Counting Idling Cars

pickupI’m sitting in my car, waiting to pick up my son from school. It’s too cold to wait outside  this time of year so I keep the heat on, the engine running, and continue listening to the Dunc’d On Basketball Podcast, the nerdiest podcast about basketball out there. I’m also quite anti-social, so I prefer to sit in the car, rather than, like, talk to people.

The driver of the car in front of me is doing the same (presumably, minus the podcast listening), ditto for the car behind of me. Maybe they’re reading “The Pickup Line,” an e-mag specifically for parents who sit in the car, waiting to pick up their kid from school. It occurs to me: boy there are a lot of cars idling in front of the school right now. I’d guess about 40. But y’know, someone should really count these up.

I get typically get to the school about 10 minutes before the release bell rings and I’m sort of in the middle of the pack of idling cars. I’d guess it’s about the average of when most cars arrive, again, most of which are idling. While I don’t conduct this environment-destroying practice all year long – when the weather is nice I’ll get out and check my phone, rather than talk to other parents – I practice it for maybe half the school year. That’s about 80 days or so.

80 days x 10 minutes of idling per day. Boy, 800 minutes of idling seems like a lot doesn’t it? And if there are indeed 40 cars at my son’s school, averaging a similar amount of idling time, we’re looking at 32,000 minutes of car idling. That’s over eight days of just idling.

We have a train that goes through town and we have signs encouraging us to turn off our car, rather than sit there idling, while we wait for the train to pass through. And I sometimes follow that instruction! I should probably follow it more often and more aggressively. But what about idling in the school pickup line? Or along the side of the school for us anti-socialites?

How much gas are we wasting?

How much Carbon Monoxide are we putting in the air?

How much gas waste / CO is the entire town/state/country contributing?

Would it be better to just switch off the car and start it later?

Boy, oh boy, someone oughta do the research on this…

What about at your school? How much gas is wasted in a day, week, or school year? Could students do the research? Could they create an awareness campaign for reducing gas waste (and presumably promoting cleaner air at their school)? Seems like something a bunch of go-getter students could handle.

 

Posted in elementary, problem based learning, projects, Uncategorized | Leave a comment

Why we teach the “other stuff”

reluctance

“I don’t know what to say.”

“I don’t know how to talk to him.”

 

I’m sitting in a coffee shop with my back facing a mentor and her mentee, a college student who is apparently struggling through her semester. I can hear them clearly, even though I’m trying not to eavesdrop. The mentor is pleading with her mentee to email one of her professors to get help with an assignment, or even figure out when office hours are. “I don’t even know what to say!” the student response. The mentor patiently describes what questions to ask and how to start off the email, to no avail. “I don’t know how to talk to him!” she keeps responding. Pretty soon the student starts doing that thing that teenagers do where they start laughing when they’re really uncomfortable . It’s an unintentional defense mechanism employed by nearly all adolescents. She’s embarrassed by her inability to perform a seemingly simple task, so she starts blushing and laughing.

“I don’t want to talk to someone else.”

“That sounds like so many words.”

Later on, the mentor is trying to get the mentee to call the registrar’s office to find some information about something or other. Again, the student giggles that she doesn’t know how to talk over the phone. The mentor clearly cares deeply for her mentee. The mentee is clearly embarrassed at how nervous she is communicating to professionals.

***

Teachers sometimes scoff when we implore them to teach those other things. Things like communication skills, groupwork skills, self-reflection, these are “soft skills” that don’t appear in our scope and sequence. The state test doesn’t address them, and we have too much content already to cover to worry about these phony-baloney skills. I’m a math teacher, I teach math, that’s what I do. That’s my responsibility.

I can’t speak to the mentee’s instruction, but I’ve seen it frequently enough. Listening to her, she was paralyzed when it came to communicating with other adults, or at all. This is something she did not learn, let alone practice, while in High School. And now it’s preventing her from succeeding at the post-secondary level. Her paralysis wasn’t that she didn’t know her content well enough, it was that she didn’t have the ability to find out how to further her content knowledge. Whether that was technically the purview of her secondary math teacher or not, the responsibility to prepare students for post-secondary life falls on each of her teachers and the system in which they teach.

Does that mean that it is your responsibility – as, say, a math teacher – to teach students how to make phone calls? Or email professionals? Or create a study group? Or manage their time? Or teach all of those non-math skills?

