A Defective Method

No system is perfect. And no school will ever be perfect. But there's a difference between not achieving perfection and purposely creating a system that you know won't work. My school currently has a system for "credit recovery" that is designed to fail.

Like just about every school, we have some students who struggle in our classes. For a small number of those students, we have a "credit recovery" system in place, where they work with an online learning platform to make up classes they have failed. I have a ton of problems with this, not the least of which is that it's completely designed around the idea of "recovering credit" and not around the idea of learning (or what the student even needs). But even with those concerns, I would be willing to give it a pass if it provided a viable way for these students to jump through the hoops, graduate and move on with their lives.

I haven't ever had any interaction with our system but, yesterday, I had the opportunity to help one of our students who was working on their Geometry class on the platform. I was a tad bit surprised when the problems I was helping her with involved the Law of Sines and the Law of Cosines. Back when I was a full-time math teacher we taught that in Trig, but I figured perhaps with the changes due to Common Core that too had moved down into Geometry.

When I had a chance to look later, however, I discovered that while it's an option in Geometry, it falls in the "+" category, which means it's "Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics." That hardly seems appropriate for a student who is struggling in mathematics and is participating in our "credit recovery" option as sort of a last-chance.

But, again, I thought perhaps it was something we had decided as a school was to be included in our Geometry classes in which case, while I still didn't think it was appropriate for this student, it would at least be consistent with our regular classes. So I went and talked to our Math Department and we don't teach Law of Sines and Cosines in our Geometry classes. Which means this struggling student, who is in our online-only, credit recovery option, is being asked to do more than the students in our regular, teacher-led classes.

But it gets worse. Because after the relatively straightforward Law of Sines and Law of Cosines problems (assuming that's not an oxymoron), she was presented with a problem something like the following. (Because it's in the online platform, I don't have access to it to see exactly what it said but, for reasons that will become clear in a moment, I feel relatively confident that this is essentially it.)

Using the defects method, which relationship represents the Law of Cosines if the measure of the included angle between the sides a and b of ΔABC is less than 90°?

Well, I read that a few times and was stumped. I had never heard of this "defects method." The student couldn't help me with what it was, so I asked her if we could go back and look at the "instruction" she had presumably had over this method previously on the platform. She said we couldn't because she was "locked out" now that she had finished that part. (I can't independently verify whether that is accurate, but she certainly thought it was.) So I googled "defects method Law of Cosines" . . . and found nothing.

Well, that's not entirely true. I found four or five links for it - all with various versions of that same problem that students had posted to various sites looking for answers (like this one). Unfortunately, I had a meeting to get to so I couldn't investigate further at that point, but later I spent more time googling and still came up with nothing. I did find something similar when talking about hyperbolic triangles (and I'm pretty sure even Common Core doesn't include that in high school Geometry), but nothing for 2D geometry. That night I asked on Twitter, and no one knew. And the next day I went in and asked our Geometry teachers, and they had never heard of it.

Now, none of that necessarily means it doesn't exist or that there perhaps wasn't some instruction in the online platform that would help explain it, but it does again make you wonder why it's being included in a credit recovery course for struggling math students. We don't cover it in our regular Geometry classes, none of the math teachers in the building (or who saw my tweet) have ever heard of it, and Google can't seem to find it either. Why in the world was this question there?

There are larger problems here, of course. How and why did my district select this platform? Who is overseeing the content and ensuring that students are actually getting content similar to the courses they are theoretically "recovering credit" for? Why do we think that students who struggled in a regular classroom, with a teacher and classmates to help them, is suddenly going to be successful as a learner in a learn-on-your-own online platform (even if the platform wasn't serving up the wrong content)?

Clearly, this "credit recovery" option is not at all about what the students need. It's not about what they want or need to learn to be successful in their future, it's not even about them being successful right now. It's just a desperate attempt by the adults in our system to somehow, some way, get these students to pass our required courses. As I said earlier, as horrible as that sounds, given our current system, if it actually accomplished that then I'd be okay with looking the other way (while still vigorously arguing to change the system). But it doesn't. We're taking these students that we've already failed and setting them up to fail again.

I still don't know what the "defect method" is in relation to triangles and geometry, but I have a pretty good idea what a defective method looks like in practice. If "defective method of instruction" was a standard, we would "exceed expectations."

What Does It Take to be an Elite Athlete?

I posted this on my Algebra class blog, I thought I'd share it here as well.

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Watch the video below to find out, but basically innovation, democratization and imagination. More specifically, math, science, technology and mindset.




Huh. Math. Science. Technology. Mindset. Kinda sounds familiar . . .

An Open Letter to the Littleton Public Schools Board of Education

This post is kind of an addendum to my last post. On Tuesday of last week the district asked our Math Department for a list of our concerns over the materials that were being recommended. Since the Board meeting was on Thursday, the department met after school on Wednesday and generated the letter below. The letter was shared with the district and, to their credit, they shared some of the bullet points with the Board when they made their presentation. To the best of my knowledge* (see update at bottom), the entire letter was not shared, so I thought I would share it here.

There are two other high schools in our district, plus a small, alternative setting. At the Board meeting the Math Department Chair of the next largest high school (we are the largest, 15 teachers in the department) spoke against the materials adoption, stating that 10 out of the 11 math teachers in her building opposed it (you might recall from my previous post that we had been told something different). The third high school is apparently in support of the materials although, again, we're hearing second hand from at least some of those teachers that, and I paraphrase, "we felt like we didn't have a choice so why fight it."

The School Board will decide on the materials adoption at their next meeting on Thursday, May 8th.

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To: Littleton Public Schools School Board

From: Arapahoe High School Mathematics Department

Re: Concerns over materials adoption

As you know, LPS is in the process of adopting new materials in order to implement the newly revised Colorado Content Standards in Mathematics (which, in turn, align with the Common Core State Standards - Mathematics, or CCSS-M). As is the usual process, a committee was formed to preview what materials were available, then review selected materials, then make a recommendation to the Board on what materials to adopt. While this process has worked reasonably well in the past, we have concerns that the materials that are being recommended this time are not in the best interests of our students.

First, a bit of context. While there has been a lot of discussion both locally and nationally around the Common Core State Standards (not just the Mathematics ones, but the Language Arts ones as well), it’s important to keep in mind that these standards are still relatively new, especially in the context of textbook development cycles. Consequently, many of the choices that are currently available from textbook publishers are not (yet) of the quality we would like.

