I heard that question a lot towards the end of my last school year. It was often paired with a look or a tone that asks one (or often, both) of these questions, “Aren’t you glad to be getting away from everything going on in schools today?” and “How will you keep yourself occupied?”

I could, if I chose, take the easy way out. I accomplished a lot in my 35 years as a professional educator. I taught thousands of students. I wrote dozens of curriculum documents. I collaborated with hundreds of other educators. Retirement is supposed to be a time to slow down, spend time with the family, read a book or five, travel, and enjoy life. And I do plan to do all of those.

But even though I’m done with full time teaching, I’m not done being a teacher. Not yet. I still have ideas to share and work to do, and retirement is giving me the freedom to do it. The reason why has a lot to do with the things I learned along the way since I began this journey in 1991.

My teaching career almost didn’t happen. I was a terrible first-year teacher. And I had more than one setback in my years in the classroom. But I dedicated myself to figuring out what I was doing poorly and making it better. In the process, I started noticing a few things about the system in which I was working. At first, I just wondered if I wasn’t cut out for this work, but eventually I realized that it was a misalignment between how schools were set up and what I believed instinctively about students and learning.

Here are five key things I’ve learned in the course of three and a half decades as a teacher that led me to the work I am doing now. None of these arrived fully formed. They came from repeated moments like the ones I describe here. I also don’t claim to be the first person to identify these—in fact, many others contributed over the years to my awareness and understanding. But these are the reasons I’m not ready to stop yet.

1. Learning opportunities are not equally accessible to all learners

For more than fifteen years I taught gifted students, and in that role I felt like I’d finally found the freedom to teach the way I always wanted to, using creative projects and allowing students to explore their passions. I eventually became the gifted supervisor in another district, and started to understand the cost of that freedom. I remember one conversation with a parent whose son hadn’t met the district gifted criteria. She was adamant we give him the gifted label anyway. “I don’t want my kid in class with those kids.” Though she danced around it, it became clear she did not just mean the non-gifted students, she meant the Black students who were overrepresented in those classes. Conversations like that one, again and again, made it clear that gifted education was not entirely about meeting needs. It was about deciding who got access to the best opportunities, the best resources, and the best experiences. Once I noticed that, I began seeing the same pattern across the whole education system.

2. Schools are designed for compliance, not engagement

I knew from the start of my career that I wanted to engage my students, though at the time I did not have the vocabulary to explain that or the skill to accomplish that. My very first day of teaching, I had spent hours planning a set of individual puzzles to get them thinking and working right away. I was eager to try it out, but the activity collapsed almost immediately into chaos. I struggled for weeks to figure it out. My principal could see the disorder the moment he walked into my room. Rather than helping me develop my skill at engaging learners, he misdiagnosed it as a lack of compliance. His solution was to hand me a copy of the book Assertive Discipline in which I learned that marbles in a jar and names on the chalkboard were the path to an orderly classroom. The clear message: compliance is the main precondition for learning.

3. Curriculum is built to be measured, not to be effective

For several years I worked with my district to align our curriculum to the new Common Core standards, using Webb’s Depth of Knowledge levels to evaluate the quality of student tasks. No matter how much we talked about adding depth and complexity, we kept finding our way back to things that were easy to count, easy to script for teachers, easy to reduce to exercises and worksheets. Even while striving for depth, our assessments rewarded recall, and the curriculum regressed toward mechanical and superficial processes to match. It wasn’t any single decision. It was subtle, and so ingrained that most teachers never even noticed it, because it was just how things were built. Steve Hargadon’s words a few years later crystallized this idea for me:

This struck me as a powerful articulation of an idea that had been simmering at the back of my mind for a long time. So many things in the curriculum are built entirely around what we can measure: acquisition and retrieval of facts, demonstration of discrete and isolated skills, observable behaviors. True learning is difficult—if not impossible—to measure cleanly. True assimilation and transfer of concepts can take months, years, or even decades. Some of the seeds we plant in elementary school may not sprout, let alone bear fruit, until students are long gone from the building.

4. The obstacles are structural, not personal.

I spent the last ten years of my career developing the STEM and makerspace program in my school. A district realignment in 2025 brought both significant changes to the program and an administrator who was not present during its development. I remember a meeting over the summer where we were working out some issues with the schedule for the new program. “I’m excited about this STEM program,” she said as we sat down. I was happy to hear that, since I’d had a lot of support and positive input from other administrators for several years. “This is going to be a real boost to our PSSA scores.” A knot of dread formed. I’d had similar conversations many times before. For the next hour I tried to explain that this STEM program was focusing on the technology and engineering parts of STEM. Her frame of reference, and the lens through which she saw elementary school, could only conceive of test-driven instruction. This wasn’t her failure though--it’s how the system is built. Standardized tests are for sure not the only structural obstacles in the way of student-centered learning, but they are one of the most visible.

5. Cultural relevance must be central

My entire career has been spent in schools with a diverse population, but it wasn’t until about 2016 when I first encountered the idea of cultural competence and culturally responsive pedagogy in education. For a long time I struggled with my own lack of competence and lack of awareness. It felt overwhelming to think about the lessons and plans that I had built and then figure out how to make them more relevant to the students in front of me. Through my doctoral research, I began to realize that cultural relevance isn’t an adjustment you can make to a project. It has to be one of the core ideas you start with when you’re designing an experience for learners. If it’s not in the structure, it’s not going to work well, and that actually showed up in my dissertation data. Due to a collection of constraints I had to work with, the culturally relevant treatment I designed ended up being an add-on instead of the central principle, and the results showed that not only did it not work as expected, it had a somewhat negative impact. My work now is focused on finding ways to help teachers put their students at the center of learning, including how to build experiences that are culturally relevant.

Here’s the thing, though. Even when all of these challenges are addressed, even when schools are truly and deeply student centered, the work is still hard. It always will be. It’s hard because it’s complex, because it involves diverse human beings, and because learning is not transactional. I believe learning is always happening, and that it is not a direct result of having been taught. At its best, teaching is about creating the experiences and conditions in which learning can occur.

It took me thirty-five years to see all of that. I see my work now as creating the conditions for other educators to learn this earlier so they can put it to work for schools and students. I will keep doing this work as long as I can, and keep helping teachers do it as well as possible, because it matters.

Many teachers are being asked or required to teach online while school districts, cities, and states are shutting down normal operations to slow the spread of coronavirus.

A lot of well-meaning companies and teachers are sharing gigantic lists of resources and tools and websites to do this quickly and easily. Facebook groups have launched where teachers are asking each other how to do this and sharing ideas and solutions. I’ve seen questions like, “How do I turn all of my worksheets (with a single click) into a PDF that students can fill out online?” and “How do I give a timed quiz to make sure that students aren’t looking up the answers?” and “My district told me I have until tomorrow to post ten days of lesson plans on the class website. Can anyone help?”

Few people were asking questions about why and whether we should do all of this. It was mostly about how to instantly transform a brick and mortar, face-to-face system of instruction into distance learning.

In short, in the span of one weekend, I saw the entire teaching profession trying to answer all the questions and solve all of the issues that the ed tech community has been wrestling with for at least ten years.

I think before we do anything else, we need to slow down and consider a few more basic principles. Here is my attempt. It is surely flawed, and you may not agree with all of my thoughts. I welcome your feedback and additions. But regardless, let’s take a breath and do some reflection.

1. Keep things simple. You and your students are dealing with a hundred new things that you’ve never quite had to deal with before. Stick with a few light, simple learning ideas that can keep brains active without asking too much.

2. Don’t try to replicate the “normal” school experience. Doing live instruction is extremely challenging online. Stick to things you can provide asynchronously, and when in doubt refer to point #1.

3. Include things that are purely aimed at social and emotional health. Share resources for mindfulness, family games, and fun experiences with no obvious academic goal.

4. Now is not the time to learn a new tool or website. Use resources you are familiar with, and that students are familiar with. If a tool or website is mandated and you’ve never used it before, allow at least a week (or better, two) of exploration and “getting familiar” activities that do not include new or complex academic content.

5. Lower your expectations. This is the opposite of our usual approach to learning. But please keep in mind that the home environment is much more variable than school. Some families have one device being shared by everyone (including mom and dad who are also working from home). Some children can only access the Internet on a mobile phone. Some have no access at all. Families will have other urgent things vying for their attention. And at the very least, remember that meaningful learning can only happen when other needs (food, rest, safety, security) are taken care of first. Some families will be struggling to figure those out, especially for the first few weeks.

