Tag math

Friday Link Fest…*

Friday Link Fest | rethinked.org | Photo by Elsa Fridman


Welcome to the ‘Sharing Economy’ ~ “It used to be that corporations and brands had all the trust,” added Chesky, but now a total stranger, “can be trusted like a company and provide the services of a company. And once you unlock that idea, it is so much bigger than homes. … There is a whole generation of people that don’t want everything mass produced. They want things that are unique and personal.” via New York Times, published July 20, 2013.

The Mistake Smart People Make: Being In Motion vs. Taking Action~ Motion is when you’re busy doing something, but that task will never produce an outcome by itself. Action, on the other hand, is the type of behavior that will get you a result. via James Clear on Medium, published June 27, 2013.

Innovation Isn’t an Idea Problem ~In most organizations, innovation isn’t hampered by a lack of ideas, but rather a lack of noticing the good ideas already there. It’s not an idea problem; it’s a recognition problem. via Harvard Business Review, published July 23, 2013.

Encouraging Students to Imagine the Impossible ~ Dreams inspire learning, according to the founders of The Future Project, a venture for social entrepreneurship in high schools. via The Atlantic, published July 23, 2013.

Compassionate Mind, Healthy Body ~ Compassion research is at a tipping point: Overwhelming evidence suggests compassion is good for our health and good for the world. via Greater Good Science Center, published July 24, 2013.

Test the Rules Of Creativity ~ CEOs across the country are calling for more creativity from their workforces. Andrew Benedict-Nelson, of Insight Labs, talked with Matt Wallaert, a behavioral psychologist who has founded and advised several startups, to unpack what they really mean. via Insight Labs, published July 22, 2013.

Meet the 17-Year-Old Who Created A Brain-Powered Prosthetic Arm ~ “The educational system has boundaries, and you don’t have to work within the boundaries of systems. You can do things to achieve your own outcomes–that’s what I’m doing.” via FastCo.Design, published July 23, 2013.

How Diagrams Solve Problems ~ 3 common problems that trip up your creative process & how diagrams will help you solve them. Via Joe Ringenberg on Medium, published July 22, 2013.

Encouraging Connected Learning Means It’s Okay for Students to Opt-out ~ Facilitating Choice: Value & relevance around a learning approach must be something the child determines on their own. via Connected Learning Research Network, published July 23, 2013.


A Tea Party That Encourages Random Acts Of Kindness ~ Clare Twomey sets up tea for 1,550–and an artful way to promote good deeds–at London’s Foundling Museum.via FastCoDesign, published July 18, 2013.

Free Comic Books Turns Kids Onto Physics: Start With the Adventures of Nikola Tesla ~ PhysicsCentral, a web site run by The American Physical Society (an organization representing 48,000 physicists), has created a series of comic books designed to get kids excited about physics. via Open Culture, published July 21, 2013.

20 Places to Educate Yourself Online for Free ~ via LifeHack, published July 22, 2013.

City in Sky / Mu Wei + Sam Cho + Yu Hui ~ 39 kids & their families explore the boundaries of architecture. Raises some brilliant questions…~ via ArchDaily, published July 17, 2013.

The Weirdest Typewriters You’ve Ever Seen ~ from the Mailing-Hansen Writing Ball, 1865 (Nietzsche’s favorite) to the Chromatic Typewriter, 2010, which paints with oils, these typewriters are sure to delight. via Flavorwire, published July 25, 2013.

Seven New Courses Coming from the School of Open: Sign Up Today ~The School of Open is offering its second round of free, facilitated, online courses. Through August 4, you can sign up for 7 courses on open science, collaborative workshop design, open educational resources, copyright for educators, Wikipedia, CC licenses, and more. Courses will start after the first week of August and run for 3 to 7 weeks, depending on the course topic and organizer.  via Open Culture, published July 24, 2013.


How do you build a culture of innovation? ~ How does a successful company maintain a climate in which new ideas and risk-taking are encouraged? Tim Brown, CEO and president of the design consultancy IDEO, describes how he thinks about innovation and why empathy is an important part of the equation. via Yale Insights, published May 2013.

How An “Impossible” Aviation Challenge Led To An Innovation Breakthrough ~ { YES…* } Atlas won the Sikorsky prize by zeroing in on the right box to think inside–and then rigorously, intensely, and persistently analyzing it. “Achieving the so-called ‘impossible,'” he says, “is a matter of removing unnecessary constraints, and understanding what’s in the box.” via FastCo.Design, published July 23, 2013.