In addition, we are very much in a transition period between print resources and digital resources. While we clearly are headed toward digital resources, textbook publishers have not yet figured out the best way to utilize this new medium. (There are also questions of how the publishers will maintain revenues and profits, but we will not go there as part of this discussion.) Many publishers initially just tried to port their existing print resources to an online format, usually as some combination of non-editable PDF’s and non-editable web pages behind a login. While that was a natural first step, it really didn’t provide any advantages for the end user over a print textbook (in fact, it was probably more difficult to use). (It did, however, provide a cost-savings to the publishers as digital is much cheaper than physical; a cost savings that sometimes was passed along to the customer, but often was not.) This is an example of “Substitution” phase in the SAMR model that LPS uses for 21st Century Literacy.

Over time publishers began receiving feedback that customers did not like this and began to investigate better ways to take advantage of the affordances of digital platforms. The Agile Mind materials that the committee is recommending we adopt is an attempt to both address the new CCSS-M Standards and take advantage of those digital affordances. In our opinion, however, they have not successfully addressed either one.

Here’s a brief - although not comprehensive - list of some of the concerns we developed in a department meeting.

• Much of it is not editable (exams, lessons, activities in PDF form or online) - can’t be easily customized. A physical text would not be editable either, but we feel like other digital resources are much more customizable (our own fledgling efforts on ck12 (still very much in alpha form), test generator-type software from previous publishers, Google Sites/Drive, etc - all have the ability for us to modify).
  
  
• Not adaptable across our level of instruction such as remedial, on track, and advanced. This ranges from concerns from our Learning Support Services folks about reading level of the text (not adaptable to lower reading levels) to concerns about the ability to extend for our more advanced students. This also includes concerns about how we implement the various intervention models we have developed in our PLCs over the last few years using these materials, including how our Study Center personnel will utilize it.
  
  
• There are not enough examples and daily practice provided without considerable supplementation.
  
  
• There are concerns about being able to utilize the Smart Board environment like we currently do while simultaneously accessing the Agile Mind materials on screen. Many of us have developed many digital resources that we use with students in class. We understand that you don’t have to follow the Agile Mind script exactly, but that calls into question what the advantages are of buying this resource.
  
  
• These materials are built to be delivered in a fairly particular way. While the publisher argues that the teacher has great flexibility, the materials themselves only work for a while if you follow the “script”. While teachers are under no obligation to follow that script, if they do not, then these materials are not of much use to them. In addition, the Agile Mind script requires more days of instruction to complete the curriculum than we currently have.
  
  
• There is a concern with all students having access to the Internet at home in order to fully utilize this program. While that is certainly a goal of ours and we are heading that direction (both at AHS and in LPS), the district currently cannot guarantee this. If we are going to adopt materials that are only available with an online connection, then we would have to guarantee (and provide for those who cannot afford it) both equipment and high-speed Internet access for all of our students. (In comparison, the ck12 book we are creating is online, but can also be downloaded in PDF, ePub, or mobi formats for use offline without an Internet connection if necessary).
  
  
• While we haven’t had time to explore the materials fully, we have already discovered some technical issues (for example, there are issues on pages with scroll bars and the “interactive” dragging and dropping). In addition, the user interface is not particularly well designed. There are issues with the size of the print (if you’re projecting and kids are very far back in the classroom). While there are zoom options available on browsers, the interface itself doesn’t adjust well making it not very usable with a class.
  
  
• Cost (including additional cost of printing the student activity sheets). While we have not been told an exact cost, we’ve heard numbers like $500,000 thrown around. Whatever the final number is, we think that would be a reasonable investment in materials that would help our students become better learners, but we don’t feel it is a reasonable investment given the quality of these materials. Especially when you consider the following budgetary concerns (these are just three recent examples that come to mind):
  
  
• Our Deaf and Hard of Hearing Teacher is being let go due to budgetary reasons, despite the fact that we still have students in need of those services, and the fact that we have two sections of students who are taking ASL as their World Language and will now not be able to continue with that.
  
  
• Apparently spending $15,000 on blinds to cover the windows next to our classroom doors is too much, even though we need them in a lockdown situation in order to prevent intruders from seeing into our classrooms and targeting our students.
  
  
• Apparently we can no longer as a district support individual student logins to the network. Instead, all students at Arapahoe will use a single login. This affects all students and teachers, but particularly affects instruction in Technology Education, Business and Journalism.

While not a comprehensive list, we feel these concerns are more than enough already to question the adoption of these materials. We want to be clear that we are not resistant to change, nor are we unwilling to look at new approaches, we just don’t feel like the materials we have seen so far (and, specifically, the Agile Mind materials), meets the needs of our students. Instead of adopting - and spending the money on - materials that are not up to our quality standards, we would propose the following.

• Don’t adopt anything at this point. Perhaps some outstanding materials will come along in the future that will be worth adopting but, at the moment, these are not outstanding materials.
  
  
• Instead, let's use a small part of the money that would’ve gone to this adoption and invest in professional development. Since we’re beginning this transition with Algebra, why don’t we get a group of Algebra teachers together and develop materials and come up with the types of activities we want to do with our students? We feel that we could come up with materials that were at least as good as those proposed for adoption, and probably better for our students, for substantially less money.
  
  
• In addition, that professional development is much more likely to impact our students in a positive fashion than simply purchasing these materials. Learning theory tells us that humans actively construct their own knowledge and are active meaning-makers. This is not only true for our students, but for our teachers as well. Adopting canned, pre-scripted materials is unlikely to actually impact classroom practice or student learning. If we want to actually impact classroom practice, then professional development - with teachers co-creating materials and activities - is the way to do that.
  

We feel that there has never been a better time to be a teacher or a learner. We fully agree that the affordances of digital technologies and resources can improve our instruction and our students’ learning. We simply disagree that the Agile Mind materials - or any of the materials that were previewed - will actually do that. We feel that investing in professional development - investing in us - would not only be less expensive, but much, much more helpful for our students.

You trust us with your children, please trust us with this.

Sincerely,

Arapahoe High School Mathematics Department

Update 5-1-14: We've been told that the entire letter was shared with the Board of Education.

Burden of Proof: A Textbook Example

My district, like many I imagine, is in the process of making the transition from our existing math curriculum to one aligned with the updated Colorado Math Standards (pdf), which in turn are aligned with the Common Core State Standards - Mathematics. This post is not going to be about the Common Core State Standards themselves (you can thank me now), but about the "Materials Selection Process."

Traditionally in my district (as in many), when new curriculum is adopted a committee is formed to select new materials to support that curriculum. (Although, interestingly, I recently found out that in my district there is no dedicated budget for that, they just "find" the money each time they need to do this.) Once the committee researches, previews, and reviews the various materials available, they make a recommendation to the Board of Education. After a period of time for public comment, the Board then decides whether to adopt the materials.