6. All schoolwork should be optional right now. Provide ideas and resources for families who want and need it. But let them know that if they ignore them completely and take care of each other in other ways, that’s entirely OK too.

It is no coincidence that there is overlap with my own framework for nurturing a problem solving culture in the classroom. If our goal in education is to create the leaders and problem solvers of the future, we need to ensure that we go beyond content delivery and provide experiences where students learn these 21st century skills.

Recent events highlight the critical importance of making this a priority. Real world problems require complex thinking and sophisticated understanding of relationships. In my observations of how people attack problems, both in the world and in the classroom, I have seen four bad habits that get in the way of developing 21st century skills in any meaningful way.

Jumping to Solutions

Over and over again, when a problem arises, I have witnessed people responding almost instantaneously with their solution. Frequently the solution is presented as the only viable option, and no other possibilities are considered. Whether it’s students designing a device to protect an egg from a high fall (here’s one version I particularly like from NASA) or a community trying to prevent mass shootings, we jump immediately from recognizing the existence of a problem to implementing the intuitive solution.

I believe the way we deliver our K‑12 curriculum promotes this kind of thinking. There are few opportunities for real problem solving. Instead, we present facts and algorithms as pre-packaged chunks for students to consume and later recall. We occasionally tell the story of how the facts and algorithms came to exist, but rarely let students experience that process themselves. When we teach history, for example, as an inevitable sequence of events instead of showing the messy and time-consuming complexities of making decisions and considering alternatives, students may believe that there must be one right answer to every situation. They will then either pick one from whatever happens to be instinctively obvious to them at the moment, or they will wait for someone else to show them the answer key.

We need to begin teaching students about the additional steps between and beyond recognizing a problem and implementing a solution:

1. Clearly define the problem

2. Analyze and understand the problem and its context

3. Developing multiple solution alternatives

4. Analyze the solutions and select one

5. Implement or test the solution

6. Evaluate the outcome

7. Repeat the cycle

Risk and Loss Avoidance

Related to our desire for instant solutions is our tendency to pick the options that involve the least personal risk or loss, even if they are the least effective. “I’m all for preventing global warming as long as I don’t have to pay more for electricity.” “I want an A on this paper, as long as I don’t have to give up my video games or quit the soccer team.” This artificially limits our options when we’re developing solution alternatives.

Teach students how to really analyze solution alternatives and recognize potential long-term benefits from a short-term risk. Show them how to identify and distinguish needs from wants. Help them learn how to do deeper research about the implications and consequences of the alternatives.

Appropriating Opinions

Because we have been trained to accept what we’re told without critique or analysis, we treat all media as a source of authority. In an age when anyone can publish anything, this is dangerous. One symptom is the proliferation of fake or satirical news articles shared as fact. No, a man playing the Pokemon GO app did not cause a major traffic accident. A more serious symptom is that many people appropriate opinions expressed on social and traditional media as their own. Psychologists have shown that when the people we connect with have the same opinions as we do, those opinions are significantly resistant to change. The nature of social media in particular promotes the sharing of opinions disguised as unambiguous fact.

Schools should spend more time teaching how to parse the difference between fact and opinion, and in analyzing opinions. Learning to question the source, recognize bias and hidden assumptions, fact-check information, and consider alternative explanations and possibilities will help students form their own opinions instead of merely adopting those of others

Shallow Listening

In order to recognize opinions and analyze them, it’s necessary to really listen to and understand other people. Too often we hear little of that they are really saying as we focus on formulating our own response. A great deal of conflict arises because we bring our own assumptions to a relationship and don’t truly understand from the other person’s perspective.

This week I observed this in a summer class I’m teaching. Two students who are collaborating on a project had two different ideas about what their end product should be. The first student described his idea about solving a particular engineering design problem. The other student interrupted him and explained his solution. When I asked the second student to tell me what he thought about the first solution, he just looked at me blankly. I probed further: “What specifically is it about his design that you think isn’t going to work well?” The blank stare continued for a moment, then he said, “Mine is better because.…” The second student hadn’t listened well enough to make even a single thoughtful statement about the first solution.

If we spend more time understanding how the brain listens and teaching active listening strategies, students will begin to listen more deeply.

Addressing these four barriers to 21st century skill development will go a long way towards improving outcomes in schools. What other obstacles do you see in schools and in society that we should consider as we help students become better critical thinkers and problem solvers? Share your ideas in the comments.

Image credit: Barrier by Rae Allen (https://www.flickr.com/photos/raeallen/27533649/).

Statements like these are part of the reason that gifted programs are controversial. So in places like Newington, Connecticut, schools are moving to eliminate gifted programs. While cost is a significant factor in these decisions, here are four reasons gifted programs are irrelevant in the 21st century:

Limited resources shouldn’t be wasted on kids who are already proficient.

Our mandate is to get students ready for college and career, and we are judged on how many of our students are proficient on grade level exams.

Gifted students are likely going to be ready for those despite what we do in school, and in many cases they walk into school already proficient on grade level content, so there is no need to expend precious dollars and personnel boosting the achievement of kids who need no boost.

Gifted programs are the only remaining acceptable form of segregation.

Gifted programs allow schools to keep the serious students who want to learn isolated from the slackers and slow learners. On the surface this seems appropriate until you look at those classes. In practice, gifted programs, even in ethnically and economically diverse communities, are filled with primarily wealthy white and Asian students. African American and Latino students, and those from lower income families, do not have the opportunity to participate. When we base admission to gifted programs on apparently objective criteria, schools and parents can say, “It’s just how it works out. We can’t control how smart they are.”

The best instructional practices shouldn’t be reserved for the privileged elite.

Because gifted programs are freed from many (or even all) of the normal constraints placed on general education, they can adopt methods like project-based learning and avoid low level drill and practice. Unfortunately, innovative methods often stay in the top track classes, limiting students who don’t make the cut to a less rich experience.

Today’s tech personalizes everything anyway.

When it was first invented, one of the selling points of gifted education was that it could personalize learning for gifted children, allowing them to work at their own pace and on their own goals.

Today, companies like Dreambox tell us that digital technology allows us to personalize the experience and learning for every child, effectively making gifted programs obsolete.

Gifted programs may be irrelevant…BUT gifted education is not.

Let me explain. The way we have always done gifted doesn’t work in the 21st century. Two of the “reasons” above, however, are red herrings, and the other two have real alternatives that don’t involve ignoring the needs of high ability learners.

1. Although we may only be measured by the state exam, I don’t know any educator who would argue that striving for adequacy is enough. We should be able to help every child fulfill her or his potential, and it doesn’t have to involve allocation of large amounts of resources.

2. If schools invested more in talent development in earlier grades, we can close the excellence gap. Districts like Fairfax County, Virginia, are finding young students with latent strengths and intentionally building them through experiences and activities available to everyone. And incidentally: our old concept of IQ as a fixed, inherited trait? Not so much. Turns out we probably can control how smart the kids are.

3. If instructional methods are working well for the best and brightest, why wouldn’t we try them with everyone? Approaches like the Schoolwide Enrichment Model or Genius Hour are bringing strategies that were traditionally used in gifted programs into all school environments.

4. The promise of personalization via technology is a hollow one if all it means is picking just the right multiple choice question or just the right drill exercise for a student at a specific moment. True personalization happens when teachers develop thoughtful curriculum that accounts for student personalities.

Real gifted education (not gifted programs) involves seeing every student as an individual, finding out what they need, what they want to learn, and what they care about, and then adapting the instructional environment and curriculum to those needs, wants, and passions. There’s no reason we can’t do this for everyone, letting gifted students soar without the downsides of selective gifted programs.

People give more than money: clothing, bottled water, food, and blankets come in to disaster areas from well-meaning donors trying to make a difference. Unfortunately, not all of it actually helps.

CBS Sunday Morning recently ran a story talking about what disaster workers call “the second disaster”: the relentless crush of stuff that flows in from these givers. Juanita Rilling is the director of the Center for International Disaster Information in Washington, D.C. She says it’s not just that there’s too much stuff. “Generally after a disaster, people with loving intentions donate things that cannot be used in a disaster response, and in fact may actually be harmful. And they have no idea that they’re doing it.”

The story gave an example of a hurricane relief effort in Honduras where donations included high-heeled shoes and winter coats. Rilling makes the point that often when people give it’s more about them than the recipients. They give personal items so they can feel like they’ve at least done something. But there is little thought about what’s actually needed by the recipient, and people rarely try to find out.

