Monthly Archives: September 2012

Flipping the Flipped Classroom

In an earlier post I questioned the trendy use of foldables. Today I want to question the flipped classroom model which is all the rage right now. If you’re somehow unfamiliar with this model, here’s a handy infographic you should check out.

So the basic premise of the flipped classroom is that the lecture portion of instruction is recorded in some way and students watch this lecture on computers at home for homework. Then, in class, the students work on more engaging activities (practice) because they’ve already “learned” the content of the lesson at home. The teacher, free from having to lecture, is able to walk around and help students with problems as they arise. Educators like to talk about transitioning their role from the “sage on the stage” to the “guide on the side” and this model definitely allows for that transition in roles…in the classroom only.

Here is my primary concern:

What is with the insistence on the lecture (direct instruction) model?

Teachers appear to be loving the ability to offer more engaging, open-ended activities in class now that students are watching lectures at home.

What was stopping these teachers from offering these kinds of activities before?

Why do teachers think students have to be told what to do before they actually do any math?

The use of instructional videos as “pre-learning” shows that the transmission model of education is in no danger of going away. In all these years, hasn’t the field of education learned enough about how students learn best to know that talking at them is not ideal? Don’t get me wrong, having access to these kinds of videos as a resource is great. If I’m working out a problem, and I realize I need to brush up on the Pythagorean theorem, then watching a 5-7 minute video might be super helpful. Why do we assume students need to be told everything they need to know about a concept or a strategy before trying out a problem or two for themselves?

Flipping the Flipped Classroom

If anything, I would rather suggest flipping the classroom in the other direction. First, start with an engaging problem. Look at Dan Meyer’s three act problems for one approach. Don’t spend a lot of time talking at your students from the get go. Have a brief discussion about the situation and then let them go. If it’s challenging, let them work in pairs or small groups to brainstorm together. If they finish quickly, give them some other problems related to the big idea of the lesson. Finally, pull the class together and debrief. Talk. Have discussion, not lecture. At this point, if you want to tell the students something, they are much more receptive to hearing it and asking questions about it. I have witnessed this first hand. Students are more talkative after engaging with content, not before. Students love to think and talk, but they are more readily engaged if they have some connection with what you’re talking about. And if you still want to make an instructional video, great! The students have struggled with the content, they’ve talked about it with each other, and they’ve talked about it with you. Watching a video might help cement ideas that they weren’t quite sure about yet.

With this model you’re showing students that they can learn content without having to be told exactly what steps to take. Instead the role of a student is being problem solvers engaged in their own learning and processes, rather than passive recipients of information that may or may not “stick” or that they may not understand how to apply.

The Medium is the Message: (3) Constraints of print textbooks

I was going to do a post on print materials in general, but then I realized there are two types of print materials that I want to discuss separately. The first is print textbooks, which are ubiquitous in public education. The other is print curriculum that is not a textbook. If you’re not sure what I mean by that, bear with me. I’ll get to it in a post or two.

So, without further ado, let’s dive deeper into the design of print textbooks. What design choices were made intentionally or unintentionally that yield the stack of books you may or may not be using in your classroom?

I’ll start with the constraints. Remember, a constraint is something that hinders. What features of a textbook hinder the users? How do they hinder teaching? Hinder learning? Hinder understanding?