In many areas, particularly Math, this has traditionally been a textbook-selection process. I was not part of this committee, but the process this year was a little different for a couple of reasons. First, because the Common Core State Standards are still fairly new (at least in terms of textbook publishing cycles), there are not a lot of good choices out there. Second, we are clearly in a transition period between the traditional print-based textbook and online "techbooks".

The committee ended up deciding on Agile Mind. (Well, sort of. Apparently some folks on the committee weren't entirely thrilled with the choice, and others felt like they really didn't have much choice so didn't say anything. But, in any case, that's the recommendation that's going forward.) The math teachers at my school were then asked to review the materials briefly before a webinar from the company and to share our thoughts and concerns. Here are some of my thoughts.

To summarize those thoughts, my feeling is that this isn't a good choice. While I like some of what Agile Mind is doing (I've used some ideas from the Dana Center in my Algebra class), overall I wasn't really impressed with their online techbook (with the caveat that I haven't spent enough time with it to do a fair and thorough review). It just doesn't seem to leverage much of the affordances of digital over print (see the thoughts for more on that).

I found it both interesting and convenient that for the webinar Agile Mind chose "Topic 18: Modeling with Quadratic Functions" to demo their product. I had recently taught an abbreviated version of this topic (abbreviated because we are transitioning to the new curriculum this year, so we have some of the old and some of the new), so I could compare what they clearly felt was their "good stuff" with what I had just come up with on my own.

Conveniently (again), Agile Mind starts their unit with a modeling activity built around shooting a basketball. They have an animation of two players shooting a basketball, one overhand and one underhand. You really have to see the animation to get the, umm, full effect, but I'll share a screen shot here that should give you an idea.

Source: Agile Mind, Algebra 1 CCSS Edition, Topic 18, Student Activity Sheet 1

It turns out that I used a similar activity borrowed from the MTBoS (MathTwitterBlogosphere). Which version do you think makes better use of digital resources? Which version do you think is better pedagogically? I think the MTBoS version is much better, but that's certainly debatable. What's not debatable, however, is that I can modify, alter, adjust, customize, and add to the MTBoS version as I see fit, where it's difficult to do that with the Agile Mind version (their techbook is behind a login, student activity sheet is a PDF, you can't customize their techbook).

I could go on about things I don't particularly like about Agile Mind (as well as things I like - for example, it has a cohesiveness and flow that a "put-together" set of lesson plans like mine may lack), but the point of this post is not really to criticize Agile Mind. The point (I knew I would get to it eventually) is that the "materials selection process" we (and I imagine many districts) have in place is fundamentally flawed. The default assumption is that if we are revising the curriculum, then we need to purchase new materials, and those materials are going to be in the form of a textbook (either print-based or digital, but still essentially a textbook).

I think that is wrong. I think it's a fundamental misunderstanding of the context of what it's like to be a learner today. It completely misses the advantages and affordances of digital over print (or at least open digital over pre-digested, closed digital resources). I think that for all "materials selections" from here on out, the default should be to not purchase a new textbook. That doesn't mean a new textbook can't be purchased if it's decided that's the best option, but it means the burden of proof should be on those that want to purchase a new textbook to justify why we should. To use the trendy term, what's the "value add" of these materials?

We haven't been told how much this adoption is going to cost, as I don't think they've negotiated that yet, although the figure of $500,000 has been thrown around (not sure if that's an initial cost, or a 7-year cost, or what). I'm going to assume that this will cost somewhere between $50,000 and $5 million. Whatever the final figure, I think that's an egregious waste of money.

Here's what I propose instead. Don’t adopt anything at this point. Perhaps some outstanding materials will come along in the future that will be worth adopting but, at the moment, these are not outstanding materials. Instead, let's use a small part of the money that would’ve gone to this textbook adoption and invest in our teachers. Wouldn’t it be amazing to get a group of Algebra teachers together for two weeks over the summer and come up with the types of activities we want to do with our students? (Maybe $15,000 or so, depending on the number of teacher and number of days - we currently pay $150/day stipends for teachers doing curricular work.) That would give at least one full day to work on each unit in CCSS-M - wouldn’t that be a better use of our time and money? Wouldn't that end up developing materials that were at least as good as - and perhaps better - than the materials we could purchase for substantially more money? And, more importantly, wouldn't investing that money in teachers developing the activities be much, much, much (did I mention much?) more likely to impact teachers' practice?

Adopting Agile Mind (or anything else I've seen out there) isn't likely to change what happens in the classroom with kids. (Or, if it does, it will change it in a negative fashion by providing a script-like experience for students.) But give teachers time, guidance and resources (including tapping into the MTBoS), and I think you will not only develop an outstanding resource that will get implemented in the classroom, but will also influence teachers' practice, and therefore student learning.

If the burden of proof is indeed on those wishing to adopt/purchase new materials, I would suggest that they haven't fulfilled that burden in this case. And I would suggest that districts and School Boards everywhere reevaluate the processes they have in place for curriculum adoption and materials selection. If you can't justify how and why a new curriculum or set of materials is going to help your students become better learners, then you can't justify the purchase price. Instead, consider investing in your people, and their ideas. That's truly a better way to develop agile minds.

Basketball Quadratics

It's been awhile since I've had a math post on here, so I thought it might be time. At my school we are in the process of transitioning from our previous Algebra 1 course to an Algebra 1 course that aligns with the Common Core (Semester 1, Semester 2, although much of Semester 1 will go away next year as we complete the transition). As a result we are going much more in-depth on quadratics than we did previously.

To put this particular activity in context, we will have already discussed factoring, solving by factoring, graphing, completing the square, and quadratic formula. We then touch on graphing using the vertex form of a quadratic equation. As usual, I've borrowed ideas from wherever I can and, once again, this activity is from Dan Meyer.

I've previously done this activity using Geogebra, but with the recent addition of the ability to add images to Desmos, I decided to try to go that route. As is becoming a habit for me, I host the activity in a Google Doc and then link out from there.

One of my struggles is always how much direction to give the students, and I tend to fall on the side of probably giving too much scaffolding for them (compared to some other folks). My experience has been that if I don't, we don't get very far, but I still struggle with where that middle ground should be. So my compromise with myself is to give them a lot of scaffolding as we step through the first example, then turn them loose from there.

As always, I would love your constructive feedback on this.

Air Travel: Google Apps Style

Like pretty much anything good I do in my Algebra class, this is simply a slight modification of something someone else has created - in this case, Dan Meyer. Please go read his post - and the comments - for all the goodness.

But I thought it might be helpful for somebody if I shared the slight modification I've made to it to take advantage of Google Apps. Like many districts, we are a Google Apps for Education district, so I wanted to try to leverage that for this assignment and use Google Spreadsheets instead of Excel. I'm going to have the students gather the data outside of class, following these directions and using a copy of this Google Spreadsheet.

