Wednesday, December 28, 2011

Exit Slips

For several years, I've wanted to do exit slips, but I just never could get it organized to my liking. I understand the benefit of them and can see them being an awesome thing in my classroom.

Enter in some discussions with my bestie, @approx_normal... she does her warmups on index cards and then hands them back for the students do to the exit question on the back and put it in a box by the door. But, like @approx_normal, I also suck at closures and often run out of time....

So today, while she and I are discussing some ideas for the spring semester, I get a brainstorm.... What if I made a poster of generic exit-questions and posted it in my classroom? For example...

1. Summarize the important points of today's lesson

2. Write 3 things you learned, 2 things you are fuzzy on, and 1 question you still have.

3. Etc

Then, at the end of the hour, I could just direct student's attention to the poster and tell them to write their response to question number ___ and put their index card in the box as they leave the room.

I need more exit ticket prompts though.... Ideas? :)

Tuesday, December 27, 2011

Simulations based on Game Shows

The PCMI Probability problems had a "Game of the Day", oftentimes related to the King of Game Shows - The Price is Right. I don't know about you, but as a kid, whenever I was home sick, I always loved watching TPIR. (Honestly, though, I miss Bob Barker....)

Anyway, one of the "Game of the Day" activities in the PCMI packet is the "Spelling Bee" game, in which contestants select cards and hope to spell the word "CAR". I plan to show a clip of the game from TPIR website and ask my students to figure out the proability of winning. Of course, the probability isn't the easiest one to calculate, especially right after a 2 week break, so it will be a natural lead-in to simulations. I found this worksheet/writeup online and plan to use it as a guideline. In their partners, the kids will run through the simulation several times, then combine their data with another pair of students to calculate the simulated chance of winning.

P.S. Like many people, my favorite TPIR game was Plinko. I really want this game board from Oriental Trading...Disc Drop Game

Real or Fake?

Yesterday I went through the PCMI probability problems from 2007 and found some really neat ideas to use over the next few weeks. I plan to use one of the activities to start us off on day 1 next week.

The basic idea is for groups to create two datasets of a coin flip. First, they will fake a dataset of 240 coin flips, then they will create a real dataset by actually flipping the coin. They will write these two datasets on index cards. Using their two datasets, they will discuss with a partner and come up with a way to determine if a new dataset is real or fake. I will then have them exchange their cards with another pair of students and use their "test" to determine which card has the real data and which card has the fake data. If time allows, there are some additional coin flip datasets in the PCMI packet that I will put up for discussion.

At some point after that - not sure if I'll do it the next day or a few weeks later - the PCMI packet went on to use an inference test to determine if a dataset was real or fake. By splitting the coinflips into sets of 2 (or 3 or whatever), you could keep track of how many HH/HT/TH/TT combinations there were and compare them to the expected 1:3:3:1 ratio. This would provide an interesting introduction to inference testing and p-values, as well as tying in to binomial expansion and pascal's triangle.

This activity should be a good way to get them back into the school frame of mind, thinking about the start of inference techniques, and drawing conclusions from data. If I'm really good this week, I'll get it together in a google form.... We'll see how that goes :)

Monday, December 26, 2011

Problem Sets and Probability

Winter break is halfway over - where, oh where, did it go?? :) Last week, I spent time cleaning house, reading novels, and in general, just enjoying the off time. However, all good things must eventually come to an end, so this week, I vowed to work at least one hour per day on school stuff. (wishful thinking?)

Probability is one of my weakest areas as a stats teacher. Prior to going on break, we had covered basic probability, disjoint events, independent events, venn diagrams, tables, trees, etc. Next week, when we go back, we'll do simulations and probability distributions. In the past, I've not been pleased with how this unit turned out, so I'm hoping to do it better this year. A few weeks ago I ran across this problem set from the 2007 PCMI and today I've been working through it. So far, I have some ideas I think will work, especially for simulations. I really like the Game of the Day activities and plan to use several of them to spark conversation in my class.

Thursday, December 15, 2011

Semester Reflections

As I sit and watch my students working diligently on their semester
final, I am so grateful that winter break is upon us. It has been a
whorlwind of a semester, filled with new challenges, new triumphs, new
frustrations, and a huge lack of time to sit and write about it.

One of my biggest challenges at the start of the year was how to
manage 130 kids in AP Stat. If you've never looked at the AP
Curriculum, it's very writing intensive and conceptual - not your
run-of-the-mill right/wrong math class. It has worked out fairly
well, and while I am not able to grade assessments as quickly as I
would like, I have amazing students and they have really shined this
year. Part of how I've managed is by two things - active learning and
standards based grading. Over the past few years, I have transitioned
more and more away from lecturing and this year is even more so.
Since AP Stat is my only major prep, I have really put a lot of time
into developing quality lessons, making connections, and tying things
together this year. In class, the *kids* are the ones working their
tails off. They sit in partners, so they have someone to turn to when
they are stuck. They work with their partners on a daily basis while
discussing and working problems. The problems that in the past I
might have assigned as "homework" get worked in class instead. They
do not sit and watch me work problems and do examples - THEY tackle
the problems, work through it with their partner, then we discuss it
as a class. Overall, this has led to high engagement, which has shown
up in their assssments.

The second thing that I tackled this year was using Standards Based
Grading in my AP class. I had started this journey last year with
Algebra 2, and at the time, had no idea how it would work in AP.
While it's still a learning process, overall I do really like having
the more detailed information about student's understanding of each
concept. There are still some kinks to be worked out, like the crowd
of people in my room this week for reassessments, but the pros far
outweigh the cons. The kids have embraced SBG with open arms and over
time have seen the benefit of having to remediate and reassess, of
having detailed grade reporting, and learning from their mistakes. I
have heard the statement, "I wish Mrs/Mr X did SBG too!", many, many
times over this semester. There definitely have been challenges to
SBG though... writing assessments that really get to the heart of the
objective, writing reassessments that cover the same concept without
being identical to the original, the time it takes just to grade that
volume of papers, etc. But overall, I'm happy with how this semester
has turned out.

As I reflect back over the past year and a half, I realize how
different I am now as compared to when I started this journey. My
philosphy on what really matters, what grades should mean, how to
structure my class, so many things. I was one of those teacher that
would have sworn "if you don't grade it, they won't do it" and now I
see how wrong I was on a daily basis. My kids work their butts off
every day and it's NOT about how many grades I take - it's about being
engaged with the material and tapping into their intrinsic motivation
to learn. It's not always been a smooth path, but this was a journey
well worth the time and energy it took to get where I am today.

Tuesday, October 11, 2011

#statchat anyone?

First, let me preface this by saying I am having a *great* year.
Statistics has long been my passion and this year I am blessed to
teach AP Stat all day, plus one Intro to Stat class at the uni. I
really love only having one core class to prep for, my lesson plans
are quick to write, and in the case of a lab day, I don't have to set
up and tear down the labs multiple times. It's been great to branch
out and work with the science teachers on the integration of math and
science as well as exploring new ways to use technology in my

However, what I did NOT anticipate about this year was how much I
would miss the daily collaboration of my Algebra 2 buddies. For the
past several years, I have taught next to Partner Teacher and we have
joked that if we could put both our brains into one teacher, that we
would be unstoppable. This year, though, I moved across the parking
lot to a new building, leaving behind many of my close friends AND I
no longer teach Algebra 2, so I don't have the collaboration partners
that I am used to. This adds up to a year of feeling pretty alone in
my math world. I am one of those teachers that really learns through
brainstorming and discussion. I love the flow of ideas that can come
from a discussion on "How do you teach this topic?" or "My kids keep
messing up here - what do you do?" or "Dang, they bombed that quiz -
what now?"

This past Sunday, my feeling of isolation really came to a head and I
was very frustrated. In general, I believe in being proactive, so I
got on twitter that afternoon/evening and asked if anyone would be
interested in a weekly #statchat discussion. It doesn't have to be
ultra formal, I just want a time to talk to other stat teachers and
bounce ideas, labs, activities, suggestions, etc. I got a few
positive replies, so I thought I'd post here too - so, let me see a
show of hands... Anyone up for a weekly #statchat?

