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Topic: "Integrating technology: What does it mean?"

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Topic started by: Brian Drayton on 10/18/16

A remarkable amount of policy around education (teaching, learning, and assessing) is interwoven with “technology,” by which is usually meant “digital technology” and most often something Web-based and commercial. As you know well, our Information Age is said to have transformed the way people learn (or “consume knowledge”) andtherefore the role of the teacher has to change (or, has changed). Moreover, the infiltration of the Web into every nook and cranny of life is generating Big Data, which will provide unheard of insights into the education process, putting Utopian tools into the hands of schools, bureaucracies, and teachers (or whatever they will become).

There is, however, still nowhere near enough research to enable us to critique such claims, or even decide which widgets to buy. Moreover, most technology innovations getting a classroom connected to the Internet, for example are in fact more than one innovation in parallel, making it pretty hard to make rigorous or even well-formed claims about impact. Such work takes time and lots of careful analysis, and time is a commodity that is rarely lavished on research once the sales have been made, the machines or software is installed, and actual people use the new system for a solid length of time (something our team at TERC spent some time exploring a few years ago with respect to 1-to-1 computing).

Allow me, therefore, to direct your attention to a growing series of posts at Larry Cuban’s blog. Larry is (sort of) live-blogging a recent research project trying to get at the mysteries of technology education, and just what kind of impact it is having. In the first post, Larry makes the case for a series of closely observed case studies of integration. His research questions are:

How have classroom, school, and district exemplars of technology integration been fully implemented and put into classroom practice?
Have these exemplars made a difference in teaching practice?


In hissecond post, Cuban discusses how he decided todescribe varying degrees of integration, a notoriously vexed term, and takes a bottom-up approach to creating a definition, asking practitioners to direct him to examples of “best cases”. From these, he derived a set ofindicators for tech integration:

*District had provided wide access to devices and established infrastructure for use.
*District established structures for how schools can improve learning and reach desired outcomes through technology.
*Particular schools and teacher leaders had requested repeatedly personal devices and classroom computers for their students.
*Certain teachers and principals came regularly to professional development workshops on computer use in lessons.
*Students had used devices frequently in lessons.

In part 3, Cuban, noting that integration is not “all or nothing,” discusses some “stage models” for integration, reflecting on some of their assumptions about what is happening in each stage, or what enables the shift from one stage to another (such as the popular but debatable notions of PCK, or even TPCK) . Most importantly, he notes that these models tend to assume that when these various levels of use are reached, each can enable us to infer what it is the student is doing and especially what she is learning. As he says (in post #4), just because you see lots of functioning technology, being used by the students very often, this does not tell you anything about student learning, nor even about the pedagogy of the class.

Cuban fans will not be surprised that it’s for this reason that Larryasks (his question #2)Has the integration of technology actually changed teaching in the classroom, and in what ways? As he writes,

Far too little research has been done in answering this question about changes in teaching practices. So in researching and writing this book, I, too, focus on the process of classroom change and not yet how much and to what degree students have learned from these lessons. Once changes in classroom practices can be documented then, and only then, can one begin to research how much and to what degree students have learned content and skills.

Our “wireless high school” study examined teaching practices in high school science in our case study work, looking at dimensions like curriculum content, pedagogical practices (with a particular interest in student inquiry) and assessment; all in relation to the intended goal of the technology innovation. We could not look at change in practice, since we had not done a “pre test” on these classrooms, though we did ask teachers to report changes in their practice that they were aware of. Given how many kinds of instrumentation and technologies (including things like microscopes, multimeters, and glassware) science teachers have, the process of integrating the Web into all that is pretty formidable, and represents not just “teacher learning,” but in a broader sense, teacher growth, as they make choices about what is most important for their students to encounter and wrestle with; the student experience, and the design of tasks, is constantly being revisited. It takes time to figure out your pedagogical values again, especially when the technology keeps changing. As Cuban is quite aware, case study work is still pretty important, because our models of the challenge posed by technology integration, and the learning and experimentation needed to make good use of it are quite incomplete

Larry follows his 4-part reflection on his study design with a guest article by Mary Jo Madda of EdSurge, entitled “Did that edtech tool really cause that growth?” In this post, Madda makes some recommendations for how to evaluate studies claiming student learning impacts from new technology.