A Look At The Devastating Effects Of Food Waste ~ Data visualization video “Food Waste, A Story Of Excess” presents a quick look at food consumption in America. via PSFK, published July 24, 2013.

How to Teach Math as a Social Activity ~ A master teacher in Anchorage, Alaska, establishes a cooperative-learning environment in an upper-elementary classroom. via Edutopia, published February 8, 2013.

Shouldn’t Personalized Learning Be Personal? ~ “It’s not about actually finding the information anymore. So, I think the model we’re trying to develop with connected learning is to say, how can we use the capacity of these network resources, these social connections, to bring people together that want to learn together.” via Teach Thought, published July 26, 2013.

Friday Link Fest…*

photo 5


Gearing Up for a Summer of Making, Connecting and Learning by Doing  ~ Suzie Boss, on project-based learning ideas for summer. via New York Times, published May 15, 2013.

Daniel Dennett’s seven tools for thinking ~Cognitive scientist and philosopher Daniel Dennett is one of America’s foremost thinkers. In this extract from his new book, he reveals some of the lessons life has taught him. via The Guardian, published May 18, 2013

{ Pattern Thinkers } How an Entirely New, Autistic Way of Thinking Powers Silicon Valley ~ Three kinds of minds — visual, verbal, pattern — naturally complement one another. Yet society puts them together without anybody thinking about it. via Wired, published May 23, 2013.

Stanford Builds Strong Innovators with New “Design Thinking” Curriculum ~ via Product Lifecycle Stories, published May 8, 2013

16 Learning Strategies To Promote Grit And Delayed Gratification In Students  ~ In psychology, intelligence is not the primary predictor of success. It is the ability to persevere in hardship, persist and learn after failure, and have a resilient spirit in the face of obstacles. Intelligence is a gift that can be developed and nurtured, but continuing on a difficult path when the gratification is far away? That is an invaluable skill for all of us to learn. via TeachThought, published May 3, 2013

Technology for Learning vs.Technology for Education ~ Learn about Sylvia’s Super Awesome Maker Show and what researchers Rich Halverson and Benjamin Shapiro at the University of Wisconsin-Madison call “technologies for learners” as opposed to “technologies for education.” The latter include student information management systems, adaptive learning software, and computerized assessment tools. Technologies for learners, however, are designed to support the specific needs, goals, and learning styles of curious individuals—like Sylvia. via Remake Learning, published May 15, 2013.

How to Expel Hurtful Stereotypes from Classrooms across the Country ~ The fear of confirming derogatory stereotypes can hinder academic performance. Researchers are scaling up relevant interventions to statewide programs.via Scientific American, published May 22, 2013.

Collaborative Platforms Empower Citizens to Shape Their Communities ~ Design Thinking comes to the neighborhood: Participatory online platforms and visual tools help gauge and meet the actual needs of the population. via PSFK.

Why getting new things makes us feel so good: Novelty and the brain ~how intricately novelty seems to be associated with learning, which means we can use this knowledge to our advantage for learning new things and improving our memory. via Buffer, published May 16, 2013.


BMW Guggenheim Lab Maps the Trends Shaping Our Cities ~The BMW Guggenheim Lab, a traveling think tank/community discussion space, released their latest list of urban trends, gleaned from almost six months’ worth of workshops held in Mumbai, Berlin, and New York City. via Wired Design, published May 22, 2013.

Harvard Scientist Creates Incredible Microscopic Crystal Flowers In A Beaker ~ via Beautiful Decay, published May 22, 2013.

See The Works, And Stories, Of Renoir And Van Gogh As Comics ~ The Museum of Art of São Paulo brings the dramatic stories behind famous art works to life. via comics via FastCo.Create, published May 16, 2013.

Ernest Hemingway Creates a Reading List for a Young Writer, 1934  ~ via Open Culture, published May 23, 2013.

Boring Math Equations Turned Into Whimsical Animal Illustrations ~ In her illustrated series ‘Drawing Mathematics’, Zurich-based illustrator Kasia Jackowska turns boring math equations and concepts into adorable, whimsical animal illustrations. via Design Taxi, published May 20, 2013

{ Lucien Hervé: Le Corbusier in India } A Stunning Survey Of Pics By Le Corbusier’s Trusted Photographer ~ via FastCo.Design, published May 16, 2013.