Professional development often feels like this. Every professional I know wants to grow and learn and get better at their craft. Unfortunately, PD is usually sent to us from a distant administration building. The people in that building, with the best of intentions, provide training that has no meaning to the teachers or benefit to students. But at least they’ve done something. Right?

What can a teacher do, though, besides gripe about the disconnect between what Administration seems to think is needed and what is actually happening on the ground? Here are two steps you can take to improve the situation (and some bonus advice you can share with your administrator).

1. Plan ahead

Just as it’s too late during a disaster to think about what might be needed, it’s too late during a terrible PD session to think about what you could or should be doing instead. Think ahead to what you need to learn in order to be more effective as a professional, and start developing a list of goals and needs. This should be both personal and collective. Create your own individual list, and also work with your colleagues to craft goals and needs for students and teachers in your building and your district.

2. Communicate with your administration

Well in advance, talk to the administrators responsible for planning and organizing the professional learning you want and need. Be sure to share your goals, but also demonstrate why your goals and needs align with the direction and mission of the organization. Remember that you aren’t a solo practitioner–if you work for a school or district, you have a responsibility to to the community of learners as well as yourself. Show your administration how meeting your needs also serves the whole district, and you’ll be more likely to get a yes.

3. Be ready to show results

Administrators need evidence of success. It isn’t that they are inherently distrustful or that they need to micromanage. Administrators are charged with managing precious, valuable, and often very limited resources. They need to know that those resources are going towards something that will make a real difference for individuals and the organization. So think ahead about what you’ll be able to show as a meaningful outcome. Over time, repeatedly bringing back results will build confidence and you will get more opportunities to own your own professional learning.

And a note for administrators…

The CBS story makes two points about what actually does work in a disaster to relieve needs: networks and money.

Juanita Rilling says, “For me, the network is key. Who has the knowledge? Where are spaces that goods can live if there’s a disaster? Who’s really well-connected on their blocks?” The parallel for professional learning is to allow and encourage your teachers to get and stay connected. If they have opportunities to work as an internal team and also to collaborate with others outside the building and district, the network will be better able to assess needs and manage resources than you can.

And if you’re going to give something in a disaster, Rilling says, give money. “Money sometimes doesn’t feel personal enough for people. The reality is, it’s one of the most compassionate things that people can do.” The reason money is best is that it’s liquid. It can go towards whatever the immediate need is at the moment. In PD, the most precious resource is time. Give it to your teachers in abundance, and let them decide what to do with it.

If there needs to be accountability, don’t micromanage how it gets used. Instead work with teachers to agree on mutually beneficial outcomes and support them in achieving them.

When we are proactive and plan ahead for meaningful and effective professional development, everyone wins. This is the perfect time of year to be thinking ahead to what will make summer and fall learning experiences better. What other strategies are working for you to avoid disastrous PD? What are you doing as a teacher or administrator to help everyone learn and grow and achieve meaningful goals? Share your thoughts in the comments.

Fresh starts often involve fresh commitments. I propose that every educator should make the commitment today to take sixteen new steps in 2016 to deepen their knowledge, sharpen their craft, and stretch out of their comfort zone. In no particular order:

1. Read every day. I’m not talking about all those unread emails from central office, either. Blogs, picture books, journals, news, professional articles, YA literature, or poetry. It’s all input that helps shape and inform your thinking and provides cognitive fuel to keep your mind going.

2. Write every week. Input isn’t enough. Process what you read and think about by turning it around and putting it into writing for a real audience. Everyone (that includes you) has something worth sharing, and most probably several somethings. Write a blog post. (If you don’t have your own, ask your favorite blog or blogger if you can guest post there.) Write an article for the district curriculum newsletter or for a professional journal. Start writing that book you have been planning in your head for the last eleven years.

3. Present to your colleagues. Corollary to #2 is to share something in person. Did I mention that everyone has something worth sharing? Other teachers want to learn from you, too. Share a technique at a faculty meeting, run an inservice workshop, or present at a local or national conference. This wine pairs very nicely with entree #7 below, too.

4. Learn a new tool every month. Digital tech or low tech, find something new you don’t know how to use yet and start using it. Find other people who use it well and learn from them. Try stuff out. Break things. Then figure out how to fix them.

5. Listen to someone who disagrees with you. And not just to plan your rebuttal. Really hear them. You will learn something new, and you’ll expand your awareness of different points of view in the world. It’s healthy for you and for your students.

6. Build something with your students. Make something together that didn’t exist before and that none of you knew how to make before you started. Solve a problem, construct a toy, build a website, or create a work of art. Use your hands and your minds.

7. Attend an Edcamp. They’re free, they’re everywhere, and they’re awesome. ‘Nuff said. (You say you’ve already been to one? OK, then become an organizer.) Oh, and since every Edcamp attendee is a potential presenter, you can check two items off your list on the same day.

8. Expand your network. And your students’. The wider your circle, the more ideas you’re exposed to that can help you deepen your understanding. This works for your students, too, so help them connect with other students and other adults around the area and around the world.

9. Travel someplace new. Whether you go across the ocean or across town, visit someplace you’ve never been. Repeat as often as possible, then use the experiences to feed #2, #3, #6, and #8.

10. Teach someone else’s class. Pick a subject and grade you’ve never taught. Plan a lesson, a project, or a whole unit and teach it to a new group of students. Collaborate with the other teacher, or switch classrooms entirely.

11. Throw out grades and homework. Examine carefully why you do what you do, and think about whether it is really as important as you think it is. If it gets in the way of actual learning, throw it out. Grades and homework are two things that most teachers do just because they’ve always done them. Take the time to really think about the purpose of your practice.

12. Teach something you’ve always wanted to teach. Yes, you have time in your packed schedule to squeeze in one thing that you teach because you want to instead of because someone told you you have to.

13. Try Genius Hour. To go a step further than #12, let your students tell you what they want to learn. Then get out of their way and let them learn it. Help where needed.

14. Get up and move. Whether you add movement within your classroom routine or you get out and go somewhere else, movement is good for brains and learning. The change of perspective and environment helps keep things interesting and engaging.

15. Make a mess. Learning should create dirty hands and piles of stuff and discarded scraps. Color outside the lines and put parts together differently than the directions say. Don’t clean up before it’s time. Or until you’re ready.

16. Remember why you teach. Every day of 2016, you will be faced with things that discourage you and make you wonder why you should still bother. Be sure to take the time, every day if necessary, to remind yourself why you chose this. Your reasons may be different than anyone else’s, but they are still there if you look.

What would you add to this list? What personal steps are you going to take in 2016 to recharge, refresh, and grow yourself?

Special thanks to Ann Leaness, Beth Still, KL Peters, Starr Sackstein, Steve Johnson, Seth Reichgott, Tony Baldasero, and Lisa Nielsen who contributed ideas to this list.

Photo credit: “Take the First Step” by imanka

I get it. You’re frustrated. You want to help your child with his or her school work. It’s supposed to make sense. After all, if an adult can’t grasp it, how is an 8‑year-old supposed to? So when it doesn’t make sense and you can’t help, something must clearly be wrong. And since the only obvious change was the Common Core, that must be the culprit. There are definitely some cogent arguments against the Common Core State Standards. This isn’t one of them:

Mocking the Common Core is a popular amateur sport these days. You surely know about the dad who wrote a check to his kid’s school using “common core numbers”:

As has been pointed out elsewhere, despite the image’s viral popularity, the dad really didn’t get the point of the exercise his kid was being asked to do. And that’s my point. This post is not about whether Common Core makes any sense. It’s about the message you send to your children when you share posts like the ones above:

If something doesn’t immediately make sense to me, then it must be stupid, and it is therefore appropriate to ridicule it.

Think about that for a moment. When your child is in school the next day, and something the teacher presents doesn’t make sense, do you want him or her to mock the teacher? To mock the lesson?

Unless your child already knows everything that’s being taught in school (in which case, why is she still in school?), she is going to encounter things every day that don’t immediately make sense. Things that you want her to spend time exploring, wrestling with, thinking about, talking about, and working through. That takes a certain mindset that values curiosity and perseverance. If you have a beef with the material, by all means present your arguments and build your case. Explain your thinking and give persuasive evidence to support it. Just don’t dismiss it out of hand with ridicule and sarcasm. Curiosity, perseverance, and persuasive argument are more useful life skills than being able to get a Facebook post to go viral. Oh, and by the way, they are also part of the Common Core. For whatever that’s worth.

