I've got a number of goals for this next school year. There's Interactive Student Notebooks (which administration has given the ok). Standards Based Grading (which the admin is less than fully supportive of) and pre-teaching.

I will devote a post at sometime to the process of pre-teaching I am considering. This post is about how I want to use that idea to solve a problem which comes up at least 2-3 times a year in each of my classes.

"When will we ever use this?"

I have lots of responses for this question, this post is not about them.

Next week my students will arrive. They are coming with baggage, many of them cripplingly so with regard to mathematics. They've struggled, OR WORSE YET, they've never had to struggle, to work, to imagine how to solve math questions.

Still, "when will we ever use this?"

Their newness to me is a benefit, believe it or not. Many of these students are, being high school aged, thinking of what they'd like to do as a career for the rest of their lives. I'm thinking this might be one of my only chances to get an honest answer from them about what they might like to do. I'll take it.

They're asking the right question, especially given the age they are. Problem is, they're asking the wrong person. Look at the pronoun. "When will WE ever use this?" This question should not, nah CANNOT be answered to the satisfaction of the student by the teacher.

So, I want to know what each of my students wants to do when they grow up, and then I want to use their answers to have them tell me, and the class when we'll ever use this.

I see the big pitfall already. I won't need math to be a choreographer (told to me last year by a lovely young lady). Or, I don't know what I want to be. Well, each of my students will one day be a member of our society, preferably a productive one. (That's the part which is up to us)

I'm going to collect this data. I want to sit on it for at least a month. I want to know the students better, and I want them to know me better before we discuss this little project.

Then I'll wait for someone to ask that magic question. "When will we ever use this." I'm glad you asked.

Gotcha!

I want a research paper. How does HIGH SCHOOL leveled mathematics appear in the job you wish to one day hold? No high school leveled math involve in your chosen career? (Very unlikely) then I have a list of math topics which affect many adults, just in being citizens and residents of our modern civilization

Voting, demographics, borrowing money, lending money, taxes, population, accelerating in relation to cars, decelerating in relation to airplanes/boats, lunar cycles, average climate (temperature, rainfall), triangulation, etc...

Can't find an appropriate topic, the pick one at random from my hat.

How is this pre-teaching? Seems to me any time I get students reflecting and/or predicting (and doing more work than I am) them I'm doing something right.

## Tuesday, August 27, 2013

## Monday, August 26, 2013

### Dan and Desmos present: Penny Circle!

Big THANK YOU to Dan Meyer and Team Desmos for their latest creation. If you haven't seen it, here it is: Penny Circle.

Dan and Eli Luberoff shared what they had created, invited math teachers (and others) to play with it and, here's my favorite part, to make suggestions of other ideas which could be developed.

This is incredible, a tipping point on some level. Up until now most online curriculum has been created, sometimes without teachers being involved in the material, and offered up to teachers looking for resources. The idea that we might want/need/expect a hand in creating materials for our own classes would have been a nigh impossibility just a few years ago (given the large numbers of teachers and the limited number of curriculum publishers) The discussion in education has focused for a while now on engaging students, well I want to be engaged too!!

Ok, maybe its because I'm in such a sequences mood, but I have an idea for a game/activity relating to this topic. Remember the game Galaga? (if not, play it). In this game, an armada of invading ships was coming and it was your job to defend the planet. Imagine if the ships were being released from a number strip and it was your job to predict where the next ship would be released from. As I imagine it, ships would continue to generate (and you couldn't attack the invaders) until you managed to destroy a spawning ship from the next number in the sequence. Different modes with progressively harder to predict sequences could be made and points could be scored (what's a space shooter game without points and bragging rights?)

Imagine walking through the lunch room and seeing kids trying over and over to beat their friend's high score, learning and practicing sequences all the while.

Finally something in the lunch room besides the chicken surprise to bring a tear to my eye.

It could happen....

Dan and Eli Luberoff shared what they had created, invited math teachers (and others) to play with it and, here's my favorite part, to make suggestions of other ideas which could be developed.