Fostering Growth Mindsets ~ Why fostering a growth mindset can give your children the drive to succeed. Part of a discussion series between Christine Carter and Kelly Corrigan. via Greater Good Science Center, published October 2007.

How Coca-Cola Used Vending Machines To Try And Unite The People Of India And Pakistan~ Rethinking…* the vending machine as medium for exchange, expressing empathy & promoting peace: Specially designed Small World Machines placed in both countries in March served as live communications portals. via FastCo.Create, published May 20, 2013.

{ Limor Fried’s Circuit Playground } A Web Series For Kids Aims To Be The “Elmo for Engineering ~ Engineer and Adafruit Industries founder Limor Fried saw an unmet need in the educational-video space. “We looked around and didn’t see an ‘Elmo for engineering’ or a kid’s show that celebrated science and engineering,” she tells Co.Design. “Every kid seems to have a cell phone or a tablet, but they know more about SpongeBob than how a LED works on the device or TV they’re watching, and we wanted to change that.” via FastCo.Design, published May 22, 2013.

Shannon Rankin’s Gorgeous Collages Made Entirely Of Old Maps  ~ “Maps are subjective. Every map is an interpretation. We bring our own personal meaning when we view them. They can reference the physical and psychological simultaneously. They elicit our memories and become a metaphor of life and personal cosmologies.” via FastCo.Design, published May 20, 2013.

Why Our Brains Get Addicted to the Internet (and How to Avoid It) ~  via Lifehacker, published May 10, 2013.

Teaching Youngsters About Medical Science With A Game–And Killer Muenster ~ Genentech teams with Ideo to create Ralph’s Killer Muenster, which makes science weird & fun enough for kids to care. via FastCo.Create, published May 21, 2013.

Friday Link Fest…*

Friday Link Fest...* | rethinked.org



The Importance of Quick & Dirty ~ Jason Fried, co-founder and president of 37signals, on why ‘The ability to run with scissors is a blessing, not a curse.’ via Inc.com, published April 30, 2013.

5 Ways To Innovate By Cross-Pollinating Ideas ~ via FastCo.Design, published May 10, 2013.

Many Parents Push Academics Over Play Which May Harm Kids’ Health  ~ On the critical importance of play…* in life and learning. via Inhabitots, published January 1, 2012.

Want Kids to Become Scientists? Don’t Arrest Them For Experimenting ~ #ScienceIsNotACrime . via GOOD, published May 3, 2013.

Profiling Serial Creators ~  Scott Barry Kaufman on why it’s essential that we continually question and attempt to improve the methods by which we identify, mentor, and cultivate those who are ready and capable of becoming our next generation of innovators. Tragically, we are failing these students, often unknowingly letting them fall between the cracks in an education system that rewards characteristics that dampen creativity, such as conformity, standardization, and efficiency. via The Creativity Post, published May 8, 2013.

Well Designed Schools Improve Learning by 25 Percent Says New Study ~ via Dezeen, published January 2, 2013.

John Dewey’s Vision of Learning as Freedom ~ “The inclination to learn from life itself and to make the conditions of life such that all will learn in the process of living is the finest product of schooling.” via the New York Times, published September 5, 2012

5 Innovation Lessons You Can Learn On The Dance Floor ~ “Through movement we can inspire creativity, deep listening, & cross-generational learning” via Fast Company, published May 3, 2013.


Things Come (Very, Very) Apart ~ Toronto-based commercial photographer Todd McLellan disassembled 50 design classics for his book: Things Come Apart: A Teardown Manual for Modern Living. McLellan’s photographs seek to challenge our disposable culture by making transparent all the things that we regularly throw away. “I hope people think a little bit more about the things they use. Not that people should have feelings for objects, but instead think about ‘reuse and recycle,’ not just ‘use and discard.’ ” via NPR, published May 1, 2013.

10 Playgrounds That Would Put Your Childhood Hangout to Shame ~ From a colorful crocheted alligator, to a surreal, warping jungle gym, to a playground made out of recycled iron drums, here are 10 truly innovative and unusual playgrounds. via Atlantic Cities, published May 7, 2013.