Sincerely,
A Concerned Educator

What do you think? Do we resort too quickly these days to mockery? Or are there times it’s okay to make fun of the Common Core and other activities we don’t comprehend?

To Maine From the Main Line

When I was ten years old, my family took a trip to Maine. It was the first time I’d been on an extended car trip out of my home state of Pennsylvania, and my father gave me a critically important job: trip navigator. It was my responsibility to help plan the itinerary and the route from suburban Philadelphia to Acadia National Park. My most important tool? A set of brand new maps of the mid-Atlantic and New England states.

I studied those maps for days before the trip, plotting out the best route to our destination. My planning was slightly complicated by the fact that we had specific stops we wanted to make: a day in historic Boston, and a visit to my mom’s college roommate. By the time we left, I knew those maps very well, and when the inevitable glitches arose along the journey, I was able to sort things out and get us back on track.

There were other times I didn’t have as much success. After I learned to drive, I frequently began to rely on my standard route to specific destinations. And there were more than a few times I had to go miles out of my way because I only knew those familiar roads to and from my house.

Teaching has developed much like my driving history. We’ve begun to rely heavily on purchased, packaged programs that give teachers the turn-by-turn directions without giving them enough time getting to know the map. This is highlighted in a recent editorial in Oregon’s Baker City Herald (Solving 5J’s Math Problems). The local school district had mandated use of EngageNY, a math program provided for free by the state of New York, and now teachers and parents were questioning its effectiveness. The editorial opens with an unapologetically blunt assessment:

“The Baker School District has a problem with its math curriculum. What’s not clear is how big this problem is.”

Driving Blind

The editorial outlines three main problems:

1. EngageNY may work well for some students but not others, but we have no idea how many or how well.

2. The district implemented the program with little input from important stakeholders, resulting in a lack of flexibility for teachers who are expected to follow the math program verbatim.

3. Flexibility needs limits, however. Teachers can’t be expected to juggle multiple programs every day to try and meet the needs of a diverse group of learners.

The newspaper calls for surveys of teachers and parents to find out more about whether EngageNY is working and to understand the problems more deeply. Without this information, the board and school district professionals are essentially driving blind, following the turn-by-turn directions in the program without having any way to know if they’re getting closer to their destination.

Road Closed One Mile Ahead

Before I recommend some possible paths forward to resolve these challenges, there are some additional problems we need to consider which weren’t directly addressed in the editorial.

Flexibility is more complex than it first appears. We tend to use the words “program” and “curriculum” interchangeably, but they are not synonyms. Let’s extend our travel metaphor further to better understand some of the components involved:

• Curriculum is the map

• Program is the vehicle and turn-by-turn directions

• Standards define the destination

• Instruction is the journey

• Learning is the experience

A well-written curriculum gives teachers the whole map of the territory, while a program can give a recommended (or in the case of the Baker School District, mandatory) route through the territory.

The problem with rigid adherence to a program is when the unexpected takes place. On our trip to Maine, for example, we had a minor car accident in Boston that sidetracked us for a brief period of time. We might run into heavy traffic or a road closure. Weather can change the conditions or someone might need an unplanned rest stop. Wrong turns happen. If I’m following turn-by-turn directions and get off course, I may be completely out of luck. If I know the map, though, I can plot an alternative route that gets me back where I need to be.

Programs aren’t inherently bad, though. They provide consistency between schools and teachers, allow for a common language, and permit natural flow from one grade or school to the next because teachers know what to expect from the students they are receiving. Programs are also efficient in terms of time, teacher planning, and financial investment.

Surveys won’t tell the whole story. Surveys will reveal comfort more than effectiveness. Responses during early implementation will also be based on perceptions of self-competence rather than effectiveness. As Black and Gregersen pointed out in their book, Leading Strategic Change: Breaking Through the Brain Barrier, “Many prefer to be competent at the wrong thing than incompetent at the right thing.” Selecting a program and designing a curriculum can’t be a popularity contest. Surveys will also be filled out by those with the strongest feelings, skewing results. Feedback about EngageNY is likely to be conflated with overall opinions of Common Core, so those strong feelings will color perceptions.

Meaningful change takes time. Assessing the effectiveness of any new program should be ongoing, but you can’t make firm decisions about keeping or abandoning a path too soon. According to Michael Fullan (@michaelfullan1), a leading expert in systemic change in education, “Significant change in the form of implementing specific innovations can be expected to take a minimum of two or three years; bringing about institutional reforms can take five or ten years.”

Related to this, there is a very real and well-documented implementation dip that happens in any new endeavor. Those first two to three years will see a decline in performance, and to make long-range decisions based on those initial results means you will miss the opportunity to show eventual growth.

Are We There Yet?

I propose three considerations as the Baker School District–and any other school facing a similar problem–looks for a way forward.

Instruction matters more than program

The Baker School District should invest heavily in embedded professional development and coaching in excellent instructional practices. And while a good program such as IMP will give you a head start on good instruction, emphasizing instruction will give teachers confidence to be more flexible when given the opportunity. This also means districts should emphasize fidelity to outcomes and goals rather than a program. Instead of checking whether teachers are using the right book or teaching the right page on the pacing guide, ask for evidence of learning that shows students are getting to the right destination.

Beware the implementation dip

It’s absolutely critical for a district to commit at the start of an initiative to persevere through it for the long haul. Educate stakeholders about the difference between what is comfortable, convenient or familiar and what is truly effective. Prepare everyone for the dip by setting reasonable short-term goals in addition to long-range ones, understanding that there is a predictable process of change. Use multiple ways of gauging effectiveness beyond annual test scores and surveys.

Empower teachers to make choices about the journey

Give teachers both the vehicle (a well-designed program), and the map (a thorough curriculum) and empower them to make choices about the best way to get to the destination. Some teachers may choose to stick with the program. Others will find their own route. For those who want to take the road less traveled, provide a formal pathway for teachers to communicate their plans to leadership so that the district can maintain the common goal, common language, and ensure there is appropriate support for the teacher and students.

Where’s Our Next Trip?

If you’re in a community that’s wrestling with these issues, here are a few questions for your own reflection and which may help you start this conversation with your leaders:

1. What are your priorities and goals for student learning?

2. How would you balance the need for consistency and fiscal responsibility with the desire for flexibility and professional discretion?

3. When a teacher chooses to go “off route”, what are the important ways that your school and system can support that teacher to ensure students are learning? How should that be communicated to parents and the community?

4. What other questions or concerns are raised from your unique perspective that we need to consider in implementing a new curriculum?

Educating hundreds or thousands of individual children in a school or district is a highly complex task, requiring a great deal of effort, energy, resources, and time. With adequate planning, thought, and teamwork, we can make it the trip of a lifetime.

photo credit: Should I ? via photopin (license)

There’s a lot we can learn about teaching math skills from language arts teachers. For example, think about how we build writing fluency and grammar skills in language arts. Among other things, we certainly do these:

• Explicitly teach important skills and rules.

• Provide students with “mentor texts” and many examples of excellent prose to read and analyze; students who read a lot also write better.

• Ask students to review and correct examples which contain errors; this is often done in a “daily edit” format.

In math, most of our instruction traditionally focuses on the explicit teaching of math skills and rules, so we have that one down cold. Mathematical mentor texts are also used, though not as frequently, when we model solutions for students and share examples of worked problems.…

Read the rest of this post on Brilliant or Insane.

photo credit: NCSSMphotos via photopin cc

This post first appeared on the Education Insider blog at It’s About Time.

Back to the Future

I’ve been a cook since I was big enough to kneel on a chair to reach the kitchen table. I remember my father teaching me to measure flour, a small cloud rising above the canister as I leveled the measuring cup with the back of a butter knife. A quick sift, cut in some ice-cold butter, roll and cut the dough into rings, bake for 15 minutes at 450°. I couldn’t wait to taste those fresh biscuits, the flaky, buttery crust dripping with even more melting butter. Before I’d ever really heard of Paradise, I already knew its official food.

Dad wasn’t my only cooking teacher. My mom was equally talented in the kitchen, and in a house with books in every room, cookbooks dominated the shelves. On weekends, Julia Child and the Frugal Gourmet were like extended family members.

In school, my first love was always math. Solving a difficult problem has always been satisfying. I started elementary school towards the end of the “New Math” movement, so we learned about set theory and base 8. By the time I entered high school, though, the “back to basics” shift was in full swing and my schooling was much more traditional.