Constraints – Print Textbooks

  • Content is fixed at the time of printing.Once a print run is complete, there’s no going back. What is written in the book will always be written in the book (at least until a new edition is published).
    • The teacher cannot change or update any information in the book. If she finds an error or an extra example to share with her class, she cannot modify the book in any way. Sure, she can take the effort to add a sticky note inside her book, but is she responsible for doing that to every textbook in her class? What happens if sticky notes fall out of some books and not others? Fundamentally, the teacher has no control over the content in the book itself.
    • Even more troublesome, the students can’t make any changes either. Textbooks are knowledge students can hold in their hands, but they cannot change or challenge it in any way. This may yield the unintended consequence of altering a student’s perception of knowledge, where it comes from, and whether knowledge is something that can be created. The textbook for each subject is like a bible for that subject. It’s the students’ job to…what? Read it? Memorize it? It isn’t obvious from looking at a textbook that nearly every subject is in flux in some way. There are people out in the world studying new facets of every subject, expanding our knowledge, and even creating brand new subjects to study and learn more about.
  • Textbooks are heavy.Textbooks are printed on hundreds of sheets of paper per book and they usually have a hard cover to help them last for many years. As a result, they’re heavy!
    • They are portable in the abstract, but in reality textbooks are a pain to transport. They are much larger than paperback novels and much heavier. Carrying one around can be a nuisance. Carrying around a backpack full of textbooks is even worse. The unintended consequence of this is that some students may choose not to take them home for homework. Maybe it’s not cool to be seen weighted down by a full backpack. Or maybe you have an instrument case, gym bag, and backpack to lug around. You might start making some difficult decisions about what “must” come home with you because you don’t want to carry all of it. Or maybe you don’t go home right away, or you walk home, or you ride a bike. Carrying textbooks in any of those situations makes you feel like a pack mule, and on a bike it may even be dangerous.
  • Textbooks are light…on teaching.
    • Let’s consider a math textbook. If I open my textbook to teach a lesson, I get very little support with how I should actually be teaching the concept. Sure, there are a few worked out problems at the front of each lesson and those are followed by various problem sets. Great. But how do I teach the lesson? What should I be doing and saying with my students so that they build a strong understanding? The teacher manual may include a few questions you can ask your students about the worked out problems, but beyond that there is very little pedagogical guidance. The unintended consequence of this is that it reinforces a transmission model of education. Each lesson contains information that the teacher needs to transmit to the students. By reviewing the worked out problems together, probably in a lecture format, the students are supposed to learn the skill(s) they need in order to succeed on the problem sets. Does success on problem sets mean you know math?
    • Now let’s consider a science book. Many science books I’ve seen and used are dense repositories of information. They may make great reference material, but what they imply about teaching science is an entirely different matter. The science textbook I used in my last school started out each chapter with directions for a hands-on experiment. That sounds great, but all that taught my students was that experiments are already written; you just need to follow the directions. This leads directly into numerous science fair projects that are mislabeled as experiments. They usually turn out to be demonstrations – the end result was known before the student ever started working. Beyond the science “experiment” at the beginning of the chapter there are pages and pages of text and illustrations. What does this tell me as a teacher? My students have a lot of information to learn! What does this tell my student? Science = reading. Lots and lots of reading. Usually followed by reading comprehension questions.
  • Textbooks are not good at controlling information.
    • Imagine a textbook writer. She has the best of intentions. She wants to present a really meaty problem. She creates a diagram to accompany the problem just in case students need it. Unfortunately, she has little control over the presentation of the diagram. Most likely it will be printed mere centimeters from the problem. Rather than construct their own model or diagram, students will assume they need to use the one provided in the book, even if that wasn’t the writer’s intent. The same goes for worked out problems at the front of the lesson. The answer is usually right there on the page. Students are just going through the motions everyday to recreate the answers in the book.

That’s all I have on constraints for now. In the next post in this series I’m going to take a look at the affordances of print textbooks. After talking about how textbooks hinder teaching and learning, it may surprise you to find out there are actually features that enable the same.

Collaborating for fun…and profit?

I witnessed a heated exchanged on Twitter this morning that I want to address in more than 140 characters. Here’s the gist:

Twitterer1 (T1) posted a game to Teachers Pay Teachers (TPT). From what I could tell, the game was based on a game from someone else’s blog. Twitterer2 (T2) called her out on it, saying that she was making money off of the ideas of other bloggers and plagiarizing their work. She went on to say that the members of the mathtwitterblogosphere do not like TPT and do not support its use for this reason. T1 claimed she did give credit to the person who she was inspired by, but T2 said that’s not good enough. T1 also pointed out that there are other mathtwitterblogosphere members with TPT stores, so obviously some people are okay with it. Eventually T1 removed the offending game from her TPT store.

At first blush, this is a pretty straightforward issue – T1 took someone else’s work, made slight modifications, and attempted to sell it for profit. However, upon reflection, I find an interesting double standard here. In my eight years working in the classroom, I saw countless examples of copyright infringement perpetrated by fellow teachers.

  • Copying entire commercial workbooks that someone else bought so the teacher has a copy in their files
  • Making posters for their classroom using licensed characters such as Winnie The Pooh, Mickey Mouse, and Dora the Explorer
  • Playing full movies and songs for which the teacher does not have express permission

And I get why teachers do these things. For one, teachers are not made of money. They aren’t copying workbooks because they don’t like spending their own money. They’re doing it because they can’t afford to buy an entire library of instructional materials. As it is, teachers often purchase many supplies and materials for their classroom using their own money, but there is a limit to how much they can spend. Schools sometimes have budgets to help teachers purchase supplies and resources, but not always. Second, teachers want to make their classrooms fun and engaging for their students. Using licensed characters is appealing to many students so teachers include them. I don’t personally care for it because students are bombarded with enough advertising to buy products associated with these characters, but that’s a whole different matter.