Explaining Complicated Philosophies With Gorgeously Simple Postcards ~ Philographics by Genís Carreras:  Making it easier for us to talk philosophy by removing words & replacing them with pictures ~ via WIRED Design, published May 6, 2013.

Tour Google Moon and Google Mars with Bill Nye the Science Guy ~ via Lost At E Minor, published May 9, 2013.



The History of Typography Told in Five Animated Minutes ~ via Open Culture, published May 6, 2013.

The Best of Humanity Caught on Russian Dash Cams ~ via Colossal, published May 3, 2013.

Can A New Symbol Make You Better At Math? ~ Math popularizer Rob Eastaway’s ‘Zequals’ sign is a reaction against the learned helplessness that most of us have accepted in our relationship with numbers. via FastCo.Design, published May 6, 2013.

Graffiti Artist Uses Rotten Fruit and Vegetables As Paint ~ Tropical Hungry by Narcelio Grud. Grud scavenged for produce in the streets and created sustainable, organic murals with it. ~ via PSFK, published May 8, 2013.

High schoolers design robotic locker for disabled classmate ~ via GOOD, published May 9, 2013.

Friday Link Fest…*


Make and mend: Designers are finding ways to counter today’s throwaway culture ~ Rethinking…* the ways we make things, shifting the discourse from incessant production to intelligent adaptation. via Financial Times, published March 29, 2013

Engineering Serendipity ~ via New York Times, published April 5, 2013.

Great Scientist ≠ Good at Math ~Discoveries emerge from ideas, not number-crunching ~ via Wall Street Journal, published April 5, 2013.

How to Create Your Reason ~ “We need a reason, because our reasons are what liberate us from lives that feel senseless.” via Harvard Business Review, published April 9, 2013.

The link between art and innovation ~ via Politico, published April 7, 2013.

Musical Training & Language Skills Enhance One Another ~ via New York Times, published April 8, 2013.

How IDEO brings design to corporate America ~ via CNN, published April 11, 2013.


Everything You Know by Wendy MacNaughton ~ via Explore, published April 9, 2013.

The Grinders Vs. The Dreamers. Who Wins? ~  Lovely Infographic rethinking…* grind by Joey Roth. via FastCo.Design, published April 8, 2013.

Street Artist Roadsworth Transforms the Streets of Montreal into a Visual Playground ~ via Colossal, published April 10, 2013.

Sick of the boring commute? Straphanger photobombs fellow commuters ~ via New York Daily News, published April 5, 2013.

Every Day a Different Dish: Klari Reis’ Petri Paintings ~ The Daily Dish by Klari Reis: a new petri dish painting every day. via Smithsonian Magazine, published April 5, 2013.

Artist Turns Abandoned Cars into Public Art Installations ~ “Ocupe Carrinho” (Occupy the Car) by Felipe Carrelli. via Junkculture, published April 11, 2013.



Dan Pallotta: The way we think about charity is dead wrong ~ via TED, published March 2013.

Circuit Playground Sparks Electronics Education ~ Introducing the sippy-cup set to soldering irons & the world of wires ~ via Wired, published April 4, 2013.

60 Second Adventures in Astronomy Explains the Big Bang, Relativity & More with Fun Animation ~ via Open Culture, published April 8, 2013.


Spring Demo: A Night of Ideas at EdLab

Last Thursday I attended Teachers College’s Ed Lab Spring Demo Night. It was high energy with a focused discussion and well thought out ideas.  One of the presenters demoed TuVa labs, an online platform to support students learning through their interests. They posed the questions: How do we get kids to learn from what they are already interested in? Is it the Miami Heat’s winning streak? Italian food? From here, students would pick up a subject and learn about it through something that really fascinates them. TuVa Labs focuses on the subject of math, since, as the presenter stated, math is the subject our nation struggles with the most.

The concept of connecting learning with student’s interests in a rigorous way seems to be a winning start, but of course the challenge is keeping the program tailored and rigorous for each student. Another group that presented was called Chalkable. Chalkable selects the finest technology apps out there and brings them on to one hub where students can pick and choose programs and teachers can track student results.


The follow-up questions from the audience were quite insightful for TuVa Labs. One person asked about how reflection was incorporated into the online lessons to helps students be metacognitive about their learning. It’s not. Yet. But the question does represent a major challenge in online learning.


