Module 1-E Content revisions

[siwelwerd]

Issue to track non-trivial content improvements to 1-E; will add one comment with discovered issues after each class day.

[siwelwerd]

Module E Part 1

1. Observation 3.2 could easily be omitted.
2. Activity 3.8 didn't seem especially worthwhile. I would have rather had that 5 minutes for the last activity.
3. Activity 3.10: The phrasing of Part 1 with the r, s, t was confusing to the students.
4. Activity 3.11: Replace the t_i with ? to be more consistent and less confusing.
5. Activity 3.16: I felt like I needed more time here, 10 minutes for teams and 5 minutes for classwide discussion.

[StevenClontz]

Observation 3.2 could easily be omitted.

sounds good

Activity 3.8 didn't seem especially worthwhile. I would have rather had that 5 minutes for the last activity.

agreed

Activity 3.10: The phrasing of Part 1 with the r, s, t was confusing to the students.

agreed

Activity 3.11: Replace the t_i with ? to be more consistent and less confusing.

I agree. I also split activity 3.11 into two parts: first find the solution as a single vector, then split that vector into a linear combination of vectors.

Activity 3.16: I felt like I needed more time here, 10 minutes for teams and 5 minutes for classwide discussion.

Done.

[StevenClontz]

Part 2: it may be useful to take the Gauss Jordan illustration from part 3 and provide it as an illustration of circling pivot positions and working through the problem methodically.

Also fix that stupid typo in activity 4.2.

[StevenClontz]

Circle leading terms in definition. Emphasize that pivot positions are where we want to put leading terms

[StevenClontz]

Illustrating pivot positions in an explanation of activity 4.2 would help enable students for 4.4. We could require a different row echelon form in 4.4 to prevent retreading the same steps.

[StevenClontz]

Should we require specifying row operations when showing row reduction?

[StevenClontz]

Maybe part two activities should be written to focus on matrices, with observations calling back to the corresponding linear systems. Less moving parts might help focus students on developing the mechanics of row operations. (Part 3 is where we really dig in and talk about those solutions anyway.)

[siwelwerd]

Part 2 comments Timing issues: Activity 4.4 needs more time, 4.5 less. Somewhere I used 60 minutes instead of 50.

I think activity 4.2 can be omitted. I would rather have them discover the operations, but give them intermediate target steps. First, fix the first column. Then, fix the second column.

As I mentioned in conversation, I disagree with your last comment. Matrices are a means to an end and should be treated as such. This is linear algebra, not matrix algebra. <\algebraist snobbery>.

[StevenClontz]

I think activity 4.2 can be omitted. I would rather have them discover the operations, but give them intermediate target steps. First, fix the first column. Then, fix the second column.

This. We can address timing when we address this.

I definitely like the motivation of phrasing in terms of linear systems. I think my concerns about too many moving parts might be addressed when we redesign the activities into smaller chunks as you suggest.

[siwelwerd]

I think we are on the same page--I'm okay with phrasing parts of one problem in terms of matrices, provided it is tied to a system at the beginning and end of that sequence of activities. For example, activity one is "Turn system into corresponding augmented matrix into matrix of X form", activity two is "Turn resulting matrix of last activity into matrix of Y form", ... last activity is "Turn back into system and solve".

[StevenClontz]

Something I'll point out: we're moving away from Same Response. I'm okay with this, but it's worth noting that if we scaffold our activities this way, they will likely diverge until they get to RREF(A) at the end.

[siwelwerd]

Same Response is not a TBL thing. Same Problem, Significant Problem, Simultaneous Response, and Specific Choice. It would be boring if they all had the same response anyways.

[StevenClontz]

Whoops, I meant Specific Choice, which I think is usually interpreted as "all correct responses should be the same" based on our workshops. But I think our interpretation, which is that we should always specify a well-defined goal even if the correct answers are not unqiue, is a good fit for TBIL.

[siwelwerd]

I have already reinterpreted Specific Choice as Specific Commitment. The goal is for them to commit to an answer, which we are doing. I disagree with the assertion "all correct responses should be the same", as I think TBL is a great venue to pose questions without unique correct answers.

[siwelwerd]

Part 3 felt like a bit of a train wreck today.

• After 30 minutes they were still not quite through with activity 5.5.
• The notation in activity 5.8 was confusing. We should probably get rid of anything with $a_{i,j}$ in it.
• Activity 5.12 ended up rushed because we were at least 10 minutes behind.
• Activity 5.8 should be 4S-ified. Maybe multiple choice and a quick time limit.
• Actually the whole day felt like it lacked 4S structure.
• For Activity 5.7, because of the preceding Remark 5.6, as soon as I put it up every single student reached for their calculator, instead of first writing down an augmented matrix.

