After a slew of math workshops all crammed together in one summer, I can generate a list of things I've either learned or relearned from my experiences:
1. Your math text is NOT your curriculum. Not for what you should teach, not for how you should teach, not for why you should teach something.
2. Every workshop seems to have the same set of characters (other than perfect people like me ... cough cough):
- the know-it-all that has to shout out all the answers quickly just to show they know things.
- the on-the-sly-constant texter
- the nary-a-peeper
- the challenged learner that asks TONS of questions
- the I-know-this-&-am-too-cool-to-REALLY-process-what-you're-saying person who will probably be unpleasantly surprised when they have to actually apply this current knowledge next year.
3. I'm set in my ways. Before my 1st out of town workshop, I was stressing, "oh no, I won't have my favorite tea, my vegetarian food, my own bed, ..." waa waa waa. I *mostly* had a change of attitude and used it as an opportunity to try new things ...... mostly.
4. I love my new school-provided laptop. When I was getting homesick, I could stream our local NPR station, and I could Skype my husband, and I could send e-mail and impatiently wait for replies to feel connected to friends.
5. "yelp.com" is a great new asset in my traveling life. I could just type in a city and "thai restaurant" or "breakfast" and get tons of opinions to scroll through to find places to go.
6. "mathforum.org" has a section called "math tools" and you can enter the subject you teach and the topic you're interested in, and it returns a list of resources for you to browse through to use: applets, calculator tasks, worksheets.
Wednesday, July 29, 2009
Saturday, July 25, 2009
Even Better Calculator Trick
We explored a "different ways of payment" problem and learned a new calculator trick to boot. Suppose plan A gives you $20 the 1st day and increases your salary by $1 per day. Suppose plan B gives you $0.01 the 1st day and doubles your salary every day.
Calculator:
{1, 20, 0.01} (to represent 1st day, plan A, plan B)
ENTER
{ANS(1)+1,ANS(2)+1,ANS(3)*2}
ENTER, ENTER, ENTER, ..... to keep seeing current day, plan A, plan B updates.
Nice. And sandwiched between 2 nice pictures of a recent trip.
Tuesday, July 21, 2009
Ooh Cool Calculator Skill
Today at my math workshop, I learned some new-to-me calculator skills that I believe I'll use this year.
Let's say you want to compare 2 functions at various values. They don't need to be, but for ease sake here I'll assume the x values are integers, and the y values linear, say some geometric patterns where x represents the pattern number, and y represents the number of sides. In the main window type:
{1, 3, 7} and ENTER
This would mean: 1=1st pattern, 3=#sides for one shape in 1st pattern, and 7=#sides for 2nd shape in 1st pattern.
Then TYPE/GET
ANS + {1, 2, 6} and ENTER
This would mean you're adding 1 to the 1st number (1) in list, adding 2 to the 2nd number (3) in list, and adding 6 to the 3rd number (7) in list.
Now you can keep hitting ENTER, and you have a nice way of visualizing what pattern number you're at without keeping track of how many times you pushed ENTER, and what the 2 other functions are, so this list would look like:
{1,3,7}
{2,5,13}
{3,7,19}
{4,9,25}, etc.
Second skill: you know how sometimes you're populating L1 and L2 where L1 is just integers and L2 is some function of the integers? Well, in the past, I would just go to L1 and physically type in 1,2,3,4,5,... then type in the equation at the header of L2. Well. In your main window you can easily populate L1 by:
seq(x,x,1,100,1)--> L1
I guess it would only be quicker this way for large amounts of integers. "seq" is found under LIST>OPS.
The first value is your expression/function,
the 2nd value is the variable,
the 3rd value is where you want to start,
the 4th value is where you want to end, and
the 5th value is what you want to increment the input by.
Now the ironic thing would be if I "learned" this in the past, and just don't remember it because I haven't used it.
Let's say you want to compare 2 functions at various values. They don't need to be, but for ease sake here I'll assume the x values are integers, and the y values linear, say some geometric patterns where x represents the pattern number, and y represents the number of sides. In the main window type:
{1, 3, 7} and ENTER
This would mean: 1=1st pattern, 3=#sides for one shape in 1st pattern, and 7=#sides for 2nd shape in 1st pattern.
Then TYPE/GET
ANS + {1, 2, 6} and ENTER
This would mean you're adding 1 to the 1st number (1) in list, adding 2 to the 2nd number (3) in list, and adding 6 to the 3rd number (7) in list.
Now you can keep hitting ENTER, and you have a nice way of visualizing what pattern number you're at without keeping track of how many times you pushed ENTER, and what the 2 other functions are, so this list would look like:
{1,3,7}
{2,5,13}
{3,7,19}
{4,9,25}, etc.