This is incredible, a tipping point on some level. Up until now most online curriculum has been created, sometimes without teachers being involved in the material, and offered up to teachers looking for resources. The idea that we might want/need/expect a hand in creating materials for our own classes would have been a nigh impossibility just a few years ago (given the large numbers of teachers and the limited number of curriculum publishers) The discussion in education has focused for a while now on engaging students, well I want to be engaged too!!

Ok, maybe its because I'm in such a sequences mood, but I have an idea for a game/activity relating to this topic. Remember the game Galaga? (if not, play it). In this game, an armada of invading ships was coming and it was your job to defend the planet. Imagine if the ships were being released from a number strip and it was your job to predict where the next ship would be released from. As I imagine it, ships would continue to generate (and you couldn't attack the invaders) until you managed to destroy a spawning ship from the next number in the sequence. Different modes with progressively harder to predict sequences could be made and points could be scored (what's a space shooter game without points and bragging rights?)

Imagine walking through the lunch room and seeing kids trying over and over to beat their friend's high score, learning and practicing sequences all the while.

Finally something in the lunch room besides the chicken surprise to bring a tear to my eye.

It could happen....

## Sunday, August 25, 2013

### Sequence and Series group lesson

I've got this idea for a sequence lesson.

I see it as a group assignment. I want to give the students 2 terms of a sequence and have them identify a sequence which could contain those two terms. I figure that if I given only two terms, that a number of different sequences could be made using those terms.

I've never made a Prezi before, but I did work on one for this lesson. It is still a work in progress. (I am hoping for feedback on the lesson, not the Prezi) sequence prezi

The groups will all be given the same starting information (in case you didn't look at the Prezi). I will be giving them:

My thought is that the groups can either look at this as 5 cents and 20 cents, or they can see 1 thing and 4 things. I want the groups to each come up with a different sequence. Once each group comes up with their sequence they need to write the first 4 terms and a rule to get those terms on the board. As each group adds their terms and rules, that particular sequence becomes off limits to the other groups.

Next I want the groups to figure out if their sequence would end up including the term $5.00 or not.

I can see lots of different options for a third term, giving each group a different sequence of numbers and rules. I want different groups to view the given information differently. I don't want the final challenge to influence the kind of sequence they choose.

ok, thoughts?

I see it as a group assignment. I want to give the students 2 terms of a sequence and have them identify a sequence which could contain those two terms. I figure that if I given only two terms, that a number of different sequences could be made using those terms.

I've never made a Prezi before, but I did work on one for this lesson. It is still a work in progress. (I am hoping for feedback on the lesson, not the Prezi) sequence prezi

The groups will all be given the same starting information (in case you didn't look at the Prezi). I will be giving them:

My thought is that the groups can either look at this as 5 cents and 20 cents, or they can see 1 thing and 4 things. I want the groups to each come up with a different sequence. Once each group comes up with their sequence they need to write the first 4 terms and a rule to get those terms on the board. As each group adds their terms and rules, that particular sequence becomes off limits to the other groups.

Next I want the groups to figure out if their sequence would end up including the term $5.00 or not.

I can see lots of different options for a third term, giving each group a different sequence of numbers and rules. I want different groups to view the given information differently. I don't want the final challenge to influence the kind of sequence they choose.

ok, thoughts?

## Wednesday, August 21, 2013

### Sorry to Drexel University

I have heard that Drexel University has copy written "I notice......I wonder....."

My problem comes from knowing that my students will see "I notice" as less than Drexel U. is anticipating. My modification will seem insignificant, a matter of semantics but I know that for my students it should make a significant difference.

To me the questions should be:". I SEE......I NOTICE.....I WONDER..."

First off threes seem more complete than two's. (at least to me and Blind Melon they do)

Next, I know that if I don't separate "see" from "notice" the students won't either. To see means to observe with the eyes. To notice implies the brain being involved in the observation. I want my student's brains involved before the wonder portion.

