1 comment on “Active Caring (and Epilogue): the essential ingredient”

Active Caring (and Epilogue): the essential ingredient

This is a post in the ongoing Emergent Math mini-series: Routines, Lessons, Problems, and Projects.

Active Caring - Card.png

As we stand on the balcony and gaze out at our own version of the MCU (Math Class Universe) that consists of Routines, Lessons, Problems, and Projects, we must be sure we’re not missing the crucial ingredient that stitches it all together: caring. More specifically, active caring.

Many, if not most teachers demonstrate passive caring. Such teachers show a general, blanket kindness to their students. They’re open to students’ questions. They typically like their students and certainly don’t show unkindness. Often, the student-teacher relationship hinges on the student’s academic aptitude or natural charisma. A teacher might have a decent relationship with all his students, but truly special relationships only with students who excel in their classroom or have otherwise magnetic personalities.

A teacher who is actively caring cares for each student as an individual and views each student as a mathematician. He reaches out to students individually, not broadly. Consider the difference between “if anyone needs help come and see me” versus going to each student to see if they need help. Think of the difference between welcoming the class all at once versus greeting students individually, by name, at the door. These individualized acts of kindness and care are as essential as the task at hand – the routine, the lesson, the problem, or project. Well thought out curricula and tasks are nice, but active caring will ensure that they land for each student in your classroom. Active caring often involves a disruption of social or academic norms: students who typically don’t engage in math receive the same level of care as students who do.

To be sure, active caring is a challenge for a teacher who may see upwards of 100 students a day (or more). It’s difficult to get around to each student in such a compressed amount of time. Don’t beat yourself up if you’re unable to. But make an achievable goal: perhaps every two days you’ll have a personal conversation or check-in with each student. It’ll require a level of intentionality that might seem forced at first. You may have to print out a class roster and check off your interactions with each student as they come. But in the end it’s worth it. An excerpt from a, uh, certain book:

Briana is a 10th grader, talking about her middle school math experience. “I was invisible to the teacher,” she begins. “I always got my work done. I never got in trouble. I would raise my hand to ask a question but my teacher would never call on me. It got to the point where I would ask my friend to ask a question for me so I could get something answered.” Briana is soft-spoken, but clearly motivated. It’s tragic and understandable how she would feel “invisible” to her teachers. In the hustle and bustle of a noisy middle school classroom, soft-spoken students get short shrift.

Recently an administrator I know took part in a “shadowing a student” challenge, in which the administrator identified a student and followed her around for an entire day. From the moment she got off at the city bus stop in front of the school until the moment she got back on it at the end of the day, the administrator followed the student around to each class, every passing period, even lunch. Debriefing the experience, the administrator was stunned by how little teacher-interaction the student received. Other than a greeting here or there, the student received few words from her instructors.

Shy students, or students who don’t have as much academic status, or who are still learning the English language can easily become invisible in a school day, for weeks at a time. Make sure this doesn’t happen. Try some of these strategies:

  • Document your interactions with students to ensure you’re having conversations with everyone.
  • Host “community circles” in your class.
  • Greet every student by name at your door.
  • Demonstrate vulnerability by sharing details from your personal life.

How do you demonstrate active caring for your students? Let us know in the comments.

***

Epilogue

Let’s review.

Your daily classroom has a lot of moving parts. I’ve attempted to categorize those parts into Routines, Lessons, Problems, and Projects, acknowledging that these are imprecise buckets and you might go between them several times throughout a day. Holding these all together is an atmosphere of active care for each student.

As you think about the upcoming school year, which of these are you curious about? Which do you want to get better at? Do you want to try a project this year? Would you care to create an assessment structure of using “Portfolio Problems” for students’ portfolios of understanding? What’s the right ratio of routines, lessons, problems, and projects?

In addition, what will you do in the first couple weeks of school to demonstrate active caring? How will you touch each student and make sure they’re welcome at the table of our oft-uncaring discipline?

I hope you enjoyed this mini-series. As much as anything it was a think-aloud for myself to wrap my head around all the different ways of being for a math class. I may update the posts going forward as new resources come across my radar. As always, feel free to share insights and ideas.