Til next time... :)

Sunday, October 9, 2011

Active Learning

Tomorrow is my yearly Pre-Evaluation conference with my principal. Last week, he sent out an email asking for our professional goal for this year and suggested that it tie into our high school's goal of "increasing student engagement both in and out of the classroom." I decided that my goal for the year would be using Active Learning strategies on a regular basis.

I wrote about Active Learning last summer in this post. However, since then, I've become even more concerned that "classrooms are a place where students go to watch teachers work." The problem, for me at least, is how to solve this. I have a large collection of games, labs, activities, etc that I like to use, but I want more activities that are quick 5-10 minute activities (like Think-Pair-Share) that could be used during instructional time. Another issue I have is that I teach seniors and so many of the collaborative activities are fairly corny and would not go over well with my students. Yet a third issue I have is that while I have a large classroom, it feels fairly small with 32 bodies, so a lot of "move around activities" are hard to do.

Here are some of my tried and true favorites:

Partner Discussions
My classroom is set up in pairs. Daily, students talk to and work with their partners to discuss problems. I would like to develop some more specific strategies to use with the partners, beyond Think-Pair-Share.

Half Sheets
This strategy was first known as Relay Race and came from an ebay book that I got many many years ago. It is a definitely favorite amongst my students. Students work in pairs (or groups of 4) to work through problems. They get one problem (half sheet) at a time, bring it up to be checked, then get the next one to work on. The kids love this and I really like the individual feedback I can give to each group. This is again more of a review game though.

Gallery Walk
I have used a Gallery Walk with several concepts and I'm always impressed by the discussion that comes out of it. I love this idea and wish I could use it more often, but it's again a "move around" activity and that limits its usability. I have 8 groups of 4, but only whiteboard space for 6 groups, so I really need to invest in some of the "showerboard" whiteboards.

Exit Tickets
I really like the idea of Exit Tickets, but I just can't seem to make them work for me. I would love to hear how they are used in other classrooms.

What are your favorite strategies?

Math/Science Partnership - part 2

I have to admit, I'm so glad September is over! For most of the month, I felt so overwhelmed and behind and unable to catch up.

Anyway, the AP Env Sci (APES) teacher and I were able to get our students together to do the Quadrat Analysis activity. On the first day, we all met in her room as she talked about what QA is and why it is useful to scientists. I jumped in a few times to ask my students why we wouldn't want to take a census and what kind of sampling method QA was for us. Then we split up into groups of 4, with each group having 2 APES students and 2 Stat students. We gave each group a map and a yellow square of acetate and they were off to collect their data. They dropped the acetate 10 times, recording the species found in their sample. After their 10 trials, they found the average for each species, then multiplied by a conversion factor to find a population estimate for the land area. Finally, the groups put their data into a Google Form.

On Day 2, we started out in my room as I discussed the analysis that we were going to do. From the previous day's G-Form, I had compiled the population estimates for the 16 species on the map and each group was going to have one species to analyze. This proved to be a great review for my students on how to make well-done graphs, write descriptions, and test for outliers. Each group was given an 11x17 piece of paper to make a mini-poster for their species. The posters were then displayed for our Open House festitivies.

Overall, I was happy with how our first collaboration went and I think the students walked away with a better knowledge of how the course content overlaps.

Friday, September 23, 2011

Math/Science Partnership

One of the goals for my high school is to develop a math/science partnership to help students make connections between the content areas. The commitment to this goal can be seen in our new building, where math and science classrooms are side by side rather than in different wings, as in a traditional facility. This opens up some unique collaborative opportunities for us since I now have daily access to the biological science teachers and the activities/labs they do in their classrooms.

Enter the AP Environmental Science (APES) teacher. She and I have collaborated before and actually took a week long workshop together last summer in an effort to see where our curriculums collided. Stat has the unique ability to fit in with so many curriculums that I could easily tie into just about any teacher's lesson plans if I truly tried. Anyway, earlier in the week, the APES teacher came to me with a lab she was doing that involved Chi-Square tests. Ultimately, the idea behind her lab was Natural Selection - the ability of a predator to find and kill their prey and the ability of the prey to hide from a predator. Her students had taken 3 types of beans and spread them into two differing habitats (aka the sidewalk and the grass) and recorded which prey was killed in each habitat. They organized the data into a table and that's where the Chi-Square Test came in. Now, I don't get to Chi-Square until April, but I had just finished contingency tables and segmented bar charts, so I was pretty bummed to miss out on such a neat collaborative activity.

Today was test day, so I went over to my APES neighbor and asked her for a copy of a couple of the labs she had mentioned so that I could read over them and jot down notes for next year. During our short chat, she mentioned another lab that she said she would find and bring over to my room. Low and behold if she didn't show up with this map:
With this lab, the students have to count the species of plants to determine the potential environmental impact of the plants. My students have already been through the idea that a census isn't usually practical and is oftentimes inaccurate. We have also discussed the different random sampling methods used to generate data. This lab will let them see a real example of cluster sampling and using that to estimate a population parameter. They will drop the yellow acetate square 10 times, count the various species in the square, find the average of their 10 trials, and then use a conversion factor to estimate the population parameter. The next day, each of my student pairs will get the data for one species, have to display it in both a histogram and boxplot, and then describe the distribution of their species. I'm thinking this will be a great summary of the material we've covered thus far.

If you have any other ideas on how to integrate math and science, please leave it in the comments... We're in the baby steps phase right now, but eager to learn more!

Wednesday, September 7, 2011

What a great day!

Today was one of those days that you just feel good about. Lessons went smoothly, the a-ha moment happened at just the right time, and kids were engaged.

First off, let me preface this by saying that for the most part, I am enjoying teaching AP Statistics all day long. Sometimes I get into that "Did I already say that?" rut, but overall, it's fun to be sharing my passion for stat with the students. I kind of miss Algebra 2 and I definitely miss collaborating with my Algebra 2 buddies, but after a couple of years where stat got pushed to the back burner, it's great to have the time to really devote to engaging lessons and an active classroom.

Right now in AP Stat, we are deep into the Experiments chapter. This year I am trying to bring in more real life articles and having them analyze them. Last week we discussed the vocabulary of experiments and the required elements of experimental design, then ended the week by analyzing some articles. Each group got their own article and an analysis sheet. Working with their partner, they broke down the article using the language of statistics. That brings us to today.... When class started, each group (my kids are seated in pairs) had a copy of this article about the Placebo Effect. They had to read and discuss it with their partner, then write a summary of it in their warmup folders. Then we had a sharing session to see what they had found interesting in the article. That immediately got us thinking that if the placebo effect can be so powerful, how well does the REAL treatment have to perform to be considered the "winner". We had briefly talked about the idea of Statistical Significance earlier in the year, so I pulled out another psychological experiment (Zener Cards and ESP) and we tested our class for ESP. This lead us into a discussion of how many right answers they expected to get, how many they actually got, and if that was a big enough difference to convince them of our class's ESP ability.

Then the grand finale (and lead-in for tomorrow), I told them we needed to do some quick review of all of that vocabulary from last week. I pulled up the Fish Tank problem from the 1997 exam. (Can I just say I really *love* the Snipping Tool in Win7!) I asked the students to identify the experimental units, the explantory variable, the treatments, and the response variable. Then we designed a Completely Randomized experiment for the fish tanks. We sketched the experiment on the whiteboard, then talked about randomization. I had the groups discuss how they would assign the fish food and really had some great responses (spinners, dice, etc). When someone said "Put the numbers 1-8 in a hat and mix well", I played it up and said "OH MY GOSH! That's what I did too!!!" I brought out my paper bag with 8 poker chips and we assigned the treatments. In all of my classes someone then said "But wait!!! What about the Temperature issue???" That led to a great discussion on confounding variables and at the end of the hour, I left them with the task to determine how to assign the new and old fish food to the tanks with respect to the temperature issue. Tomorrow, their warmup will be to write down their method and we should be able to segue into blocking and why blocking reduces variability.