I think a big part of why I felt today went poorly is that TBL actually shows us student thinking, so it is much easier for us to see when they are confused. In lecture, they nod and tell you that they get it when they don't. But in TBL, their thinking is on display in a quite literal sense. So I can't trick myself into thinking that they got it when they didn't.

[StevenClontz]

I think a big part of why I felt today went poorly is that TBL actually shows us student thinking, so it is much easier for us to see when they are confused.

+1, thanks for making me feel better about yesterday; I hadn't considered that point.

My students gave me a lot of friction on doing row reduction as a team yesterday. I think we erred in not attaching value to the product they put on the Smartboards. Next year I want to "grade" (in some sense) that each team has done each activity as a team on the vertical nonpermanent surface. I want to emphasize that during class, I'm mostly concerned as to whether the group can solve the exercises; individual proficiency should be developed later at home.

[siwelwerd]

I was thinking this morning that maybe row reduction should be pushed to the individual space and tested on the readiness assurance. Free up the class time for the more important stuff. I think I'm giving a mixed message having them spend 30 minutes of precious class time slogging through row reduction only to say "Okay, now we are never going to do that again. Ever."

[StevenClontz]

I was thinking along those lines as well. I like it.

[StevenClontz]

When we revise module E, we should have students label the row operations in a Gauss-Jordan elimination, but not ever have them actually do it as a team (instead add note to tell students to practice at home for E2).

[StevenClontz]

E4 might be more useful for students if we focused on # of solutions at this point, rather than its basis. (We could loop back around and talk about a homogeneous system' solution set basis in module S if we like.)

[siwelwerd]

Circling back to this, starting to think we might want to put some set builder notation questions on the first RAT. I am asking them questions like "Show that the set of all points on the line x+3y=0 is a subspace" and they start throwing around vectors like [x // 3y] . This comes up in writing a solution set in E3, and the first RAT was a little light anyways.

[siwelwerd]

Came across an interesting student error today. When I do row reduction, at least at first, I label my operations with something like "R2->R2-5R1". Then I start getting lazy, and write something like R2-5R1 next to row 2. I noticed earlier in the semester, some students liked do things like 5R1-R2; no problem as far as row reduction is concerned. But then today I had a student unable to figure out why their determinant calculation was off by a -. She had done R2->5R1-R2, which had an implicit scalar multiplication by -1 in there.

Maybe the answer is to emphasize the matrix multiplication interpretation of row operations (I think you suggested adding that as a standard). Maybe the answer is to be stricter in our notation on row reduction. But throwing this out there as something to think about.

[StevenClontz]

FWIW I haven't suggested any notation for my students because we didn't cover notation in the activities. Some students are using notation, but I'm mostly just inferring the operation by comparing their matrices. If we want a specific type of notation then we should include it in the notes.

I think I like exploiting matrix multiplication for simplifying determinants. It's easy to show that det(AB)=det(A)det(B), and we took the time to show that all row operations (similarly, column operations) may be written in terms of matrix multiplication. So we can use this to establish det(A)=det(A^T) as well.

[siwelwerd]

Module E has been reworked to use only 2.5 days as discussed. No row reduction is done in class. Added an applied activity based on determining forces on a truss (one of the things suggested by Dr. Knopf).

Readiness materials still need to be updated.

[StevenClontz]

Cool. I haven't looked at those closely, but I did note that at least one activity is too large to fit in our slides currently.

For whatever reason, I imagined doing applications on totally separate days than theory. I guess there's no reason that has to be the case.

Note that I've merged the refactored file structure into master. It should be straightforward to continue development on, but let me know if I organized anything oddly.

[siwelwerd]

Okay, @StevenClontz take a look at module E now.

[StevenClontz]

Closed by 16a936b - only major change I made is removing mostly redundant discussion of pivots in E.2.

[StevenClontz]

I guess there was one other significant change: I reworded questions to consistently ask for solution sets instead of just saying "solve", to emphasize that we want things written as sets.

[siwelwerd]

I was pretty happy with how this module worked this semester. The only real change I would make I already integrated in e697854

[StevenClontz]

Looks good.

[StevenClontz]

Small change: I'd like to add the following instructions for using CoCalc:

pkg load symbolic
A=sym([3 0 1; 0 2 1])
rref(A)

[StevenClontz]

I think this looks good now. I changed CoCalc to Octave-Online - it's much easier to pick up and use during class, and runs much quicker. I only mention Octave-Online in one slide and refer to "technology" otherwise, so before distribution it may make sense to replace this activity with a generic "use technology to find RREF" activity, and provide a couple handouts for CoCalc and Octave-Online that instructors can use or replace with their own.

Of course the perfect solution is to change formats from PDF slides to a web-based format where we can embed our own technology, but that's out of scope for now.