Also in this mini-series:

3 comments on “Projects: what they’ll remember in 20 years”

Projects: what they’ll remember in 20 years

This is a post in the ongoing Emergent Math mini-series: Routines, Lessons, Problems, and Projects.

Projects - Card

I graduated high school twenty years ago this year. What’s remarkable is how little I actually remember about my classes. I remember certain feelings I had towards particular teachers or classes, but not the actual classroom action itself. There are three exceptions. There are four distinct activities I remember from my classes and they’re all projects:

  1. In my combined Physics/Calculus course we divined the accelleration due to gravity based on an experiment me and Eric Durbin concocted. And we were pretty close! We’ll call this the Learning Project.
  2. In AP Stats we conducted soil testing and surveyed the neighborhood to determine whether they cared about this issue. We’ll call this Project-Based Learning.
  3. In English we had to recreate various scenes from The Lost Horizon. We’ll call this the Dessert Project, for reasons which will become clear.
  4. In Biology we had to collect a bunch of leaves. I don’t remember why, but we had to do it. We had to get certain kinds press them is a special way. I hated it. We’re not calling this project anything other than The Leaf Project

That’s it. That’s all I remember about my classwork in High School. Don’t get me wrong: I remember other stuff too, like that time the time my friend Ash was talking so the teacher made him get up and teach the class,I recited “Shaft” in English class (“Who’s the black private dic that’s a sex machine to all the chicks?”), and my creepy Algebra 2 teacher making about ten too many jokes about “french curves.”

But by and large I remember the projects. Don’t get me wrong, there’s other stuff in there. I graduated college and everything, partially with some knowledge I acquired in school. But I only remember these actions.

Projects are an opportunity to illustrate how crucial your discipline is to the world or our understanding of it. They’re also an opportunity to waste several days or weeks of class time and force students to jump through imaginary hoops concocted by the teacher. In both cases, students will remember.

Projects apply mathematical knowhow to an in-depth, authentic experience. A project occurs over the course of two to four weeks. Ideally, projects are outward facing, community based, and/or personally relevant to students.

Let’s take a look at three types of projects. As with this entire mini-series, I’m painting with a broad brush and I’d happily concede that what I call one thing, might actually be another in another’s eyes.

The Dessert Project

I’ll withhold why it’s called the “dessert” project for now. These are typically given at the end of a unit intended to sum up the content. These often occur as a retelling of the content, such as my Lost Horizon example above. We read the book, we identify crucial scenes, and then we reenact them. We’re barely doing any analysis, let alone synthesis.

The best Dessert Projects take what a student has learned and unleashes it on an appropriate real-world scenario. Now that we’ve learned the content, we’re going to see how it looks in a different context. Most end-of-chapters offer this kind of project.

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A Dessert Project

The Learning Project

In a Learning Project, we learn something germane to the topic at hand through the use of an in-depth investigation. The structure of a Learning Project is more-or-less dictated by the teacher, but there is enough agency awarded to the students to experiment on their own. The WHY and HOW are often provided and the WHAT is relatively self-contained.

In my gravity example above, we were given the task (calculate the accelleration due to gravity), the materials (a video camera that allowed you to fast forward one frame at a time – this was the 90’s mind you), and the format of the product (a lab report). We had

It was a deeply memorable and engaging task. Unlike Dessert Projects, we are asked to actually find out something new, rather than repackaging information. Despite the fact that Learning Projects may not have a community partner, a public presentation, or a shiny final product (ingredients of Project-Based Learning which we’ll get to in a moment), we construct or deepen our understanding of some new knowledge or knowhow.

I’d suggest these as other examples of Learning Projects:

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A Learning Project

Project-Based Learning (PBL)

PBL has gotten the most headlines lately. Schools across the country want to provide deep, authentic, and motivating experiences for kids in all subjects. And to be sure, the best of PBL absolutely achieves that. Students are given a open ended, authentic challenge and students develop and present a solution. Through this process, students acquire new mathematical knowledge and skills.

In PBL (like Problem Based Learning), the task appears first and necessitates the content. Students learn the content in order to achieve their final product. Often – if not always – PBL occurs in groups.