However, every great day usually has a bummer moment too. I plan to also talk about matched pairs tomorrow and wanted to intro it using the Boots problem, so when hubs was running errands after work, I asked him to check on some really cheap boots that I could use as a prop. For some reason, in past years, students have not really understood that the new water proofing method does NOT change the appearance of the boots, they look identical. I was hoping with the two physical sets of boots that the kids would get that you could assign one boot of each type to a person and see which one resisted water the best, but it was going to cost close to $50 for 2 pairs of boots and that was quickly vetoed!

Now to figure out the blocking dogs activity to see if I want to tackle that this week too. :)

Monday, August 22, 2011

Another year has begun...

And what a year it has already been! New building, new technology, new hallmates, new gradebook, the list goes on and on! Overall, it's been pretty good, but having never moved into a new building, I wasn't prepared for the little details that were commonplace before, like pencil sharpeners. :)

My schedule also changed in the days leading up to the official start of school. Last year, we had 90 AP Stat students in 4 sections. This year's senior class is the first class that took 8th grade Algebra 1 as an on-level class (rather than honors as before), so that left a lot of juniors that took Pre-Calc and wanted a 4th year of math. Enter AP Stat - our enrollment jumped to 215 in 7 sections at last count. (And for those AP Stat teachers out there that are half jealous and half "how the heck are you going to grade all that" - I don't know yet....) So needless to say, I now teach AP all day long (and one hour for my AVID seniors).

So today was day 3 with the kids and I really am enjoying them overall. Thursday and Friday we did some introductory material of "Stats in the news" and today was our first real day of material. Because of the success of the Gallery Walk that I did last year, I did something similar today. The first chapter of my textbook talks about how important it is to know the context of data - the W's if you will (Who/What/When/etc). After a brief introduction to the W's and a class example, off to the boards we went. One nice feature of my new classroom is LOTS of whiteboard space. I can fit 8 groups of students at the whiteboards, so I had taken some scenerios, printed them on cardstock, and posted them around the room (held to the board with magnets) with a #1, #2, etc above them. I numbered my students and sent them to the boards to the corresponding number. As a group, they read the problem, discussed and agreed upon the Ws and wrote it on the board. When they were done, they took the problem card down, flipped it over to reveal the answers and graded themselves. Then they erased their work, rotated to the next station and did it again. We continued until they all felt comfortable with identifying the W's.

All in all, I'm pleased with the first days of school and I'm excited to see what this year brings. For the past two years, AP has kind of been on the back burner because of Algebra 2, so I'm eager to get back into the planning of AP and really trying some new things.

Now if only that morning alarm wasn't quite so early.... *sigh*

Saturday, July 23, 2011

Summertime Reading

One of my favorite things to do in the summer is to read and one of my favorite books to read once the reality of Back-to-School sets in is a trio of books by David R. Johnson. I found Mr. Johnson's first book "Every Minute Counts" early on in my career and quickly bought the sequels "Making Minutes Count Even More" and "Motivation Counts". I don't even know if these books are in print any more, but they have been my summer staple for years. I also lend them to student teachers and new teachers to read. The books are short, more like booklets, with around 100 pages in them, so they are quick to read but they definitely pack a punch.

Last night, I decided it was time to start my yearly re-read and decided to pick up the third book. The first two are more about classroom management and how to set up your routine, while the last book is more about best practices in math. "Motivation Counts" was published in 1994 and while I was reading it, it really struck me how slow education is to embrace change in our teaching methods. Other than the fancy technology that now populates classrooms, I would venture to guess that most classrooms have the same structure that they did 50+ years ago. Even with the research on best practices, how to engage learners, teachers that fully agree that change needs to occur, it is sometimes so overwhelming that we quickly fall back into old habits and comfortable routines. We tend to teach the way we were taught by teachers who taught the way they were taught by teachers... (rinse, repeat).

Here's the quote that got me: (remember, this book is close to 20 years old now)
Lesson plans for the traditional classroom routine, as you can see from this list, detail *my* activities; they do not include what *the students* should be doing during class....

..In a recent television interview, a CEO in a major industry cited the main objectives for our schools as follows:
  • Teach problem-solving experiences and skills.
  • Teach communication skills.
  • Teach students how to learn.
  • Teach students how to work effectively as a team member.
  • Give students an ability to handle change. is very obvious that what industry wants, and what the traditional rountine offers, are not at all compatiable - or even complementary. Industry wants involved, active thinkers who can work together and deal creatively with the unexpected....

I think most of us know and agree with the above and even strive to accomplish those goals. For years, this quote has really hit me in the gut. I know I start the school year with big plans, but as reality sets in, it can be easy to fall back on that traditional routine where *I* am doing the work and the students sit back passively. I find it wild, though, that today's goals are still what they were 20 years ago and that little progress has been made in changing what a traditional math classroom looks like.

I can easily say that, of all the professional books I've read through the years, this trio of books have had the most profound influence on me as a teacher. Even though I've read these books numerous times, they never fail to inspire me and make me think about how to be more effective in the classroom.

What is your must-read book for teachers?

Thursday, July 21, 2011

Incorporating Writing in Math

With students returning in just a few weeks, I am digging through old materials looking for lesson ideas. Tonight, I ran across this...

The question "why so much writing?" can be answered in three basic ways:
1. Writing promotes clear thinking.
2. Writing promotes effective and long-term retention of what has been learned.
3. Writing provides individuals and groups in a complex world with a voice and a record.

Students need to understand that writing is the single most powerful tool for thinking, learning and participating in the broad culture of a society.

Source: Write Path Mathematics from AVID

Now my question... how do you incorporate writing in your classroom?

Wednesday, July 6, 2011

Using SBG in AP Stat

Last year I implemented SBG in Algebra 2 and loved it. However, I just could not wrap my head around how to implement it in AP Stat, so I spent a lot of time this past year thinking on how I could make it work. This is more of a mind-dump of ideas than a complete plan - a way of getting my thoughts down on paper and put it out there so that I can analyze it further.

This Past Year
For SY 2010-11, grading in AP was pretty traditional for me. I had three categories in my gradebook - Tests/Quizzes (65%), Assignments (20%), and Final Exam (15%). The Assignments Category contained pretty everything that wasn't a test or quiz. This included weekly AP MC practice, POWs (Problem of the Week AP problems), worksheets, labs, etc.

Tests and Quizzes
I already set up my Learning Targets (LTs) and provided them on my assignment sheets for each unit over this past year. (See Unit 3 HERE). I think each LT Quiz will cover 2-3 LTs. Where I struggle here is how to set up the LT Quiz. In Alg2, each LT has 3 problems (basic, average, and advanced levels), and I don't know how well that will work out with AP. I'm thinking maybe a MC question and then two FR questions. Of course, the layout will be different than the current Alg2 layout, allowing a question stem to be used for multiple LTs. I would still use a 4 point scale for each LT, like I do in Alg2. I think Unit Tests would pretty much stay the same as they are currently are, with a MC and a FR section, with the grade being a traditional test grade. This would allow the quizzes to be more skills based and assessed, whereas the tests would be more summative.