Yes. Yes, it is.

The reason I taught math was because I love math. The reason I taught math the way I did was because I wanted students to grow as communicators and problem-solvers. Thankfully, I taught in a school in which we were unified that these were indeed skills we wanted our students to have when they graduated. I now coach in a model that aspires to make that happen for all students.

In our classrooms, we have students call and set up meetings with mentors in the business or academic communities. We have students stand and defend their work. We assess students on eye contact as well as content knowledge. And we teach them how to do it, not just tell them to and let them flounder. We do these, not in isolation, but as an entire school. In my class, this included these activities, as well as complex math problems that required collaboration, presentation of new and novel ideas, and practice and structures to handle it when these proved exceptionally difficult.

 

***

I’m heartened by these mentor-mentee relationships. Whether they were established via a specific program or they grew organically, there’s genuine care there. As exasperated as the mentor was, she showed active, authentic caring. I’m glad the mentee has that support system in place now that she’s in college. She’ll need the skills her mentor offers, as she clearly didn’t receive them in High School.

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Vivienne Malone-Mayes and Waco, Texas

Vivienne Malone-Mayes grew up in Waco, TX, a highly segregated community in a highly segregated state. She attended a highly segregated high school where she graduated two years early at the age of 16 so she could pursue Mathematics at Fisk University, where she graduated in four years with a bachelor’s’ degree and another two years with a masters’. She worked as a professor at Paul Quinn College and Bishop College.

In 1961, she applied to take additional courses to begin her PhD work at Baylor University – my alma mater – but was rejected explicitly for her race. Required by federal law, the University of Texas admitted her (Baylor is a private university). Though she was admitted, she was not welcomed. “My mathematical isolation was complete,” she noted as she described her experience being the only female and the only African-American in many of her courses*.

Despite these challenges, Malone-Mayes obtained her PhD in 1966 with her thesis A structure problem in asymptotic analysis. Throughout her education she took part in civil rights demonstrations.

After she graduated with her PhD, she became the first full-time African American professor at Baylor University, the institution which had rejected her from taking courses just a few years prior. There she was voted the most outstanding faculty member by the student congress in 1971.

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This is an excerpt profiling mathematicians from my forthcoming book. It’ll be in the appendix along with other famous mathematicians and should-be-famous mathematicians.

I say “should-be-famous” because I’d never heard of Malone-Mayes. And I graduated from Baylor University, where she was rejected from taking classes because of her race and later a high profile university professor. I lived in Waco, TX for four years.

Part of the reason I’d never known Malone-Mayes was because of my own stupidity and probably-desired ignorance. But it’s kind of also on the University, isn’t it? I would have liked to have known of the achievements of this incredible woman while I was there. My classmates would have as well.

Why isn’t a fucking building named after Vivienne Malone-Mayes? Again, maybe things have changed since 2008. I’m sure there is a plaque somewhere on campus while I was attending, but I feel such shame for not knowing about Vivienne Malone-Mayes then and up until just a few days ago. I encourage you to look for what mathematical heroes may have been buried in your community. Please share them in the comments so we may unearth this invaluable, generally unspoken history and these amazing men and women.

For more on Malone-Mayes, I recommend this article from the Waco History Project, where the photo is taken from. See also, Complexities: Women in Mathematics.

*Case, Bettye Anne; Leggett, Anne M. (31 May 2016). Complexities: Women in mathematics.

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You are the Name Rememberer

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I’m just not good with names: It takes me a long time to remember them and even then I sometimes forget. 

Not anymore. For you are the Name Rememberer. The One Who Remembers Names.

It’s difficult with so many students. These first few months of school it’s hard to get names straight. I’m not a names person. 

It matters not. You will remember their names, Name Rememberer.

I’ve never been good with names. I can remember a face, but names are hard.

Maybe names are hard, maybe they are not. It doesn’t make any difference to you, the Name Rememberer.

I’ll get their names by the end of the month. It’s October, there’s still plenty of school year left.

You will get their names by tomorrow morning 8am. If this means you need to print out flash cards that is what you will do. If it means you need to find their address, drive to their house, wake their house up, and have a 30-minute conversation to remember their names, that is what you will do. That’s what the Name Rememberer does.

But I don’t know their addresses and I don’t have a car.