Evolution of Math

Skip ahead to 1996. This was an important year for me, personally and professionally. A blizzard dumped 30 inches of snow on the Philadelphia region, closing schools for a full week. After four years of teaching third grade, I moved to fifth. Pennsylvania gave its very first state assessment. I turned 30. My second child, Timothy, was born, as was the Google search engine and the TI-83 graphing calculator.

Things were also beginning to change again in mathematics education. In this same year, the US Department of Education established the Mathematics and Science Educational Panel, tasked with evaluating the quality of K‑12 mathematics programs.

1996 was also the year that Laurie Kreindler (@LaurieEDU) and Tom Laster founded IT’S ABOUT TIME™ (IAT), publisher of the Interactive Mathematics Program® (IMP). In the NSF-funded video above (Life by the Numbers with Danny Glover), an exuberant Danny Glover (@mrdannyglover), fresh from a successful run of Lethal Weapon movies, introduces IMP to an audience conditioned to teaching and learning traditional math. IMP, however, was anything but traditional. When this video was produced, featuring teachers and students from Philadelphia Central High School, IMP was only being taught to35,000 students in approximately 200 schools nationwide. IMP was a radical new way of thinking about high school mathematics instruction. With an emphasis on problem solving and understanding of deep concepts, IMP set a new standard.

“You might  not realize it, but mathematics can unlock incredible power! Mathematics is a powerful tool for exploring life on earth and discovering our place in the universe. Why would anyone teach you what the tools are without helping you learn how to use them? That’s exactly how mathematics have been taught in this country for decades. All around the country, dynamic educators and innovative professionals are finding a way to make math make sense. Who knows, you just might discover that you are really pretty good at math because you’ve had the tools all along!” — Danny Glover (Life by the Numbers, 1996)

Today, my son Tim is a college freshman. It’s enlightening to compare how math instruction (and cooking!) have evolved in the years he’s been alive.

Nerdy is the New Cool

Twenty years ago, there were only a few chefs in popular culture: Julia Child, Wolfgang Puck, Emeril Lagasse. Their television shows were primarily about making sophisticated techniques accessible to untrained cooks using the equipment available in most home kitchens. Still, to admit you were a fan of cooking shows was to embrace the label of “nerd.”

Math in school was in a similar place. The “math nerds” didn’t hang out with everyone else. In fact, it was cool to proclaim that math just wasn’t your thing. And nearly everywhere, school math focused on computational fluency and getting the right answers.

But 1996 was at the cusp of changes in both fields. The NCTM standards had started a movement away from rote learning towards an emphasis on problem solving and application, exemplified byIMP. And the fledgling TV Food Network was beginning to change the way America thought about cooking.

Today, popular media and culture are filled with cooking competitions and festivals. Artisanal pickles and small-batch craft beers are mainstream. Chefs are celebrities, and they even have live touring shows. It’s cool to be nerdy about food.

Math sadly hasn’t made as much progress. Danny Glover told us about popular nineties icons bad-mouthing mathematics, and today Hollywood still hates math. Even when Hollywood shows it a little love, math is almost always the domain of the quirky genius or the mentally ill one. It’s math as spectator sport, still not something mere mortals should attempt.

Understanding Is Engaging

The PSSA test in Pennsylvania brought with it a new kind of test item my colleagues and I hadn’t seen before on standardized tests: the open-ended question.

For me and my students, the most challenging part of these questions was the requirement to explain reasoning. For the first time, it wasn’t enough to pick the right answer out of a list. My students had never been asked to answer the questions “Why?” or “How do you know?”

So we developed some rudimentary techniques to start building those muscles. We gave students a challenging problem and asked them to work on it for a week. We encouraged them to work together and talk to each other. We spent time teaching writing and vocabulary. We even gave them problems to which we didn’t know the answer.

Although student engagement has today achieved buzzword status, it was hardly talked about twenty years ago. Nonetheless, when our students were working on complex problems, they were more deeply engaged. Our math class was being transformed into one focused on big mathematical concepts; without realizing it, we were inventing in our elementary classrooms what IMP was doing for high school math.

A similar transformation was happening in the world of cooking. As we turned to the 21st century, Alton Brown created Good Eats. Equal parts Julia Child, Mr. Wizard, and Monty Python, Brown did far more than just walk his audience through a recipe. He taught us why it worked. And did it in a way that was deeply engaging. My son Tim has probably seen all 252 episodes of Good Eats at least twice. Though he and I did spend a fair amount of time together in the kitchen, I suspect Tim learned far more from Mr. Brown.

Defragmenting the Curriculum

For my entire school career, first as a student and then as a teacher, math class was fragmented into two-week segments. We’d spend two weeks learning, say, how to add three-digit numbers. One day we’d add without regrouping. The next we’d add with regrouping. Eventually, we’d take a test with all the kinds of three-digit addition mixed together.

The day after the test, we’d start a new unit: perimeter and area. Two weeks later: fractions. And so on. Many schools institutionalized this with scripted programs and tight pacing calendars. Thanks in large part to a ten-year experiment called Project Follow Through, direct instruction was touted as vastly superior to any other method.

This design was the epitome of what David Perkins calls “elementitis”: teaching a subject by breaking it down into its smallest elements and teaching them in isolation. The instruction is more manageable, but it sacrifices understanding for simplicity.

By far the biggest change in school mathematics is now happening as a result of the Common Core State Standards. Instead of fifteen topics to cover at breakneck speed, we now have three or four major topics each year. The explicit intention of the Common Core standards is to allow teachers and students to spend more time and go into more depth.

This does not go far enough, however. The groundwork has been laid, and if the next twenty years are going to be better than the last, it is time to reinvent mathematics.

The Future of Math

While some schools may still choose scripted programs despite more recent evidence that direct instruction is ineffective, more reflective schools, like Etowah High School (“What Does Math Look Like in Today’s Classroom?”), will embrace this opportunity to rethink their instructional practices. Three things need to happen for school math to be relevant and meaningful in the twenty-first century:

Bypass the Busywork

One thing that hasn’t changed at all in the past twenty years: high school math classes still use the TI-83 calculator, even though today there are more options, like Photomath, Desmos, and Wolfram Alpha. Look at that Danny Glover video again: what was once state-of-the-art in video production today looks dated and even a bit cheesy. It’s well past time for us to have high def math.

Our reliance on old tools and methods just allows students to lose even more ground. “It’s not so much that maths education is worse than it was;” says mathematician Conrad Wolfram, “instead, real life is much more demanding and we’re running in the wrong direction to catch up.”

Wolfram’s approach to math is radical: stop asking students to do computations that can be done more easily by a computer. Although many schools may not be ready to dive head first into this deep end of the curriculum pool, we all must shift instructional time significantly towards mastering the few things that humans still do better than computers.

Understand the Brain

Any professional educator should be an expert in learning, and to do that you must understand the brain. We know far more today about how the brain learns than we did twenty years ago (as Sherry Fraser explains in an interview, “Sherry Fraser Doles Out Mental Ice Cream with Problem-Based Math.” Math educators must understand the mental processes involved in subitizing, number sense, and how the brain processes different kinds of learning experiences. They need to be aware of developmental and emotional factors and be able to recognize different causes for a student misconception. Teachers also must understand how to gain and maintain a student’s attention, when to shift gears, and how to design instruction so it aligns with the brain’s natural timing and patterns.

Design Whole Learning Environments

Connected with understanding the brain, math teachers must realize the importance of the entire learning environment on a student’s learning. Curriculum isn’t enough, nor is it adequate to rely on an instructional bag of tricks. Physical space has a significant effect on learning, as does the culture of the classroom. Math teachers must be intentional about not just designing lessons but designing the entire environment in which those lessons will take place.

The more I learn about cooking, the more complicated it becomes. Every new idea, technique, and ingredient carries with it a raft of other things to learn about making good food. I find the same is true for math: transformation will take time. We’ve come a long way since IAT and Danny Glover made that film. Programs like IMP are helping teachers do the hard work of thinking differently about what math class should look like.

But we still have work to do. Edward Begle said in 1972, “Mathematics education is much more complicated than you expected, even though you expected it to be more complicated than you expected.” If he were alive today, I suspect he might say this is an understatement.

It’s the time of year we celebrate scary things: ghosts, goblins, clowns, pumpkin spice (whatever that is). There is one creepy thing with the power to raise the hairs on necks everywhere and which rarely gets celebrated: math. This is a shame. Because the fear of math is not inherent in the subject. Rather, it’s a result of growing up in a school environment based on four terrifying myths about math:

1. Math is applied computation, and being good at math is about memorizing increasingly complex incantations done with arcane symbols.