Remediation and Reassessment
This past year, students could retake a different form of a quiz *if* they provided proof of remediation, which was the practice problems on the assignment sheet for that chapter. They could also make test corrections if they did at least one problem from each objective on the assignment sheet. For the most part, I liked this plan. This next year, it would roughly stay the same, but to reassess a Learning Target, they would have to work the problems specific to that LT, rather than the entire chapter. For test corrections, they would still have to do at least one problem from each LT, PLUS have completed the Unit's Summary Sheets (see Unit 3 HERE)

Issues I need to figure out
  • What percentage breakdown do I want to use for Tests, LT Quizzes, Assignments, and Final Exam? The Final is district mandated to be at least 15%.
  • Actual AP questions often cover multiple topics. While I could edit them for the LT quizzes to only include the current objectives, I would like to have that cumulative element. This could be a reassessment opportunity, but with only one data point, how would I grade it on a rubric? Maybe those "mixed-bag" style questions should be on the summative tests, not the quizzes?
  • What to do about the Assignments category? I could leave a small percentage of the grade devoted to this category. In Alg2, their grade is purely assessments, and all of their assignments are non-graded, feedback only. I'm not sure I'm ready to go there in AP just yet. I do see value in the items placed in this category, but would not want them in either assessment category since a lot of it is lab investigations, partner work, etc. The other issue with this category is anything that isn't done in class has the potential to not be turned in on time, which leads us down that "late work" rabbit hole.
  • Should the tests be unit based (like they currently are), or time based (like every 6 weeks)? I like unit based tests because things seem so neatly packaged, but I worry that that last chapter being quizzed won't be graded/returned/processed/remediated/reassessed prior to the unit test date. I like the idea of every 6 weeks (covering LTs up to Chapter X), but worry it might feel awkward and not flow well, but theoretically would give that cumulative element needed in preparation for the AP exam in May.
  • One of my biggest issues is that I'm a pretty slow grader in AP. With Alg2, I almost always had their quizzes back to them the next day, sometimes it took two days, but rarely more than that. With AP, there is so much reading that you have to do that it really bogs down the process.
New idea for next year One thing I've done for several years is a weekly POW that is a previous AP problem. I take these up on Friday and provide feedback and an AP score. This has worked fairly well for years, with the exception of a few kids here or there not getting them turned in, etc. This year, however, I had one class that was the class from hell when it came to turning these in. Seriously, out of 20 kids, it was pretty common to have less than half of the class turn it in. This really pissed me off, especially since they were assigned on Tuesday, given 10 minutes to work with their partner to read, discuss, and sketch out a solution, then 3 days until it was due in final format. After some thought and an "a-ha" moment earlier this summer, I think I am going to do two things to hopefully fix this problem. First, I am going to do daily warmups that consist of parts of AP problems. I can give up a few minutes a day to have the kids write a solution to a part of an AP problem. Then, I will either provide the scoring guideline to the class for whole-class feedback or sometimes take them up for more individualized feedback. Second, on a regular basis (maybe once a month?), we will have an AP quiz with maybe 4 AP problems and they have to choose 3 to completely answer and I'll grade it using the rubrics. I'm not sure where these will fit in my grading scheme yet though :) Wrapping it up
I don't have the details all ironed out, but overall, I think this is a plan I can live with for a year while I refine it. I think this provides me the detail I want on the individual objectives while still maintaining the big picture/integrated structure needed in Statistics. Now that I've identified the big issues and concerns that I have, I think I will be able to work on strategies to fix those issues. As always, I appreciate any feedback and questions to help me guide my thinking.

Tuesday, July 5, 2011

My Summer To-Do List

Oh my gosh, it's now July!!! Back to school aisles and sales are popping up all over and I have NOTHING done!! So, thanks to some inspiration from some blogger/twitter friends, I decided I had better put my to-do list down on "paper". There is just something satisfying by crossing things off of a list!

You will note that my to-do list is not something that easily lends itself to crossing off items. Most of these are a work in progress that will continue through the year. The idea behind this list is to help me focus on what I need to work on, rather than the nitty-gritty details. Some (most?) of these will not get done by August 15th, but I can make headway on putting together a plan for them.

  • Read. I am working on UbD, but have several others in line as well, including some on Habits of Mind. Need to do some personal reading too:)
  • SBG. I need to figure out how to make it work for AP, which isn't as skills based as Alg2. I also need to do some minor tweaks to Alg2.
  • WICR. I really want to work on incorporating Writing, Inquiry, Collaboration, and Reading in my math classes. I usually start off the year fairly well, but need to keep this going throughout the year.
  • Active Learning. I did this in AP and was mostly pleased with how it worked. I need to do some revisions in AP and increase this component in Alg2. I am in the process of going through and finding labs to add to my binder of ideas.
  • Warm-Ups. This year, I really struggled with Warmups and I really need to go back to them. In AP, I think I am going to do formative assessments using parts of AP problems. I'm not sure on Alg2 yet.
  • Cumulative Work. This has been a goal for several years, but it often goes by the way-side due to time crunch. I want to make a consious effort to have assessments and assignments that have previous knowledge involved.
  • Technology Integration. Supposedly we will have access to laptops in our new building, so I would like to beef up my class website to be more of a learning portal. I would like to integrate tools like Flubaroo (Thanks Fouss!), G-Docs, Wiki, etc. However, until I have full confirmation that this technology really is going to be available, this is kind of low on my priority list.

I'm sure there are more things to add. I've worked a bit at most of the ideas listed, but I don't have anything concrete yet, which is a bit frustrating. I have a jumble of ideas floating in my head and lots of dreams of what to do, but the nitty gritty details just haven't settled down yet. *sigh* I need July to go slower than June did :)

Wednesday, June 29, 2011

Active Learning and UbD

Our bookclub has been reading Understanding by Design. The first few chapters really gut-punched me in several places and I marked next to them "BLOG POST!!". However, I was out-of-town at the AP Reading and a workshop, so it's taken a while to actually get my thoughts down on "paper".

Here's what got me in Chapter 1...

"How will we distinguish merely interesting learning from *effective* learning?" (pg 14)

"But many teachers begin with and remain focused on textbooks, favored lessons, and time-honored activities - the inputs - rather than deriving those means from what is implied in the desired results - the output. To put it in an odd way, too many teachers focus on the *teaching* and not the *learning*. They spend most of their time thinking, first, about what they will do, what materials they will use, and what they will ask students to do rather than first considering what the learner will need in order to accomplish the learning goals." (pg 15)

That still has the power to take my breath away. How many times have I been that teacher? How many times I have thought about what *I* will do without considering the end goal? One of the design tips suggested going up to a student mid-lesson and asking them "What are you doing? Why are you doing it? What is its purpose/connection?" and I want to do that more this year. I want to be more explicit in the WHY, so that at any point kids should know the purpose of the lesson/activity.

A few days later, we read and discussed chapter 2... again, I felt convicted:

"Doing something correctly, therefore, is not, by itself, evidence of understanding. It might have been an accident or done by rote." (pg 39)

"Students should not be able to solve the new problems and situations merely by remembering the solution to or the precise method of solving a similar problem in class It is not a new problem or situation if it is exactly like the others solved in class except that new quantities or symbols are used." (pg 41)

"We cannot *cover* concepts and expect them thereby to be understood; we have to *uncover* their value - the fact that concepts are the results of inquiry and argument." (pg 46)

I am guilty of coverage. Especially this year :( After 11 snow days, I was in a race against the clock to cover it all. I cringe to even use that word, but it's what I did :( I am also guilty of the new problem issue, although not as bad as I used to be. Early in my career, I was bad about giving a worksheet of 20 problems that were all alike, then giving a quiz with 2-3 more and declaring a success because the kids were able to repeat a process like a trained monkey. Thankfully, I have gotten away from that as much, but it still can creep up on me if I'm not watching.

The next few chapters in UbD weren't as exciting to me, but now we're on Chapter 5, which is about Essential Questions (EQ). I'm about halfway through the chapter at the moment and am eager to finish it and discuss it with my bookclub buddies. Last week, I was at an AVID workshop and one of the cornerstones of the AVID system is the use of Cornell Notes (CN). This year, they rolled out an updated version of their CN template that includes a space at the top for the EQ. I know a lot of districts around the country have adopted UbD as a planning tool and require their teachers to post the daily EQ on their boards at the beginning of the hour. I really like this new addition to the AVID CN template because it helps focus the students in their note-taking and their summary should be a direct link back to the EQ of the day.

As always, when I leave an AVID workshop, I feel challenged to do more WICR activities in my math classes. (WICR = Writing, Inquiry, Collaboration, Reading). I really feel that the use of WICR activities may help the issues mentioned above and aid in student understanding of concepts. Today, as I was working on some literacy strategies in math, I saw a link being tweeted about PBL, which lead me to another link about Student Centered Learning. (link here) The idea behind this article is that this teacher writes a step-by-step lesson plan and has his students teach themselves. That's not a very good explanation, so please go read his article for yourself. :) I do something very similar in my AP class, where students work through lab activities to gather data, learn vocab and concepts, and work collaboratively with their groups with me acting as a facilitator. I am eager to try something similar (on a smaller scale) with Algebra 2. All afternoon, I tried to visualize this classroom dynamic and the pros/cons of it. I'm not there yet, but so far, I think this could work for me.

