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As someone who tried teaching themselves math with Khan Academy, I feel like Khan Academy suffers from the same problem most sites do, in that they tell you the

As someone who tried teaching themselves math with Khan Academy, I feel like Khan Academy suffers from the same problem most sites do, in that they tell you the information before you can discover it for yourself. This is different than how AoPS teaches math, where they ask you questions which then guide you towards self discovery, and as a result, you start asking your own questions which create paths for you to go on and explore.

barry-cotter 8y ago
You, and AoPS’ target audience of current and potential math nerds are very far from the norm. Inquiry based learning is actively harmful to learning for many students, and much less efficient for more or less everyone. > Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching > Evidence for the superiority of guided instruction is explained in the context of our knowledge of human cognitive architecture, expert–novice differences, and cognitive load. Although unguided or minimally guided instructional approaches are very popular and intuitively appealing, the point is made that these approaches ignore both the structures that constitute human cognitive architecture and evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process. The advantage of guidance begins to recede only when learners have sufficiently high prior knowledge to provide "internal" guidance. Recent developments in instructional research and instructional design models that support guidance during instruction are briefly described. https://www.tandfonline.com/doi/pdf/10.1207/s15326985ep4102_1?needAccess=true& https://www.tandfonline.com/doi/pdf/10.1207/s15326985ep4102_...
- jacobolus 8y ago
  Your link is to a very controversial polemic which IMO sets up a straw man, and then makes its own argument in a (both theoretically and empirically) questionable way, based on the authors’ pet “cognitive load” theory (which I personally think is bunk, but YMMV). It should be read in the context of its critics, and taken with a heap of salt. To understand the problem with US-style mathematics pedagogy, I would recommend reading http://www.de.ufpe.br/~toom/travel/sweden05/WP-SWEDEN-NEW.pdf http://www.de.ufpe.br/~toom/travel/sweden05/WP-SWEDEN-NEW.pd... For some advice and materials based on an alternative theoretical framework, let me recommend https://www.map.mathshell.org/trumath.php https://www.map.mathshell.org/trumath.php * * * I think Khan Academy should be thought of as a consistently average-quality US-high-school-style lecture, combined with US-style trivial exercises. It is a slow, unimaginative, pedantic curriculum. But it has the advantages of being free, always available, and self-paced (in the sense that students can keep going through as much of it as they want without needing to wait, and can return to previous sections any time). I’m glad it exists, because it sets a quality floor; live teachers have variable quality, and while many are better than KA lectures, some are certainly worse.
  - barry-cotter 8y ago
    If you can refer me to three relevant articles that critique or falsify Kirschner et al. I’ll be happy to read them. I’ve read Problem-Based Learning is Compatible with Human Cognitive Architecture: Commentary on Kirschner, Sweller, and Clark (2006) already.

barry-cotter 8y ago

You, and AoPS’ target audience of current and potential math nerds are very far from the norm. Inquiry based learning is actively harmful to learning for many students, and much less efficient for more or less everyone. > Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching > Evidence for the superiority of guided instruction is explained in the context of our knowledge of human cognitive architecture, expert–novice differences, and cognitive load. Although unguided or minimally guided instructional approaches are very popular and intuitively appealing, the point is made that these approaches ignore both the structures that constitute human cognitive architecture and evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process. The advantage of guidance begins to recede only when learners have sufficiently high prior knowledge to provide "internal" guidance. Recent developments in instructional research and instructional design models that support guidance during instruction are briefly described. https://www.tandfonline.com/doi/pdf/10.1207/s15326985ep4102_1?needAccess=true& https://www.tandfonline.com/doi/pdf/10.1207/s15326985ep4102_...

jacobolus 8y ago
Your link is to a very controversial polemic which IMO sets up a straw man, and then makes its own argument in a (both theoretically and empirically) questionable way, based on the authors’ pet “cognitive load” theory (which I personally think is bunk, but YMMV). It should be read in the context of its critics, and taken with a heap of salt. To understand the problem with US-style mathematics pedagogy, I would recommend reading http://www.de.ufpe.br/~toom/travel/sweden05/WP-SWEDEN-NEW.pdf http://www.de.ufpe.br/~toom/travel/sweden05/WP-SWEDEN-NEW.pd... For some advice and materials based on an alternative theoretical framework, let me recommend https://www.map.mathshell.org/trumath.php https://www.map.mathshell.org/trumath.php * * * I think Khan Academy should be thought of as a consistently average-quality US-high-school-style lecture, combined with US-style trivial exercises. It is a slow, unimaginative, pedantic curriculum. But it has the advantages of being free, always available, and self-paced (in the sense that students can keep going through as much of it as they want without needing to wait, and can return to previous sections any time). I’m glad it exists, because it sets a quality floor; live teachers have variable quality, and while many are better than KA lectures, some are certainly worse.
- barry-cotter 8y ago
  If you can refer me to three relevant articles that critique or falsify Kirschner et al. I’ll be happy to read them. I’ve read Problem-Based Learning is Compatible with Human Cognitive Architecture: Commentary on Kirschner, Sweller, and Clark (2006) already.