First, for educators, she recommends

#1: Look for the caveat statements, because they might discredit the study.
#2: Be wary of studies that report huge growth without running a proper experiment or revealing complexities in the data.

Then, for tech companies:

#1: Consider getting your study or research reviewed.
#2: Continue conducting or orchestrating research experiments.

Each of these recommendations is accompanied by a helpful discussion, and all the posts in this series include many links to research and other resources. In coming weeks, I will review at least some of Larry’s cases. I encourage you to at least check out the posts I’ve described here (and the vigorous discussions accompanying them!).

Originally posted Oct 18, 2016

This archived topic is open to the public.

restart conversation
This topic has 20 posts, showing all.

What do we already know about integrating technology?

posted by: Andy Zucker on 11/8/2016 12:19 pm

One hopes that Larry Cuban discovers something new in his case studies of technology integration, but that seems unlikely. There have been hundreds, probably thousands of such case studies conducted in the U.S. and abroad, and dozens of excellent reports based on those studies have been published -- including fine work Brian and colleagues conducted at TERC for the wireless high school project.

John Dewey said that democracy has to be born anew every generation, a thought that seems especially germane on Election Day. Apparently technology integration, too, must often be rediscovered, reinterpreted, and re-evaluated. But some of that effort is simply unnecessary.

For many years multiple researchers have observed that there are a variety of "necessary conditions" for effective technology integration. Some schools have posted one such report online, published by the Northeast and Islands Regional Technology in Education Consortium in 2004; I am a co-author. The lessons learned described in that concise report appear to apply equally well today. See

"Lessons learned" have appeared over and over again in research studies. So has an underlying question about technology integration in schools, and that is: What would a reasonable person expect the impacts to be? Because learners are still learners, and teachers are still teachers, and the interactions they have in school are central, as are students' experiences outside school, it seems unreasonable to expect a revolution merely because technology is used in schools. Yet that is too often the benchmark some researchers use: We did not observe a revolution, so technology in schools is a failure.

I have argued that utopian thinking should not be our guide, although some technology proponents, such as Seymour Papert, have held utopian views. Over the past 100 years civil and military fixed-wing aviation has been transformed, and the results are both obvious and significant; the world is a much smaller place now, and we all know it -- but it is not a utopia. I believe that over decades schools will also be transformed (many have been), that technology will play an important role -- but that no one should expect utopia. (I would add that concerns that technology is too often viewed by policymakers as a magic talisman are probably correct -- but then look again at the "necessary conditions" and the lessons learned that have been written about for a long time and decide if the offending policymakers paid attention to what we already have learned.)

Technology supports understanding. It doesn't replace it.

posted by: Amy Cohen on 11/9/2016 10:37 am

In almost 50 years of teaching freshmen at a very diverse institution of higher education and about 10 years of working with math education colleagues and with in-service teaching, I have heard versions of the following comment all too often:

"I understand the concepts of this word problem. I want to use my calculator. Should I add or subtract?"

Our students need a "both/and" approach - not "either/or" to be able to select appropriate tools strategically. They must have experience with hand computation to develop fluency and insight. They must have experience with reasoning and multiple approaches to problem solving to choose likely approaches and to develop the stamina to try other approaches if the first one(s) they try don't work out well.

Technology supports understanding. It doesn't replace it.

posted by: Sara Silver on 11/10/2016 8:29 am

Hi Amy,
To your quote:
"I understand the concepts of this word problem. I want to use my calculator. Should I add or subtract?"

If students have a conceptual understanding of the word problem, they will also know whether to add or subtract. A calculator will not direct them as to which operation to use!!

Utopia limited

posted by: Brian Drayton on 11/10/2016 7:39 am

Andy, thanks for this thoughtful post! I love your analogy with flight technology. It's so hard for the "Education business" to keep its collective mind on learning itself, and try not always to think of it as a tool for shaping economies etc.
Anyone (like all the people posting on this thread!) who's aware at all of the history of science education has to wonder, What does it take for people to actually recognize how much as been figured out? Maybe we have done a disservice to education policy by stating so often how complex and poorly understood the learning process, the classroom, etc. are as researchers or teachers, such admissions only seem like honesty in the face of complexity but it's not like we don't know a lot! I see an analogy with climate change science, or evolution people inside the field are painfully aware of the unknowns and they take for granted the vast amount that is actually well established and not in dispute.
I wish that some ed policy people could read the comments in this thread yours included and get a sense of how much is known about right use and right understanding of technology in schools.

