of talk about classrooms where instruction is “individualized,” “student-centered,” and “customized.” So-called reformers from the ed-tech community especially favor this language, touting the latest software they’ve created to expertly deliver a curriculum to a passive learner in front of a computer or tablet.

In theory, no one should be against personalization. But if you believe, as many educators have for quite some time now, that learning almost always occurs in a social context, then some of this talk of creating an individualized curriculum for each child might give you pause. If one of our central aims in schools is to build vibrant communities devoted to learning, then we need to think about how individuals usually learn within communities.

In his landmark book, The Book of Learning and Forgetting, Frank Smith maintains that for millennia humans have learned from “the company we keep.” We are driven instinctively to seek out what he terms clubs – communities of influentialbook learning forgetting people – and as we identify with the members of the club, we begin to establish our own sense of identity:

…as we identify with other members of all the clubs to which we belong, so we learn to be like those other members. We become like the company we keep, exhibiting this identity in the way we talk, dress, and ornament ourselves, and in many other ways. The identification creates the possibility of learning. All learning pivots on who we think we are, and who we see ourselves as capable of becoming.

While there are undoubtedly times when individuals learn something on their own – for example, reading a book on a topic, perhaps to understand some new concept or to complete a task or a project – Smith insists that even in this case, one is joining the “literacy club,” joining the company of authors, participating in an exchange of ideas towards the ultimate fulfillment of one’s intended goal.

Learning within your club

So, along this line of thinking, we are constantly learning about our world, and there are a variety of clubs that we identify with that deeply influence this learning. Some clubs we are born into (i.e. the American club, the rural or urban neighborhood club,) and some that we are more naturally compelled to join (what Smith terms the “spoken language club” that all infants and toddlers join at some point.) The clubs that we choose to identify with not only influence learning, but actually create conditions for the kind of deep learning that we carry with us throughout our lives.

Looking at the clubs that our students at The Willows gravitate towards, I notice that there are, of course, certain common examples: some children identify with clubs centered around sports or games, others identify with art, music, or dance. By middle school, when the pressure to join one specific club or another seemingly intensifies, children begin signing up for clubs like Rock Band or the Robotics team.

One new, informal club that has emerged this year is our Maker Club. Since establishing our makerspaces within the school two years ago (spearheaded by our Director of Technology Amy Dugré) and beginning weekly maker classes during the school day last year, we have wrestled with how to give interested students more devoted time to work on self-directed projects. This year, we found four blocks of IMG_7519time, two lunch periods and two afterschool sessions, where students are invited to work alongside fellow makers and maker teachers, often learning new skills and developing deeper expertise with familiar tools and programs.

However, in addition to being interested in becoming a better programmer or learning how to print with (and often repair!) 3D printers, we have also noticed other worthwhile interactions amongst our Maker Club members. Kids are genuinely excited to have this time and space available, and are quite disappointed when we have to cancel Maker Club. One student’s excitement about their particular project has the real power to inspire others in the same room to try something new, leading to a scene we recently came upon, where four fifth grade boys were crowded around a Youtube video on how to use a sewing machine after seeing the pillow a sixth grade boy had recently finished assembling. IMG_7514

These observations align with some of the latest research on maker-centered learning, specifically research from a recent initiative associated with Harvard’s Project Zero. In a white paper reporting initial findings (that are being prepared for a forthcoming anthology called Makeology), the researchers found that “the most salient beliefs of maker-centered learning for young people have to do with developing a sense of self and a sense of community that empower them to engage with and shape the designed dimension of their world.” Young empowered makers, they argue, see themselves as people capable of finding and solving worthwhile problems, as individuals within a supportive community “who can muster the wherewithal to change things through making.”

Implications

 Thinking broadly about identity and association, several questions persist:

  • Are we aware of what draws us to our clubs, to the company we keep?
  • Do we belong to different kinds of clubs, representing diverse or divergent points of view?
  • Are we aware of clubs (or better yet cultures) that are different than our own?
  • Is it possible to learn much about a club you are not a member of?

            Further, given that all of us are compelled to join communities and learn alongside their members, what does this mean for us as educators? Exactly, how do these issues play out daily in classrooms?

For example, think of the students who have already decided by second or third grade that they are either deficient in reading or math (or both, or school in general); these students seek out classmates who feel the same and reinforce this desire to be a part of the “non-reader” or “math hater” club. What steps can teachers and school leaders take to deal with all-too-common phenomena like this?

Hello World!

Wisdom of The Willows provides a forum for members of our unique community to share their knowledge and reflect on a variety of topics. Certain posts will highlight innovative teaching and learning within our community; others will address broader issues on the minds of educators and parents worldwide connecting the experiences of our Willows community to broader, global conversations in education and parenting.

The Willows is a strong, collaborative community of lifelong learners. Wisdom of The Willows opens a window on the learning undertaken on our campus by not just students, but also by teachers, administrators, and parents alike. For example, here on this blog we will share details of the issues discussed by our teachers and administrators during our monthly Learning Lunches and at our Willows Academy (all-day professional development held once each trimester.) In addition, these articles will be accompanied by references and connections to research and theoretical bases supporting our school’s program.

In-depth profiles of parent and family educational events, as well as those centered on technological, creative or personal development topics, will also be featured.

The overall intent is to make the learning that takes place regularly in our community visible to all.

We look forward to posting more soon, and we invite you to expand your vision, explore the blog, get inspired, and join the conversation!