How to Think About the Future

I'm reading a few different books right now (always my curse - 12 unfinished books at all times), and a few different ones have me thinking about my vocation, my career, my job, and "what's next?"

A change will be needed, even though change comes every school year. "Just wait, and it will be different in a few months," is a good motto for a teacher. Everything changes, every year. Some years feel exhilaratingly successful, and others feel like a snail's crawl across a salt lick. So, a change won't be needed in order to experience change.

A change will be needed because my strengths are in analysis, synthesis, learning, finding connections between ideas, and "making it better," whatever "it" may be at the time. Returning to this list of strengths about a year after filing them away, I can see now that if the person possessing them has good intelligence, she's got a great deal of potential. Perhaps influence. Perhaps leadership. Certainly growth potential.

And since I'm finally able to objectively see this, I'd best not be hiding it under a bushel much longer.

I don't refer to hiding and bushels because I think what I do is "just teaching," or because I don't think it's the most exciting job out there. I say it because I know I have spent 9 teaching years slinking around, trying to hide from parent or administrative attention. I suppress opportunities that could be open to me by trying to just do my job very well, but in secret. I'm so hidden, I don't even know what the opportunities could BE.

So, I happen to LIKE the bushel basket on my head very much, thank you.

But, I think it may be time to hoist up onto the lampstand.

Sigh.

P.S. to the Parabola discussion:

Here's a really great website that explains why suspension bridges are made of parabolas and not catenaries. But even better is at the very bottom of the page is a Geometer's SketchPad simulation of a hanging chain, demonstrating the difference between the two.

Luckily, I've got GSP through the school license.

Cool!!

Answers to Questions About Parabolas

In Math 1, we're studying various functions, including quadratic functions. When we talked about the function being in the shape of a parabola, the following student questions spewed forth. Here's what I could find, answer-wise:

1. Is the St Louis arch a parabola? Answer here.
   
2. Are skateboard ramps parabolas? Answer here .
3. Is the Golden Gate Bridge made of parabolas? Answer here.
4. Are roller coasters built from parabolas? Answer must be inferred here. (Basically, the answer is, "perhaps")
5. Are there any songs about parabolas? The empty link to someone's project is here. There's also a song titled, "Parabola," by the band Tool, but it seems more philosophical than mathematical.
   

How Poverty Affects the Brain

Unbelievable analogy in this article. Made my jaw drop.

Confidence

I did a pre-quiz today in Math 1, with two questions per topic (FOIL, Distribute, Solve, Factor) to see where we stand in light of potential quiz on Friday. I walked around and did a checklist to see how many got each problem right or wrong.

I showed them the one problem they all got right, and the one problem that they all got wrong. Then we talked about all the in-between problems. We concluded that everyone has a basic idea of what's going on for each topic, but that there's both a lack of accuracy even on the basic problems, as well as a high degree of panic and dismay when the problems become more complex, even with an idea they got in an easier format.

I took a poll of my freshmen, who return after their lunch period for an additional hour of Math 1 Support with me, asking the following:
1. Do you need more opportunity to practice and build confidence with the simpler versions of the problems, or
2. Are you ready for me to push you with the more complex versions?

They unanimously begged for confidence-building problems, so during my next class I grabbed a few minutes here and there to make up a 20-question practice sheet with 5 each of the four types of problems, in their easiest permutations.

They loved it. And they still had plenty of opportunity for immediate feedback and correction, but they seemed so much more emotionally able to handle it! I felt like I made progress in correcting some errors in understanding for some kids I felt stuck over, before. And they seemed so much more relaxed when it was over.

They were in an excellent frame of mind to work effectively on their homework worksheet, which contained 50 problems (GASP!!!), which I'll post and talk about tomorrow.

"Baking Ratios" Group Task

I'm typing this while my 2nd period class is working on the group task I wrote this morning: "Baking Ratios" Group Task. Who know that six teenage boys would be motivated by cookie recipes?

The unit I'm on is "Ratios, Proportions, and Percents."

(back at the end of class)

I tried to do a quick-and-dirty backward design approach to the unit by looking at the standards on the county website first. Several of the objectives for the subject also had assessment questions released from the state testing, so I used those to form the base of the quiz for the end of the unit. The state listed the same questions for both ratios and proportions, but I think there is a difference in the two subjects. Ratios are comparisons of two values, but proportions are comparisions (using an equal sign) of two ratios. Proportions are a way of finding an unknown value, but ratios by themselves don't involve unknowns.

So the quiz questions I wrote for ratios were all about practical problems: ratios of girls to boys in a group; ratios of amounts in cooking; and ratios of other practical quantities.

I've been reflecting on what to do as a practical, investigative, group activity to introduce the need for ratios, and I settled on baking recipes. Every student received a page of measurement equivalents from cookbooks, two cookie recipes (choc chip and peanut butter), and a set of questions.

Some students had trouble staying on task, but others were very engaged from start to finish. Along the way, I answered questions and gave advice about calculator use when they struggled with how to represent their ideas.

I had them self-score (1-10) on three topics: 1. Your effort; 2. Your understanding of the math; and 3. Your cooperation with your group. Most students honestly self-assess with this; some grades I will actually boost, and one I will lower.

For a separate accuracy grade, each question will get a score of 0-3:

• 3 - all parts of answer complete and accurate, showing excellent understanding;
• 2 - all parts of answer complete, but less understanding shown;
• 1 - any part missing or very inadequate understanding;
• O - no answer or totally off topic.

The questions I posed are here.

Tiles and Patterns

The current Math 1 group math task ultimately will take them to discovering the use of a quadratic equation to describe a pattern, but today it was just fun to watch them think about modeling the pattern in different ways.

One group just wanted to stick with the units blocks in the Algeblocks set, but they had to go get another set to have enough of the size they were using.

Another group used the Cuisenaire Rods, using the graduated sizes to substitute for each row length.

I wrote a note to myself on the board so I could remember what had impressed me. It was fun to watch how each group correctly, but differently, made a visual for the ever-growing pattern.