Then they'll come to class, hopefully with the printouts of their two graphs but, if not, I'll hopefully have their shared copy to pull up on screen if necessary. We'll then talk about sketching a line of best fit (they on their printouts, me on the smart board) and coming up with a rough equation for that line. We'll then discuss, hopefully teasing out the same questions that Dan talked about in his post.

Some folks might refer to this as a "flipped" lesson, as I'm having them doing the research outside of class and then we discuss in class. I don't much care what we call it, I'm just trying to maximize my face-to-face time with them and hopefully get them to engage in some interesting mathematical thinking. They'll have two nights to complete the research, which I'm hoping will only take them 20-25 minutes total.

While I'm not a huge fan of homework, given the restraints of our schedule (my Algebra class meets four days a week, 59 minute periods when no special schedules - PLC, assembly, testing, etc.) and the curriculum (still too much for even a 5-day a week, 90 minutes a day Algebra class), I feel reasonably good about 20-25 minutes with two nights to get it done. (Next year I'm hoping to give them 3 or 4 nights to do it, I just didn't figure it out in time this year.)

My interest here wasn't so much in plotting the points, which is why I've created the two graph tabs in Google Spreadsheet for them. My interest is more in the relationship between time and distance and cost and distance, and whether they can think that through. And then translating all of that to an equation to model it. I debated for a while with just giving them the flight/time/distance/cost information up front, as gathering that information isn't the essential part of this activity, but in the end I decided there was some value both in them learning about flights/cost and how to gather the information, and about how to organize it in a way that might help analyze it. I would be interested to hear your thoughts on that decision (as well as any of the other decisions I made with this lesson.)

Minimum Expectations

I spent the last two days in some district-provided professional development around the Common Core Math Standards. Overall it was a pretty good two days, in spite of my misgivings about Common Core in general, and other than I went away somewhat depressed with my own ability to do this well (but that's another post or three).

I wanted to take a moment to put down some thoughts/questions about a couple of problems we did today. Early in the day we did an activity where we were rating the complexity of various problems. One of the problems was:

Solve the following equation:  (3x - 2)² = 6x - 4
When you are finished, enter your answer below.

The group generally agreed that this was not an overly complex problem, but there was a debate going on about exactly how complex it was. Because this was after rating a bunch of other problems, I was growing a bit tired of this (I see some value in comparing problems, but it felt more like we were determining where this would fit on the PARCC test and not discussing what a good problem looks like), so I said I thought this was really a 1 (being the least complex, and the debate previously was between whether it was a 2 or a 3).

I basically said something like, "Well, if your goal is simply to solve it and enter an answer, then I'd just use Desmos. How hard is that? It's a 1." (Yes, I know, I can be a pain sometimes. But they invited me.)

A little later in the day (or maybe it was earlier, I've lost track now) we then encountered this problem:

Once again we worked with it for a while and analyzed the complexity of the task and what students would need to know in order to complete the task. This time the discussion was about how difficult it was to find the minimum and how much that should factor into the complexity of the task. Again, I brought up Desmos, and suggested that if the students knew the appropriate formulas, this was a relatively trivial problem.

The scoring rubric we looked at assumed most students would make a table of values and the points they got was determined by whether they got the formula, did the substitution, and then how precise they were with their guess-and-check.

Now, I'm not saying that's a bad way to do this, but I think it brings up an interesting question. Let's assume this is not a calculus course where we're talking about finding maximum and minimum, and I think that's not a bad assumption to make considering it was labeled a Geometry problem (and considering that Calculus is no longer the assumed capstone course in Common Core - heck, even the College Board apparently agrees). So, in the age of Desmos, or Wolfram Alpha, or whatever, how much value is there in finding minimums and maximums by tables of values, or by factoring, or even by calculus?

I'm not saying there isn't value in those approaches, but I found it interesting that no one other than me thought to graph it (and these folks proved over the two days that they are generally brighter than me mathematically). I don't know this, but I would guess the reason is because they either don't know about Desmos (although most had graphing calculators with them), or simply don't think of a graph to solve this because we think like math teachers and graphing has always been difficult.

So I'm not making any grand pronouncements (for once), but I'm curious what the math folks out there think about this (and similar issues). What should be our "minimum" expectations?

Update 8-8-13: Desmos suggests perhaps having students design the can.

Help Me Make This #howtolearnmath Poster Better

I'm still enjoying my How To Learn Math class. In a recent session, Professor Boaler talks about her own "Mathematical Thinking Process" and how we often don't make that very transparent to our students. (She describes her process in the first few minutes of this video.)



As a result I got to thinking that perhaps I should create a poster for my classroom that illustrates some of these ideas, both for students to refer to and to remind me to make my own thinking transparent when I glance at it.

My design ability is, ahem, less than awesome. So I thought I'd ask for your help. Here's my first attempt. It's just text right now, but I think it could be improved in a lot of ways. Perhaps change the wording, or the font, or the colors, or the layout, or add pictures or illustrations. I'd like to have it on one page so that I can create a large poster of it and perhaps print it out for students to put in their notebooks.

It's in Google Docs, so go ahead and make a copy, improve it, and then post a link in the comments. Or, if you'd prefer to use a more robust piece of design software, go ahead and do that and then leave a link in the comments. I'd really appreciate your time and talent if you'd like to spend a few minutes making this better. As with everything on this blog, it will be freely available to everyone, so please don't include any copyrighted images.

Mindset

My How to Learn Math class is going very well - I'm halfway through the sessions and feel like it has been very worthwhile. A good portion of the first part of the class was built around the ideas in Carol Dweck's Mindset. As a result, I decided to create an "assignment" for the parents and students of my incoming freshmen. Here's the email I just sent to them:

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Algebra Parents and Students,

I hope your summer is going well. We'll be starting school in just under three weeks (woo-hoo!) and in a few days I'll be emailing some more information about our class and some tasks for the students to do. In the meantime, however, I wanted to give both the parents and the students a joint "assignment." Now, just to be perfectly clear, this assignment is optional, but I really, really, really (did I mention "really"?) think it would be helpful for each one of you to do this assignment between now and the start of school.

Okay, so here it is. As your student is about to begin high school they likely (and naturally) have a lot of fears. Many of those fears are social (we've never had freshman stuffed in a locker, although I've wanted to a couple of times), and many of those are academic (we've never had a freshman's head explode from doing too much homework, although a few have cracked a bit).

This assignment tries to address some of the academic fears that many students have. By the time they start high school, many students have decided that they are "smart" at some things, and "dumb" at other things. While this is true of all subjects, it seems to be especially true in math. The thing is, those students are wrong, and not just the ones who think they are "dumb" at something, but also the ones who think they are "smart" as well.

