Some of the comments here indicate that the Khan Academy videos also include instruction on the meaning behind the math as opposed to the idea that it's just teaching rote memorization of procedures and applications without context. As a student who has recently taken math methods courses some of the arguments against this approach is the idea that students should be developing their understanding of the underlying meanings on their own. One resource I've used recently classifies activities into four areas: memorization, procedures without connections, procedures with connections, and doing mathematics. The first two are considering as having lower-level demands and the last two are higher-level demands[1]. Thus it is possible that the Khan Academy videos are actually a great resource for students as there are no guarantees that we're within the bounds of the lower-level demands tasks, and this seems to be possible considering the comments I've read and some of the sections of video that I've watched.
In contrast I've also looked at one of the mathalicious.com lessons[2] which if approached correctly can also fall within the bounds of the higher-level demands tasks. However, that is something that close attention must be paid to. We can always modify activities such that the level of cognitive demand is either increased or reduced. More importantly though I feel as though the mathalicious lessons have an opportunity to further make connections by having students do mathematics that is practical. The one lesson I examined seemed to not do this, which is disappointing. Granted I don't have my BS in mathematics nor my teaching certification yet as I'm in my final semester but I don't think this lesson represents any kind of activity that is realistic. I remember reading an article by IIRC Richard Feynman about analyzing textbooks for use in classrooms in California. This was one of the arguments he presented as well; example activities we have students do to learn the underlying mathematical concepts should be realistic and not contrived examples.
Overall, the key here is that students should be doing the mathematical work. Obviously I have a vested interest in the subject as I'm in the classroom for the majority of my week actually working with students to teach and help them learn math. Is it possible that Khan Academy can be ineffective if used incorrectly? Absolutely. But I feel the same can be said of the mathalicious lessons. If someone isn't there to correctly use the resources they can have a smaller impact than originally intended.
[1] 5 Practices for Orchestrating Productive Mathematics Discussions, Smith & Stein. NCTM.
N.B. I'm also a little concerned with one of the sections in the Lesson Guide that I read through. It states the following:
Before we find the equation of the line, we want to focus on the meaning of slope. A helpful shorthand for slope is “y per x,” which is how we’ll measure slope (i.e. its units). In this case slope will be measured in “heart beats per music beat,” and will tell us what happens to Billy Jean’s heart rate when she increases the music tempo by one [beat]. By focusing on this real-‐world meaning, we can avoid tricks like “rise over run.”
At first glance it seems to me that "y per x" is a trick too, which they're calling out "rise over run" for being. I feel that "rise over run" is closer to the mathematical definition that is presented in most textbooks which refers to the "difference in y over the difference in x" or "vertical change over horizontal change". While using "y per x" allows them to then refer to "heart beats per music beat" in this context, that doesn't get at the heart of the idea that it's really the ratio of the change in heart beats compared to the change in music beats.
In contrast I've also looked at one of the mathalicious.com lessons[2] which if approached correctly can also fall within the bounds of the higher-level demands tasks. However, that is something that close attention must be paid to. We can always modify activities such that the level of cognitive demand is either increased or reduced. More importantly though I feel as though the mathalicious lessons have an opportunity to further make connections by having students do mathematics that is practical. The one lesson I examined seemed to not do this, which is disappointing. Granted I don't have my BS in mathematics nor my teaching certification yet as I'm in my final semester but I don't think this lesson represents any kind of activity that is realistic. I remember reading an article by IIRC Richard Feynman about analyzing textbooks for use in classrooms in California. This was one of the arguments he presented as well; example activities we have students do to learn the underlying mathematical concepts should be realistic and not contrived examples.
Overall, the key here is that students should be doing the mathematical work. Obviously I have a vested interest in the subject as I'm in the classroom for the majority of my week actually working with students to teach and help them learn math. Is it possible that Khan Academy can be ineffective if used incorrectly? Absolutely. But I feel the same can be said of the mathalicious lessons. If someone isn't there to correctly use the resources they can have a smaller impact than originally intended.
[1] 5 Practices for Orchestrating Productive Mathematics Discussions, Smith & Stein. NCTM.
[2] http://www.mathalicious.com/lesson/can-music-kill-you/
N.B. I'm also a little concerned with one of the sections in the Lesson Guide that I read through. It states the following:
Before we find the equation of the line, we want to focus on the meaning of slope. A helpful shorthand for slope is “y per x,” which is how we’ll measure slope (i.e. its units). In this case slope will be measured in “heart beats per music beat,” and will tell us what happens to Billy Jean’s heart rate when she increases the music tempo by one [beat]. By focusing on this real-‐world meaning, we can avoid tricks like “rise over run.”
At first glance it seems to me that "y per x" is a trick too, which they're calling out "rise over run" for being. I feel that "rise over run" is closer to the mathematical definition that is presented in most textbooks which refers to the "difference in y over the difference in x" or "vertical change over horizontal change". While using "y per x" allows them to then refer to "heart beats per music beat" in this context, that doesn't get at the heart of the idea that it's really the ratio of the change in heart beats compared to the change in music beats.