It's been a busy summer and while I love going to workshops and learning new methods/ideas, sometimes I walk away feeling pretty down on myself. I don't know if it's something other teachers feel or if it's the perfectionist in me. I know I always have room for improvement and I think that quest for continuous improvement is a good thing. At the end of the day, all I want is to be able to answer "YES" to this question... "Have you done everything in your power to be the best teacher/person that you could be today?"

Wednesday, June 8, 2011

SBG - Reflections on SY 2010/11

Last summer was a changing point for me as an educator. Fed up with my then method of grading, irritated at the "points-game" that my students played, and a lack of consistency in grading amongst teachers led me to reach out to the twitter/blog-o-sphere to build a better mouse trap. As a result, I became drunk on the Standards Based Grading (SBG) Kool-aid and I'm so glad I did.

If you go back and read the posts from last summer, you will see a lot of uncertainity in my posts as I tried to figure out how to best implement SBG in my classroom. Now that a full year has gone by, I want to provide some information on implementation, what worked for me and what didn't, and how I plan to modify it for next year.

Disclaimer #1: I only did SBG in my Algebra 2 classes and I'm still working out the details on how to implement in my AP classes for this upcoming year

Disclaimer #2: I am writing this post with the assumption you are already familiar with the basics of SBG. If not, I would definitely recommend Robert Marzano's Classroom Assessment and Grading that Works. A lot of my ideas are borrowed from his research.

How SBG works in my classroom...
At the beginning of a chapter, students are provided with an assignment sheet (Click HERE) which has a list of Learning Targets (LTs) and practice problems for each LT. In general, the LTs were from the lesson objectives of my textbook, but I did sometimes combine or even eliminate smaller objectives. For each LT, I broke down the traditional assignment from the textbook to 5 or so problems per LT, trying as hard as I could to provide a range of difficulty for each LT. I also tried to select odd problems so the students would have access to the answers in their textbook.

After 2-3 lessons (roughly 4-5 LTs), we would have a quiz over the material. Each LT had 3 problems, the first one was fairly straightforward and basic, the second problem was of average difficulty, and the third problem was of more advanced difficulty, often asking them to apply their knowledge in a new way or combining multiple skills. (Click HERE to see a sample quiz). Each LT was graded as a C (for Correct), P (for Partial), or I (for Incorrect). The C/P/I's were then combined for a rubric scale grade for each LT, with the more advanced problem's score weighing a bit heavier than the basic problem's score. I used a 4 point rubric, which I then converted to a 10 point "gradebook" grade due to limiations with my district gradebook.

In general:
CCC = 4 = 10/10 - You totally have this concept mastered!
CCP = 3.5 = 9/10 - You are almost there, just a minor error (usually a sign issue!)
CCI = 3 = 8.5/10 - You've got a pretty good grasp on the material
CPP = 2.5 = 8/10
CII = 2 = 7/10 - You have a basic understanding of the material
PPP = 1.5 = 6.5/10
PPI = 1 = 6/10 - There is a glimmer of knowledge of the concept
III = 0.5 = 5/10 - You have no clue, but you gave a valid effort
--- = 0 = 0/10 - You left it blank or no valid effort
**Note, not all combinations of C/P/I are listed... this is just a general guideline of what I did. Sometimes a CPP was a 3 depending on the strength of the Partial.

The night of a quiz, I went home and graded them, then recorded them in my gradebook on the 0-4 scale. I kept a paper gradebook (Blank copy HERE) because I wanted to keep track of student scores and reassessments, plus we don't have online access to our gradebooks at home :) Each square in the gradebook is large enough to write several scores, so it worked well for me. (See Sample GB HERE)Probably the most difficult thing for me was that I've always been a slow grader so I really didn't know how well I would do at getting quizzes back the next day. However, after a few quizzes, I was amazed at how speedy it was to grade, and so it wasn't the dreaded chore that it had been in the past.

The next day I handed the students back their quizzes. On the first few quizzes, I took the time to re-explain the system and what the rubric score meant. I really think that the time I took to model and explain the SBG system paid off in more ways than I could have expected. In the past, students had looked at their overall grade and then thrown their quiz away (or in their backpack, never to see the light of day again). However, with SBG, students really took the time to read the feedback, do an error analysis, check with a buddy to compare methods of solving, and rarely did I find a quiz in my trash can or recycle bin. In fact, most students kept their quizzes in their binders, in numerical order and even in May, they were able to produce quizzes from the fall semester when they were asked to. I had *never* had that happen in the past!

After the students received their quizzes, we discussed as a class what it meant to remediate and reassess. We talked about their score was a reflection of the mastery they had demonstrated, and if they felt their mastery had improved, then they needed to come in to demonstrate that improvement to me. On my podium was a weekly sign-up sheet (Click HERE for a blank copy) for students to schedule reassessments. I only allowed reassessments on three days of the week so I would have some off time for tutoring, meetings, etc. We also have a built in Advisory period on Thursdays that students could come in, but since I already had 20 Advisory students, I limited reassessments to the first 10 students that signed up.

When a student showed up for reassessment, they had to provide me proof of remediation. The idea behind this was that I didn't want them wasting my time or theirs on reassessment if they had not put any effort into mastering the material. Initially, I had planned that their remediation would be the practice problems from the assignment sheet, but as the year went on, that idea was modified to include an error analysis of their quiz, notes/problems worked with a tutor, etc. Overall, I was pleased with how students handled their remediation. As the year progressed, you could definitely see the students taking more control of their learning as they decided the amount and type of remediation they needed to do in order to master the material. We did have a few big rules regarding reassessment - the students could only do the LTs from a single quiz during a single session, and they could not received tutoring and reassess during the same session. These rules helped us keep our sanity and helped with the short-term memory issue :)

The Lessons We Learned
I was really shocked and amazed at how easy parent communication became with SBG. Since their grades were totally based on quizzes, there were no discussions on extra credit, turning things in late, etc. The gradebook was laid out in a very clear manner about their student's level of mastery per objective, so most parent questions were easily addressed.

At first, I was really dreading the actual grading, but I quickly adapted and overall I ended up with less to grade, yet able to provide my students with more specific and detailed feedback about what they knew or didn't know. I was also able to grade much faster, which let me have more time for planning interesting lessons.

In our original design, we had planned to continue with traditional chapter/unit tests, but this quickly went by the wayside. Part of this was a time issue, part of it was keeping all of the terminology straight, and part of it was just that traditional tests didn't seem to fit in well. We ended up going to just quizzes, which were every 5-8 class days and it worked out just fine in the end.

Definitely have a partner to try this with! If I had gone at it alone, I would have bombed out early just from being overwhelmed. However, I had spent most of last summer reading, researching, blogging, tweeting, discussing SBG before I ever stepped into my classroom. Having Neighbor Teacher there to try it with me, to help shoulder the responsibilities of writing quizzes, coming up with LTs and Practice Problems, asking advice while scoring a quiz was simply invaluable.

Changes for Next Year
One change I would definitely like to make for next year is an easier way for students to keep track of their scores. The assignment sheet has boxes for this, but I wasn't very good at insisting that students write their original score and their reassessment scores in those boxes. I need to look at some of the other blogs to see what they do for student recording.

I would also like to look into using tiered remediation. In other words, if you scored a 3.5, you only had a single minor error, so you don't need to do as much remediation as a person that scored a 0.5. I'm not sure that I could keep up with this paperwork, but I did have a few kids that did the minimum amount for remediation and then were shocked when their reassessment still wasn't very good!

Would I do it again?
Heck yeah! This was a long process but SO worthwhile. I've grown professionally through this process and I don't regret a minute of it. I just hope that this record of my journey helps someone out there as they start sipping the Kool-aid :)

Friday, June 3, 2011

In the Good Ole Summertime...