Integrating tech survey findings

posted by: Sara Silver on 11/8/2016 3:26 pm

Hi Brian,
I've been out of the discussion loop in a long time. Just saw your post and wondered if you had seen this: -to-use-tech-to.html?intc=EW-TC16-EWH

It confirms several of your points.

Sara Silver

Tech counts etc

posted by: Brian Drayton on 11/10/2016 7:16 am

Good to hear from you, Sara!
Thanks for bringing the Tech Counts report to mind. I wonder how that report is used, as a discussion starter in schools or faculty meetings, for example?

Tech tools contd.

posted by: Sara Silver on 11/11/2016 2:22 pm

Hi Brian, not even sure if such a report is brought to staff attention in schools. Building leaders with strategic vision may choose to do so. Here is another link to an Ed Week series- this one on digital literacy

It intersects with the broader topic in your string on tech tools.


What Andy said . . .

posted by: Talbot Bielefeldt on 11/9/2016 1:23 pm

I agree with Andy Zucker. So much of the discussion about educational technology takes place as if it were started yesterday. I worked for years for ISTE, the author of a widely used set of ed tech standards that have been adopted or referenced by many states. The standards are explicit that the quality of technology use depends on looking at things like questions asked, decisions made, information gathered and organized, and so forth. Yet even in states where the ISTE standards are the state standards, I would visit projects that devoted precious grant funds to imagining new rubrics and frameworks for ed tech.

Of course part of this is the rapid change in technology. The things we have to integrate don't stay the same. But I also suspect there is some fundamental need for people to reframe subjects for themselves. Most of my work now revolves around math and science, and I see a similar phenomenon with the NGSS Science & Engineering Practices. Here again I see educators devoting precious time to reformulating the existing standards.

I note the best results (that is, in this context, learning experiences that address the highest numbers of technology and content standards attributes) when educators and professional developers focus on concrete learning experiences (lesson plans, experiments, discussions) and use common frameworks to ensure and enhance the details of student interaction with people and things. This is as opposed to starting with a definition of, say, technology integration, and then trying to come up with something that fits the definition.

post updated by the author 11/9/2016

technology inside and outside

posted by: Brian Drayton on 11/10/2016 7:30 am

Talbot, I appreciate your comments, especially from the ISTE point of view --
You know, it makes me think -- a lot of the language around standards of any kind implies that they are something to be achieved or accomplished, rather than to characterize a learning experience, piece of curriculum, etc. Standards, like technology, can be seen as "outside" or "inside" ingredients.
What I'm thinking is sort of a re-statement of what you have said already except in very specific settings, you grab the "right" tool to do the task before you, rather than shaping the task around the tool ("We spent all this money on these computers, we should use them for something other than doorstops!!")
But I can't help believing that part of the problem is that teachers are often asked to "integrate" a new tool which they have not had the chance to use in a natural way to solve a problem for themselves. Having a feeling for the time and way a tool comes in handy means that you use it purposefully and in a sense with authority or (intellectual) integrity.
When I was first around science ed., a big hope was that kids would come to use spreadsheets (on apple IIs!) to enable new kinds of inquiry and understanding. But it was years before spreadsheets became so well understood, a sort of "lingua franca," that their use in classrooms was taken for granted and started to deliver on the promise and from my observations, a big reason was that the teachers had become very used to spreadsheets as a tool that they valued and could think with. They had to have an "inside" experience of the tool.
I wonder if the need to reinvent or re-write standards, rather than applying them, reflects the process of getting inside them, and getting to the point that they are actually serviceable in the way that things have to be in a classroom -- flexible, fluid, and unobtrusive, as long as they support real learning, rather than being the goals to accomplish.

"concepts" and calculators alone are not sufficient

posted by: Amy Cohen on 11/11/2016 8:11 am

The quotation marks on "Concepts" are intended to suggest that many students who think they have conceptual understanding do no. And many students who depend on calculators also depend on procedural guides (what buttons to push in what order).

