The Absurdity of One-to-One Initiatives

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As comes up every year, someone in our department suggested we go one-to-one. Of course, this sparked lively debate. So much so that do to the frequency of these debates and the cycle of outrage I invariably go through after each one, I’m motivated to write out the multitude of reasons that going one-to-one with textbooks is an absurd idea.

First, let’s talk about costs. A good textbook costs close to $100. Sometimes less, sometimes more, depending on how many you buy. If a kid has five classes, that means it’s going to cost roughly $500 dollars per student to go one-to-one textbooks. And it’s not just $500 one time. Of course not, because in a few years much of what’s inside the books will be dated. They will need to be updated and some of them will be so obsolete they’ll need to be replaced entirely. Do we want to go through the up front costs and then the future costs to update and replace them?

Second, let’s talk about letting teenagers carry around several hundred dollars in textbooks. Have you seen the average teenager’s bedroom? Of course not! There’s too much stuff on the horizontal surfaces (and maybe even the vertical surfaces) to actually see any substantial part of the room. Are we going to let kids, who can hardly get a dirty tissue to the trash can across the room, be responsible for hundreds of dollars worth of school property? I think this is a nightmare that no administrator or teacher wants to deal with.

Third, I’d ask you if the cost is worth the benefit. Sure, textbooks have lot’s of knowledge in them. Give students books corresponding to the subjects they’re learning allows them to easily and quickly look up information, helpful diagrams, maps, and other media, but don’t we have teachers for that? Teachers have much of this knowledge, and if they don’t, then they can look it up in their book and deliver it to the students. What’s the point of a teacher if all the information is easily available to the students? Sure, the best teachers might use the books in coordination with their teaching ability to create near sublime learning experiences, but this would surely only be the most motivated of teachers, not the norm.

Fourth, it would be a logistical nightmare. Suppose your high school has 1000 students. Then we are talking about THOUSANDS of textbooks to keep track of. Not just keep track of, but record those that go missing and those that are damaged. Then schools have to make determinations about how much the damages cost. Then who pays for it? The students? What if it’s an accident? What if the student can’t afford it? What if they get lost in a house fire? Who’s on the hook for the bill then? And who does this burden of tracking fall upon? The library? The administrators? The teachers? There’s no good options. And then, who fixes them? Do we offload this responsibility on the already short staffed library personnel? We’d probably have to hire somebody to spend part of their day repairing textbooks, so tack that on to the bottom line.

It seems clear that the costs of trying to put the these resources into the hands of each student almost certainly outweigh the benefits. But this fight will never die. Year after year we’ll continue to hear how we should “give students access to the tools they’ll be using when they leave us”. Given what I’ve outlined above, I can’t see the logic that results in this being a good idea.

Update: I should make something clear. This is purely satire. I am simply trying to make the argument that when it comes to discussions of 1 to 1 technology I think the problems that are brought up are often ones that we have solved in other contexts. This situation never came up in my department. And even if it had, I would never throw them under the bus like this publicly. Once again, this is purely satire.

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I’ve underestimated the importance of vocabulary

"Words" by Shelly on Flickr

I thought for a long time that I could get by teaching math while deemphasizing vocabulary. Obviously we would discuss the meaning of words, especially the ones that come up frequently. But I thought that if I was able to help students get a feel for the math, and show kids how to do math, without getting too caught up in what the new vocabulary meant, that would be success.

Part of this was time. Or rather to save time. Spending time helping students really understand vocabulary takes more time, especially if it’s something that is more easily shown/practiced. For example, I feel like one of my struggles with helping students understand domain and range is that I don’t do a good job at really helping them understand the words. In algebra II, if I present a new type of function to them and ask them to find the domain and range, they often struggle until they see a few examples. It’s as if they’re simply replicating the process for each type of function.

At risk of this turning into a domain and range post, let me explain a bit further. When we study quadratic functions I tell students the domain is always “all real numbers”. The student thinks, “Sweet. Whenever I see a question over domain on the quiz, I’ll just write ‘all real numbers’.” When we learn a new family of functions they have no understanding of how to find the domain, beyond “that’s something with the x values, right?”.