So basically, I’ve seen many teachers willingly cheat the system and steal from outside businesses. In their minds, I’m sure it feels out of necessity to provide the best learning for their students. However, it intrigues me that when a teacher takes an idea from another teacher and makes some money off of it, other teachers get up in arms about plagiarism. That’s not to say that T1 was right to do what she did, but it still strikes me as a double standard.

The other part that gets me about this is that teachers should know that ideas are recycled over and over and over. Games especially are rehashed throughout the years. I’ve seen 4th graders playing variations of games I played when I was a kid. When I told them I played that game when I was younger, I’ve had them reply I couldn’t have because so-and-so’s sister just made up the game. Look at foldables as another example of content that is invented over and over. Dinah Zike might be the queen of foldables, but do you think every idea is originally hers? Do you see her going after every teacher who shares foldables ideas for free or profit?

There is a definite gray area as teachers are planning lessons because for the many ideas they have, it is not feasible for them to check if there is a copyright on every single one. Also, is it the idea that is copyrighted, or just the materials that come with it? For example, I love the game Close to 100 that I learned from using TERC’s Math Investigations curriculum. I don’t have the materials anymore, but if I was to make a version for my class now, would I be breaking copyright law? Do I even know if TERC invented and copyrighted the game? Do I have time as a teacher to navigate all the legal waters just to play a game with my class? I definitely don’t have the time to do this for everything I do on a daily basis.

Okay, on to the other side of this issue. I don’t just have a problem with what T1 did. I also take issue with T2’s response. The way T2 characterized it, the mathtwitterblogosphere is some kind of entity that has specific members and specific rules. I don’t agree. From what I have gathered since starting blogging a few weeks ago, the mathtwitterblogosphere is an initiative, not an organization. A few people who have seen the value in blogging and twittering with fellow educators were inspired to encourage others to join them. And join them they did! There was a huge group of educators who started blogging in August, myself included. We did not join an organization, however. There was no application process so I could connect with these folks. There are no membership fees. There is no charter. The “members” of the mathtwitterblogosphere are a loose collection of educators who share a similar interest in talking about math education and sharing ideas with each other.

Don’t get me wrong, I completely understand why T2 was upset. There is something sketchy about freely sharing ideas with people only to find out some of the people you’re sharing with are taking your ideas and selling them for profit. There are some issues with integrity and professional ethics there. However, I don’t appreciate T2 speaking for the entire mathtwitterblogosphere since it is not a defined entity. I would have preferred T2 to keep it personal – I don’t like TPT. I don’t like sharing ideas so others can make a profit. Others are then welcome to add their voices if they agree. As T1 pointed out, there are other members who have TPT stores. Heck, I’m sure that is true throughout the twitter and blogging realms. I’ve seen numerous postings on #edchat advertising sales in TPT stores. I have no doubts that some of these people are reading blogs, getting ideas, and creating materials to put in their stores. Are they getting permission to use other people’s ideas? Probably not.

Honestly, I feel sad mostly for the teachers who are turning to TPT for their educational resources. From what I’ve seen in my short time blogging and twittering there are so many people willing to share ideas, lessons plans, and instructional materials for FREE. Perhaps finding and keeping up with blogs is too much work. There is something to be said for the convenience of going to one site, searching for a specific topic, and getting the materials you need right then and there. It might cost you a few bucks, but pretty much everything comes down to time vs. money. Some have more time, and some have more money.

In the end, I’m glad T1 took the materials out of her store. It did seem like the right thing to do. So what am I taking away from all this? The mathtwitterblogosphere is a collection of educators who want to stay connected and support each other. Unfortunately, our shared interest in education does not necessarily mean that everyone shares the exact same values. I’m okay with that. The rewards definitely outweigh the trade offs.

UPDATE: So shortly after posting this message I came across a news story about a teacher who has earned over $1 million selling lesson plans on Teachers Pay Teachers. It raised an interesting ethical question for me. Is there a legal conflict in this situation? Who owns teacher lesson plans? If I was a teacher, and I made lesson plans for my students, I am doing that as a paid employee of a school district. If I then take those lesson plans and sell them elsewhere, do I have the right to do that? Do my lesson plans belong to me or my school district? Do I have the right to double dip?