2. Math achievement comes from implementing quality programs “with fidelity.”

3. Problem solving is the last in a long series of teachable math skills.

4. Some people just aren’t math people.

So let me turn on the lights and pull off the rubber mask to reveal the truth behind the myths.

Math is the language of problem solving

The point of learning math is to understand how to make sense of problems and communicate with others about them. The structure, vocabulary, and grammar of a language shape the way people think. The rules of math are not just recipes we must blindly follow in doing computations. They are a precise and sophisticated way of structuring ideas and understanding solutions. Learning math is therefore far more than just memorizing the vocabulary and grammar. It’s about becoming fluent in the idioms and subtle features of math, which leads us directly to the next truth:

Language is learned best by immersion

If we treated world language instruction the way we teach math, we’d have students drill on grammar rules and vocabulary for several years and the only sentences they would hear, read, speak, or write would be in isolated, contrived situations. There would be no conversations, no discussions, and no need to come up with your own thoughts in the other language. Now imagine one of those students was dropped into a foreign city for a week: that’s the annual state math test.

A better way to learn is to spend most of your time immersed in an environment where the language is used naturally. You still have instruction in the grammar and vocabulary, but it’s always done in the context of the way the language is really used by native speakers. In math, this means all skills, content, and structured algorithms are taught in the context of problem solving. Students solve problems every day, and they have abundant opportunities to collaborate just as adult problem-solvers do.

Problem solving is a complex collection of learnable skills and habits

We often treat problem solving as just another isolated skill, as if it’s a simple checklist we can give students. “Understand, Plan, Solve, and then Check,” we tell kids. Just follow the recipe and you’ll solve every problem.

Just like communicating in a foreign language, problem solving is actually a complicated and sophisticated collection of skills and habits of mind. The power is not in accumulating all of the isolated problem solving techniques, but in being able to use them together in interesting and often messy ways. Like learning a language, learning how to solve problems is something that students do over a long period of time, and there is always more depth to discover from new and different kinds of problems they can encounter.

Everyone can be a “math person” if given the right environment

All of this presupposes that students are regularly encountering the right kinds of experiences to be immersed in problem solving. This doesn’t happen automatically or by accident. It has to be systematically designed. Ideally, a district team will create structures and provide resources to enable this, but an individual classroom teacher can also do this. The 5 Principles framework is a guide for developing aspects of your classroom and school culture that supports problem solving and innovative thinking:

• Conjecture. Promote student inquiry and critical thinking. Never end with an answer, and always follow up with questions like, “How do you know?” and “Are there other ways you could solve that?”

• Communication. Students learning a language need to use it. A lot. So give them opportunities not just to do rote computations but to express their reasoning verbally and in writing. Let them translate from the math language of symbols into English and back again.

• Collaboration. Few problems are ever solved by one person working alone. More often, people work together to generate ideas and build on each others’ solutions. These are skills in themselves, and students can learn a lot about how to solve problems themselves when they see how others attack a problem.

• Chaos. Let’s face it: there are few problems in life that are neat, organized, and prepackaged with exactly the right information needed to solve it. Students need to experience messy, complicated problems as often as they do the more straightforward ones we usually present them in math class.

• Celebration. Yes, this means finding ways to make math enjoyable. But it is also about recognizing the positive value of mistakes and letting students celebrate the growth that happens afterwards. Students should have plenty of opportunities to recover from failure and show new learning.

Building the Culture

Every educator has an obligation to create the right conditions for learning how to solve problems. Even if you don’t teach math, you can create a classroom culture that promotes the 5 Principles. Encourage your students to ask questions and communicate clearly, to work together and tolerate the messiness of real problems, and to celebrate not only the right answers but the learning that comes from mistakes.

What’s one thing you can do today to change the culture of your classroom? Share your ideas in the comments, and join the discussion at http://www.geraldaungst.com/5cmath. To learn more about creating a classroom culture that promotes problem solving and innovative thinking, check out my new book 5 Principles of the Modern Mathematics Classroom.

There’s lots of research to support acceleration as a strategy for gifted learners. The Acceleration Institute, part of the Belin-Blank Center at the University of Iowa, recently produced a report entitled “A Nation Empowered” which details the enormous benefits to accelerating a student when he or she is performing well above grade level.

Researcher Jonathan Wei of Duke University says, “All students deserve to learn something new each day.” In math, the obvious way to learn something new is to accelerate the instruction, letting the student go on to the next topic or grade level. But “learn something new” is not the same as “learn the next thing on the district’s scope and sequence.”

Read the full post on the Brilliant Or Insane blog.

This app is going to ruin math class this year, and here are four reasons Photomath should be summarily banned:

1. It will make routine textbook exercises worthless. In the past, when teachers assigned #2–40 (even), they could ensure that students would have at least a good twenty to thirty minutes of solid mathematical practice. Now, avoiding the odd problems because the answers are already in the back of the book is pointless because students can just use Photomath to get instant answers to the even ones too.

Read the whole post on the Brilliant or Insane Blog.

My wife loves her vegetable garden. Michele will spend hours with her fingers in the rich soil, nurturing her tomatoes, zucchini, lettuce, green beans, jalapenos, watermelon, and sweet potatoes.

I love Michele’s garden too: I get to eat the produce it generates. The problem is, so do all of the local wildlife which didn’t get the memo from the township that we own this land now and they need to move along.

So over the past several years, I’ve built three fences for my wife’s garden. It’s not that they were bad fences, or that they didn’t stay up. It’s that the problem we were solving kept changing.

My first fence was awesome: nice, straight metal posts hammered into the ground at equal intervals around the garden’s perimeter; welded wire fencing tightly stretched between the posts and anchored into the soil to prevent forward-thinking groundhogs from digging underneath. And it worked exactly as intended. Those groundhogs stayed out all summer, as did the foxes, cats, squirrels, and other small mammals.

The deer? Not so much. To them, the fence merely defined the boundaries of a conveniently-located salad bar. We didn’t get much of a harvest that first year.

Year two brought fence number two. Taller posts. A second tier of fencing above the first one. This fence kept out the deer, and a lot more of the food made it into the house.

I thought I was done with fences, until this year when Michele said, “I want to expand my garden.” So with the help of my son, we added more fence around the new section, and the result is the verdant miracle you see in the picture above. And in case you were wondering: ratatouille made with fresh-picked zucchini is absolutely spectacular.

Math as an Innovation Incubator

What’s all of this have to do with math? you ask. Well, the fence was built to solve a particular problem, and it wasn’t a solution I could look up in the answer key to a book. It wasn’t a nice, neat problem created by a textbook-writer either. It was messy (both literally and figuratively) and complicated, and the parameters kept changing as the situation evolved.

There was certainly computation involved in solving the problem: how much square footage we needed to have in the garden, how much fencing to buy, how far apart we’d put the posts. But it was more than that. Every version of the fence needed to innovate–granted, on a very small scale–in order to work in our unique situation.

I learned how to innovate by solving problems throughout my life. It’s not something I learned in school, at least not directly. But our modern world needs more innovators, and if we’re going to build these skills in our students, the mathematics classroom is a fantastic place to start. There are two habits of mind you can build into your math instruction to begin creating more innovators. I call them Conjecture and Chaos.

Conjecture: Capitalizing on Curiosity

The human brain is naturally curious. We are wired to wonder. John Medina, molecular biologist, explains in his book Brain Rules that it comes from our need to explore our environment.

Babies are born with a deep desire to understand the world around them, and an incessant curiosity that compels them to aggressively explore it. This need for explanation is so powerfully stitched into their experience that some scientists describe it as a drive, just as hunger and thirst and sex are drives. (Medina, 2014, p. 247, emphasis mine)

Most math classrooms never capitalize on this curiosity. We hand students predefined and preprocessed problems for which there is one, single correct answer and then walk them step-by-step through the procedure for finding that answer. Worse, we wait until after they’ve drilled the skills to even introduce them to that problem.

Instead, try sparking their curiosity by introducing your students to an intriguing conundrum and then using it to introduce the skills they’ll need to solve it. You may be surprised at how many of your students figure the skills out on their own in the course of solving the problem.

When students struggle to get an answer, encourage them to guess and explain their partial reasoning. Never end with the answer to a question, either. Always ask your students follow up questions like these:

• Why do you think so?