For every student that is in your class tomorrow whose name you do not know, you will give them free 100’s on assignments for a month. You will give each of them $100 a day until you remember their name. You will do 50 pushups for each student whose name you can’t immediately recall. And you will NOT under any circumstances make that face where you’re trying to think of their name.

But I have these kids that sit next to each other and they really look alike. What if I —

QUIET! You will learn every student’s name and you will learn them all now. Tomorrow morning you will stand by your door, greet each student BY NAME, and welcome them in to your classroom BY NAME.

But – 

SILENCE. You are wasting valuable time, Name Rememberer. Time that could be spent on remembering students’ names. The school day starts in 10 hours and you have names to remember. Or, as the Name Rememberer, do you have them all memorized? You have the proper pronunciations down seamlessly? First and last? There will be no beat skipping when you want to call on a student with his or her hand raised? 

Good. For tomorrow, you – in addition to being the Student Name Rememberer – will also become the What Students are Passionate About Knower. 

 

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Find, Adapt, Create: A Path Towards More Agreeable Task Design Time

In the past I consistently struggled with making the turn from the excitement toward problem-based learning (PrBL) to the actual design of complex, engaging problems. Typically I would spend the morning building the buy-in (the “why”), another part of the morning conducting some sort of problem simulation to showcase PrBL (the “how”). Then my instructions were along the lines of “OK gang, after lunch you’ll start designing your own tasks!” If you’re like me, you find it difficult to be creative on demand*. (I mean, if you’ve been keeping up with the infrequency of my blog posts in the past year you probably know that already).

Don’t get me wrong, I have little patience for math teachers who say “they’re not the creative type.” And I do think creativity is an under heralded attribute teachers need to have. It’s difficult to be creative at gunpoint.

I’ve started codifying what I believe is a more agreeable framework. Many of the successful implementation of inquiry-based, complex tasks has followed this progression (often over the course of multiple coaching sessions):

First: Find

Then: Adapt

Finally: Create

We start by finding (and often trying out) a task; then, at a later date, we try adapting a task (which we then implement); finally – and this is a tall ask – we try out creating a task more-or-less from scratch. This final step is probably more of a slow-walk from adapt than a full on design sprint.

FAC

Find

There are countless websites with open accessible tasks of ever-increasing quality and navigability. You know ’em, you love ’em. You can find a bunch on the “Math-like Blogs” list on the right side of this page. You can also find well organized tasks at IllustrativeMathematics, Shell Centre, Teacher.desmos.com, openmiddle.com and NCTM’s Illuminations.

An afternoon of PD spend simply clicking through your favorite, say, three of these resources is an afternoon well spent. That’s how the ol’ curriculum maps came to be.

Find something compelling and pretty soon you’ll find a ton of stuff you find compelling.

Adapt

Once you’ve found some good stuff, try to see if you can take something that’s pretty good and make it better. I’ve presented about that before: [NCTM] Adaptation.

This requires a bit more discussion and contemplation. You start to turn from “I like this task” to “What do you like about it?” Once we start adapting we are developing an implicit or explicit criteria for what makes a quality problem.

Maybe you adapt a problem by removing the sub-steps. That would suggest you like problems that allow for a lot of “open middleness.” Maybe your colleague adapts a problem to a hands on activity a la Fawn. That speaks to how much you value tactile experiences and students actually doing stuff.

Now – and only now – ought we turn to the ever challenging work of creation.

Create

Most of the time, creation of a task comes from either inspiration and/or sheer luck. I’ll see an advertisement or watching a movie and see something that’s kinda mathematical. Like I said, really tough to do on-demand, and also really tough to do in any kind of standards-aligned way.

But it’s also absolutely crucial! Not only does it work out your creative muscles, it generates tasks for the rest of us to find! It’s a give-a-penny / take-a-penny situation. Even if you’re not teaching, say, geometric constructions in your Algebra 2 class, maybe you get struck by a divine lightning bolt of inspiration that the rest of us can draw on. In that respect the Find –> Adapt –> Create framework could be seen as a cycle.

Find –> Adapt –> Create –> Other people find your creation

But yeah, it’s difficult to do on a good day, it’s much more difficult to achieve when I’m hovering over individuals harping on them: “got anything yet?

And this isn’t just true for tasks. Consider other instructional tools.