We know from brain research that people aren't "smart" or "dumb" at things, but that everyone can learn, and that it turns out students' attitudes about learning have a surprisingly strong effect on how well they learn. This is referred to as "mindset" in the research, and the assignment I have for you to do involves learning a bit more about how your brain works in order to perhaps change your mind(set).

Again, this is optional, but I really, really, . . . (oh, you get the idea) . . . think you should consider doing this. Ideally this assignment will be completed by a parent(s) and student working together, at the same time. I've divided it up into three "sessions" as a way to break it up a bit (perhaps even over several days or weeks), but you are welcome to do it however you'd like. Simply visit this website and work through as much or as little of it as you'd like. I think you'll find this assignment very worthwhile and I hope you consider completing it.

Either way, enjoy the next few weeks and I look forward to meeting all of you soon. Again, look for another email from me in a few days that will have additional information about our class as well as some specific tasks for students to do.

Thanks for your time,

Karl Fisch
Arapahoe High School

-----

It will be interesting to see if any of them take me up on it. I'd also love any feedback you might have on the mindset assignment itself.

My First Semester Algebra 1 Lesson Plans (CCSS Edition) - Draft

As I indicated in a previous post, my school is in the process of rewriting our Algebra curriculum to more closely match the Common Core. I've now completed my first run through of my (very rough) first semester lesson plans to match up with this, so I thought I'd share.

Before I do that, a few important things to keep in mind:

1. Read that previous post for the specifics of my situation (the biggest one being that I see my Algebra students fewer days/minutes than a lot of folks).
   
   
2. Here is the rough outline of our translation of the Common Core Math Standards to our Algebra course.
   
   
3. When that document refers to the "CK12 Textbook", that's the textbook alternative we are creating on the CK12 site. This is even more in draft form, so you won't find it on the CK12 site just yet. We are planning on working on it throughout the school year and, with a little luck, will "publish" it to the CK12 site for 2014-15. But here's a PDF that is the result of a very quick run through to try to modify an existing CK12 text to match CCSS-M and our Algebra course. It's a good start, but has a long way to go.
   
   (Note: Our philosophy for this textbook is that it is a resource, not our curriculum or our lesson plans. As such, it is simply a place students can go to see additional examples, explanations, and practice problem sets, and therefore does not have to be perfect or match our individual teaching styles. Our additional "philosophy" is that we hope we can do a good enough job on this to convince our district not to spends tens of thousands of dollars purchasing a new "Common Core Aligned" Algebra textbook in 2014-15.)

Okay, so now on to the lesson plans.

1. These plans are written for me, so sometimes it will not be clear to someone else what I'm talking about. I do link to some things that are linkable, but if you have questions about something, feel free to ask.
   
   
2. There are also lots of question marks where I'm still debating what I want to do and/or whether I have enough time to do it.
   
   
3. As always, these are my "big picture" plans and they will get adjusted frequently based on how things go with my students throughout the semester, so don't think of these as set in concrete. For me, though, I need a pretty specific plan to work from initially, both to make sure it flows mathematically/pedagogically, and to make sure I "cover" what I have to (as much as I dislike that word).
   
   
4. You'll notice that there are five blank days at the end of the semester (as of this writing, anyway). Those are my "cushion" as inevitably things don't go as I planned (see #3). I really would prefer more than five, but given that I only get 62 class periods (with at least 9 of those shortened periods), that's the best I can manage at the moment (subject to revision as I go through it several more times - and hopefully with some feedback from you).

I'd appreciate any feedback (or questions) you'd like to share, either in the comments or via email or other means.

Three Acts/101qs/#WCYDWT - A First Attempt

So as I'm creating my lesson plans for Algebra 1 for next year (more on that in a future post, hopefully) I'm feeling pretty bad about something. You see, there's all this great material out there developed by other math teachers and I feel bad that I haven't really contributed much to it (other than to publicize it). Not bad enough, however, to not stea . . . borrow all the material. But still, I feel bad.

So as I'm planning I came across a linear equations activity I've done the last few years that involves a story of me going to my recreation center to work out, stretching first and then running on a treadmill, and figuring out calories burned. It's a perfectly fine activity, and it has worked reasonably well, but it's completely text based.

Within the last year, however, we've purchased a treadmill for home. And this morning when I was running on it I thought that perhaps I could dip my toe into creating something useful. So this could fit into a lot of categories, but I'm guessing it might fit into Dan Meyer's three acts, 101qs or perhaps #WCYDWT.

I'm not sure if it really matters where it fits, but I'm posting it here to get some help. My problem with creating material like this is that it's not "natural" for me. I can recognize great stuff that other people create with no problem, but creating it myself is a challenge. My other problem is that I can do basic video editing in iMovie, but that's about it. With those caveats, I think this is a decent start.

In my head, this is how this would sequence.

Update 7-17-13: Split the first video into two videos to make it more obvious where Act 1 ends and the info they're likely to request in Act 2.

Treadmill 1a (Act 1?) - How fast am I running?


Treadmill 1b (Act 2?) - Information they need



Treadmill 2 (Act 3?) - The answer

Treadmill 3 (continuation) - How many calories am I burning? (Internet research based on speed, etc.)

Treadmill 4 (answer to continuation)

Treadmill 5-1 (extension) - How long have I been running?

Treadmill 5-2 (the answer)

Treadmill 6 (Second problem Act 1?) - How long did I walk and how long did I run?

So, constructive criticism/feedback is appreciated - keeping in mind the caveat of limited video editing skills and software :-).

• What would you add/remove/change?
• Does the sequence work?
• In the end, is it any better than an equivalent text-based problem?
• Anything else I should've thought of to ask.

Thanks.

How To Learn Math

I've decided to attend Stanford. Sort of.

I just enrolled in EDUC115N: How to Learn Math:

In July 2013 a new course will be available on Stanford’s free on-line platform. The course is a short intervention designed to change students’ relationships with math. I have taught this intervention successfully in the past (in classrooms); it caused students to re-engage successfully with math, taking a new approach to the subject and their learning.

In the 2013-2014 school year the course will be offered to learners of math but in July of 2013 I will release a version of the course designed for teachers and other helpers of math learners, such as parents. In the teacher/parent version I will share the ideas I will present to students and hold a conversation with teachers and parents about the ideas. There will also be sessions giving teachers/parents particular strategies for achieving changes in students and opportunities for participants to work together on ideas through the forum pages. The ideas I will share will be really helpful as teachers prepare to implement the new Common Core State Standards.

Taught by Jo Boaler, this course is for both teachers and parents and will focus on the following eight concepts:

1. Knocking down the myths about math.
2. Math and Mindset.
3. Mistakes, Challenges & Persistence.
4. Teaching Math for a Growth Mindset.
5. Conceptual Learning Part I: Number Sense.
6. Conceptual Learning Part II: Connections, Representations, Questions.
7. Appreciating Algebra.
8. Going From This Course to a New Mathematical Future.