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Project Based Learning

But don’t be fooled: quality PBL entails a lot more than just giving the students and letting go of the process entirely. The teacher/facilitator crafts the daily lessons and activities to support the process. The following graphic is taken from the New Tech Network, my employer. It explains well the various phases of a project and a menu of options for lessons, activities and assessments throughout a project.

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The project launch occurs at the beginning of the unit. It kicks off and drives the unit. In this case the project is the “meal” as opposed to the “dessert” (recall from early Dessert Projects). The project is how students will learn the material.

As an example, here are a few artifacts from one of my PBL Units about the 2000 Election. I’ve blogged about it before (twice, in fact!).

Project Launch: Have students read the Entry Document (the letter) and collect “knows” and “need-to-knows”.

To the students of Akins New Tech High School,

The US presidential election of November 7, 2000, was one of the closest in history. As returns were counted on election night it became clear that the outcome in the state of Florida would determine the next president. When the roughly 6 million Florida votes had been counted, Bush was shown to be leading by only 1,738, and the narrow margin triggered an automatic recount. The recount, completed in the evening of November 9, showed Bush’s lead to be less than 400.

Meanwhile, angry Democratic voters in Palm Beach County complained that a confusing “butterfly” ballot in their county caused them to accidentally vote for the Reform Party candidate Pat Buchanan instead of Gore. See the ballot above.

We have provided you the county-by-county results for Bush and Buchanan. We would like you to assess the validity of these angry voters’ – and therefore Al Gore’s – claims. Based on these data, is the “butterfly” ballot responsible in some part to the outcome of the 2000 election? What other questions do the data drum up for you? And what can we do to ensure this doesn’t happen again?

We look forward to reading your analysis and insight, no later than May 5.

Sincerely,

Your county clerk

Example project pathway – the 2000 Election

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In this example, we still retain many of the lessons and workshops that we would typically teach during this unit, but notably they occur as students are working towards various benchmarks and the final product. The lessons inform the student products.

There is enough to write about PBL to merit its own miniseries. Structures and routines are crucially important in a PBL Unit. Assessment must look different. Managing groups becomes an entirely different challenge. How the authenticity of the product and the external audience enhances the quality of student work.

For now, here are some other tasks that adhere to PBL.

How often?

The genesis of this entire mini-series stems from questions I receive about Problems and Projects. Mainly, “how often should I use problems? How often should I use projects?” The unstated part of that question is, “when do I actually, y’know, teach?” (Actually, sometimes that’s stated). I’ll save another post for “putting it all together” or “adjusting the levels” but know for now that’s why I put together this framework of Routines, Lessons, Problems and Projects.

As for the “how many projects?” question, I’ll give a squishy answer and a non-squishy answer.

My squishy answer: design a project whenever (A) the standards uniquely align such that you can create multiple lessons around one scenario and (B) when you can identify a project scenario that will maintain momentum over the course of several weeks.

My non-squishy answer: One or two a year. Most standard clusters don’t lend themselves to multiple investigations around one, single context. But some do! Content clusters around things like Data and Statistics, Area and Perimeter, and Exponential Growth and Decay are ripe for real-world scenarios that can be analyzed through the lens of multiple content standards.

As challenging as it is to design and facilitate projects, and as little time we have as educators to carve out the time for it, we don’t want to deprive students of the real-world insight math can have. We want to provide these experiences that will live on in students’ minds as the power of mathematics, whether or not they go into the field. So be on the lookout. Look for news articles and community opportunities that might embolden students to use math for maximum impact.

Also in this mini-series:

(Editor’s note: The original post had “dessert” written as “desert,” which is a different kind of project altogether, I imagine.)

4 comments on “Problems: then a miracle occurs”

Problems: then a miracle occurs

This is a post in the ongoing Emergent Math mini-series: Routines, Lessons, Problems, and Projects.

Problems - Card

Ah problems. I have to reveal my bias here: I love problems. Problematic problems. Problems are where I honestly cut my teeth as an educator. If you’re reading this blog, might have stumbled across my Problem-Based Learning (more on that specifically in a second) curriculum maps. I’ve blogged about Problem-Based Learning (PrBL) a bit. I’ve learned so much from teachers and math ed bloggers about what makes a good problem, how to facilitate a problem, what kinds of problems are out there. Some of that I’ll share here. Let’s just start with Problems.