  Find Adapt Create
Rubrics NTN Learning Outcome Rubrics (Math) Pull from a few of the rubric indicators Design your own, based on your grade level, school context and content area
Lesson Plan Template Problem Planning Form Modify based on your class time Design a lesson plan template that works for an entire department
Math attitudes survey Here’s one I developed Steal a bit from it, but identify a few of the specific things you’re trying to deduce On your next iteration, make it totally your own!

I do believe that the best instructional experiences students have are by-and-large teacher-designed. Getting to that point is challenging so start with the stuff we have and slow-walk yourself into creation mode.

Y’know, unless inspiration strikes you like a lightning bolt while you’re sitting on the couch. In that case, disregard everything I said and go nuts, Creator.

* – Note: to contradict myself, this was not true of PBL Chopped! That was absolutely a fantastic experience of solely creation with incredible project ideas.

Posted in task design, Uncategorized | 2 Comments

2017 New Tech Network PBL Chopped Recap

I had the honor of co-designing and MC’ing the first ever PBL Chopped competition at the New Tech Annual Conference in July. While this is typically a blog about math instruction, this experience welcomed all content areas and all grade levels, teachers, principals and instructional coaches. It was an absolute blast and the teams were incredible. It’s so fun to be an observer to this cross-curricular design sprint. Below is a recap, followed by a link to additional resources and commentary – geoff

ST. LOUIS, MO — The only thing more intense than the current of the Mighy Mississip was the sweltering PBL Kitchen. Eight teams entered the Steelcase room on an overcast Saturday afternoon hoping to design the “tastiest” of projects based on three mystery “ingredients.” These ingredients came in the form of three randomly selected standards from across the curriculum.

Each team had 20 minutes to design the outline of a PBL unit based on the following standards which were drawn at the time of the competition.

  • Natural selection leads to adaptation, that is, to a population dominated by organisms that are anatomically, behaviorally, and physiologically well suited to survive and reproduce in a specific environment. (HS-LS4-3),(HS-LS4-4)
  • Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. (CCSSM.A-CED.A.4)
  • Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts. (CCSS.ELA-LITERACY.RH.6-8.7)

As soon as the standards were drawn, the first round of the competition began in a flurry of ideation and activity. Teams scribbled on whiteboards provided by Steelcase. Participants. The end of the 20 minutes was punctuated by a “3…. 2….1… Markers down! Cooking time is over, chefs!” Exasperated from the intensity, participants – teachers and principals alike – let out a cry of triumph. While the design of a PBL Unit – with carefully selected and uniform standards – can take hours, competitors had come together to create an engaging, meaningful project in 20 minutes.

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Sadly, only three teams could advance to the final round. This proved to be the most difficult part of the competition – for the judges. After some deliberation, looking through the eight project ideas, they identified the three projects that allowed their creators to advance to the final round. At this point, standards were drawn again:

  • ELA: Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
  • SS-Geo: Use geospatial and related technologies to create maps to display and explain the spatial patterns of cultural and environmental characteristics.
  • Sci: The complex patterns of the changes and the movement of water in the atmosphere, determined by winds, landforms, and ocean temperatures and currents, are major determinants of local weather patterns.

As before, 20 minutes flew by in a flash and the three teams developed PBL Units that would be uniquely engaging and meaningful to their students. They presented to the judges who asked them critical questions to get a sense of the scope of the project and the team’s understanding of the project.

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After two rounds of high pressure, minimal time PBL design one team was left standing. The judges – after much deliberation and pained conversations – came to the unanimous conclusion that Scottsburg New Tech‘s final project was the one to take them over the finish line. They were announced as the winners at the next morning’s plenary session.

But while Scottsburg got to take home the lovely 2017 NTN PBL Chopped Trophy (which we can only assume is currently being prominently displayed in a proper trophy case), everyone who competed won something. Some teams walked away with a greater understanding and empathy for teachers of other disciplines. Some teams walked away with a greater camaraderie with their peers. Other teams walked away with an actual project that they promised to refine and implement in a cross-curricular experience.

So congrats are in order to the winner, Scottsburg New Tech, but given the creative explosion in the Steelcase room on that Saturday afternoon, congrats are also in order to the thousands of students who will benefit too, from PBL Chopped 2017.

(Note: in addition to the recap here, you can find additional information, commentary, and details on the New Tech Network blog. [link coming soon!])

