High School Math

[Craig Jessop]

Since the system is so institutionalized, we judge based on regurgitated answers and pre-programmed rhetoric, rather than analysis and problem-solving skills. Should we really be so surprised when students are reticent to do it?

Which is why the liberal arts are so valuable; they're all about analysis and original thought.

[wired]

Since the system is so institutionalized, we judge based on regurgitated answers and pre-programmed rhetoric, rather than analysis and problem-solving skills. Should we really be so surprised when students are reticent to do it?

Which is why the liberal arts are so valuable; they're all about analysis and original thought.

For a moment, I had to decipher what you meant. Then I thought of this.... http://www.youtube.com/watch?v=UBztjzDr ... re=related

[Katya]

Our educational system as a whole devalues independent thought.

And by high school, this attitude is likely to be well ingrained.

[C is for]

Our educational system as a whole devalues independent thought.

And by high school, this attitude is likely to be well ingrained.

Which is why I really think seriously about home-schooling my children. Unless the educational system changes fairly drastically by the time my unborn children are school-age, I think that they will be smarter if I keep them home. (The current educational system is also why I'm a little hesitant to become a teacher, because I think I would find the curriculum confining.)

But we'll see how I feel when I have 3 little kids running around screaming and there's never any escape.

[thebigcheese]

But we'll see how I feel when I have 3 little kids running around screaming and there's never any escape.

That and...(I'm about to get in trouble for saying this, but here goes) all the homeschooled kids I knew were just plain socially awkward.

[Laser Jock]

I don't have any real solutions to why some people don't even try at math, but I wanted to put in my vote on the most applicable math (that I've taken so far, anyway). I loved calculus, since integrals and derivatives were so useful for actual problems, but I think my vote for "best describes the real world" would have to go to partial differential equations. With normal differential equations I started to see their usefulness, but then it turns out that PDEs are the real answer to SO MANY real-world things. It was exciting. Even though it still wasn't an easy class.

(Um, also, I'm not trying to one-up anyone here. I promise. I just was pretty excited when I discovered PDEs. You math majors are welcome to top me. )

[Marduk]

Wired, I wasn't being sarcastic. I'm a little confused. I don't think Craig was either. Did you think one or both of us was?

[Katya]

Wired, I wasn't being sarcastic. I'm a little confused. I don't think Craig was either. Did you think one or both of us was?

Here's how I read the situation:

Marduk says the school system is based on giving pre-programmed answers, not on investigation and discovery (in the context of a conversation about math education, specifically).

Craig says that the liberal arts are valuable because they're all about analysis and original thought (as opposed to pre-programmed answers), meaning that subjects such as English and history aren't typically taught with pre-programmed answers in mind.

Wired assumes Craig is employing sarcasm, either because he (Wired) has found English and history classes to be every bit as full of pre-programmed answers OR because he (Wired) knows that the phrase "liberal arts" actually encompasses math and science as well as history and literature, etc., and so assumes that Craig must be employing sarcasm, because it makes no sense to contrast "liberal arts" with "mathematics" when the former includes the latter.

I invite any of the above-mentioned parties to correct any mistaken assumptions on my part and I take the opportunity to volunteer that I was mistaken about the meaning of the phrase "liberal arts" for many years (having assumed it to be equivalent to those fields in which one would receive B.A., rather than a B.S.).

[wired]

Katya reads my thoughts correctly. Both of her assumptions about my post hold. Liberal arts classically includes math, science and science AND the rest of the liberal arts (from my experience at the undergraduate level) is that it is as much about regurgitation as math is. And, again at the undergraduate level, I felt like the social sciences were even more focused on regurgitation then the math classes I took. While application is the ultimate goal of a liberal arts education, the courses students take are primarily about regurgitating previous theories in a field. Philosophy, history, political science and economics (all the social sciences I took courses in) all focused primarily on learning about movements or methods and being able to spill those back on to an exam paper. The main exception I can think of is Econ110 which taught methodology and gave genuinely new situations to apply the principles from those on the exam. Every other class I took in those field, including 400-level courses in Phil, PlSc, and Econ, focused on just learning everything that had been said before and saying it back.

Edit: for clarity

[Whistler]

Our educational system as a whole devalues independent thought. Our form of teaching is far less Socratic than just about any eastern method; when we do ask questions, they are overly simplistic and closed.

Hmm... maybe their way of teaching math is more socratic, but from what I know of the Japanese English teaching system, there is a whole lot of rote learning going on there.

And I think our educators, at least, value independent thought. At least the ones I've encountered.