It's official - summer is here! Today's highs were in the upper 90s and it's downright yucky outside!

Last Friday was our official last day of school, but I went back for a two day workshop this week. To say I'm conflicted would be an understatement... As I had understood it, the goal of the workshop was to work collaboratively on inquiry based lessons. However, most of my inquiry focused more around the "Huh??" realm. :) One definitely positive outcome was having conversations with the science teachers on how they use math in their classrooms and what I can do to support their program within my math classroom. I think the key challenge will be finding places in our math curriculum where the science fits naturally as to not create a "square peg/round hole" forced situation. It was pretty natural to find places where statistics fit in (duh!), but it was challenging to find areas for Alg2. The best we came up with was literal equations, parabolic motion, and graphing stories (distance vs time, etc).

After our workshop, several Alg 2 teachers got together to plan out the first part of next year. One of our frustrations is that we spend too much time on Alg 1 review, which then creates a bottleneck when we get to the actual Alg 2 material. Our goal was to try to condense the first few chapters of material while reviewing the Alg 1 material in the context of Alg 2. For example, instead of reviewing slope and writing equations of lines and such, we would do linear piecewise functions and have them write equations and find slopes of the various segments. I'm very excited about the changes and reorganization that we worked on and hope that it really helps with making connections for our students.

By the way, for those naysayers that think teachers have all this time off, today was my first day with nothing planned out and what did I do? I cleaned my office and worked on some activities for next year. I did get a nap in though! :)

Edited to add....
I asked my twitter PLN for any examples of how math can support what they are doing in science. For sake of my memory, I am cataloging the responses here...

macsmath - linear & quadratic eq's --> 3d position & prediction - I'll post what I do with it soon (hopefully)

jsb16 - I'd be happy if my students came in with Alg1 concepts solidly understood. Most of my sophomores can't solve F=ma for m.

torquedu - direct/inverse/inverse square/sqrt/logarithmic/exponential variation as common relationships among variables (not x &y)
- Not strictly Alg2/Precalc, but stus could always use practice with unit conversions, sci notation, non-integer numbers & graphing

fnoschese - equation of line, slope, area under graph (by hand, no calculus), solving equations, systems of equations, right tri trig, vectors.
- stop using x and y as variables eg if height is unknown use h not x.
- Truck starts 100 m north of school going south at 20 m/s. Car starts 40 m south of school going north at 35 m/s. When/where meet?
- Another is when they need to use slope eqn and area equation for a graph at the same time b/c of unknowns.
- for example: slope = (10 m/s/s) = v/t, area = (45 m) = (1/2)(v)(t) . What is v and t?
- You have a graph of velocity vs. time. Slope is acceleration (given). Area under graph is displacement (given). What's v and t?

I really appreciate the information given by the science teachers!! Thanks to you all!

Saturday, May 28, 2011

Sweet summertime....

Another year has come and gone and what a year it has been!

This past week...
Thursday we had a Professional Development day and Neighbor Teacher and I presented on our implementation of Standards Based Grading. We had a classroom full of teachers, mostly math, but a few from other subjects too. The presentation was supposed to be 1 hour, but many people stayed over for about 30 extra minutes to ask questions. Overall, I was really pleased with how well the presentation went and I am excited to see where next year takes us in terms of assessment. From the questions and comments, I think several of my colleagues will be trying SBG next year in their classrooms. After the presentation, I started packing my classroom as I will be moving to our new math and science facility next year. After 30 boxes, my cabinets are completely empty and I am headed back up there today to do my desk area.

Next week...
One of the future goals of the math and science departments is to create inquiry based collaborative projects and lessons. This next week, several of us will be gathering for a two day workshop to learn about this initiative. I'm eager to see what the outcome of the workshop will be.

Over the summer...
As always, it will be a busy summer. In addition to next weeks workshop, I have three more weeks of workshops planned, several items on my to-do list for next school year, unpacking my new classroom, and lots of naps :)

Friday, May 13, 2011

Things to keep... Things to change...

Yesterday was my favorite day of the year. It was my annual "Trash Me" day. That is the day that I tell my kids to let me have it, tell me what they liked and dislked about the class, what needs to be kept, and what needs to be revised or even tossed completely. I tell them it's okay to tell me the honest truth and to feel free to tell me that I'm the worst teacher they've ever had and they wouldn't wish me on their worst enemy and I won't take it personally. For me, it's the most rewarding day of the year because the kids really are brutally honest and that's what allows me to grow from year to year. I start out by asking them to get out a piece of paper, then they free write for a few minutes. Then, I open it up to verbal discussion and write their comments on the board.

Here are some of their comments:
- Really liked working with a group/partner, but many felt they were too dependent on their partner, so they struggled when working independently. (My response: This year is the first year I've gone to almost a completely active classroom. As a result, the students worked on labs and activities almost daily to learn the material. While I did appreciate the reduced dependence on me as the teacher, I
did not anticipate the increased dependence on their groupmates.)

- Students felt the Gallery Walk activity was very successful. It forced them to read over the previous groups work and look for error and to see different ways that other students did the steps. (My response: I'm glad they felt this was useful, I had never used it before and now I will try to find ways to use it more often)

- Students appreciated that homework was only required for remediation/reassessments. The majority felt that we worked so hard in class (remember, they are the ones working, I don't lecture much at all), so additional homework they felt was unnecessary for most students. However, they did recognize that sometimes they needed to work more on a concept in order to really get it. (My response: I totally agreed with them here)

- One suggestion they had was to do more FR questions at a time. We do a weekly Free Response question, but many of them requested a monthly/quarterly Free Response practice that was multiple FRs at a time over mixed topics to help them prepare on pacing and seeing multiple topics at a time. (My response: I think this is a great suggestion and I will definitely implement it for next year)

Overall, I really appreciated their honest feedback and I will admit that this is the first year that I've had more positive comments than negative comments. I always learn so much from their suggestions and feel that this is one of the best growth opportunities for me from year to year. Now that the AP exam is said and done, I love reflecting on my year and planning for next year :)

Tuesday, May 10, 2011

Random Thoughts...

Tomorrow afternoon is the AP exam... I've done what I can do, now it's up to the kiddos.

Now the race to the end begins... Graduations, assemblies, banquets, final exams, professional development, packing up.... Seems like every day on my calendar has something written.

I've started my to-do list for the summer and it keeps growing. Sometimes I look at it and think "Dang, I really did a horrible job this year"... I know that's not true, but it's so easy to get overwhelmed by all of the things I would like to improve upon. I need to trim and edit the list to a manageable level...

Two more weeks....

Saturday, April 23, 2011

Looking Back... Looking Forward....

It's that time of year where I start reflecting on the past and looking toward the future. We now have one month left of school and a lot to get done in that month. The Algebra 2 End of Course exam is just days away and the AP exam is coming in a few short weeks. The month of April has just flown by and here we are at the end of it!!

Yesterday I got to see my new classroom for the first time. My district is building a new math and science facility and in just a few short months, I will be moving in. It is bittersweet for me - I'm excited to have the amenities that come with the new facility, but very sad to leave my current hall-mates that have helped me through thick and thin. Some of the perks of the new room - a thermostat that *I* can control, lights that turn on automatically when you enter the room, and light controls both by the door and by the teacher station, which will be great for videos, etc, lots of white board space and the ever important storage.