 

 

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Active Caring, or, “Give a Crap”

I’m in awe of my son’s 3rd grade team.

Last year, when he was in 3rd grade, he had two teachers, a counselor, a GT specialist, a principal, and three specials teachers that cared for him. Not in a passive way, like a “my door is always open” kind of way. But in an active, give-him-hugs, come-to-multiple-parent-teacher conferences, “let’s figure this out” kind of way. One kid, eight adults just pouring love onto him. And he’s a kid that needs outward expressions of love.

As he enters fourth grade, he’ll have a lot of the same adults in his life next year as he did this past year, thankfully. I’m confident in fifth grade he’ll get that same level of care as well. Consider this blog post a partial paen to elementary schools that get that it truly does take a village.

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A while back I critiqued myself for not writing about Social and Emotional Safety as I do Tasks and Facilitation. If I’ve evened out the ratios of those three elements, it’s only because I’ve written less on the blog in aggregate in the past year.

Nevertheless, I have been writing. And much of that has been about caring.

You see, we secondary teachers think we’re caring. I told kids they are welcome to hang out and talk after school. I left an open invitation for kids to come before school to get work done. I invited all students to participate. I said “good morning” at the beginning of the day. Shoot, I even greeted every kid with a handshake at the beginning of every class period. And, with a few students, I truly did have that special relationship such that I made an impact on their lives.

I showed passive caring. I opened the door and beckoned kids to come through.

Elementary teachers – at least the ones my son has – they show active caring. They open the door, beckon kids to come through, and when they don’t they’ll leave their room, grab them by the arm and bring them in. They don’t just invite kids to participate, they demand  it and make it a norm in their classroom. They don’t just say “good morning” at the beginning of the day, they hug my son, ask him how his dance class was, give him a specific word of encouragement, and then give him another hug.

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I worry about the level of care it’s realistically possible to show a kid as he or she progresses through middle and high school. While it Takes a Village, kids graduate into an assembly line. They get 50 minutes with a Social Studies teacher, then they move down the assembly line to obtain their Science Parts. How many days in a row can a kid go without being shown care? I’ve talked to students who feel “invisible.” I’ve shadowed students that don’t get called on for an entire day.

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I write about this in my book that will eventually be written, if I’d ever stop using the damn passive voice (see: this sentence). I was talking with a 10th Grade teacher who suggested, “maybe you should just call that chapter ‘Give a Crap.'” I laughed. And she’s right! While I don’t think I can get away with that title for a section (let alone a chapter), that’s probably the biggest differentiator between effective classrooms and ineffective ones.

Becca may have put it best:

I know it’s incredibly challenging for secondary teachers, who have limited time and expansive content to get through and, like, hundreds of students. But I’ve seen secondary teachers do it. And it’s absolutely a beautiful scene to behold, if only because it’s relatively rare in the hustle-and-bustle of the secondary learning ecosystem. I encourage you to show active caring, rather than just passive caring this year. Because that third grader who needs a word of genuine encouragement, still might need one in 10th grade.

 

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Post-It Problem: Grades 2-3

If imitation is the purest form of flattery, then Graham should be pretty darned flattered. I imitated (read: stole) his The Big Pad problem for slightly younger grades. Graham’s task necessitates fractions, which was a bit further down the line for my intended audience, roughly grades two or three. In this task, the giant Post-It is 15 inches x 15 inches and the small Post-Its are 3 in x 3 in. Enjoy!

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(Coming soon: a 8 in x 6 in Post-It Problem for grades 4-5, with additional commentary)

Act 1

Facilitation:

  • Watch the video. What do you notice? What do you wonder?
  • How many small post-its will it take to fill up the big post-it?
  • What do you know? What do you need to know in order to solve the problem?

Act 2

Post-It Problems 15x15 Act 2.png

Post it Problems Act 2 Post its.png

Act 3

Posted in elementary, Uncategorized | 1 Comment

Systems of Linear Inequalities: Paleontological Dig

(Editor’s note: the original post and activity mistook Paleontology for Archaeology. Archaeology is the study of human made fossils; paleontology is the study of dinosaur remains. The terminology has since been corrected and updated. Thanks to the commenters for the newfound knowledge.) 