The deeper issues of understanding a contextualized task, modeling it with mathematics, and developing an appropriate computational plan are not automatically resolved by teaching only "concepts" and "calculator syntax"

Sorry for my classroom experience at variance with theoretical predictions about the almost absolute superiority of technology over productive struggle with a variety of computational attacks on problems.

do we give this learning the time it takes?

posted by: Brian Drayton on 11/14/2016 4:43 am

Yes. But as I read your post, I wonder: do we give this kind of learning: " understanding a contextualized task, modeling it with mathematics, and developing an appropriate computational plan"
the time it needs? There are many things to learn, embedded in your words.
I see some similarity here with one of the challenges of teaching science -- I mean, we want students to get a feeling for science as a way of knowing (that is, of coming to know). So early on we start asking students to "ask questions" or "develop hypotheses, and think about ways of testing them -- when they have so little experience with the phenomena that the first questions that arise are atheoretic and often deeply unproductive of the kinds of learning that we desire.
So to overcome this hurdle, the students need more time and experience than we usually give them. They don't have need yet of the conceptual tools we are eager for them to use.

Finding the channel

posted by: Talbot Bielefeldt on 11/12/2016 5:55 pm

I see us navigating between two reefs. On one side is the absurd proposition that we have these computers, so we have to use them for something. On the other is the puritanical dogma that if you can write a decent sentence, only then we will let you write in on the computer. I think what we want is a population that can at least do useful work and make appropriate decisions. Once our work is cut out for us (building a flight of steps, fixing a tail light, writing a dissertation), we usually manage to pick up the STEM knowledge we need for the job. The problem with kids is that in our society they dont really need to do anything. With project-based and problem-based learning, we try to give them things to do that are as close as possible to adult activities. Part of that approach is using available technologies the way they would be used on a real-world problem. Without knowing the context, I am not necessarily bothered my Amy Cohens students not knowing whether to add or subtract on a calculator. Im often in the same position when my statistics package asks something like, orthogonal or oblique rotation? One criterion for effective technology use is, did technology help or hinder the students getting to the point where they realized they needed to look something up? Another criterion might be, can technology help the move through the barrier? Ideally, Amy could say, figure it out, and the students would have a range of resources and the time to use them. Im speaking as a mathphobe who has to use statistics. To the extent that I learned the required concepts, I did it through manipulating numbers, rapidly and repeatedly, until I began to see the underlying relationships. For students like me, that is one example of an instructional approach that is only possible through technology.

"technology" a term that muddles things

posted by: Brian Drayton on 11/14/2016 5:00 am

There is a lot of value in the scenario you describe, in which "technology" is a tool that one learns to use as needed and with a purpose in mind. Then in a way the tool (as I know it) and the task are part of a concept that I build for myself -- or a schema or script. Sometimes at first these serve as what someone once called a "pragmatic ritual," but as with all matters of meaning, once we have a concept (or the nub of one) we can continue adding to it until it has something of the richness that experts see in it (a version of "Quinian bootstrapping")
But I think that another important thing to bear in mind, in getting at the true complexities of the challenge, is that "technology" is an umbrella for a LOT of different tools. Quite aside from all the non-digital or non-computational tools that are essential in life, computers and the Internet offer a huge range of tools -- the computer is a tool box, not a tool. So "looking something up," as you say, actually can mean "find a word definition using Google," or "finding a how-to-do it video on Youtube," or "learning an experimental procedure from JoVE," or "reading about Bosnia on Wikipedia," or "reading about John Dewey in the online Stanford Encyclopedia of Philosophy," or "getting into an on-line community to get expert tips about science teaching." We all know that there is a lot to learn about information retrieval and critical use in any of these operations.
Meanwhile, there are also data sets, computational environments, tools like spreadsheets or stats programs, Geometer's Sketchpad, tools for creating video... and all of these can be used with more or less understanding, as learning tools, or as tools for making and expressing meaning.
What I hope is that (to go back to Sara Silver's posts) STEM departments in schools learn to develop a coherent approach (articulated across years and disciplines) about how they will realistically build students' purposeful use of SOME of these many possible tools, and their embedded languages of thought and their understanding of the further range of tools they can reach to when their purpose dictates (or start to play with tools, to think of new purposes).

Purposeful use of tech

posted by: Sara Silver on 11/14/2016 9:29 am

Brian et al., I think this is key: purposeful use. And the time it takes to develop the habits of mind that permit discernment. All too often, practitioners--like students--get seduced by the next "sexy" tool. For example, 3D printing was /is the rage in MSP (ED) projects that infused technology into STEM programs. All our data show is that actual classroom implementation of 3D printing was influenced by resource capacity. And it was just an episodic thing. There was little if any reasoned justification how this tool could advance STEM (integrative) thinking. The MSP learnings that are likely to endure are those taught by MSP participants who stayed in the PD program 3+ years, AND- whose programs were faithful to the strategic vision of what habits of mind the district wanted their students to acquire.