I don't want my students simply giving me visual observations before posing questions about the situation being offered to them. I want them thinking, and preferably thinking deeply about their questions. Our brains need to warm up before asking truly valuable questions. Getting the brain working from concrete to abstract is a natural and valuable progression. Without this progression I am afraid that my students will not delve deeply enough into the problems which I am giving them.

How do I see this playing out in the classroom?

Me: Take a look at this:{1, 4, 9, 16...} What do you See?

Multiple students: I see a group of numbers. I see a set of numbers. I see 4 numbers.

Me: What do you notice?

Multiple Students: positive numbers. +3, +5, +7. Squares

Me: What do you wonder?

and so on.

Of course, perhaps I'm just looking for a reason to use the previously linked song in my classroom/blog. (Note to Drexel University...there's a copy write thing at the bottom of my blog too....lol)

My problem comes from knowing that my students will see "I notice" as less than Drexel U. is anticipating. My modification will seem insignificant, a matter of semantics but I know that for my students it should make a significant difference.

To me the questions should be:". I SEE......I NOTICE.....I WONDER..."

First off threes seem more complete than two's. (at least to me and Blind Melon they do)

Next, I know that if I don't separate "see" from "notice" the students won't either. To see means to observe with the eyes. To notice implies the brain being involved in the observation. I want my student's brains involved before the wonder portion.

I don't want my students simply giving me visual observations before posing questions about the situation being offered to them. I want them thinking, and preferably thinking deeply about their questions. Our brains need to warm up before asking truly valuable questions. Getting the brain working from concrete to abstract is a natural and valuable progression. Without this progression I am afraid that my students will not delve deeply enough into the problems which I am giving them.

How do I see this playing out in the classroom?

Me: Take a look at this:{1, 4, 9, 16...} What do you See?

Multiple students: I see a group of numbers. I see a set of numbers. I see 4 numbers.

Me: What do you notice?

Multiple Students: positive numbers. +3, +5, +7. Squares

Me: What do you wonder?

and so on.

Of course, perhaps I'm just looking for a reason to use the previously linked song in my classroom/blog. (Note to Drexel University...there's a copy write thing at the bottom of my blog too....lol)

## Saturday, August 17, 2013

### Thank you, Park City Mathematics Institute

I was blown away following the Park City Math Institute online from twitter this year. I knew about the Park City curriculum, but wasn't aware the summer institute existed. I found it fun, and the little comments in the margin really made me feel like someone was cheering me on. Kudos to you guys and I'm soooo jealous of the ppl who were actually there. (Any t-shirts still available? I'll pay!!)

I'm looking at teaching algebra 2 and statistics and I want to thank you, because you got me thinking as to how I will challenge my kids. Probability is not my first unit, it's actually supposed to be second, but I think it will be third this year. I need a little more time to get my students to want to know things. I'm trying to consider what kinds of questions I can ask before starting a topic. (see the previous posting about pre-teaching) I want my kids ripping probability situations apart, in more than 1 way before I teach it.

I can't assume prior knowledge in inner-city students, especially in the suburbs of Detroit. I need to put it in there. I need to introduce low entry probability questions to use as warm-ups. The pre-teaching has two effects, it gets the kids used to thinking about probabilities and it gives me the chance to see how they are looking at those ideas. I really like the train problems from 2007 (day 5) as it is a real low entry question, which can be scaled up to allow me to use the idea a couple times. Also the paper ripping problems (day 1), for the same reasons. Also, from 2007 (day 4) I want the kids playing with the finding the area of a staircase problem.

There are a bunch of other great questions in there. I have starred about 5-6 of them, from the 2007 set I've mentioned and from this year's set (also on probability). Those I want to save for when I'm actually in the probability unit.