Here’s an activity on systems of inequalities that teaches or reinforces the following concepts:

  • Systems of Linear Equations
  • Linear Inequalities
  • Systems of Linear Inequalities
  • Properties of Parallel and Perpendicular Slopes (depending on the equations chosen)

In this task students are asked to design four equations that would “box in” skeletons, as in a paleontological dig.

DOC version: (paleo-dig)

This slideshow requires JavaScript.

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Facilitation

  • Give students the entry event and instructions. Have one student read through it aloud while others follow along.
  • Consider getting started on the first one (Unicorn) as a class. Should our goal be to make a really large enclosed area or a smaller one?
  • Students may wish to start by sketching the equations first, others may chose to identify crucial points. Answers will vary.
  • If you have access to technology, you may wish to have students work on this is Desmos. Personally, I prefer pencil and paper. Here’s the blank graph in Desmos:  https://www.desmos.com/calculator/y1qkrfnsw2
  • For students struggling with various aspects of the problem , consider hosting a workshop on the following:
    • Creating an equation given a line on a graph
    • Finding a solution to a system of equations
  • Sensemaking:
    • Did students use parallel and perpendicular lines? If so, consider bubbling that up to discuss slopes.
    • Who thinks they have the smallest area enclosed? What makes them think that? Is there any way we can find out?
    • Let’s say we wanted to represent the enclosed area. We would use a system of linear inequalities. Function notation might be helpful here:
      • f(x) < y < g(x) and h(x) < y < j(x) (special thanks to Dan for helping me figure this notation out in Desmos!)

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=== Paleontological Dig ===

Congratulations! You’ve been assigned to an paleontological dig to dig up three ancient skeletons. Thanks to our fancy paleontology dig equipment, we’ve been able to map out where the skeletons are.

Your Task: For each skeleton, sketch and write four linear functions that would surround the skeleton, so we may then excavate it.

Check with your peers: Once you have it, compare your functions to your neighbors. Their answers will probably be different. What do you like about their answers?

Optional: For the technologically inclined, you may wish to use Desmos. (https://www.desmos.com/calculator/y1qkrfnsw2)

Challenge: What’s the smallest area you can make with the four functions that still surround each skeleton.

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https://www.desmos.com/calculator/6v0rb28bsl?embed

Posted in algebra, linear functions, linear inequalities, problem based learning, systems of equations, Uncategorized | 6 Comments

Is bad context worse than no context?

In elementary classes we consider it a good thing to be able to move from the abstract to the concrete. We ask students to count and perform arithmetic on objects, even contrived ones. We ask students to group socks, slice pizzas, and describe snowballs. A critical person might suggest these are all examples of pseudo-context, and they’d be right! These are more-or-less contrived scenarios that don’t really require the context to get at the math involved. Why do we provide such seemingly inessential context? I’m venturing a little far away from my area of expertise here, but I’d guess it’s because it helps kids understand the math concept to have a concrete model of that concept in their heads.

My question is this: in secondary classrooms, is there inherent value in linking an abstract concept to an actualized context? Even if the context is contrived?

I mean, yeah that’s bad. Comically and tragically bad. It doesn’t do anything to enhance understanding. I’d say the context actually hinders understanding. The thickness of an ice sculpture dragon’s wing? That’s about three bridges too far.

But what about a slightly less convoluted, but also-contrived, example. Say:

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This problem is still most certainly contrived: dimensions of tanks aren’t often given in terms of x. I’m not even suggesting this problem will engender immediate, massive engagement, but it might help students create a mental model of what’s going on with a third degree polynomial. Or at least the context allows students to affix understanding of the x- and y-axes once they create the graph of the volume of this tank.

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We provide similarly pseudo-contextual in elementary classrooms in order to enhance understanding of arithmetic and geometry.

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From Burns’ “About Teaching Mathematics”

Of course, we also compliment such problems with manipulatives, games, play, and discourse, which secondary math classrooms often lack. In the best elementary classrooms we don’t just provide students with that single task. We provide others, in addition to the pure abstract tasks such as puzzles or number talks.

Perhaps the true sin of pseudo-context is that it can be the prevailing task model, rather than one tool in a teacher’s task toolbox. In secondary math classrooms pseudo-contextual problems are offered as the motivation for the math, instead of exercises to create models and nothing more.

(See also: Michael’s blog post on Context and Modeling)

Posted in commentary, problem based learning, Uncategorized | 7 Comments