Purposeful use of tech

posted by: Betsy Stefany on 11/15/2016 9:33 am

I am reading along with the Integrating technology topic watching for a point to jump in. The MSP I managed and continue to coordinate actively engages in STEM integration. I am frustrated by the lack of capture of the accuracy of the STEM integration process with early projects however understand that this frustration is basically is due to the fundamental changes within the progression that are still a challenge to evaluate. Please accept this view as a product of the continued commitment beyond the MSP to support changes that improve understanding of the process for all learners.

The change that sweeps us into technology integration is a huge force and evaluation by current assessment is difficult to point out what is success in a manner that will be valued.

I agree with you that sales drives tool interest and that the companies teach the operation of the item but struggle with the application into projects. To nudge the term purposeful to match with relevancy of project and further timing is key to STEM success. These smaller steps may be more obvious with ESSA, as an outcome of sustained advances are measured at the student level. Part of the past problem with integration is that the process is often thought to be leaped by just purchasing an item without developing the relevant application. Disappointment crashes with the effort to demonstrate full grade or classroom results with tools.

Return to the 3D printer as a further view from the small MSP perspectiveOnly one district out of the multiple districts joined to form a rural based MSP reached the point of a 3D printer by the end of the 4 years of MSP support. Does not mean that the tool was not an appropriate for their progression point? After the MSP closed, theres no evaluation system to record their progress and before the close the percentage of engagement was low. How would that progress be even evaluated as it blended in with expanded student programs in the following years?
The evaluation of STEM integration is important to revise and thie past project remains as a Community of Practice continuing to support projects and assisting their integration through their use and application with expanded programs.

It is not the tools that we need to focus on as we assess, but the application over time by students. Thats still on the drawing table although funding systems like Donors Choice are capturing and documenting the continued progress by individual teachers.
The 3D printer use involves a huge step from flat thinking to spatial that is core to STEM success.

That teak in terms towards relevancy is the bridge to the elusive term engagement however still not the full conditions under which STEM expands and is sustained. As a Community of Practice we continue to wrestle with the varied topics identified by Harvards MOSART tests in science of citizen misconceptions. We all know it takes time to revise them once they are set. Digital tools are individual learning conditions and moving from classroom set and plug and play is important to explore.

Glad for this topic and look forward to hearing more from others still out there in the process of integration.

Betsy Stefany

3-D thinking

posted by: Brian Drayton on 11/16/2016 8:21 pm

I was intrigued by many points in your post, but for now will just ask this: In your area, was the move "from flat thinking to spatial" seen as desirable before 3D printers came into the picture? If so, how was it addressed before? I am just thinking about your idea that perhaps many schools didn't get to adopting 3D printing because it wasn't appropriate for their level of integration (or other preparation) So does that mean that some other approach to 3D visualization should be in place, before introducing the sometimes frustrating new technology (with its expenses and limitations)?

3-D thinking

posted by: Betsy Stefany on 11/17/2016 10:26 am

Great questions. Yes, the progression toward spatial thinking was well in place prior to the option to use a 3D printer.

Answering also requires stating that the project was conceived as a Community of Practice, resolving the potential conflict between teacher and district goals. This later factored into the pressures to introduce specific technology, however the initial focus was on internet content access not digital tools. Technology integration was a way to that goal, not the focus of the project.
Our MSP project considered teachers interest as part of the integration process as well as their needs to learn specifically identified areas in science education that had been introduced since their degree. Student testing highlighted the need for more physical science for students. Specific areas of the teacher knowledge, light applications/properties, heat transfer and graphing were the teachers needs, identified by testing. ( Harvards MOSART tests). These content areas tend to lean toward physical project activities and the application of physical objects, forming a base for spatial thinking.

Beyond the content, the participants could request how and when they would progress, requiring that they show student evidence of their PD. Digital tools were the seamless way to provide the evidence.