As I look back on this year, here's my list of things that I'm really excited about:
  • Standards Based Grading really worked well for me in Algebra 2. The kids really took ownership of their grades and realized that the important thing was that they learned the material. I am extremely proud of how well my kids adapted and how much they matured over the year.
  • Converting AP to a completely active classroom. I really couldn't tell you the last time I lectured in AP. Instead, I set it up as a lab style classroom where the kids worked daily in groups, really emphasizing that "productive struggle" we keep hearing about.
  • My online PLC via Twitter - I learn so much from these people! From the online book clubs to just having a network of like-minded educators, this has been one of my most rewarding professional activities from the year.
  • Vertical Team - several of my colleagues and I have been working this semester on vocabulary alignment, Pre-AP ideas, and opening the lines of communication, all of which were sorely needed.
  • Overall, because of the things listed above, this was my best year ever!!
Things to think about for next year...
  • Flipping my classroom - making videos to teach, review and refresh concepts from earlier in the year
  • Standards Based Grading for my AP classes
  • Determining which labs were most effective for AP and which need to be revised
  • Integration of articles into my AP classes
  • More technology - in the new facility, we are supposed to have laptop carts in our classrooms. If so, I would like to work more with google forms, wikis, blogs, etc to really integrate technology
  • Pre-AP integration - Assuming that I am still teaching Algebra 2 (we've not gotten our schedules yet), I would like to work on more Pre-AP activities.

It's going to be a very busy summer..

Saturday, March 26, 2011

Developing Understanding in Algebra and Geometry

Last week, my district brought in a Pre-AP math consultant to work with us on Pre-AP Strategies. Initally, most of us were not pleased with having to miss a day of school to attend a PD day, mainly because we had missed 2 weeks of school in February due to a blizzard and we have end of course exams coming in mid April, so a lost instructional day was not high on our to-do list. However, we were also very grateful that the district was trying to bring in PD that would be applicable and ready to implement. In a nutshell, we had a great day :) Here are some tidbits of knowledge that I took from it...

General comments
"You (the student) will feel uncomfortable in this room! Your brain will hurt daily!"

The "Rule of 4" should be on every assessment and potentially every problem.

Make the kids communicate in complete mathematical sentences. Communication helps ALL kids - the answer alone does not. With just the answer, the struggling kid still doesn't know what to do or where to start.

Students should be asked to read, interpret, communicate, draw, label, compute, and explain/justify on a regular basis.

We as teachers should not have to put "Show all work" on every test - this should be an implied directive that they do no matter what.

More Specific Ideas
One of the key components of the workshop was the focus on how to communicate mathematically both your process and your product. One of the activities she used came from the Math Connections book by Dale Seymour. She used the "What are you likely to be asked" activity, but in the Amazon link, you can see an example of the "How do you know" activity. I can really see both of these as great warmup/journal prompts or even as exit slips.

Another idea she had was based on the game "Would you rather?" I think it would be neat to sit down and brainstorm a bunch of these for various courses. This again could be a neat journal activity.

She also refered us to the Algebra Lab website and we looked at the All Tied Up in Knots problem, which explores a system of equations using two ropes, tying knots in each of them and measuring their length. This could be a great pre-ap Algebra problem as you could go into what the y-intercept and slope really mean, which is a vital skill in AP Statistics. I'm eager to go through the other activities on that site to see what else I could use in my classes.

We also explored some neat geometry problems such as constructing a tangram using compass/straightedge, a fun manipulative proof the Pythagorean Theorem, 3D solid constructions using pipecleaner pieces and coffee straws, and peeling an orange to discover that the surface area of a sphere is 4(pi)r^2.

All in all, it was a fun and productive day that really allowed us to get some creative juices flowing.

Saturday, March 19, 2011

Mastery of Objectives

So during a discussion on twitter today, @misscalcul8 and I were discussing the number of objectives taught per week. On average, in Algebra 2, I would say I cover 3-4 objectives. Her question, and a very valid one was this:

So how do you teach to mastery in one day of experience with a LT? I don't meant that critically.

Now that response is way over 140 characters, so I told her I would blog my answer :)

In short, the answer is "You don't." Mastery is not a one-day process - it is a long term process that differs for every child. You have to continue spiraling the curriculum so that over time, mastery is obtaining. Some of you may have seen the "forgetting curve"...

Here's how the forgetting curve works for me...
On the first day of an objective, I teach, they take notes, do problems, etc like normal. Then the next day, I give a "Checkpoint" - this is an ungraded formative assessment so I can provide written feedback and correct errors. On day 3, they get the checkpoint back, look over it, read my notes. (Note: during days 2 and 3, I am teaching new, but related objectives that I try to continue tying into each other). A few days later, there is some kind of cumulative activity to see how objectives work together, review multiple objectives, etc. There are also Jing videos that I have created and put on the class website that they are supposed to refer to if they need additional instruction. About once a week, there is a SBG quiz that covers that week's objectives. Again, lots of written feedback if needed. Over the next few weeks they are working on those objectives using self-check materials, the Jing videos, tutoring, etc so they can reassess. (In order to reassess, they must provide evidence that they have worked on mastering the objective)

In a nutshell -
From start to finish, the student has seen and worked with the objective many many many times, so that they are constantly bringing it to the forefront of their mind, spiraling the material so that they will achieve mastery.

Definitely longer than 140 characters :)

Tuesday, March 15, 2011

Spring Break :)

I have been meaning to post for a few days, but I'm struggling with forming coherent thoughts right now... This post will be somewhat of a rambling one, so bear with me...

At school, some of the teachers have decided to get together for lunch once a week in order to discuss vertical alignment. This has caused me to pull out old Pre-AP materials from workshops, do some research online, and even do a few calculus problems. What I have learned is that at the time I took calculus in high school and college, I really was clueless about what was going on. It makes so much more sense now that I've taught geometry and algebra 2 and have the conceptual maturity to get it!

As an extension of that, I've really been feeling a need to do a better job in Algebra 2, specifically with making connections. So I am going to steal borrow from the wisdom of my amazing blogger and twitter friends to rework the exponential/logarithm chapter with more active learning techniques. That was part of my goal today and I have 1 lesson done out of 8.. woot! :)

While I definitely enjoy having a break and being able to sleep in, I really am not a fan of this time of the school year. For some reason, each year in March and April, I look back over the year and thing, gosh, I did a cruddy job :( Then I start my to-do list of things to do better next year and the cycle repeats itself....

I need a nap...

Tuesday, February 15, 2011

Gallery Walk - Stat Style

Remember that blizzard that hit the midwest two weeks ago today? Yeah, well, yesterday (Feb 14th) was the first day I had seen my students since Jan 31st. In AP, time is a very precious thing because we have a lot to cover and every day is really special to us. Thankfully I was a bit ahead before the storm AND the AP exam was moved to the 2nd week of testing this year, so I'm not frantic - yet! I was in the middle of teaching confidence intervals for proportions when the storm hit and I really feared that the cobwebs would take awhile to clear in order to get us back on track. Yesterday I did the half sheet review and it went very smoothly. The kiddos settled back into the routine like no time had passed at all! Since for each halfsheet, they have to come up for me to check it, I was able to clarify thinking and remind them of details quickly and more effectively than I could have through lecture. However, I knew I needed more practice on confidence intervals before the chapter quiz, and then a brainstorm hit - GALLERY WALK! :)

The idea behind a Gallery Walk is pretty simple and I had used it before in workshops, but never with my students. I didn't know how well it would work at all, but I really liked it! Last night, I took a worksheet with 7 confidence interval problems and printed it. Today, I cut those problems apart and posted the problem and a piece of chart paper around my room. When the students got to class, they worked on their warmup in their groups while I went around and gave each group a different colored marker. Then we got started. Each group went to a piece of chart paper and read the prompt. Then as a group, they decided what the parameter of interest was and wrote that down. When all of the groups were done, we rotated clockwise to the next chart paper station. The group then read the new prompt and the previous group's work. With a new group member as the writer, they corrected the previous group's work and then continued the problem by checking the conditions needed for a confidence interval. Again, when all groups were done, we rotated clockwise again. Repeat with a new group member as the writer, read the prompt, check the two previous groups' work, then continue the problem with the name of the procedure and the calculations of the interval. Again, when done, rotate to new station, marker goes to a new writer, read the prompt, correct the previous groups' work, and write a conclusion for the problem. Finally, the writing is all done. They rotate once more to read and check the previous work. Now comes the self-checking part. Each group rotates back through the posters they had written on to see what errors had been caught by someone else. Here is a completed poster:

So how did it go? I think today's activity was a success. For the most part, the kids did really well working together and moving about. When I read over their work, rarely was there an error, so I was glad to see that. I have pretty much taught this chapter with no direct instruction, so I am eager to see how they do on Thursday's quiz. Overall, I would deem this a success and will try it again when we do hypothesis testing... which reminds me, I need more chart paper :)

Til next time.... :)

Thursday, February 10, 2011


Yeah, so tomorrow is the 9th straight snow day we've had. The last time I saw my students was January 31st. Crazy, huh?