This course is completely online, and free, and is loosely structured so you can more or less go at your own pace. I've already connected with several folks on Twitter who are enrolled (hashtag #EDU115, unless we're instructed otherwise), so I'm hoping the discussions will be rich, relevant and meaningful.

The class "starts" on July 15th and "ends" on September 27th (although I anticipate "finishing" it sooner if the course allows as things get really busy once school starts up). If you have an interest - as a teacher or a parent - consider joining us. There's no cost, and really there's no huge commitment - if you end up not fully participating - or not participating at all - that's okay.

Algorithms, Quadcopters, and the CCSS-M

So, as usual, the end of the school year (and then subsequent visit from my in-laws) ended up leaving not enough time to do my self-assigned homework around #algorithmchat in a timely manner. But, in keeping with my belief that it's more about the learning then the exact date of that learning, here's the results of my thinking.

First, I think my general thinking hasn't changed that much from the original post, where I stated:

algorithms, when used as a result and in conjunction with understanding and meaning, can be a good thing, while acknowledging that we have often emphasized the algorithm at the expense of understanding and meaning

I appreciated the detailed descriptions and explanations of the various algorithms in the Fuson and Beckmann article and they certainly got me thinking. The authors argue that the CCSS-M includes the meaning and sense-making as part of students' development and understanding of algorithms, which I agree with. They also state that in the past the algorithm was often taught without that meaning and sense-making portion, and I think most of us agree that is not a great approach.

The part I still disagree with the CCSS-M (and maybe Fuson and Beckmann as well, I'm not sure) on is the idea of the standard algorithm. I think the crux of this argument boils down to folks who argue for one specific standard algorithm because it is the most "efficient." I would argue that the most efficient way to do most of these calculations is with Siri or Google Glass or Wolfram Alpha. I'm more interested in students understanding the mathematical underpinnings of the algorithm(s) then in being able to quickly apply them. I want them to have number sense and mathematical understanding, but I don't think that necessarily means being able to "efficiently" compute a four digit by four digit multiplication problem by hand.

So, as long as I can change the standard algorithm to a standard algorithm that makes both mathematical sense and is most helpful to that particular student (which, I admit, doesn't flow quite as freely), then I'm good.

As a side note, this TED Talk happened to get posted just as I was trying to compose this blog post.


I think it's interesting in and of itself, but I also found it interesting how often he refers to "algorithms" and "mathematical modeling." I think this shows the power of algorithms, but also the need for our students to understand the algorithms, and also to understand that algorithms are first and foremost developed by humans and are not always set in stone, as when the algorithms appear to "adjust" or "learn" in the flipping sequence.

If our students can be begin to understand that algorithms don't supersede our understanding, but can help enhance it, then I think we're on the right track.

Ninth Grade CCSS Algebra 1 Scope and Sequence

I had some requests on Twitter to share this out, so here goes.

As many of you know, in addition to my tech duties I teach one section of ninth grade Algebra (occasionally some sophomores in there as well). Colorado has adopted the Common Core State Standards so our math curriculum - like most folks' - will be transitioning to match the new standards over the next couple of years.

If you've read this blog before you know I have concerns with the Common Core. Nevertheless, it's what we are tasked with so - while still advocating for something different - I'm attempting to get my head around the scope and sequence for Algebra 1 next year. As I looked into it I was surprised to not find very many examples that have already been created, so I decided to try to take our current scope and sequence and see how well I could "translate" it into CCSS.

Before I link to that document, I think it's important to remember that everyone's school and situation is different. There will be local variables and constraints that will make each school's implementation look different. For example, here is some information about my school that affects what I've done so far.

1. My algebra class meets for 59 minute periods four days a week (MTWF for me). When all is said and done, I see my students for approximately 126 class periods in a year, with about 110 of those the full 59 minutes and the rest anywhere from 20 to 40 minutes depending on the day (PLC days, assembly days, ACT testing days, state testing days, etc.). Because this is less time than in many Algebra classes, we do not typically cover quite as many of the "advanced" topics that some Algebra classes do. We have a six period day and freshmen (which is the vast majority of students in our Algebra classes) have between one and four unscheduled periods a week.
   
   
2. We are divided into semesters and, while most students have the same Algebra teacher first and second semester, not all do, so we attempt to have a clearly defined break at semester (winter break, we start in August and end in May) and all the Algebra teachers have "covered" the same material by then. So you'll see the year divided up into two 18-week semesters.
   
   
3. Our class sizes in Algebra are typically between 27 and 33. Not saying that's either good or bad, but it gives you information to compare to your classroom. We have 2150 students total in our school and the equivalent of 13 full-time math teachers (plus me teaching one section), and (this year at least) seven of those teachers that teach at least one section of Algebra (with 13 total sections). Whatever we develop has to meet the needs of the district, the school, those seven teachers, and the rest of the math department, and be both "backward" and "forward compatible." (And, oh yeah, it should meet the needs of the kids, but hopefully you get my point.)
   
   
4. We have four middle schools in our district, two of which are our primary feeder schools. They are also transitioning to the Common Core 6-8 Math standards, and should complete that transition next year. But we also have roughly 30% of our students open enrolled - from public schools in surrounding districts and from many private/religious schools (over thirty total feeder schools each year). So while we more-or-less know what the students from our middle schools have experienced in math class, we have about 30% of our students that come from widely varying backgrounds.
   
   
5. We currently use the 2007 edition of McDougal Littell's Algebra book. As we fully transition to the Common Core by fall of 2014, we may be able to purchase new materials (assuming they exist by then) but, until then (at least), we'll be using our existing book. (I'm campaigning not to purchase a new textbook, but that's a discussion for another blog post.)
   
   
6. We are a suburban school serving a primarily middle class clientele. The community values education and our school is generally considered a very good school.

Okay, that's probably more than you wanted, but hopefully it will address some questions that people might have.

So I took our existing scope and sequence, matched it with the ninth grade CCSS Math Standards, and came up with this still very much in draft Google Doc. Feel free to copy, edit, add comments, do whatever (appropriate) things you'd like to that document. It really is rough draft thinking to give us something to build on this summer as we try to translate that into actual lesson plans. I'd love to hear your thoughts (on the doc or in the comments to this post).

Algorithm Nation

As many of you are aware, I'm the "Director of Technology" (read, "building level technology coordinator) for my high school, but I also teach one section of Algebra. As a result I often find myself drawn into the math conversations happening on Twitter and on folks' blogs. This weekend I somehow ended up deciding to join a "reading group" around an article (pdf) titled "Standard Algorithms in the Common Core State Standards" from the Fall/Winter issue of the NCSM Journal.