The reason I ask is because working as an instructional designer for a curriculum company, I know my company would take serious issue with me taking lesson plans from my job and selling them on another site for my own profit Heck, they would probably even take issue if I made lesson plans on my free time and just sold those lesson plans. And I would understand their concern. If I made lesson plans on my free time that are worth selling, does that mean I am not giving my company my best effort during the work day? Am I holding out, so to speak, saving my best ideas for the work I do in my free time? It’s an interesting issue, and I wonder if there is an answer with regards to public school teachers. I’ll have to check around.

The Medium is the Message: (2) Laying out my perspective

So what started as an interesting topic I’d like to entertain is quickly ballooning into something that will likely take me several blog posts to thoroughly explore. I’m okay with that. If you ever meet me in person you’ll learn that I can (and like to!) talk at length about education matters, so really this is no surprise to me.

Source: Amazon

I’ll be up front that I’m going to approach my analysis from a user-centered design perspective. If you are unfamiliar with user-centered design, I encourage you to check out the provided link for additional information. I also highly recommend the book The Design of Everyday Things by Donald Norman. It was one of the first books I read in grad school, and it had a tremendous impact on my thinking with regards to designing curriculum materials and instructional technologies. Here’s a quick summary of user-centered design from the Wikipedia article I linked to:

“The chief difference from other product design philosophies is that user-centered design tries to optimize the product around how users can, want, or need to use the product, rather than forcing the users to change their behavior to accommodate the product.”

Now, I’m not saying that any curriculum materials were designed according to this perspective, but they are definitely worth analyzing from this perspective. The end users – teachers – often have very strong opinions about the materials they use with their students. Throughout my posts you’ll hear me refer repeatedly to constraints and affordances. These are key ideas from Donald Norman’s book. I’m probably not using the terms exactly as Donald Norman did, so I’ll give my working definitions.

A constraint is something that hinders. For example, a constraint of a wooden pencil is that it has a finite supply of lead. Once you have exhausted the lead, you need a new pencil.

An affordance on the other hand is something that enables. For example, the casing of a mechanical pencil enables you to use the same pencil continuously because you can add lead any time you run out. (Granted this quickly raises the constraint that if you run out and have no supply of extra lead, then your mechanical pencil becomes just as useless as the wooden pencil.)

In addition to constraints and affordances, I also foresee myself talking about assumptions and unintended consequences. I’m writing this post before I’ve written any of the meat of this blog series, but I’m interested in both topics so I’m sure they will come up as appropriate. For example, what assumptions does a textbook publisher have about the teachers who will use its product? Or, what are the unintended consequences of introducing digital curriculum materials in a classroom?

And with that question, I’d like to close this post with a quote that sums up the work of curriculum designers:

“The best laid schemes of mice and men go often awry…”

Or if you have a more cynical view of the relationship between publishers and teachers:

“No battle plan survives contact with the enemy.”

The Medium is the Message: (1) Taking a closer look at curriculum materials

Earlier this week I read a post on Dan Meyer’s blog where he proposes a hypothesis that print curriculum materials interfere with students’ and teachers’ ability to abstract while doing math.

“It should go without saying that if the contexts in your textbook are predigested with those symbols, tables, line drawings, and coordinates, we’re already in trouble. The context has already been abstracted and we can only hope that every student already understood how to apply that abstraction.

My hypotheses here is that this predigestion is a fundamental condition of print-based curricula and very hard to counteract.”

This led to an interesting question in the comments from Bryan Meyer that really resonated with me as an instructional designer. I’m going to summarize a bit, but the question he puts forward is whether the problem is inherently one of print curriculum specifically or prepackaged curriculum in general (regardless of delivery method).

“I’m just not sure that the release of pieces of a lesson should be in print (or video, or otherwise). Possible trajectories that students might take with a question/task/problem can be hypothesized, but never predicted with certainty. For this reason, I don’t see how we could ever prepare a scripted curriculum in this sense….it should always unfold in response to students and their ways of thinking.”

I didn’t want to reply to this and overtake Dan’s comments. It’s his blog after all, and he’s looking for feedback related more to the hypotheses he’s making this week about the ladder of abstraction. Instead I decided it would be better to address this on my own blog where I have all the space I want to write about it. Rather than dump all my thoughts in one post, my plan is to address various curriculum modes individually – print and digital – followed by my thoughts on prepackaged curriculum compared with “home-made” lessons by teachers.