• How do you know?

• Why did you solve it that way?

• What was hard about solving that problem?

• How did you overcome the difficulty?

Professional mathematicians exhibit this kind of curiosity all the time. It’s what propels them to explore new ways of thinking about the world and math. James H. Simons, founder of the National Museum of Math, turned his incessant curiosity into a billion dollar empire. And he did it by studying math.

Chaos: Embrace the Mess

Math class needs to be a place with a healthy dose of chaos. I’m not talking about the kind of chaos my students experienced during my first year as a teacher, when I struggled with even the most basic classroom management tasks. I’m talking about the messiness of real problem solving. Thomas Edison famously said, about the path to finding the right filament for his light bulb, “I have not failed. I’ve just found 10,000 ways that won’t work.”

One of the biggest problems with math instruction is that we show students the one way that someone else figured out would work, and then ask them to rehearse it to perfection. We never let kids experience the ten thousand ways that won’t work. I’m not talking about aimless, endless anarchy here, but we can’t expect kids to learn to cook without making a mess in the kitchen.

Terry Tao is another world-class mathematician, one who embraces the Chaos of real math work. When he tackles a complex problem, he never takes a straight line from problem to solution. The work usually involves weeks or even years of false starts, failed attempts, and flawed logic.

If one of the world’s greatest mathematicians is a messy problem solver, why wouldn’t we let our students be messy? When students struggle to solve a challenging problem, don’t be too quick to come to their rescue and provide them with the next step. Focus on the process.

One way to do this is to give students the correct answer to the problem up front. Now there’s no pressure to find an answer. Instead, the challenge is to figure out exactly how someone got to that answer. Another strategy is to use lots of non-routine problems. Consider this one:

If Citizen’s Bank Park were completely filled with popped popcorn, how long would it take the Phillies to eat it all?

Given the Phillies’ level of success during the 2015 season, perhaps we ought to seriously consider filling the ballpark with popcorn. But I digress.

The point here is that there is no way to be certain about the answer. Students need to defend and explain their thinking, moving them towards deeper thinking practices that will serve them well and help them be more innovative.

Tomorrow’s Innovators in Today’s Classroom

With these two ways of thinking embedded in the culture of your classroom, you can begin to nurture students who can think creatively and find innovative solutions to complex problems. What other ways do you use math instruction to promote innovation and reasoning? How do you get your students to think outside the box? Share your ideas in the comments below.

5 Principles of the Modern Mathematics Classroom

Want to learn more? You can explore Conjecture and Chaos more deeply, as well as three more habits of an innovative mind, Communication, Collaboration, and Celebration, in my new book, 5 Principles of the Modern Mathematics Classroom.

References

Medina, J. (2014). Brain rules: 12 principles for surviving and thriving at work, home and school (2nd ed.). Seattle, WA: Pear Press.

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Let’s consider another quote: “Some of you who have small children may have perhaps been put in the embarrassing position of being unable to do your child’s arithmetic homework because of the current revolution in mathematics teaching known as the New Math.”

This did not come from another frustrated parent or a political stump speech railing against the Common Core (or “Satan’s Handiwork” as one Iowa mom put it in the same NBC article). It was in the introduction to a 1965 song titled “New Math” by mathematician and satirist Tom Lehrer. In the song, Lehrer goes on to say, “But in the new approach, as you know, the important thing is to understand what you’re doing, rather than to get the right answer.” Sound familiar?

So why do we keep circling back to the same place? Why on earth does “this conceptual thing” matter in math, even for younger children?

Read the full post at the Brilliant or Insane blog.

photo credit: Late Night Mathematics via photopin (license)

8 ways to make students love math

1. Let students ask (and answer) their own questions.

Instead of relying on the teacher, or the textbook (see next tip), to provide all of the questions, get your students to start asking some of their own. What are they curious about? What intrigues them about mathematical ideas you’ve been exploring? For a fun way to create engaging, thought-provoking questions, try using what I call iWonders. Here are a couple of examples:

• iWonder if Lincoln Financial Field were filled to the top with popcorn how long it would take the Philadelphia Eagles to eat it all.

• iWonder if everyone in Seattle got in cars for a road trip to Boston at the same time how long the line of cars would be.

2. Ditch the textbook and solve problems.

Last year, Mark Barnes wrote about his visit to a problem-solving centered classroom where students were actively engaged in mathematical thinking instead of drudging through page after page of worksheets and exercises. The students owned the work, and when they didn’t know the answers to something, they just kept at it and worked it out together. How powerful would that be in your classroom?

3. See math everywhere.

Math isn’t just about numbers and algorithms in math class. Math is everywhere, from video games to nature to poetry to current events to fashion design to food to music. I could go on, but I’d run out of room for the other five points. Short version, look everywhere, all day, for ways to connect with math. (And see tip #7 for the flip side of this.) Point out places where you see mathematical ideas that crop up in unexpected places. Create a space, either physically in your classroom, or digitally online, to capture, share, and celebrate the math you and your students find in the world. Once you start looking, you may not be able to stop.

4. Fill your classroom with mathematical toys and games.

Games, toys, and puzzles that require logic, sequence, patterns, and shapes give students opportunities to explore these ideas in highly engaging and non-threatening ways. Sometimes (but definitely not all the time), take the time to dive deeply into the structure and mathematics behind them. The game of NIM is a spectacular way for even very young children to begin to explore the math behind the rules of strategy games.

5. Play!

This may seem redundant after the last tip, but this goes beyond just playing games. Play with numbers and mathematical ideas. Math shouldn’t always be about relentless pursuit of a solution. Sometimes it’s good to just mess around and see what you find out. A great source of ideas for mathematical play is the Math Pickle site. In particular, check out the section of Unsolved Problems. Beware. Your mind may be blown. And who knows: your class may even win a million dollars.

6. Be OK with mistakes.

In a recent article in Time, mathematics professor Jordan Ellenberg talked about how important trial and error are in real mathematics, and how we need to bring it back into math instruction. Mistakes are important, and we need to let kids make lots of them. They will gain much more by recovering from a mistake than they ever will by getting things right the first time.

7. Let math leak into other subjects.

OK, so this sounds like it’s just a repeat of #3. The difference is instead of just finding math where it happens to be lying around, look for ways to actively bring mathematical ideas into your instruction and conversations in other subjects. Science is easy, since math shows up regularly. But when you’re teaching about poetry, have students analyze the rhythmic patterns and try to decide if there’s a formula for poems that “sound good” compared with those that don’t. Or have them collect data about their performance in phys ed and use it to analyze their own progress, or even the effectiveness of different physical activities.

8. Learn to love math yourself.

I suspect that if you have tried all of the first seven tips, #8 may well take care of itself. But if you are teaching math but don’t like math, that attitude will leach out into the air in your classroom, and your students will spend all day breathing your distaste. If you are someone who really, truly doesn’t enjoy math but find yourself required to teach it, find something–anything–that you can like about it, and latch onto that. Actively explore these first seven tips in your own life outside of your classroom. Identify the things about math that cause you to cringe. Face those fears, and chip away at your anxiety so that when you’re with students, you can honestly convey positive vibes.

[This post originally appeared on September 10, 2014 at Brilliant or Insane.]

Photo credit: Edutopia

The word “rigor” is hard to avoid today, and it provokes strong reactions from educators. Policymakers tout its importance. Publishers promote it as a feature of their materials. But some teachers share the view of Joanne Yatvin, past president of the National Council for Teachers of English. To them, rigor simply means more work, harder books, and longer school days. “None of these things is what I want for students at any level,” Yatvin says. Part of the problem is that we have adopted the jargon without a clear understanding of what we really mean.

Calculating Cognitive Depth

For classroom teachers, the more important question is one of practice: how do we create rich environments where all students learn at a high level? One useful tool, Norman Webb’s Depth of Knowledge Levels, can help teachers meet that challenge. Depth of Knowledge (DoK) categorizes tasks according to the complexity of thinking required to successfully complete them.

Level 1: Recall and Reproduction

Tasks at this level require recall of facts or rote application of simple procedures. The task does not require any cognitive effort beyond remembering the right response or formula. Copying, computing, defining, and recognizing are typical Level 1 tasks.

Level 2: Skills and Concepts

At this level, a student must make some decisions about his or her approach. Tasks with more than one mental step such as comparing, organizing, summarizing, predicting, and estimating are usually Level 2.