Basically the conversation on Twitter began with some folks describing ways in which algorithms got in the way of learning and understanding mathematics. Then other folks pushed back a bit and asked if perhaps there was some value in algorithms. Christopher Danielson then pointed us toward the article in NCSM and suggested a "reading group" to discuss the issue. Feel free to "join" the group, which basically means you read the article and discuss it on Twitter or blogs using the hashtag #algorithmchat.

I thought I'd take a moment to put down my thoughts about algorithms in mathematics before I've read and begun discussing the article, just so I/we could see if my thoughts change after the discussion. While this is certainly a topic I have thought about, I also have not done a "deep dive" into the research or people's thoughts about algorithms. Right now I think I come down squarely in the middle (if that's possible). I agree that there are many times when algorithms have gotten in the way of learning and understanding mathematics. That we try to get our students to master the algorithms as quickly as possible so that they can be "efficient", even if it's at the expense of understanding. Then later we complain when they don't seem to have what we would consider basic number sense.

On the other hand, I don't see that as an inherent problem with algorithms, just the way that we sometimes deploy them. I do see algorithms as a valuable tool in working with mathematics (and other content and problems, for that matter). I think as long as we focus on understanding before (and while) we use algorithms, they can be very valuable in ways at making our thinking and processing "efficient" in order to then move on to thinking about more advanced mathematics, as well as to apply the mathematics.

So I guess my position right now, before this discussion, is that algorithms, when used as a result and in conjunction with understanding and meaning, can be a good thing, while acknowledging that we have often emphasized the algorithm at the expense of understanding and meaning. Feel free to join our reading group and contribute your own thoughts (on Twitter, on a blog, heck, even face-to-face if you have someone to talk to in your own building).

What I Learned in College (two days ago)

I was at the Colorado School of Mines on Saturday for a Science Olympiad competition my daughter was participating in. By all accounts Mines is a good school and we've had many graduates of the high school I teach at continue their education there and love it, and it's a beautiful campus.

In many ways, Science Olympiad is like a track or swim meet, a whole lot of waiting around until your event begins. In my daughter's case, she was in two events, right in the middle of the day, only one of which I was allowed to watch. So I had a spare eight hours or so to fill. Naturally I brought some books to read and a laptop, figuring I could hop on their wifi and get some work done. Conveniently School of Mines does have a guest network setup where they give you a guest login credential for temporary access. The only problem - they wouldn't give us the login credentials.

According to the person we talked to, it would be a "security risk" and a "liability issue" if they allowed us to use their network. Now, I don't know the details of their network, but I was a bit surprised by this, given that my public, K-12 school district has a guest wireless network available to anyone with no login credentials needed. Here they are hosting thirty teams from around the state, grades 6-12, and their parents, and the way you say "welcome" to these prospective students (this was Science Olympiad, after all, at a math/science/engineering college) is "we don't trust you to use our network?" (And, of course, the students were pretty busy, it would've been mostly parents and the teacher-sponsors using the network.)

But, I was polite, and returned to the classroom that was our home base . . . where I noticed that the teacher computer was turned on and logged into the network. Not only was it logged into the network, but it was also logged into the professor's home directory on the server and his Mines email account. So I proceeded to periodically use that machine throughout the day to check email and do a little bit of work.

What I briefly considered, but then refrained from doing, was emailing the CIO of the university (and copying the President) - from the professor's email account, of course - and pointing out that perhaps giving guest wireless access to prospective students and their parents was not the security or liability issue they should be most worried about. (And, no, I did not read any of the professor's email - although I did notice he had over 4000 unread messages . . .)

The second thing I learned at college on Saturday is in a slightly different vein. When I launched the browser on that teacher machine the professor apparently has it set to automatically open the tabs that were previously open. Here are screenshots of the three tabs that opened:

One was in the professor's Google Drive account, open to a PDF of a research article. The second was open to Wolfram Alpha, with a graph of an interesting square root function. And the third was open to a Wikipedia article about the Munsell Color System.

I don't want to read too much into which tabs were open, because I lack the context of knowing what the professor was doing with the information. But I think asking some questions about these open tabs would make for an interesting discussion in your school, and particularly in your high school math department.

For example, one might ask, "What implications might there be for your high school math curriculum (and classes) when a math professor at a high-end science and engineering school like the Colorado School of Mines has Google Drive, Wolfram Alpha, and Wikipedia open in his web browser?"

Or maybe you'd phrase it slightly differently, something along the lines of, "For the very small portion of your high school students who are going on to major in math/science/engineering in college, what should you be doing in your classes to prepare them for college math classes that utilize Google Drive, Wolfram Alpha, and Wikipedia?"

I imagine you can think of a few more questions as well, but I think it just might be a discussion worth having. As is a discussion surrounding, "If you have wireless, but you don't let anyone use it, is it really there?"

Pick My NCTM Sessions For Me. Please.

I'm pretty sure if there was an award (or perhaps a badge?) for "Worst picker of sessions at any educational conference", I would be in contention. So, on the off-chance that anyone still reads this thing, I'd like to enlist your help. I'll be attending most of Thursday and Friday of the 2013 NCTM National Conference in Denver this week. (Arriving late on Friday as I have to teach my first period Algebra class first, leaving relatively early each day as I need to pick up my daughter at 4:30 after track practice. Not going Saturday because same child is doing Science Olympiad that day.)

I've done a quick run-through of the available sessions on Thursday and Friday and tagged some that looked interesting using the leaves-much-to-be-desired-online-conference-planner thingy. "Interesting" for me right now involves any of the following: Relates to Algebra I, relates to technology use in Mathematics, relates to early elementary mathematics (my wife teaches 1st grade and doesn't get to go), or is presented by someone that I'd like to see present. (And, occasionally, one just seems interesting.)

What I'd like from you is advice, and perhaps your vote. I've created this quick Google Form to ask for your "votes" for each time slot, as well as any comments you'd like to leave about the choices (or something that I didn't pick that you'd highly recommend). I'm particularly interested if you can recommend a speaker based on your experience attending one of their sessions. I've listed all of the sessions I could possibly attend, including ones that I can only attend if my daughter's track practice is cancelled or I can get over my guilt at being gone and also talk someone into covering my Algebra class on Friday morning.

So, here's the form - I would appreciate your input (and passing it along to others for input). All submitted results (if there are any) will be available for everyone to see online.

For additional reference, here are Dan's, Christopher's, and Raymond's session plans, as well as this post on tech-related sessions and the Math Recap site.

What Job Would You Hire a Textbook To Do?