It’s not just that topic. In fact, the concept that propelled me to write on this topic was grading a quiz over factoring polynomials and finding zeros in polynomials. Way too many of my students don’t know the difference between factors and zeros and constantly get them confused. My most significant observation was that I find students are trying to get by with the least amount of vocabulary understanding, and I don’t think I’m helping things by demphasizing it.

Since I’m having this realization at this point in the school year, I think the fix going forward will be trying to find and develop small activities to help reinforce vocabulary. Simply emphasizing it more is a start. I’ve also done some activities, like concept maps and “functions back-to-back” which help with vocabulary understanding. Next school year I’d like to take a more systematic approach and deliberately build in vocabulary activities into each unit.


Drop your favorite vocabulary activities in the comments below or send them my way on Twitter. Thanks!

Image Credit: “Words” by Shelly on Flickr

Thoughts on “GPSing our Students”

In June Dan Meyer posted Your GPS is Making You Dumber and What that Means for Teaching. In it he makes the argument that providing step by step instructions for math concepts results in students being able to get from point A to B, while not understanding much about the concepts they’re supposed to be learning. His argument can be summed up with this paragraph, and is somewhat inspired by what Ann Shannon wrote in what teachers should Look for in the CCSS Mathematics Classroom.

Similarly, our step-by-step instructions do an excellent job transporting students efficiently from a question to its answer, but a poor job helping them acquire the domain knowledge to understand the deep structure in a problem set and adapt old methods to new questions.

I would tend to agree. I do give students steps occasionally but it’s often in order to simplify concepts and, if I’m being honest, to some degree avoid students truly struggling and grappling with the concepts.

I’m curious as to what others think about his post and the notion that GPSing students leads to less learning.

Lesson Plan Version 4.0: Networked Learning Revision

For the next revision of my original lesson plan I want to look at how networks (both my own and my students’) can be leveraged to create a higher quality lesson. I want to quickly recap my lesson with it’s revisions. First, students will engage in an inquiry activity where they will do an exploration using this Wolfram Alpha widget. We will then have a group discussion looking at the patterns students noticed in exploring different functions with the widget. I will then transition into the proof of the Fundamental Theorem of Calculus. During this, or immediately following, I will ask students to backchannel, explaining the questions they still have with the proof, a part they understood the best, and how it fits with the activity they just did. I will then move into modeling a couple problems. They will then try some problems in small groups using the mega whiteboards, sharing out solutions with the class when they’re done. Finally, they will have independent work time. The following day we will follow this system for clearing up misconceptions on the assignment. At the end of the week they will write a blog post with the prompt “What kind of inductive and deductive reasoning did you utilize in constructing your understanding of the fundamental theorem of calculus?”

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Image credit: http://innovatribe.com/tag/connected-workplace/ 

How I Currently Utilize Networks

The biggest way that my lesson currently uses networks is through their blogs. I can do a better job of making this an effective use of networks (see below), but I will often tweet out quality blog posts to my network and will occasionally get feedback from people in my network. In addition, I knew Wolfram Alpha was a great math and science resource so I explored that and (surprisingly quickly) found a simulation that increased the quality of the lesson. Although I use networks a small amount in this lesson, I think that they can be implemented in a much more effective way that will further enhance the quality of the lesson.

How Networks Could be Better Utilized

I want to focus on two specific aspects of using networks: how can I leverage my network to increase the quality of the lesson, and how can my students use their networks to gain a better understanding of the concept.

One way that I can use my network is to have them look at the backchannel the students do during/after the proof. Let me explain. The backchannel will happen on a Google doc. I won’t change anything in the Google doc (I may leave students comments but I won’t change what they originally wrote). I will then ask specific math teachers that I’ve connected with previously to scan the Google doc and give me feedback on students’ misconceptions. What do they think I need to go back and reteach? Do they have ideas for extending the concepts? What trends do they notice that I should address? I really think this would be a powerful use of my network that would certainly help me increase the quality of follow up instruction on the topic.

Another idea I’d like to explore is connecting with the physics teacher to discuss overlap in our lessons. I know the fundamental theorem has implications in science and I’d like to look at how to leverage that overlap to bring a more real world context to the concept. It might be worth my time to develop a project for the end of the unit in collaboration with him.