The other question was about how the program helps students who get stuck. It doesn’t. Which isn’t a bad thing necessarily. It means there is a firm place for the teacher in the room.


Teacherly was the last group to present. Teacherly also addresses math learning, but it focuses on students who struggle. It supports differentiated learning through a video game. It mimics, at the lower age level, manipulatives needed for counting. The program draws on multiple ways a child might add and subtract–tallies, number line, coins–so that a child can use whatever way he or she is most comfortable counting to learn. Providing multiple options for counting strategies is very innovative and is something I found useful when teaching Kindergarten and 1st Grade.

These three programs are still in the early stages. Teacherly aims to tailor their programs to students learning through their own interests and passions and create environments that feel intuitive to the student.


I look forward to more demo nights at Teachers College’s Ed Lab and to exploring the landscape of new education startups. It’s good to support and help these groups prototype their ideas into final products.

Friday Link Fest…*


Relax! You’ll Be More Productive ~ via The New York Times, published February 9, 2013.

In praise of failure: The key ingredient to children’s success, experts say, is not success ~ On grit as a key component of success. via National Post, published February 2, 2013.

Social Emotional Learning Core Competencies ~ Rethinking…* the definition of academic success. via Q.E.D. Foundation, published February 11, 2013.

How to Save Science: Education, the Gender Gap, and the Next Generation of Creative Thinkers ~ via Brainpickings, published February 12, 2013

Arbonauts: of trees, data, and teens ~ The challenges & rewards of rapid prototyping as pedagogy. via Harvard’s MetaLab, published February 6, 2013.

Lighter, Quicker, Cheaper: A Low-Cost, High-Impact Approach ~ Rethinking…* the way that we do development. via Project for Public Spaces.

How Malawi is improving a terrible maternal mortality rate through good design ~ via TED News, published January 30, 2013

Tina Seelig On Unleashing Your Creative Potential ~ via 99u.

Why Even Radiologists Can Miss A Gorilla Hiding In Plain Sight ~ Rethinking…* the instructions we give to professionals to account for the fact that what we’re thinking about — what we’re focused on — filters the world around us so aggressively that it literally shapes what we see. via NPR, published February 11, 2013


Artist Can Only Draw in his Sleep ~ via PSFK, published February 13, 2013.

Landscape artworks at Hogpen Hill Farms open house ~ photographs by Fredrick K.Orkin of Edward Tufte’s Hogpen Hill Farms LLC, his 242-acre tree and sculpture farm in northwest Connecticut. via EdwardTufte.com.

Four Amazing Mini Libraries That Will Inspire You to Read ~ More accessible to a larger population than a classic library, the Pop-Up Library preserves the intimacy and experience of the book. via GOOD, published February 13, 2013.

In Photo Series, When Math Meets Art ~ Nikki Graziano’s photo series, ‘Found Functions’, defies the commonly-thought notion of the boring and geeky subject. via Design Taxi, published February 9, 2013.

A Floating School That Won’t Flood ~ On cultivating a new type of urbanism on water in African cities. via FastCo.Exist, published February 8, 2013.

Pixar Artist Designs New Facebook Emoticons ~ Matt Jones is creating a set of digital images that reflect more complex or subtle emotions. via PSFK, published February 11, 2013.


David Kelley on Making ~ via General Assembly, published February 2012.

The Scared Is Scared: A Child’s Wisdom for Starting New Chapters (Creative or Otherwise) in Life ~ Delightful meditation on embracing uncertainty. via Openculture, published February 11, 2013

Michael Jordan on Failure ~ via Nike, published August 25, 2006.

Color Me____ by Andy J. Miller & Andrew Neyer ~ via joustwebdesign, published October 23, 2012. (h/t Swissmiss.)

Tiny Sugar-Covered Bandaid Could Replace Needles For Vaccinations ~ Rethinking…* vaccines ~Scientists at King’s College London have developed a new way to administer vaccines, using a pain-free microneedle array. via PSFK, published February 12, 2013.


25 Mini-Adventures in the Library ~ via Project for Public Spaces, published 

Want to Start a Makerspace at School? Tips to Get Started ~ via MindShiftKQED, published February 12, 2013

rethinkED Math Workshop: Topics in Teaching Math

On Friday January 11th a group of math teachers and administrators stayed after school, the first week back of school no less, to participate in a math workshop.  The workshop was led and organized by the rethinkED team with a guest presentation from Jed Silverstein, upper school English teacher, a session led by the tech integration team and a sessions designed by the rethinkED team.