It was a fun and thought-provoking two days at Discovery Education's Beyond the Textbook event. Thanks so much to Steve Dembo, Dean Shareski, Hall Davidson, Laura Wenograd, and all the other folks at Discovery who not only planned this thing, but took very good care of us while we were there (Full Disclosure: I did not get paid to attend, but Discovery covered all expenses). And thanks to my fellow attendees for making this a great learning experience. (Oh, just a reminder Dean, there are still a couple of light bulbs you need to change.)

Here's a quick overview of the two days, and then I'll try to process a few thoughts. The first day (which was optional, but I attended) was a chance for attendees to meet in small groups with different teams from Discovery so they could pick our brains about a variety of topics around professional development, learning, digital resources, etc. (As was typical for me, I was pretty quiet at the beginning of the day, and then wouldn't shut up by the end of the day. Somehow I need to figure out a way to balance that out.)

The second day was the main event, where we spent some time brainstorming what a "21st Century Digital Resource" might look like, and then more specifically sketching some prototypes of what a "mathematics techbook" might look like. (Discovery Education already has a Science Techbook that is available, and will be shortly releasing a Social Studies Techbook. They are just starting on Math and are expecting their first techbook sometime in 2014.) Here's a picture of Darren Kuropatwa in front of our group's mockup as he's explaining to the whole group some of the ideas we came up with (photo courtesy of Tom Woodward).

Six different groups came up with six different mockups and, as you would expect, there were many commonalities as well as some differences. The main commonalities were that a "techbook" should be very customizable (by both teacher and student), media rich, provoke wonder/curiosity/inquiry, stimulate mathematical thinking/habits of mind, and have a social component. I'm not sure what exactly Discovery is going to do with these results, but I'm hopeful that we contributed at least a small part into making their next techbook better.

I'm left with two (at least) big questions after this event. These are questions I've had for a while and this event confirmed that they are still central (to my thinking, at least) to any discussion of a mathematics techbook.

The first question (and I don't think this one is necessarily shared by any of the other attendees), revolves around the essential question, "Is curriculum necessary?" This is not a new question for me, but it's still one I'm struggling mightily with. It seems to me that a central assumption of a text/techbook is that there is a readily identified, relatively fixed set of content/standards that all students need to learn and master.

While there's certainly a part of me that believes that in order to have a just, democratic, and functional society we do need some common knowledge, there's also a part of me that really disagrees. That part of me looks at all the children (really, humans) I've ever met and recalls how different they all are, and wonders how we could ever think that all of them should have to learn the same things at a certain specific age. This part of me doesn't see any way (or need) to create a text/techbook, because the fundamental assumption of what you would use it for is flawed.

The second question only arises if you answer "yes" to the first question. So if you believe that curriculum is necessary, or even if you don't but you think that as a practical matter it's going to exist for the foreseeable future, then perhaps this question will be more meaningful for you. This essential question is, "What's the purpose of a text/techbook?" (Or, because I just finished this book by Clay Christensen, perhaps rephrase that as, "What job would you hire a text/techbook to do?")

I think this is fundamental to this whole process, and it's the question all the Beyond the Textbook attendees were struggling with in one way or another. Is it simply a resource (digital or otherwise) with examples and sample problems for students to work through? Or is it more comprehensive, including and guiding the activities you would use with students in class? Is it a scope-and-sequence, default curriculum guide for the teacher of the course? Or is it designed simply to provoke student curiosity and mathematical thinking? Is it a central "hub" for the course that students (and teachers) will visit every day to launch and guide their learning? Or is it an occasionally-used reference?

Going along with those questions, what are the affordances that a digital techbook offers that a printed textbook does not? In other words, why digital? What can a digital techbook do that a printed one cannot and, in this case, what "value add" can Discovery bring to the table to make this better? What are their core competencies that they can bring to bear to make this a better tool to help teachers and students think and learn mathematically?

All of these were questions that I know my group thought about as we were working on our mockup. We certainly didn't come to a complete resolution on any of them (although you probably won't be surprised that we didn't think it should simply be a digital copy of a paper textbook, with examples and problem sets). One way we did try to address some of these questions was by suggesting that a techbook should be very flexible, with the district/school/teacher/student being able to customize and modify it at will to meet their needs. Darren suggested the idea of a "slider", where you could adjust what appears in the student version based not only on what your students need, but also on your skills as a teacher. (I suggested that perhaps it would have to be more granular than a slider, more like a checklist so you could pick and choose each and every piece, but otherwise we're pretty much on the same page.)

Let me try to illustrate that with an example that Darren shared. There's a fairly common trig problem revolving around a boat in a harbor and tides. The boat needs a certain depth in order to leave the harbor and you are given some information about certain depths at high tide and low tide (or other times) and then you can work through trying to solve the problem. Our thoughts are that a techbook could scaffold that in a variety of ways, and a teacher could choose how much information to include.

So, for example, a new teacher that is perhaps not very comfortable yet could slide the slider all the way to the right which would basically include everything in the student version of the techbook (much like a paper textbook typically does now, laying things out in detail). This would be the "be very helpful" version of the techbook. But a more experienced teacher might slide it all the way to the left, in which case the student would simply get the video of the boat rising and falling, with some time indicators, and ask them to figure out the question and then what they need to figure out the answer. (This would be the "be less helpful" version.) The students and teacher would then explore the problem in class via guided inquiry. And there would be several gradations in between those two versions.

I don't know if that example adequately illustrates the idea or not, but I figured it was worth a shot. We thought that one of the core competencies that Discovery could bring to this is to create those scenarios/videos. Those are the type of things that individual teachers often don't have the time or the skills to create, but someone like Discovery (who perhaps could hire some really smart folks to help with this) could create some provocative prompts and then provide pedagogical suggestions for the teacher. (And then the techbook would have the capability for teachers and students to upload/link their own creations that teachers could decide to use as well - the resource would grow over time.)

This is just one small part of our mockup, there were also pieces that addressed problems, exercises, collaboration, and the social component, but I thought it might give you an idea of some of what we were thinking. Part of the difficulty in making something that is viable is that it has to meet teachers (and schools, and districts) where they are at, and sometimes that is not where those of us in the room wish they were. So the challenge is to create a techbook that leads folks in the direction that "we" feel is the correct direction, while still maintaining "backward compatibility" with those that aren't there yet. The good news, however, is that I think digital makes that possible. I think it's possible to make an inquiry-based, technologically and web-enabled mathematics techbook that also provides support for a more "traditional" approach, and then helps lead teachers (and students) in a more constructive direction. That wouldn't be feasible in print, but - given enough smart folks and some decent server space - it is definitely possible with digital.

Now it's up to Discovery to pull this off. Even if they don't, I appreciate the way they are going about it and that they're giving it a shot. I'm hopeful they will be successful.