I also think that students could leverage their network in creative ways to increase their learning. First, I’m going to have students comment on other students blogs while considering the following questions. How does that student’s understanding of the concept differ from yours? What did he/she leave out that you would put in? What did they explain that you missed? Can you help to give that student a better understanding of the concept and if so, how? This should help each student better construct the knowledge in their own mind as well as help the person whose blog they are commenting on. This idea of explaining and discussing mathematics is especially important for gifted and talented learners to extend their learning beyond a surface level understanding of a topic (Sheffield, 1994, p. xx).

I also want them to tweet out their article using both the hashtag #mathchat and #calcchat asking for feedback on their ideas. Many of them probably won’t get feedback, but the potential for a random person to actually read their post and give feedback will motivate them to do better work.

Last, as an extension for the motivated learner, I’d like them to find a video online over the concept and critically analyze it with questions like “What did the creator do effectively and what did he/she miss?” They will then post the link to their analysis in the comments. This gives students the opportunity to participate and contribute to the conversation in mathematics. This is authentic, motivating (for some students) and will help them deepen their understanding of the Fundamental Theorem of Calculus.

References

Sheffield, L. J. (1994). The Development of Gifted and Talented Mathematics Students and the National Council of Teachers of Mathematics Standards. Storrs, CT: The National Research on the Gifted and Talented.

“Cooking with TPACK” Reflection

This morning we did an activity that was analogous to the Technology Pedagogy and Content Knowledge (TPACK) framework to help us draw connections between it and our teaching practices. Essentially we were given a kitchen tool at the beginning of class (a spatula for instance) and then randomly divided into groups and instructed to “make” something (fruit salad for example) using only the tools we were given at the beginning of class.

I took a few things away from this activity. First, the ability to be flexible was incredibly important. Just because you’ve never used an olive spoon to make a sandwich before doesn’t mean that it might not have a use (using the handle to spread peanut butter). Sometimes the tools that we have can be used in ways that we didn’t think possible. Our “content” in the context of the activity was sandwich making. The “technology” was an olive spoon. The pedagogy was how the spoon was used to contribute to the making of the sandwich. As teachers we are always trying to balance these three things. An appropriate intersection of the three places a teacher in a position to deliver a quality lesson (or make a quality sandwich).

Beyond flexibility, it became clear to me that a deep knowledge of all three contexts, technology, content, and pedagogy is vital to success in this model. Without the deep knowledge of each you can’t be flexible. If you are well versed in your content and various technology, but only know one avenue to delivery of the content then the quality of your lesson will not increase. The article, “Using the TPACK Framework: You can have hot tools and teach with them, too,” cites an example of a math teacher utilizing open sourced DJ software to teach about ratios (Mishra and Koehler, 2009, p.17). Without deep knowledge of his/her content knowledge, that teacher wouldn’t be able to recognize the connection between DJ software and mathematics. Likewise, without the knowledge of various pedagogies, the teacher wouldn’t be able to recognize the value that technology would have in the context of that particular concept. Without a deep understanding of each context, the overlap is lopsided and results in instruction that is not optimum.

Deep knowledge of the contexts and flexibility is important, but my biggest takeaway today was that teachers have always been doing this. They’ve always been balancing these three contexts. But in the last 50 years the technology context evolved incredibly rapidly in comparison to the other contexts. Prior to the development of computers, technology didn’t evolve terribly quickly. It was safe to assume that whatever technology you had at the beginning of your career would change relatively little by the end of your career. Or if it did change, it would change rather slowly. What we’ve seen in the last 20 years is that students now carry around more information in their pocket than entire universities contained only 20 years ago. This has the potential to fundamentally change our pedagogy for the better if we decide that there is value in developing a deep knowledge of the technological context. I would argue that there has always been value in developing that context, however at this point in history it’s much more intimidating for many educators.

References

Mishra, P., & Koehler, M. (2004). Using the TPACK Framework: You Can Have Your Hot Tools and Teach with Them, Too. Learning & Leading with Technology, 14-18.

TPACK Diagram

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