The questions on voluminous review packets? Not problems. My first resource on problems, problem-based learning, and problem solving is NCTM’s research brief on problem-solving, Why is teaching with problem solving important to student learning? (2010). In it, it hints at the “what really is a true problem” question:

Story or word problems often come to mind in a discussion about problem solving. However, this conception of problem solving is limited. Some “story problems” are not problematic enough for students and hence should only be considered exercises for students to perform.

This brings us to my personal, current definition of Problems: Problems are complex tasks, not immediately solvable without further knowhow, research, or decoding of the prompt. Problems can take anywhere from one class period to three or four class periods.

So when I say “problems” I mean problems that are genuinely challenging to the problem solver. Even the difficult, toward-the-end-of-the-section questions may not be problematic enough for some students. Also, a problem ought not to be so obtuse or convoluted as to not be accessible for all students. Just because something is real hard doesn’t necessarily mean it’s a problem. If someone were to challenge me to make the U.S. gymnastics team, I wouldn’t consider that a problem; I’d consider it futility.

I like to think of good math problems like this: a good problem is accessible enough so students a couple grades lower can attempt it, yet challenging enough so students a couple grades above have to think about it. I actually think this of all mathematical tasks, but it’s particularly apropos of problems.

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Here’s a good problem (from Illustrative Mathematics):

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I like this problem for many reasons. One, it combines two not-often mathematical things: lines and quadratics. In most curricula you have your unit on linear functions and your unit on quadratics. Why aren’t these two things combined more often? I have no idea. Most textbooks presents lines in one unit and quadratics in another, as if they’re in a different universe. It’s like we’re reading a geography textbook about pre-Columbian South America and Europe. But back to our discussion of problems, it’s the confluence of these concepts that makes this such an interesting, challenging, and worthwhile problem.

There’s straight up problems – just give students a prompt and facilitate as you see fit.

There are countless other modes of problems, here are a few.

  • Would You Rather? problems

I’m not sure of John Stevens is the first “would you rather” problem designer, but he certainly codified it with his stellar website. A Would You Rather (WYR) provides students two possible choices and students must decide which one makes more sense to choose: which one is cheaper? which one is better? what deal gives the greatest value? etc.

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There are several things that make this format incredibly appealing: 1) Providing students an initial choice naturally facilitates guesses and estimates at the beginning of the problem. 2) Making it a choice makes CCSS.MP3, making arguments and critiquing the reasoning of others, a necessary part of the task. 3) In many cases, either answer may be correct, depending on how it’s interpreted, the desired outcome, or the input variables (in the WYR above, the answer may depend on how far away one is from the airport, how much airport parking is, etc.). And 4) there’s something delightful about the “would you rather” framing. Maybe because it reminds me of the “what’s worse?” scene from So I Married an Axe Murderer.

  • 3-Act Tasks

Dan Meyer gave us this format years ago and countless of math teachers have built upon it sense. Following the narrative structure of movie, in act 1 the “conflict” is established and we’re drawn into the plot of the movie/problem. In act 2, our hero / students go questing for the solution. In act 3, we come to a resolution.

Fig 5-11.pngMost often these act 1’s kick off with a video or picture to pique the interest. What do you notice/wonder? What do you think will happen? In act 2, students will work through the scenario presented in act 1, sometimes provided with additional information or knowhow that might be useful to solve the problem. In act 3, students make their final answer and we come to some sort of resolution (often by playing the last part of the video).

Dan has the most comprehensive list of 3-Acts, but others have followed suit with their own libraries.

I’m sure I’m missing others. Please let me know in the comments who I’ve missed.

Like WYR, there’s something inherently appealing about a narrative structure that we’re already used to. We’ve all seen movies, plays, TV shows, and read books. If you can provide a successful hook, we’ll want to see how the movie ends.

  • Just straight up puzzles

While sometimes challenging to align directly to required content, give students mathematical puzzles. NRICH has a great library of puzzle-like maths, or perhaps maths-like puzzles.