[Craig Jessop]

I don't know which history classes you took at BYU, but most courses require large, 15 page papers with an original thesis. We're actually graded on how unique it is. Sure, you have to spend a page on repeating the major works on your subject, but that's only to contextualize what you've written. In history, there is no right answer once you move past the memorize-dates phase (which for me was in junior high).

[Marduk]

Agreed Craig; as an English major and Philosophy minor, I have not found what Wired presents to be the case. Yes, movements and historical perspectives are learned, but my experience has been that that is ONLY to give context to current discussion.

And Whistler, to say that educators value independent thought is not to say that the educational system values independent thought. Food for (independent) thought.

[Indefinite Integral]

Wow, sorry to start up a topic and then just abandon it - I'm glad you guys kept up the conversation without me.

@Marduk: I like your suggestions. You have a lot of good ideas, some of which I already thought of. Of course, implementing them is more than just knowing them - it's something that I'm continuing to work on, which will hopefully improve as I get more comfortable teaching (I'm still in my first year).

@42, Whistler, Marduk - regarding "Investigations" learning (or exploratory learning, whatever you want to call it), I am a HUGE proponent of investigational learning. I love the idea behind it, and during my student teaching I was moderately successful at implementing it in the classes we taught. However, it has been less successful this year, and I feel like I have had to revert to more traditional direct instruction, especially in the second semester. I can tell I've lost the interest of some of the students as I've switched back to more "traditional" methods, but I've also gained a lot of students who weren't "getting it" when we did more investigation-based learning. It's sort of a catch-22. I'm not sure if it's more valuable to have more students passing the test and feeling like they can do it, or challenging them more with investigative tasks - and risk having a bunch of students just shut down because I haven't told them what to do yet.

Our educational system as a whole devalues independent thought. Our form of teaching is far less Socratic than just about any eastern method; when we do ask questions, they are overly simplistic and closed. Since the system is so institutionalized, we judge based on regurgitated answers and pre-programmed rhetoric, rather than analysis and problem-solving skills. Should we really be so surprised when students are reticent to do it?

Interesting thing, I teach at a charter school where they encourage a more Socratic method of teaching, and many of the classes are based around classroom discussion on thought-provoking topics, yet I'm finding my students here to be less amenable to discussing or investigating in class than where I student taught at a traditional public high school. I'm wondering if it's something I did, or just the level of students I am teaching (here I have Algebra 1 and Geometry, before I had Geometry and Algebra 2).

[Indefinite Integral]

And Whistler, to say that educators value independent thought is not to say that the educational system values independent thought. Food for (independent) thought.

Just found this after I posted my last response. I feel this 100%. I often feel very constrained by the core I am required to cover. If I had it my way, there is some stuff that I wouldn't even touch because it's not very useful. Sometimes I just have to tell my students "we're covering this because the state requires me to, please learn it and let's move on to something more interesting."

I'm in a constant tug-of-war between what I believe and what I'm required to do by the state.

[Digit]

...there is some stuff that I wouldn't even touch because it's not very useful. Sometimes I just have to tell my students "we're covering this because the state requires me to, please learn it and let's move on to something more interesting."

What are some examples of unuseful things that are required?

[Indefinite Integral]

...there is some stuff that I wouldn't even touch because it's not very useful. Sometimes I just have to tell my students "we're covering this because the state requires me to, please learn it and let's move on to something more interesting."

What are some examples of unuseful things that are required?

Indefinite Integral's "List of a few things 99% of my students will never need to know, and for those 1% who will need them - they'll forget it all and have to relearn it later"*

• -Identify medians, altitudes, and angle bisectors of a triangle, and the perpendicular bisectors of the sides of a triangle, and justify the concurrency theorems.
  -Derive, justify, and use formulas for the number of diagonals and lines of symmetry of regular polygons.
  -Describe relationships between the faces, edges, and vertices of polyhedra.
  -Graph a circle given the equation in the form (x-h)2 + (y-k)2 =r2, and write the equation when given the graph.

Seriously, I never used these things, and I was a math major. A lot of the things in class I can justify - they are building blocks for later classes, or have potential real-world applications, or there are some that challenge students to think more deeply - but at this level, some are just memorization of some random fact that even the best students will forget within a month. What do I care if the medians of a triangle cut each other in a 1:2 ratio? (I'm pretty sure it's the medians - I'm the teacher and I don't even remember) How does that help anyone? I could care less if a student can parrot back the exact same thing I told them. That isn't learning - that's mimicry.

*All statements taken directly from the Utah State Geometry Core Standards