Level 3: Strategic Thinking

At this level of complexity, students must use planning and evidence, and thinking is more abstract. A task with multiple valid responses where students must justify their choices would be Level 3. Examples include solving non-routine problems, designing an experiment, or analyzing characteristics of a genre.

Level 4: Extended Thinking

Level 4 tasks require the most complex cognitive effort. Students synthesize information from multiple sources, often over an extended period of time, or transfer knowledge from one domain to solve problems in another. Designing a survey and interpreting the results, analyzing multiple texts by to extract themes, or writing an original myth in an ancient style would all be examples of Level 4.

photo credit: expertinfantry via photopin cc

Recently, educators have begun applying Webb’s DoK to help them design better instruction. Try this exercise to better understand the cognitive depth of the tasks you are using in your classroom and improve the rigor of your instruction:

1. Keep a list or collection of every task you ask students to do in a day (or in one subject for a week), including classwork, homework, and projects.

2. Sort the tasks into categories according to the four DoK Levels. Some resources which may help:

   • This DoK “wheel” (PDF, 34KB)

   • These examples of DoK levels for four content areas (PDF, 39KB)

   • These examples of using DoK in the fine arts (PDF, 102KB).

3. Work with a team of colleagues to review the groupings. Many tasks are easily categorized, but some will require deeper discussion to clarify your understanding of the levels. Strive toward consensus. A few pointers:

   • The verb does not define the level. Instead, consider the cognitive effort that a student will use to complete the task. The verb “describe,” for example, could be any level, depending on the kind of description.

   • It is common to find tasks that seem to fall in between levels. When in doubt, assign the higher level.

   • “Extended time” alone does not make a task Level 4. Lower-level tasks that are merely repeated over a period of time are still lower level.

4. Analyze your groupings. What patterns do you see? Is there a reasonable distribution of tasks across the four levels? Do you notice anything unexpected?

5. Rewrite a Level 1 or Level 2 task to be at least Level 3. These question stems are helpful in creating good tasks (PDF, 28KB).

Apply as Needed

You may be asking at this point, “Well, what is a reasonable distribution? How often should I be doing tasks at each level? What’s the right sequence?”

DOK Levels are not sequential. Students need not fully master content with Level 1 tasks before doing Level 2 tasks. In fact, giving students an intriguing Level 3 task can provide context and motivation for engaging in the more routine learning at Levels 1 and 2.

DOK levels are also not developmental. All students, including the youngest preschoolers, are capable of strategic and extended thinking tasks. What they look like will differ, and what is Level 3 to a kindergarten student may be a Level 1 task for a middle schooler. All students, however, should have opportunities to do complex reasoning.

To find the right balance, ask yourself these questions:

• What kinds of thinking do I want students to do routinely?

• If my own child were participating, what would I want him or her to be doing?

• What’s the most effective way to spend the limited classroom time I have?

Decide for yourself how often you should focus on tasks at each level so that students gain the most from the learning opportunities you design.

Regardless of how you define “rigor,” the important thing is that students are thinking deeply on a daily basis. Webb’s Depth of Knowledge gives you a framework and common language to make that happen in your classroom.

[This post originally appeared September 4, 2014, at Edutopia. To comment, please join the conversation there.]

photo credit: Simon Grubb via photopin cc

This summer I have had the privilege and joy of taking my son around the region doing college visits. Two of the schools he’s looking at are in cities I don’t visit often: New York and Pittsburgh. Thankfully, though, my car has a GPS navigation system, so we were able to do our visits to those unfamiliar cities with little difficulty. (Other than the horrible traffic around the Lincoln Tunnel, anyway.)

As I was driving my son to dinner in Pittsburgh a couple of weeks ago, I started thinking about how I used to get around without my GPS, and what it felt like to navigate an unfamiliar city. Now, I love maps, and I’m good at reading them. When I was a kid, I was in charge of navigating on our family trips. So plotting a route in new territory is something I’m comfortable with.

But even so, navigating a new city is always nerve-wracking for me. I might have a good idea of the route and my heading, I could miss a turn, or an intersection might look different in real life than I imagined it from the map, or there might be construction that detours me away from the known path. In each case, I can pull over, look at the map, and try to find my way again. But in a city this is easier said than done, and it just piles anxiety on top of worry. Worst is that I don’t really know until the end of the journey if I was successful: either I get to my intended destination, or I give up and go home.

Now, with my GPS, I have a constant awareness of where I am, where I’m going, and what’s the best next step to get there. Where before I would study a map thoroughly to get familiar with the entire territory, now I can just hop in the car, plug in the address, and go, confident that I’ll arrive where I need to arrive. Even better, I can now attend to the more pleasurable parts of the trip, enjoying the journey and the view instead of focusing entirely on whether I’m still on track. And if I do miss a turn, the GPS, with infinite patience, will recalculate the route and tell me the new best way to get there.

Grades are the old-school approach

Grades work like a map. The teacher gives students a description of how grades are calculated, what factors into them, and how they are all weighted. Then it’s up to the student to plot the route and figure out along the way whether they are still on track to get to their destination. At the end of the route, whether it’s an assignment, a test, or the whole course, the student finds out if they arrived. If not, it’s too late to do anything about it. In between, the student is focusing entirely on maintaining her course, anxious about whether she is going to arrive on time.

Feedback is a GPS for learning

Feedback, on the other hand, works like a GPS. The teacher focuses on one turn at a time, instead of the entire route. Students know that if they make a wrong turn, they will get help with finding their way back. And they pay attention to the journey, the learning, instead of worrying about the destination.

Fearless learning

My GPS has made me fearless. I have discovered that I do not hesitate to look for new places to explore, or to wander around in an unfamiliar place, because I know that I have a way out. I no longer stick with comfortable favorite places; I try new locales that I would never before have considered attempting to find, knowing that a wrong turn will just make my trip a few minutes longer. I know I can reach my destination.

Teacher feedback without grades has this same effect on students. Instead of being terrified of getting something wrong, of making a mistake that will have catastrophic results on the grade, students can hop fearlessly into the learning experience, knowing that it might take longer to get the learning done, but that with guidance from the teacher, the destination is in reach.

[This post originally appeared August 25, 2014, at Brilliant or Insane. To comment, join the conversation there.]

photo credit: Ed Yourdon via photopin cc

As a school district administrator, I have the privilege of working with all of the teachers new to our schools during a weeklong program of induction and orientation. Monday, we treated this fabulous group of educators to lunch. As we headed back, the conversation turned to field trips.

“Would you like to hear my field trip rule-of-thumb?” I asked the small group of teachers riding in my car. Eager to seem interested in the administrator they just met, they humored me by saying yes.

“When I was a teacher, I figured that as long as I came back to school with at least 90% of the students, it was still an A.” Polite laughter all around.

Of course the idea that losing a tenth of your class is an “acceptable loss” is ridiculous. Anything less than a 100% return rate would result in panicked parents, anxious phone calls, and serious professional consequences.

So why do we believe that the traditional grading scale is somehow the infallible and inspired word of John Dewey?

I was part of an interesting conversation on Twitter last week about the importance (or lack thereof) of grades. Without getting deep into the details (you can read the whole conversation here), one participant, John Walkup, argued passionately against eliminating grades, using a premise that has been seen here before:

@geraldaungst @markbarnes19 @games_frontiers @KoolKatJulian W/o grades and SATs, how r Ss going to show colleges their worth?

— John R. Walkup (@jwalkup) August 14, 2014

His point carries some weight: if colleges require GPAs on applications, and students want to get into college, aren’t we doing them a disservice if we eliminate grading in K‑12 schools?

During the conversation I pointed out one school that I thought was a counterexample: MC2 High School in Cleveland, OH. This school uses mastery-based reports instead of traditional grades, and yet their graduates are accepted into some of the best colleges in the nation (see page 3 of this profile).

The problem, as Mark Barnes pointed out to me later, is that the school shifts to a traditional grade structure in grades 11 and 12. Mark has suggested that K‑12 schools need to stop catering to the perceived needs of college admissions committees and start doing what is good for learners.

I agree, but the problem remains: how do we eliminate grades without unintentionally hampering kids’ chances of getting into college? Here’s my proposal: let’s just do it and see what happens. Call the colleges’ bluff. Send them a transcript without a GPA and see what they do.

I’m willing to bet that more schools will start taking the lead that one-third of the top colleges have taken by downplaying, or even downright ignoring, GPA in the admissions process.

[This post originally appeared August 20, 2014 at Brilliant or Insane. To comment, join the conversation there.]