In case you’re wondering about my ability to address these topics, I have experience on both sides of the issue. I’ve been on the side of the “consumer” buying and using curriculum materials when I taught in public school for 8 years. And now for a little over three years, I’ve been on the side of the “producer” creating commercial curriculum materials. My perspective has definitely expanded considerably over the past 11 years, and I’m excited to have the opportunity to stop and reflect on such an interesting issue.

Reflecting on my first live Twitter chat

Source: renjith krishnan via

Tonight I took part in my first live Twitter chat (#1to1techat). The purpose, if you can’t tell from the hash tag, is to discuss 1:1 computing in the classroom. Since I work for a company that designs curriculum for use in 1:1 classrooms, it seemed right up my alley. Little did I know what a negative reaction I would have to the discussion.

Going in I had no idea what to expect. I went in hoping for a discussion, and I left thinking that Twitter is just not the most effective mode for talking about ideas in depth. 1:1 computing is a big topic with a lot of ideas embedded in it. Trying to capture significant thoughts in 140 characters (less after you write the hash tag and even less if you’re replying to one or more people) is frustrating to say the least. Instead of a discussion, where ideas are put forth, analyzed, and discussed, I felt like I was bombarded by platitudes about why computers in the classroom are good for kids.

“Equity for all!”

“Global citizens!”

“Level the playing field!”

“1:1 help kids find their passion!”

“Makes learning relevant!”

“Critical thinking!”

I rolled my eyes more than once while following the discussion. I felt like I was at a fan club meeting – a bunch of people getting together who love 1:1 and love to gush about it. Which is great in a way. These people are obviously the pioneers with regards to 1:1, and usually those folks are the most motivated to use new ideas and share them. I applaud their commitment to integrating technology into the classroom.

There was some good questioning for sure. For example, one person asked what other schools had learned NOT to do with regards to implementing 1:1. It’s great to learn from others’ mistakes, and several people chimed in on this question. Unfortunately the useful aspects of the conversation felt few and far between. Overall, despite lasting an hour and generating a couple hundred tweets, the discussion felt shallow.

It didn’t help that I ended up reacting in a way I didn’t expect. As someone who works for a company developing 1:1 curriculum materials, I’m obviously all for 1:1 solutions in the classroom. I do think that technology can augment what teachers and students are already doing so that they can do even more amazing things. However, in my time with my company I’ve seen another side to the issue: cost, specifically as it relates to the added value of the technology.

Up until now teachers have managed to teach the required curriculum standards without the use of computers. They also managed to teach critical thinking. They even managed to connect globally through pen pal programs. What is technology adding to the mix that justifies the expense of buying every child a tablet or netbook? This is a question I’ve heard frequently.

I know technology devices are coming down in price, but they still cost a lot to outfit all of the students in a grade, school, or district. There are even more costs beyond that. What if you want to buy a digital curriculum to go with it? Or pay for yearly subscriptions to various learning sites? Or buy apps for your students to use? Oh, don’t forget you might need to put some money into getting your district infrastructure up to speed to handle all of these news devices and tech support to handle malfunctioning/broken/stolen devices.

The news is full of stories of districts that are having budgetary problems. Some districts have even had to let go of teachers. If a district really wants to take on 1:1, they better have something to show their taxpayers to justify the expense. And guess what they hang their hopes on. Test scores. Basically, if you invest thousands upon thousands of dollars to buy a computer for each child, it’s reasonable to expect your test scores are going to soar through the roof, right?

Wrong. An iPad or netbook does not raise test scores. (By the way, I’m not even a proponent of judging 1:1 based on test scores. This is just a reality I’ve had to learn to deal with in my job.) Technology is just a tool. How that tool is used will determine the effect it has on student learning. A tool can be used appropriately or inappropriately. A tool can have different features depending on what model you buy. A tool can be…a tool, nothing more.

I realize I could go on and on, but I’ve said enough for tonight. I’ll have to revisit this topic in greater depth later. I’m glad I stopped to reflect on my first Twitter chat experience. I’ll probably take part in more, but I can’t say I have the best outlook on them so far. I want to believe that Twitter is great for PD because it allows you to connect with so many people, but if you can only speak in sound bites and platitudes, how high quality can it really be?

Sadako and the Thousand Paper Foldables

Source: Brian Stockus

Gather round everyone. I’m going to paraphrase a story.