The workshops came out of interviews with a handful of the math faculty at Riverdale. Through in-depth interviews, the rethinkED team captured a few themes they then developed drawing on some design thinking techniques. The team shared a list of proposed topics with the math faculty and administrators asking for feedback and to rank the workshops. The top-ranked workshops were chosen based on the math teachers’ feedback.

With the dusk falling, teachers sustained themselves with cheese and wine as they listened to TED talks, participated in debates, and designed prototypes of ideas. Cross-grade and cross-subject collaboration was encouraged.



The first session was called the Creating the You-Can-Do-It Problem.The workshop involved an introductory TED talk, a discovery phase, and ideation and prototype phases with time for reflection. Out of the conversations, teachers brought up the question of transferability of a real life problems into the classroom. At times a real life problem may be difficult to talk about in terms of the specific math terms being developed. On the plus side, real life problems were seen as being high on the the relatability scale–something that greatly increases student engagement. Another issue raised was the engagement and fun of real world problems as being antithetical to the pressure of the college tests and preparation for next year.

The second session involved two workshops, one on Guided Student Teaching, with an intro from Jed Silverstein on some of the work he has done in his humanities classes. Jed often has students teach portions of his humanities classes so that they can learn and ask questions about the material as a teacher might. Well aware of the difference of content between humanities and math, Jed sought to find similarities across disciplines. The other workshop occurring simultaneously was led by the Tech Integration Team, who offered a tour through iPad apps geared towards middle and upper school math courses. A highlight was the ipad version of wolfram alpha which allowed students and teachers to see various different ways of solving a single problem.

The workshop ended on a high note, with buzzing energy past 6 pm on a Friday and plans to implement ideas and keep the conversation going. The rethinkED team will follow-up individually with math teachers, both through interviews and observations. There is talk of organizing a similar workshop in the spring. Stay tuned!

Interleaving and Grit

Screen Shot 2012-12-28 at 11.07.54 AMI’m intrigued by the idea of interleaving. I know, I know, it looks like a typo. I must have meant “interweaving”… When I first read of interleaving, I was sure that the authors had typed it wrong. It’s a weird word, but a cool, simple concept to incorporate into your teaching.

So what is interleaving? I tried for a while to come up with my own concise definition of it, but I couldn’t do any better than Rohrer and Pashler (2010) did, so I’ll leave it to them:

If multiple kinds of skills must be learned, the opportunities to
practice each skill may be ordered in two very different ways:
blocked by type (e.g., aaabbbccc) or interleaved (e.g., abcbcacab).
Until recently, experimental comparisons of blocked and inter-
leaved practice had been limited to studies of motor skill learn-
ing, where it has been found that interleaving increases learning
(Carson & Wiegand, 1979; Hall, Domingues, & Cavazos, 1994;
Landin, Hebert, & Fairweather, 1993; Shea & Morgan, 1979).

Rohrer and Pashler expand on their mention of “motor skill learning” and discuss how much better it is for a batter to practice against different pitches in different orders, instead of doing a block of fastballs, a block of curveballs, etc. Presumably, interleaving is better for the pitcher as well. Interleaving keeps athletes on their toes and thereby sharpens their skills.

But how could interleaving help learning in the classroom? One easy way to incorporate interleaving is to alter the structure of math and language homework. A lot of practice assignments in math and language rely on blocked drills (e.g., a long series of Spanish words to be translated into English, then a long series of the opposite), but students might benefit from having to face different types of problems as they go (e.g., one English–>Spanish translation, followed by a Spanish–>English one).

Remember homework assignments from your math book when you were a kid? In my math books, I had to do a few problems from section A, a few problems from section B, and a few problems from section C. In each section, the problems were blocked–they were basically the same, addressing the same skill, just with different numbers thrown in. At times I could more or less go on autopilot and perform the same procedure without thinking too hard. When I finished one section and went on to the next, I had to readjust my procedure to the skills being tested in that section. And so on.

If I were interleaving, however, I might have done a problem from section A, followed by one from section B, followed by one from C, then back to B, then to C, then to A. Or something like that, which would keep me on my cognitive toes.