If you haven't looked through the Park City Mathematics Institute's materials, and if you are teaching high school leveled math, then you should be. 2001 - 2012 problem sets

EDIT: Thank you to Cal Armstrong (@sig225) on twitter who gave me the link for this year's problem sets. 2013 problem sets

I'm looking at teaching algebra 2 and statistics and I want to thank you, because you got me thinking as to how I will challenge my kids. Probability is not my first unit, it's actually supposed to be second, but I think it will be third this year. I need a little more time to get my students to want to know things. I'm trying to consider what kinds of questions I can ask before starting a topic. (see the previous posting about pre-teaching) I want my kids ripping probability situations apart, in more than 1 way before I teach it.

I can't assume prior knowledge in inner-city students, especially in the suburbs of Detroit. I need to put it in there. I need to introduce low entry probability questions to use as warm-ups. The pre-teaching has two effects, it gets the kids used to thinking about probabilities and it gives me the chance to see how they are looking at those ideas. I really like the train problems from 2007 (day 5) as it is a real low entry question, which can be scaled up to allow me to use the idea a couple times. Also the paper ripping problems (day 1), for the same reasons. Also, from 2007 (day 4) I want the kids playing with the finding the area of a staircase problem.

There are a bunch of other great questions in there. I have starred about 5-6 of them, from the 2007 set I've mentioned and from this year's set (also on probability). Those I want to save for when I'm actually in the probability unit.

If you haven't looked through the Park City Mathematics Institute's materials, and if you are teaching high school leveled math, then you should be. 2001 - 2012 problem sets

EDIT: Thank you to Cal Armstrong (@sig225) on twitter who gave me the link for this year's problem sets. 2013 problem sets

## Wednesday, August 7, 2013

### Pre-teaching

I've been looking at how and what I teach for years now. I make changes each and every year, hoping to find a couple new lessons which catch fire and keep the kids interested. This next year will be no exception, and I'm sure neither will next, or the one after that or the 10 which follow those.

I've been reviewing notes, articles and books this summer. One idea I was pretty hot on last year (and sadly I will admit I'm not sure I did any better this past year than I had done previously) is SLOT, or Sustained Learning Over Time. In fact I will admit that with the exception of while I was working on my required lessons for SIOP training (sorry I don't recall the words, suffice it to say it was all about teaching to English Language Learners or Students with limited English skills) I can't recall specifically writing lessons with SLOT in mind .

SLOT is all about getting students to retain knowledge by causing them to practice those skills repeatedly over a longer period of time. In fact according to SLOT you shouldn't assess a student on a given topic until they have had over 20 opportunities to practice that topic. (which originally seemed impractical to me as I have many, many topics to cover in my 180 days and I can't start them all 20 days prior to wanting to asses them on that topic).

The concept seems sound, though.

I have a plan for warm-up activities this next school year. Some of the activities I plan on using are 101qs.com, estimation180.com and visualpatterns.org (there are others). It is the last of these that I am hoping to start off using pretty heavily. I want my students to have looked at and thought about many, many linear, exponential and other patterns well before I get to sequences and series (my 3rd unit). In fact, before I start that unit, I want my students to have been pre-taught the concept of sequences enough times that there should be little confusion once I start that unit.

I have decided I don't do enough pre-teaching. I know that I am more likely to be interested in a subject if I've already thought about it. I know that pre-teaching in this way will help seed my students with prior knowledge and hopefully instill some curiosity about what else can be done with these topics.

I'm not 100% sure how to pre-teach all the units I am required to teach, but I do have some ideas about a couple of them. Visualpatterns.org should help with the sequences and series AND Exponential/Logarithmic units. Desmos.com should help with all the transformations to functions which pop-up in many of the units. I also have a few activities I am planning on doing outside of their appropriate units so that the seeds of these other mathematical topics are planted well before I need them.

Can I afford the time to pre-teach some of these topics? I am hopeful that by doing the pre-teaching that the actual teaching of these topics will go easier and this will allow me to make up some time. I know I'd rather use the math to interest them when it isn't being assessed to allow me to harvest that interest later when an assessment is looming.

Subscribe to:
Posts (Atom)