“Once upon a time a week or so ago, a teacher made a foldable with her class to help them learn about integer operations. The day before the big unit test, the teacher decided to give the students a quiz first to help them prepare. Even though the students were able to access their interactive notebooks, none of them were using the integer operation foldable that was glued in their notebooks. The class bombed the quiz. The next day on the unit test, the students were again allowed to use their interactive notebooks, and again none of them were using the integer operations foldable. It wasn’t until after the test that the students realized that the foldable contained ALL of the rules they needed for integer operations. They could just open a flap for a particular operation and see what to do.”

I read this story on a blog this week and it struck me because I’ve been in the same situation with my students before. They had a resource in their hands that could help them, and yet they seemed oblivious to using it. Why?

As I said in my previous post, I want to question why everyone is using foldables so much. I’m not necessarily against them, but anecdotes like this make me want to pause and reflect.

What is the inherent advantage of taking the extra time to cut a piece of paper into flaps, write in it, and possibly glue it into a notebook? Some advantages I see:

Motivation. Making the foldable feels more “hands on” than taking notes, so it is possibly more motivating for students to make a foldable.

Source: Brian Stockus

Structure. The design of a foldable gives the content some structure. In the integer operations foldable, I can tell by looking at it that there are four key concepts, and each gets its own window. If students were just taking notes, they may do so haphazardly, losing the structure of the information in the process. I know my own note taking in high school was mostly just writing things down one after the other without any thought about how any of the information went together. I also spent a good chunk of time doodling in the margins, so I can’t say my mind was focused on what I was writing.

Source: Brian Stockus

Focus. Because the foldable usually has some kind of flaps, I have the ability to control the information I am seeing. If I want to learn about adding integers, I can open that flap and focus on that information. Look at how overwhelming it is when all of the flaps are open. That’s probably what it would look like if it was just notes in a notebook.

Source: Brian Stockus

Based on the opening story however, these advantages weren’t obvious to the students. It did not occur to them until AFTER the test that this tool was pretty useful, which tells me the foldable failed. Here are some musings about why that might have happened in this case and why it might happen in other classrooms:

Ownership. From my own experience and from what I’ve been reading, teachers are finding these clever foldables online as a way to summarize key concepts. They’re fun to do and they look attractive glued into interactive notebooks. The problem is that this is a teacher-centric activity. When it comes to summarizing student learning, the teacher has controlled the structure of that summary. She is even controlling the content if all students do is copy her words into their foldables. The students are basically just re-creating the teacher’s work. The activity lacks personal meaning so the students don’t think about the foldable as a tool that can help them later on.

To make foldables more meaningful, I think students need to learn about a variety of foldable templates. Then, after the class has learned about a topic, the teacher can ask students which foldable they want use to summarize their learning. (I might go so far as to say foldables are just one option. Students could also choose to make a graphic organizer or flash cards.) This would be a great discussion to hear students’ thoughts about how to structure the information they learned about. The students might not all make the same foldable, but at least what they make will be personally meaningful for them. It would be great to have students share their foldables afterwards so they can compare with classmates and make changes if they realize they got something wrong or left something out. And if you get to a point where the students feel none of the available options will work, then that’s the time to seek out and introduce a new template(s).

Making, followed by using. So, you spent 20 minutes making a clever foldable with definitions and examples of various mathematical properties. Students glue it in their notebooks, and later on when doing homework and other assignments they’ll turn to it as a helpful resource since it clearly summarizes important knowledge. But they don’t. Why?

My thought is that it has to do with the lack of experience actually using the foldable with any meaningful purpose. Once the foldable is made and glued in the notebook, it must be used. That’s what makes an interactive notebook, you know, interactive. Many students won’t do this naturally either. They need to hear the teacher at various points in class say things like, “Hmm, this problem includes subtracting two negative numbers. I know we just learned that. How can I check to make sure how to do that correctly?” or “This looks like a problem where I’m going to need to use the distributive property. Do I have a resource somewhere that I can use if I get stuck?” It sounds silly to ask these questions, but if students aren’t choosing to use their resources on their own, then obviously they haven’t learned how to ask themselves these questions. They need modeling.

In closing, I’d like to reiterate the point of asking my original question: Be critical of your practice. We’re not Sadako trying to fold 1,000 paper foldables so our education wish will be granted. The reality is that foldables are tools, and we can guide students to choose an appropriate tool for the job and model how to use it effectively.