The origins of the integration learning progression of these tools started in the first year with an activity in exploring convection patterns in classrooms and including GPS/GIS beyond the classroom. The change in mapping to think of data in layers and to use a variety of visualization techniques EVENTUALLY led to the introduction of a 3D printer.
Three years of multiple activities, products etc happened to time perfectly with the 3D printer buzz. I agree that from the time that the MSP funds were expected to support STEM, project managers were hit with consecutive summers of new educational products.
Our project design as a CoP, set collaboration and communication to deal with these pressures and the sharing of results, problems etc were basic to progress.. The early concept of a Community of Practice remains as a continually changing support to success and sustained STEM integration.

Thanks for asking questions, enabling consideration on how the learning progression developed towards spatial practice. Glad to discuss more specifics of the tool integration and the experience, especially .as the teacher just was funded for a further support tool to the 3D printer-- introduced two years ago.

spatial challenges

posted by: Betsy Stefany on 12/28/2016 8:52 am

I have been thinking further about the timing of tool integration with the benefit of holiday time and Thomas Friedman's latest book, Thank You for Being Late that refers to this era as the" Age of Accelerations". Brian's blog on the history of the three sectors also bears considering in how public schools merge outside school to benefit all to engage in STEM practices.

This pressure to accelerate does flex with the nature of the community in which a district is located as well as the opportunities within the school for access to varied programs that approach learning in varied, yet accepted methods.

The teachers who requested the 3D printer had years of leading annual Lego League teams in the fall and reintroduced into an interschool day club for Jr Solar Car Sprint for the spring. These programs introduce spatial practice as both a need to advance the product of their team but also by actual awarding team views and varied expertise between peers. In this situation, easing into use a tool that can replace fairly standard parts, is more acceptable than expecting amazing inventions to leap from its availability. Identifying and respecting interests drives the opportunity to adjust to the apparent pressure of change and accelerating expectations that can result in early challenges to adjust to what may feel in isolation like failure.
Teams and teaming that stresses the to development of a narrative around the learning process that is engaging is the key piece of any new, tool or team member. Enabling all to achieve requires a sharing of experience on which to build a forward momentum.

seeing and thinking in a 3-D world

posted by: Amy Cohen on 12/29/2016 9:45 am

I have taught at post-secondary level for almost 50 years and worked with in-service middle school teachers for almost 10 years. All this time I faced the awkward fact that most of our instructional media (paper-and-pencil, books, blackboards, computer monitors, etc) were 2-dimensional and few and fewer of my students had built or rebuilt 3-dimensional objects with hand tools (hammer, screwdriver, saw, compass, protractor, etc) These students had a very hard time recognizing and interpreting 2-dimensional representations of 3-dimensional objects - even a prospective sketch of a cube was almost unrecognizable.

I agree with the comments above that students need to (or would benefit from the opportunity to) explore and built experience and intuition for 3-d objects and 3-d machines gradually over their lives inside and outside formal schooling. A sudden intro to simple programming/coding for 3-D printers may just reinforce insecurity and/or a sense of "not belonging". Some of the "media specialists" I have spoken with at "maker movement events" report that their schools do not promote interaction with STEM teachers to integrate the "gee-whiz" stuff with the "standard curriculum".

What does the research say?

posted by: Talbot Bielefeldt on 12/31/2016 8:36 pm

Responding to Amy Cohen's last post:
This seems like a topic someone must have studied. What is the effect of physical object construction on ability to conceptualize and manipulate 3D representations in a flat (paper or electronic) medium?
I wonder if there is a contradiction within the whole ecosystem of knowledge/use-of-knowledge. For instance, when I was in college I took an introductory calligraphy class, and was told that research showed that children who were taught calligraphy were able to more rapidly learn early reading skills, such as letter recognition. Years later I encounbtered an article on U.S. Post Office automation, and read that envelopes addressed in italic or other calligraphic script are often inscrutable to the USPO scanners. In other words, calligraphy as a literacy approach (not as an art form) is demonstrably useful, but you'd better not use it if you need to create machine readable text.

Without having the research at hand, I'm wondering if physical construction (e.g., an old-fashioned shop class) is demonstrably beneficial but is impractical to implement today, just as universal instruction in calligraphy would have definite benefits that are probably not worth the time.

For the record, as a student I am with Amy. I learned both my math skills and construction skills late in life, and know that in my case the math is very difficult without some ability to visualize a physical space or event. Maybe in a future incarnation I will be a theoretical physicist, but not this time around.