Second skill: you know how sometimes you're populating L1 and L2 where L1 is just integers and L2 is some function of the integers? Well, in the past, I would just go to L1 and physically type in 1,2,3,4,5,... then type in the equation at the header of L2. Well. In your main window you can easily populate L1 by:
seq(x,x,1,100,1)--> L1
I guess it would only be quicker this way for large amounts of integers. "seq" is found under LIST>OPS.
The first value is your expression/function,
the 2nd value is the variable,
the 3rd value is where you want to start,
the 4th value is where you want to end, and
the 5th value is what you want to increment the input by.
Now the ironic thing would be if I "learned" this in the past, and just don't remember it because I haven't used it.
Monday, July 20, 2009
preAP math ideas
I'm at a week-long workshop for "experienced" preAP math teachers (for nonTexans, preAP is like an honors course or the higher level math students). After the 1st day, I already have some good ideas on what to do differently next year. In my school district, we have to get re-professionally-developed in preAP techniques every 5 years. At first I was thinking, hmph, I do so much other professional development on my own, this is not needed. Oh contraire. Even though I've taught calculus and precalculus, it is apparently still needed and useful.
Today our instructor did various things using calculus and statistics AP questions as the basis. But. The way he did it was very useful. We worked through a calculus problem. Then we brainstormed on earlier class skills it addresses. He showed concrete ideas on how to modify the problems to address alg, geo, alg2, precal.
But what I really came away with were the LOAD of things I could do with statistics and why it's useful. For example, at the end of the day, he had a sheet with a cm ruler on it, and we all measured our hand span from outer index finger to outer pinkie finger. We got that list in L1 on the calculator. Here are some of the things we did with it besides calculate mean, range, Q1, Q3,...:
1. What if the ruler on the page had a mistake, and we were 2 cm off, so we had to subtract 2 cm from each data point. Without using your calculator, discuss what that would do to the: mean, range, median, ...
2. What if instead of cm, we wanted inches. How would you change data? What would this now do to mean, range, ...
3. What if instead of the largest span we had, that person was replaced with (name some local basketball player who's tall with BIG hand span) ... and we put in a large reasonable number. What would this now do to ....
4. What if for our data of spans that ranged from 16.5 cm to 21.5 cm, someone got a mean of 15 cm. Discuss why this is reasonable or not reasonable.
There were a ton more good ideas. I liked it because it made us think and it would make the kids think and it was in context they could understand and it had them manipulating formulas and thinking about meanings (throughout the day).
Today our instructor did various things using calculus and statistics AP questions as the basis. But. The way he did it was very useful. We worked through a calculus problem. Then we brainstormed on earlier class skills it addresses. He showed concrete ideas on how to modify the problems to address alg, geo, alg2, precal.
But what I really came away with were the LOAD of things I could do with statistics and why it's useful. For example, at the end of the day, he had a sheet with a cm ruler on it, and we all measured our hand span from outer index finger to outer pinkie finger. We got that list in L1 on the calculator. Here are some of the things we did with it besides calculate mean, range, Q1, Q3,...:
1. What if the ruler on the page had a mistake, and we were 2 cm off, so we had to subtract 2 cm from each data point. Without using your calculator, discuss what that would do to the: mean, range, median, ...
2. What if instead of cm, we wanted inches. How would you change data? What would this now do to mean, range, ...
3. What if instead of the largest span we had, that person was replaced with (name some local basketball player who's tall with BIG hand span) ... and we put in a large reasonable number. What would this now do to ....
4. What if for our data of spans that ranged from 16.5 cm to 21.5 cm, someone got a mean of 15 cm. Discuss why this is reasonable or not reasonable.
There were a ton more good ideas. I liked it because it made us think and it would make the kids think and it was in context they could understand and it had them manipulating formulas and thinking about meanings (throughout the day).
Wednesday, July 08, 2009
Real Life Math (as opposed to the fake kind)
We're going on multiple longer-than-a-week trips this summer, lucky us, and our outside Texas plants are begging for dribbles of water. We decided to put a timer on a drip irrigation system, and then we wouldn't have to worry about coming back to an Adam's Family set of plants.
I was hooking up the 1 gal/hour drippers to each pot, and doing the math. I usually water them every two days with a huge dollop from a pitcher. Hmmm, how many dollops in a gallon? How many minutes every other day to equal a dollop? I guess I'll see if I did my math right when I come back to either a lush plantation or a brown oasis.
I was hooking up the 1 gal/hour drippers to each pot, and doing the math. I usually water them every two days with a huge dollop from a pitcher. Hmmm, how many dollops in a gallon? How many minutes every other day to equal a dollop? I guess I'll see if I did my math right when I come back to either a lush plantation or a brown oasis.