So during my second Winter Break, I wasn't nearly as productive as I should have been. Seems like each day was in limbo, waiting on the phone call that decided my fate for another day. However, since I've not seen my students in 2 weeks, that does create some issues when deciding what the heck to do with them after an unexpected and record-breaking blizzard and it's aftermath.

In AP Statistics, I had just introduced confidence intervals for proportions a few days prior to us being out. Based on an idea that I got a few years ago from an AP workshop, I created a lab where my students got the "big picture idea" of a confidence interval based on tossing around inexpensive inflatable globes with the task of predicting the true proportion of water on the Earth's surface. I love lab activities that require the kids to read, question, and discuss the big ideas without any direct instruction from me. At the end of the day, they had a pretty decent idea of the purpose of a confidence interval and the basic idea of how it is related to the Normal model. The next day (Friday) I did some direct instruction over the Margin of Error (MoE) and the more nitty-gritty details of the process required for a confidence interval. However during the weekend, the forecast started getting gloomy and I knew direct instruction would not work for Monday. Instead, I created another lab where the students were rolling Pass the Pigs pig dice to create confidence intervals for Razorback, Trotter, Sider, etc. This time, the lab was more detail oriented than the globe lab, walking them through a complete write-up of a Confidence Interval for Proportions. At the end of the hour, we quickly reviewed and that was the last time I saw them.

So now, here I am, thinking of the 2 weeks that I lost and trying to figure out how to get them back on track. Last weekend, I created a "half-sheet" activity to review what we had already covered about Confidence Intervals as well as introduce the idea of finding a sample size for a given MoE. I have done the "half-sheets" before and my students *LOVE* them. When they come to class, they sit with their collaborative groups and each group gets a copy of Card #1. As a group, they work through it, discuss it, make sure everyone is on board, then they bring it up to me to check. If it's correct, I OK it, then hand them Card #2. If it's not correct, I point out errors in thinking, etc and they go back to the group to find their errors. This continues until the end of class. Pretty much, any worksheet can be done as "half-sheets", but for some reason, they ASK to do half-sheets! Anyway, here's the confidence interval for proportions half-sheets in case you want them :)

For Algebra 2, Partner Teacher and I decided to review and quiz them on Monday/Tuesday over function operations, compositions, and inverses before moving on to the Radicals unit. I had found this neat "Ghosts in the Graveyard" activity a while back but hadn't had a chance to use it yet. Well, of course Monday is Valentine's Day AND we're going to review, so why not do Math Conversation Hearts? :) I created 8 heart-shaped cards with review problems that I will copy onto red and pink cardstock and laminate. Instead of Graveyards, I'm leaning toward possibly letting them choose some of the big Conversation Heart candies (or maybe just cutouts?) when they get their problem set correct, then at the end of the hour, determine which color is worth how many points. The prize will (of course) be yummy Valentine's candies!

Thankfully, it looks like we will be going back on Monday. Next week's highs are near 70, which will be sandal weather compared to this morning's -12!! To help make up the days that we missed, it definitely looks like I will be working on "flipping" my classes earlier than I originally expected! I'm ready to be back into my routine, although I'm pretty sure I have forgotten how to set my alarm.... :)

Friday, February 4, 2011

I *heart* my iPhone

About a year and a half ago, our phone contracts were up for renewal and hubby had been wanting an iPhone. A lot of my students had them, but I was not impressed, I couldn't figure out why anyone would want to spend that much money on a phone, plus an outrageous monthly fee for the data plan. So hubs ended up getting one while I got a "texting" phone that I thought totally fit my needs. About 6 months later, I finally saw the need for one as my students were studying for final exams and asked to take a picture of the review answer key so they would have it at home. *Shrug*, sure why not! One student offered to post the pictures on his facebook page and the kids were happily reviewing, but it got me to thinking about the uses of an iPhone in the classroom. A few days later, after stalking Craigslist for an affordable iPhone, I found a good deal and bought myself one. Now, less than a year later, I can't imagine what I would do without it!

For example, in Algebra 2, I use it as a scanner, to take pictures of files that I want to post on the class website (answer keys, etc), or when I want to point out specific instructions on a paper. When we were solving polynomial functions, I did a matching jigsaw like puzzle, but I knew if I just verbally told them that most of the expressions were repeated as equations, they would be clueless, so I snapped a picture, hooked up phone to my computer and projected the following onto the Promethean to show the kids what I was referring to.

I've also used it as a scanner in AP Stat, but I also like it for snapping pictures of students doing class activities or to embed into a Jing video later on as a remediation tool. I took pictures as we explored what happens when we flip a penny 10 times, recording the proportion of heads versus flipping the penny 20 times. Now these pictures will be put into a screencast for review of sampling distributions of proportions. (Note: I'm also fond of Post-It pad paper and Dollar Tree smiley face stickers when I need to make graphs in Stat). I didn't take a picture of all of the writing I did afterwards - we talked about the difference between p and p-hat, and talked about the overall Normal model pattern that would emerge if we were to continue flipping the penny and recording p-hats

(Sorry for the sideways graph....)

In addition to using my iPhone for about every avenue of my life, I sent my AVID kids on a snow day scavenger hunt to find cool education apps that they could use to help them study and/or get organized. Since I haven't seen them since I gave them the assignment, I'll have to update you next week on what they found :)

I know there has to be more awesome ways to harness the power of my little mobile computer, how do you use it in the classroom?

Snow Week....

So, in case you didn't hear, the nation got pounded by a massive storm system this week. In my neck of the woods, where a 3-4" snow is considered pretty big and closes us down for a couple of days, we got a whooping 21 inches! Needless to say, that set a few records, then we got another 3.5 inches today, with more forecast for Sunday *sigh*. The system came in overnight on Monday and hours before any snowflake even hit the ground, the schools were cancelling Tuesday's classes. Ultimately, we ended up cancelling the entire week due to the horrible road conditions. Tomorrow is the first day it is supposed to get above freezing, so I'm hoping for some melt as I go out to clear my driveway.

Anyway, so how did I use my snow days you ask? The first day or two was a total waste of course, spent the day gawking at the snow drifts and watching the news coverage while lounging under a warm blanket. But by the end of day 2, I started getting antsy, so I combed through blog after blog after blog stealing all of the good Algebra 2 ideas that I could find and organizing them by chapter of my textbook. I read through all of the Math Teachers at Play blog carnivals and brainstorming the various review ideas/structures and how I could increase student engagement in Algebra 2. There are some really awesome ideas out there, but it takes hours to comb through all of those sites and find the good ones.

A few weeks ago, I stumbled upon a new math teacher blog (because she was awesome enough to post a comment here, or I would have never found her!) and totally stole this neat Math Stations activity. (Click HERE to read her instructions). We happened to have a short day a few days after I found her blog, in which I would only see one of my Algebra 2 classes, so I whipped up a quick review of the material we had been learning. I printed it double sided, but I did do the answers by hand because I didn't want to type that much :) I gave the kids 4 minutes per card and overall I think it worked REALLY well. Here is the file:

Now to watch the news again... they are forecasting more snow in my future :(

Thursday, January 20, 2011

Function Dice

Today was a snow day (yay!), but we were supposed to teach function operations in Algebra 2. I had given a quiz yesterday and while they were quizzing, I had a brainstorm - function dice!!!

So today during my snow day, I found some foam dice in my closet (thanks @Fouss!) and using tiny post-its from Walgreen's Back to School sale, I made an f(x) and a g(x) dice set :)

By rolling the two dice, we have a large set of practice problems and example problems for tomorrow's lesson :)

Now I need to figure out an tetrahedral die for the four functions :)

(Although I wouldn't be opposed to another snow day either!)