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What are the benefits of an expertly curated learning pathway?

Like that provided by a major publisher's textbook - CPM, a school district's mandated curriculum - IM's Open Up Resources or a learning game - ST Math, Dragonbox, or Amplify Fractions.

I ask this question with no particular age-level in mind, but I could see how the younger a learner is, the more useful a defined learning pathway would be - partly due to the inexperience of the learner

Research has been done on the idea of learning maps as a way of assisting learners along a learning pathway. See Gates Learning Maps projects.

One led by Jere Confrey's team has had some interesting research results and a design concept.

However, I still find it difficult to believe that the future of learning will involve standardized linear learning pathways... true personalization will bend and weave the trajectory of each learner, right? As Knewton described or InBloom once visaged... Or as a math prof recently argued to me, "Whose canon?" when discussing canonical examples to teach undergraduate intro stats.

In an age of brokering experiences, I offer my non-expert postgraduate data science pathway and ask the question another way,

Why pay for an expert's subjective structuring of content when you can structure your own learning based on your own personal interest and passion projects for free?

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  • $\begingroup$ In the future they will install all knowledge in the brain like you install an app. $\endgroup$ – Paracosmiste May 18 at 0:44
  • $\begingroup$ Please define the acronyms you use in your question. Can you include a link to "Gates Learning Maps" projects? $\endgroup$ – Namaste May 18 at 0:44
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    $\begingroup$ Apologies @Namaste, my intention was to use the searchable names of the companies since cpm.org , stmath.com , and im.openupresources.org go by their acronym's. There were many Learning Maps projects funded by the Gates Foundation around 2014. I link to Jere Confrey's specifically and hope that an interested reader might search "Gates Learning Maps" to see more examples. Many of those projects don't have publicly available artifacts. $\endgroup$ – E_Rushton May 18 at 0:58
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    $\begingroup$ @MrRushton You can edit the question: matheducators.stackexchange.com/posts/16630/edit to include the extra information. This is a good habit to get into - edit relevant information into the question proper. Thanks. $\endgroup$ – Tommi Brander May 18 at 9:35
  • $\begingroup$ Evan, to clarify, you are asking about learning post high school, correct? It's tough to pull out the essence of your question. In the US, common core came into existence for a reasonable goal, and even that is up for debate. But I suspect you are not at that level, grade/high school with this question's intent. $\endgroup$ – JoeTaxpayer May 18 at 12:04
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What are the benefits of having experts create curriculum ? I gather the alternative you entertain is some sort of user-driven machine learning path which is custom fit to the student. Ok, so, if that automation is initiated and curated by experts in math then I don't see the distinction. In some sense it would be a return to the old apprentice system that predates the mass production of university education.

On the other hand, if experts in math instruction do not play a significant role in the delivery of this new automated custom-built learning experience then what will guide the experience and content ?

  • If students guide the content then they will likely choose candy over meat. Sometimes the pay-off of learning deep skills and/or ideas is part of building the larger mathematical whole. Inculcation into the society and customs of Mathematics is surely going to be short-changed.

  • If companies guide the content then again their will be specialization which favors the needs of the company over the needs of the student. That which is beautiful, but not seemingly practical will likely suffer.

So, I see a lot of problems with control of education resting in the wrong hands. To my knowledge, PhD's in Mathematics care the most about Mathematics. Of course there are exceptions, but those who have invested so deeply want to see the subject thrive, prosper, grow and attain proper appreciation by the wider society. Math education is a major vehicle for those goals. We know directions the student might pursue that they simply cannot know as they don't know what they don't know.

These guided learning path ways could misappropriate interest of students in the same way that TV commericals manipulate us to buy things we really neither want nor need. Of course, I think we all took courses in the standard curriculum we feel the same way about. The difference then is ultimately accountability. New products are almost by default unaccountable and self-policing doesn't always serve well. Take a look at online education at the moment. Where is the quality control ?

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Who is going to create your "non-linear learning pathway"? I agree that there's a lot of promise to the idea of customized learning paths although I don't think we're as far along in that direction as some. However, I don't see this as being any less curated than the traditional linear path that you would get from a textbook.

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  • $\begingroup$ There are a few issues with my ambiguous question. One is this idea of a linear learning pathway. The main feature of that being the idea that it is standardized, like a textbook, and all learners follow the same path. Another being how the learning paths will be customized... machine learning algorithms trained on billions of data points like IBM Watson? teachers themselves? Emergent curriculum growing out of interactions with students is something I experienced with the Algebra Project. My question is directed at math educators, asking why expertly curated content is important. $\endgroup$ – E_Rushton May 20 at 4:07
  • $\begingroup$ Let me give you an example from my own experience: I'm an entirely self-taught programmer. I made a living at it, enough to support a family, for over a decade and a half so I like to think I'm pretty good. However, I always had a nagging insecurity: Am I really doing things the best way? Or are there approaches and options the professionally trained programmers now but that I don't? If one of them every looked at my code, would I look like a gibbering idiot? Curated training ensures that you've got a complete picture of the field you're studying where I was always unsure. $\endgroup$ – G. Allen May 20 at 22:18

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