So let’s say I was designing a grammar assignment for my students. I could have them circle the direct objects in a series of five sentences, then move on to circling the subjects in a series of five different sentences. Maybe a third section of five sentences would require them to circle all the indirect objects.

That would be the blocking way of doing things, and that is exactly what I used to do (the grammar book I designed can bear witness to my unthinking tendency to work in blocks). But instead I might do this:

1. Identify the direct object:

The team won the game because of great coaching.

2. Identify the subject:

Somewhere in the forest lurks a big, bad wolf.

3. Identify the indirect object:

The old man told the children a story.

4. Identify the subject:

What do you think?

Studies suggest that interleaving the exercises this way (and the different skills the exercises test) increases student learning. But it isn’t some silver bullet that helps students learn things more easily.

Rohrer and Pashler cite Rohrer and Taylor (2007), a study in which college students were given four different types of math problems to solve. One group did blocks of each type of problem; another group faced the problems in an interleaved format. In the short term, the block-format students outperformed the interleaving students (mean scores of 89% and 60%, respectively). Yikes! What good, then, is interleaving?

Well, on a test given one week later, the interleavers’ average rose a bit and the blocking students’ average plummeted–63% to 20%! It looks as though interleaving helps you really learn something, even if if it makes things harder in the short term.

As you can see from this post’s title, I see a connection between these data and that word grit we hear a lot these days. Interleaving problems makes assignments harder–maybe even a bit more annoying–in the short term, for the sake of a larger payoff and deeper learning in the long term. Would our students see the value in that? Do our students understand that a lower initial score isn’t something to be afraid of, especially if it means they learn it better?

I think a lot of us wonder how we can really encourage grit into our classroom, and I doubt many of us think we can make our homework assignments seriously grit-fostering experiences. But it seems to me that interleaving problems offers one small way to make assignments more difficult, not for difficulty’s sake, but for learning’s sake. Interleaving might send the gritty message that “I know it’s hard now, but stick with it and you’ll really learn this stuff.” It’s certainly worth a try, right?…*

Further reading:
“Everything You Thought You Knew About Learning Is Wrong” by Garth Sundem (Wired)
“The Trouble With Homework” by Annie Murphy Paul (NYT)

Rohrer, D. & Pashler, H. (2010). Recent research on human learning challenges: Conventional instructional strategies. Educational Researcher, 39, 5, 406-412.

Rohrer, D., & Taylor, K. (2007). The shuffling of mathematics practice problems boosts learning. Instructional Science, 35, 481–498.

Re-Imagine Math

The rethinkED team has been rethinking the way we do math and in some ways it means we’re rethinking how we teach, well, everything. We have in no way been doing this alone. We have been exhaustively working with the math faculty at Riverdale Country School to reap the wisdom of how they face the quintessential disengaged frustrated math student and turn the student’s math experience around..

Through interviews with math teachers and research, the rethinkED team has been uncovering the challenges and set backs of learning and teaching math in schools. We identified many of the hopes and dreams for what math class could look like for teachers.

Next we tackled the research out there on learning math that could help pave the way for a better future in mathematics instruction. In our reading through articles we found questions about whether we should teach algebra at all. And we found vociferous yeses that we should.

We watched inspired math teachers and thinkers talk. Math teacher and blogger Dan Meyer opens his Ted talk saying,“I teach high school math. I sell a product to a market that doesn’t want it, but is forced by law to buy it.” He goes on to expound how students need to learn to build the math problems and that math learning needs to be based on intuition. In essence, the students need to be building the math models in order to use and apply them. He ends his talk saying, “We need more patient problem solvers.”

Similarly, Conrad Wolfram, brother of Steve Wolfram of Wolfram Alpha, in his ted talk speaks passionately about the need to use computers to teach math. He bemoans the fact that all of math education is around simply learning to calculate instead of allowing computers to do the calculations and having students think more creatively. He said students need to learn to ask the right questions, use real world problems, create math problems and see if they work back into the real world. “Math has been liberated from calculating” Conrad says, just the education world doesn’t realize it. What we want, he says, are “people who can feel math intuitively.” Through his presentation he shows how this can be done and why he thinks this must be done.

How do we help students build patience, reflective thinking, a metacognitive sense of their own learning? These questions tie in with some of our other projects as well.

Coming up we are working on organizing a one day workshop for the math faculty at RCS.  Stay tuned for more!

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