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https://nrich.maths.org/6903

And I don’t know if the authors (or you) would consider these puzzles, but I quite enjoy the tasks from Open Middle as puzzle-esque math.

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http://www.openmiddle.com/exponents-and-order-of-operations/

Problem-Based Learning

Let’s take a slight birdwalk into the practice of Problem-Based Learning or PrBL. It uses problems as a means to teach new concepts or knowhow. The problem creates a need (and in the best cases, a desire) that requires the intended content knowledge, additional information, or mathematical dispositions.

all

I suppose in some ways this may not differ much from just giving students the problem and teaching as-needed, as you go. In PrBL there’s an intentionality (and even predictability) with how the problem is posed and how the learning is facilitated (for instance, you prepare the lesson beforehand, rather than just winging it).

Facilitating a problem

One of the biggest mistakes teachers make when using Problems for the first time is that they think that by posing a clever enough problem, students will intrinsically work their way through it dilligently, testing out different methods along the way. And to be sure, it’s understandable to think that when you watch a presentation on problem solving in math or participate in a conference session and the participants or audience dilligently work their way through a problem. But here’s the dirty little secret about conference sessions: the audience is entirely composed of adults who are excited about math and presenters are showcasing their absolute best problems. It’s easy to present engaging problems as a panacea when the audience is entirely bought in and the presenter gets to cherry pick which problem or lesson he or she gets to present. So it’s easy to walk away from these experiences thinking that – just like in that session – I’ll present this super-cool problem to my students and they’ll collaborate, problem-solve, and stick to it just like at that conference.

It’s never that smooth. Rather than – like Carrie Underwood – letting “Jesus Take the Wheel” – you need to keep your hands on the wheel and your foot on the pedal (and sometimes the brakes as well). Problems should be facilitated, not tossed in like a hand grenade. So how do we facilitate a problem?

Use routines. The biggest tip I can provide for facilitating problems is something we’ve already covered in this mini-series: provide routines. Routines to get started on the problem, routines to facilitate discussion in the middle of a problem, and routines when students are sharing their solutions.

Consider this sample Problem facilitation agenda:

  • Introduce the problem
  • Facilitate a Notice & Wonder routine
  • Identify next steps and let students begin working
  • 20 minutes later, take a quick problem time out and have groups do a gallery walk routine to see how  and what other groups are doing
  • Give a problem “time in” and have students continue working toward a solution
  • After finishing the problem, have students show appreciations to one another via a routine.

One problem, three routines. And who knows? If students are struggling, you may want to hold a small workshop lesson in there as well. We’re starting to see our Routines, Lessons, Problems, and Projects framework become a set of nesting dolls.

Provide consistent group roles. Assuming students are working in groups, provide consistent, well-understood group roles.

Fig 6-8 alternate

And – like the problem itself – don’t just provide the group roles and hope for the best, check in with them and how they’re operating. Mix them up. Talk with them.

  • “I’d like the Recorder/Reporter from each group to meet with me at the front of the class for five minutes to discuss your progress.”
  • “Harmonizers – at this point give one of your teammates a compliment.”
  • “I’d like all the Facilitators to swap groups for the next ten minutes.”
  • “Resource Monitors – come up with a question as I’m going to go to each group and you can ask me one question.”

Use these roles, don’t just assign them.

Make Problems the cornerstone of your class

Quality problems won’t be the most often employed mode of teaching in your class, but make them the essential thing that students do in your class. Rich problems make for excellent assessment artifacts. They help teachers find the nooks and crannies of what students can do and know and what gaps in understanding still remain. They foster mathematical habits in a way that lessons and routines often can’t.

To be transparent, part of the reason I began thinking about this mini-series is because I was wrestling with the question: what’s the “right” number of problems to facilitate in a school year? And what are those problems? That’s when I began to think of the music mixing knobs analogy from my intro post.

There are endless ways to facilitate problems – use routines early, often and throughout a problem. Use Problems often and throughout a class. They are the bedrock of your class, and the discipline of mathematics more broadly.

Also in this mini-series: