Sunday, November 18, 2012

Trying not to brag, but I must

My last post was from about a week ago bragging about my Pre-Calculus students getting excited about studying exponential functions and log functions.  Well last week went even better.  They left me at the front board in awe of their skills.  I have taught Pre-calc now for 8 years.  And Trig College Math (a class between Alg 2 and Pre-calc) for the six years before that.  Logs have always been difficult for the students to grasp.  So this year I wanted to do something different, I needed to change how I presented the material.  It was a risk that paid off huge dividends.

After the lesson on the passing the drug test problem, the students were invested on this unit.  Tuesday I went in and had them graph 5 different transformations of y = 2^x.  We used all our previous information on how different transformation changed the graphs.  Because this was about the fourth time we talked about transformations, these five graphs were easy for them to understand and manipulate.   Then we looked at all five, noticed similarities and differences, identified the domain, range, and asymptote.  I tried not to get in their way.  I asked the questions, they made the connections.  Then we graphed 5 variations of log base 2 of x.  It just so happened (deliberate on my part) that each log graph was the inverse of the exponential function they just previously graphed.  They immediately realized the graphs, in fact, were inverses.  Everything we just studied about inverses was still holding true within this new set of functions.  Then we flip the note sheet over and fill in a chart with log form vs exponential form.  NO stopping them.  I threw 10 hard evaluate these log expressions by rewriting them into exponential form.  Students were defending their answers to others in the group and in the class.  They were more than ready for their homework assignment.

Wednesday - two questions... that was it.  They only had two questions on the homework.  Well on to log properties we go.  In years past, it was the ol' I tell you the properties, you then immediately manipulate the properties with variables.  This year, oh no we are changing it up!  Evaluate these... I have them 5 or 6 examples of logs being added together immediately followed by the log of the product of the arguments.  Do you see any patterns?  Any special relationships showing up?  And darn it, if they didn't arrive at the property themselves.  The lesson continued into Thursday with a discussion on how the change of base is going to be antiquated because of new technology.  But if they had an old school calculator, here you go.  Throw in the variable now that they are ready for them and give them a 10 question true false quiz at the end.    Lively discussion followed the grading of the quiz.  Who selected true and why?  Who selected false and why?  Did any of you change your mind?  Why?  What's the correct answer we can all agree upon? Bell rings.

And here we go for Friday:  Remember last Friday I asked you about passing a drug test?  Who remembers the plot?  What was that equation you came up with again?  Remind me why you all wanted .75 instead of .25 again.  Excellent.  Thank you for telling me the equation again.  Our task today is find out exactly when your body will have 1mg left.  Oh crap, they are not listening to me anymore!!!  They have whipped out their calculators and are scribbling on their papers.  Within a minute I have answers from nearly every group.  I stood at the board basking in the beauty of students solving exponential functions without ever being given the procedure to do it.


How did you all solve that?  I haven't taught it yet.  And here come the explanations of what they did.  I pretended not to believe they could solve such problems and gave them another.  Less than a minute again, they had an answer.  Well alright then.  Today's topic:  solving exponential and log functions.  Level:  apply   Assessment:  solve this equation (where they had to condense the log expressions before solving where there would a quadratic that would require the quadratic formula with two irrational answers one of which was extraneous).  We got through about half of the examples I wanted to.  I'm not in a hurry.  They are understanding it like rock stars!  The bell rings.  Three students run to the front with their assessment question completed and want to know if their answers are correct.  I didn't even finish the lesson let alone ask them to attempt the assessment question.  And these three students are not my top students.  In fact, one rarely speaks to me.

I left my class that day so proud of my students.  They left feeling enabled and empowered about math.

Over the weekend, I reflected on why I think they are doing so well.  I feel it's because I took the time to build the concept and lay the foundation of that conceptual understanding before I gave them the procedure.  The procedure came from necessity, not because it was what I told them to do.  I had to slow down to allow them time to discover it.  But I don't feel I will need to spend 3 days of review before the unit test like I have the past 14 years.  I will give them at least one day of review.  But I think that is all they need at this point.  Tomorrow we will finish the solving lesson.  Tuesday we discuss logistic curves and their purpose in the real world.  Wednesday, we will review.

And I would like to defend my class for a brief moment.  Yes, it is an honors class.  But this class has struggled the most of all my Pre-Calc classes ever.  One third came from the honors track, one third from the traditional track, and the last third skipped a year of math and came from a traditional math class.  These are not kids who love math and can't wait for the words to roll off my lips.  But they love being in control of their learning.  I have become more of a facilitator than I have ever been instead of being a straight out lecturer.  And I am loving it too.  This may sound like I am bragging, but how can I not?  They are amazing me every day.   I have to brag.

Tuesday, November 13, 2012

Who are you and what have you done with my students?

It has been far too long.  And I really wish the blog initiative was still kicking my butt to write at least once a week.  I have much to still do tonight, but I must force myself to reflect.  Here I go... and before I start, I need to say my Pre-Calculus kids are still shocking me this year.  Remember, they were all in their seats before the bell rang on the first day... back to the story at hand.

I had a second opportunity to see Steve Leinwand again with some more members of my department.  I was reminded about the following:
Evaluate 16(.75)^x  for when x = 8 in the exponential function 
You take 16mg of a controlled substance at 8am.  Your body metabolizes the drug at a rate of 25% per hour.  If you have to pass a drug test at 4pm with less than 1mg, will you pass the test?

Steve goes on to tell the story of how the Romain gymnast lost her gold medal because her coach didn't understand this problem.  Well, I just so happened to be starting the chapter on logarithms in three days from this afternoon conference.  Heck yeah, I'm so stealing this activity and having the kids get down and dirty with this function.

Three days go by and it's Friday... new unit day.  I pose the problem, give the students 10 minutes to come up with an answer.  Oh, and they had better be prepared to defend their answer and explain how they arrived at it.  They didn't even blink.  Bam, 15 minutes later I have kids telling to multiply by .75 not .25 each hour.  Paraphrased from students: Well Mrs. Berg, it's because it's too much work to keep subtracting the 25%.  You could, but this way was easier.  (HECK YEAH! - trying to keep my excitement PG here)  And no this person doesn't pass the drug test at 4pm.  Almost, two more hours and they would have, but not at 4pm.  Formula?  Sure I wrote a formula for it.  16(.75)^x.  (me in my mind - HOT DAMN - sorry for the French).  Oh, I said at first they would pass the drug test because I just kept subtracting 4.  But then I thought that was too easy, so I tried another way.  

I could not plan for my students to astound me this way.  They literally took over the conversation.  And I hadn't even gotten to the good part of how this was a true story.  They could google it when they got home, but a gymnast from the Syndey Olympics lost her gold medal because she took some over the counter cold medicine and the coach miscalculated the length of time on the banned substance.  They were eating in the palm of my hand.  

Then I said I had another real life story problem that involved exponential functions.  Are they ready?  They were ready as long as this one wasn't a sad story.  I then told them about buying our first family vehicle.  We were offered two choices $12,000 at 8% interest or $18,000 at 2% interest.  Which should my husband and I take?  I told them how we argued over it.  He wanted the lower interest rate.  I wanted the lower amount.  I just so happened to have my graphing calculator in my purse (just like Batman would wear his utility belt).  I worked the numbers.  We took the higher interest rate.  And then the bell rang.

I had assigned about 8 story problems.  They all groaned when I said that.  However, today, they came in without questions on those problems.  I asked, any questions your groups couldn't answer?  They said no.  The homework was actually easy and they liked doing it!  Ok, who are you and what have you done with my students?

Today we tackled graphing both exponential and log graphs.  Easy peasy, lemon squeezy.  Well, I hope.  Those buggars made the connections they needed to on their own.  I had very little to say today other than How do you know this?  Please, convince the class.  Do you agree with Suzy?  Who can help John out?

Tomorrow we pursue the properties of logs.  My goal:  Shut my mouth and let my students take over the learning.  After a small pop quiz.  1 story problem and 2 graphs... know or don't... show me.

Now, on to my other things I must attend to tonight.  Felt good to brag and post again.  Far too long I tell you.

Sunday, September 30, 2012

Brain dump

Yup, it's been way too long since I have posted.  Way too long.  I just needed to carve out the time to sit and thing.  So let the brain dump begin.  Here's what has been swirling in my mind the last 3 weeks.

First and foremost, I am concerned about my students.  I am not a perfect teacher.  In fact, I know of a few areas where I am weak.  I am continuing to work on these areas this year.  The biggest weakness is my questioning skills.  I have fallen into the trap of asking whole group questions, allowing students to blurt out answers, and not allowing my students the needed wait time to process.  Curses!  I am working on it.  I don't want to be the teacher from Ferris Bueller's Day Off.  "We call this blank economics.  Anyone?  Anyone?  Voodoo economics.  V-O-O-D-O-O economics."  I do need to ask those more important thought provoking questions like:  Why do you think that?  How do you know?  What if...?  I seem to do a kick ass job when I question in small group sittings and asking those questions.  Now, I just need to translate those into questions to my entire class.  I brought out the ol' craft sticks with names to help me.  And in my Algebra 2 class, the day I actually made a conscience effort to improve my questioning, the learning was better.  I just need to do it!  Dang it!!!  Maybe I should hang a poster up to remind me.  VOODOO with a big red slash ought to the do the trick.  Task number 1:  Be more effective at questioning in my classroom.  Start writing these questions in my lesson plans so I don't forget.

Still on the subject of my students and my concern for them, this year has been a struggle for me to get the results I want.  At progress report time, my D and F rates were god awful.  If I remember correctly, I had 13 F's in my Pre-Calc class out of 39.  OMG.  This has never happened to my students before.  Of course, this was just a snapshot.  Corrective instruction took place and the students were able to demonstrate they did learn it eventually.  This is why my weeks have been so busy.  Now, I do have 12 students who have skipped a year of math to be in Pre-Calc.  15 that are coming from the regular track of math, 2 repeaters who are improving their grades from last year, and 10 coming in from the honors track.  In years past, it was really 2/3 from honors and 1/3 from regular with maybe one or two skipping a year.  All this means is that I have had to slow down.  Not a big deal.  I'm meeting my kids where they are and bringing them along.  Translation:  What I have done in the past is no longer effective this year.  Let's start looking at my lesson plans and revamping them.  And to be honest, they did need revamping.  Task number 2:  Look at my lesson plans.  What worked well previously and what needs to change to ensure all my students are learning?

Which brings me to my third thought of the blog:  Lesson planning.  Intentionality.  Deliberate.  I am thinking I must have naturally just come across a good way of explaining material and creating lessons.  Wow, that sounds very arrogant and I don't mean it to be.  Lesson planning in the past didn't use to be a chore.  What do I want them to learn?  How do I get them there?  Did I cover what I needed to cover for future lessons? etc.  But being intentional and deliberate about the lessons is tougher than I thought.  It is almost like I am a student teacher all over again with myself as the mentor.  I question it all now.  And of course, where I can place that good question now as well as how do I get the third of my class to see the connections they have missed by skipping a year?  Task number 3:  Really look at my lessons, trim the fat, clean lines all the way... and make sure to include the questioning.

And finally, coming full circle with my swirling thoughts... how do I lead my department through this same experience?  Blank.  My mind goes blank.  Insert crickets chirping here.  Task number 4:  Help expose what's not working in other classrooms.  Gently and with care and support.  And if they don't understand the first time, give them more support and time to learn just like my students.

We have one more week left in the first quarter followed by our week long Fall Break.  Besides getting ready for a garage sale and cleaning my sons closets of the thousands of toys and clutter, I will be chewing on an action plan.

Tuesday, September 11, 2012

I can't even watch TV without thinking about school

My good friend Melissa is just starting her blog.  In her second post, she writes about measuring time in minutes.  It got me thinking a little, no a lot.  Then, to give my brain a break from thinking about school stuff for a bit, I turned on my TV and tried to watch one of my recorded, hour long shows.  I am watching a summer finale of one of them now.  (And as a side note, the show is getting really good.)  How can they manage to wrap this up in an hour?  Well, actually, the show isn't an hour any more.  You have commercials, etc.  So, the real question is, how can they wrap this up in 45 minutes?

Then - because this is how my brain works - whoa, this is just like my classroom!  I only have 52 minutes to wrap up a lesson, tie up all loose ends, and yet leave my students craving for more.  Whoops, hit pause (because I love my DVR) and reflect on this some more.

Really, let's think about it.  I have a story to tell.  I have only an hour... well less than that because of commercial breaks (collecting homework, office pass arrives, hey you kid - you owe the library a book, etc.)  I need to interest them to come back after the commercials, keep them guessing as to how the story ends, and invite them back for more.  Each day.  It has put a new light on what I have been doing for the past two decades.  Sure, I have had my flops.  But I also have had some real winners, too.

This year, I think I am going to treat one unit as a mini-series.  I want to have a unit like Lonesome Dove.  If you miss one day of class, you will call someone to find out what happened to Sheriff Berg.  Ha, too much.  Now to see what happens to Annie.  Don't spoil it for me, please.

Tuesday, September 4, 2012

Sharper questions

The purpose of models is not to fit the data but to sharpen the questions.  Samuel Karlin
11th R A Fisher Memorial Lecture, Royal Society 20, April 1983.

Imagine a lesson where the teacher comes into the room and says to the class, "Evaluate f(80) for f(s) = 10(s - 65) + 15" without any further discussion.  While students may understand by the end of the lesson to plug in whatever number is in the parenthesis into the function and spit out an answer by means of order of operations to get some number at the end, they may not understand what it really means.  You might get a question of "May I go to the bathroom?" or "I need to go to the nurse" instead of questions that further the topic.

Fast forward to today in my Algebra 2 class where I wrote the following on the board.  "This weekend I got a speeding ticket.  The police officer told me the fine for speeding was $10 for every mile over the speed limit I was going plus $15 to the city government."  Before I could even finish writing, I was barraged with questions like "Did you really get caught speeding?, How fast were you speeding?  Where were you speeding?".  They were actually anxious to solve this problem.  I told them I was clocked going 82 miles per hour.  What was my fine?  I heard answers of $170, $185, and $320.  I asked a student to explain how they arrived at $185 since it was the most popular answer.  Then I built the formula around it.  "So you subtracted 82 - 65?  Why?  Oh, because you wanted the amount I was over 65mph?  Ok.  Then what did you do?  Why?  Ok.  Anything else?  Oh yes, don't forget the city government fee."

As I talked I wrote:

82 - 67
10(82 - 67)
10(82 - 67) + 15

What if I was going a different speed?  What would change?  So if we were to put a variable somewhere, where would we put it and what could we use?  Talk to a neighbor about it.

10(s - 65) + 15

Interesting.  Let's make it a function since we have been talking about functions.

f(s) = 10(s - 65) + 15

What does this f(s) mean?  Excellent.  I love that you said it was the fine I paid depending on the speed I was going. 

What if I wrote this f(92).  What does that mean?  Right!  The fine of the speeding ticket for traveling 92 mph in a 65mph zone.  Now, what would be my fine?

How did some of us get answers of $170 and $320? 


And right there I went from concrete to abstract AND they had better understanding of the concept because there was meaning attached to it.  Hot dog!!!!  Now, function notation isn't something that is terribly hard.  But every year I have a handful that seem to struggle with it.  However, as I checked on their progress on a story problem they were doing on their own, they had it!

All credit by the way needs to go to Steven Leinwand.  He challenged us in a professional development during the summer.  Take the boring and make it real.  For him, it was real.  He really was pulled over in Vermont, I think.  He said it was the most expensive math lesson he ever had to pay for.

I had to break the bad news to the students that I did not get a speeding a ticket, nor have I ever had a speeding ticket in my life.  They were in disbelief but they did learn what function notation means.  So when I threw problems at them from the Pre-calculus book about the weight of an astronaut with a more complicated formula, they had no fear of it.  I'm amazed it went so well.

So for this particular speeding story problem, I created the model around the data as we progressed in class.  But it wasn't to just mold numbers into some formula, we actually got deeper into what function notation meant.  The students weren't just told to plug and chug.  They had meaning behind it.  I sharpened the questions I asked them and they had better questions to ask.  They weren't bored with rote, lame math.  They were involved and invested.  After all, they did think their math teacher was a bad ass for speeding at 82mph in a 65mph zone.

Monday, September 3, 2012

Hitting All Eight

Lesson Planning... about that.  Yeah, it's gotta be different, too.  With all the change that needs to take place in the classroom this year, that means the ol' lesson plans need to be adjusted as well.  Knowing I will be asking others how the 8 Mathematical Practices from the Common Core Standards (from here on out will be henceforth abbreviated 8MP) are demonstrated in each lesson, I am making it a point to make sure I can point out where the 8MP show up in my lesson.  Here's the thing, not all 8 are in every lesson.  Nor, do I think I can always achieve all 8 into every lesson.  Or can I?  Sigh.  The more I study the 8MP the more I think I can incorporate them all to some degree.  I just have to get out my own way.  I need to revise lesson plans from previous years to allow the students to reach my goal.  Far too often, I was comfortable spouting off info and happy if some of it stuck.  Now, I can't be satisfied with that anymore.  It's not what is good for kids.  It's NOT what's right for kids.

I was doubting myself that I couldn't include all eight.  I had this fear that the only way to achieve this would be to have some problem for the kids to work through, struggle through, and reason through to come out on the other end with a nice formula and complete understanding of it.  I am beginning to rethink that.  Sure it is a great model to use at least once a unit.  But I need to hit it everyday and I don't have a nicely packaged fabricated story problem for every day.  I am stressing about this.  However, I am going to type up my plans with the goal in mind of hitting all 8 tonight.  Pre-calculus will be studying functions this week, specifically what is a function tomorrow.  And Algebra 2 needs to learn how determine domain and range from a graph and write it in interval notation.  I've got an 80's marathon of music playing on the radio.  I'm going to bang out these lesson plans and measure it against the 8MP. 

Ya know, sometimes just getting my thoughts together on a topic is therapeutic.  It's just the self-motivation I need to get me through it.  Rock on fellow bloggers. 

Thursday, August 30, 2012

The Battle with Homework. Victory!

Traditional math class:

Bell rings.  Students might take out their homework and half listen to the teacher read off answers.  They may even hurriedly write down an answer in hopes of getting credit for scribbles resembling answers.  Any questions?  Great.  Here.  You do this, then this, and then this.  Here's your answer.  What else do you need help with?  Then, they pass in the homework to be graded by the teacher.  Usually very little feedback is given.  The homework will be placed in a stack for the teacher to place a check mark on after briefly looking to see if the work is complete.  Ten out of ten.  Good job.  Next paper.  Five out of ten.  When will this kid learn he needs to finish his assignments?  Enter the grades into the computer.  Fill in zeros for the kids who didn't turn in a paper.  WASH.  RINSE.  REPEAT.

Does this sound familiar?  Have you been in classrooms like this?  Aren't you tired of this endless cycle.  Are you the teacher in this scenario?  I was.  I was only because I didn't know any better.  Now I do.

And here is what my homework time looked like this morning: 

"Hey, take out your homework from last night on solving inequalities.  You should have checked your answers last night in the back of the book.  Now, I want you to check with your group mates.  Do you all have the same answers?  Oh, and hey, if you have questions.... ask your group peeps.  Lisa, get off of Facebook, your homework answers aren't there."  I then took attendance, attended to other minor details, then walked the room.  I checked in with each group.  I asked several students where their homework was.  When they responded they didn't do it.  I then asked, "Well, how can you help your peers if you don't do the work or how are they going to help you if you don't bring it?"  I walked around several times and soaked in the rich language the kids were using to help each other.  One final lap, this time with a pad of paper and pen in hand.  "What questions couldn't you and your group answer?"

43, 55, and 59.  Three questions.  That's all I could get from them.  They were so excited that they could answer most of the questions and they could explain it to each other!  By the final few groups, I just held up the pad of paper... Any others?  Nope.  Great!  Then I walked them through those three problems, but not all the way.  I got them to the spot where they could finish it on their own.  And I gave them 2 minutes to finish it up, check with their groups, and check the answer.

18 minutes into class and we were done with homework.  Some students still needed more time to finish up what they didn't complete.  However, they were going to leave class with the ability to do it on their own.

Today during lunch I wrote some feedback on their papers I collected.  But my writing feedback to them is not nearly as powerful as the feedback they gave each other.  BOOYAH!

The best thing I heard today in response to "How can you help your group if you didn't do your work?"  "Oh, but I still can.  I really understood this.  I just didn't have time to complete the homework.  Anna, get your homework.  Which one did you need help with?  See Mrs. Berg, I will still help.  And I promise to have my homework tomorrow."

The worst thing I did today:  I did the three problems.  I should have asked for volunteers to bring their work up on the doc camera and explain how they were able to figure it out.  There is always tomorrow!

How much more involved were my kids today?  Heck ya!  I'm doing this again!!!

Wednesday, August 29, 2012

Pick up the milk carton please.

Warning:  This post isn't really going to deal much with math.  I know, what a let down.  Well, maybe I will find a way to sneak it in.  Who knows? 

This year, my position has changed in my school.  It's exciting and scares the crap out of me at the same time.  I still teach two classes, but the rest of the day I am a math coach for the rest of the school with an emphasis on the math department.  It's exciting because I want to help my department be the best they can be.  I want to help them stretch and reach for that next level of greatness.  My principal has been a huge part of how my teaching has evolved in the past years.  He's been avuncular when I needed it and pushy when I needed it.  I want to share that knowledge with others.  It scares the crap out of me because I don't want to fail.  Because who really wants to fail at something? At anything?

Anyway, I am in this new position and I was out in another teacher's classroom talking strategies for helping with fractions when a third teacher walks into the room.  He's on a tear.  He's upset and just doesn't have anything good to say about the school leadership or the building or just teaching in general.  I stood there for a few minutes hoping it was a storm that was going to pass.  But oh no, he then turned to me and wanted me to personally know how bad he has had it here.  I tried to calm him down, play the "it's not as bad as you say" person in the room.  But he just kept complaining.  I finally left.  He picked the wrong person to talk to. 

This year didn't start off great for our math department either.  I could list, no joke, about 30 things that went wrong since the start of school and ramble on and on how "bad" things have gotten.  However, I have chosen not to.  I choose to make it better.  Complaining about the issues and doing nothing is like eating slimy okra.  Only a few people really like it and then it needs to be cooked just right.  I'm not trying to be vainglorious.  Don't get me wrong.  I do have my moments.  But I get over myself, untwist my big girl panties, and start finding solutions.

It's much like a milk carton in the middle of the hallway.  We could throw a fit about how the school is so littered and the kids don't care.  We could form a committee on how to improve school wide littering.  We could write letters to the district office.  YADDA YADDA YADDA.  Or we could pick up the milk carton as we walk by and toss in the trash.  And by one simple task or solution, we are on the way to making things better.  I'm about finding solutions and making it better.  And as a side note, I don't think things are going "bad".  It's changing and leaving us behind if we don't change with it.

With that being said, it's now time for me to focus on my lesson plans for tomorrow.  Tonight I want to sleep peacefully.  I want to dream of peacefully walking the beach near some Hemmingway-esque Key West village, not fret over the milk carton in the hallway.

Wednesday, August 22, 2012

Linear Functions Foldable

On Monday, another Algebra 2 teacher and I were discussing the sad state of affairs of our students retention on how to graph and write equations of linear functions.  I mentioned I would like to do a foldable on it and began the search through Dinah Zike's Foldable book I picked up in 2010 at the NCTM in San Diego.  I really needed something with 5 things.  Nothing was looking right and I didn't want to settle for something less than what I visioned in my mind.  Then, with 5 minutes left before I had to pick up my amazing kids from daycare today, the idea hit me.  Here it is:

Supplies:  Three pieces of paper.

What to do:
Fold all three using the hamburger fold, one inside the other.  With the crease at the bottom, I cut one inch off the top of the first 1/2 page in order to create a title page and a place to see all the tabs.

Trim the tabs above so you quickly reference the type of linear function.  On the inside I wanted to create a template.  I jotted some scribbles, rewrote the scribbles for this sample, and will type it up officially sometime in the wee hours of "I really need some sleep" and "Why did I have that cup of coffee?".  I will post the electronic copy soon.

Then I filled out a sample page in my son's crayons.  The black pen represents what will be typed.  And the lame hand drawn graph will become a pretty graph, too.  I have filled out what I think I will lead the kids through for slope-intercept form.  Then I just made the template for the other pages.  I really just needed to see how this looked torn apart so I could figure out the copying of it for Friday's lesson.  I will not cover this all in one day.  In fact, it won't be finished until the end of the month due to the special block I have for my A Hour class.  The kids will learn about graphing first, then writing the equations.  I will have them keep this all year long.  BIG IDEA: when I need the kids to graph a line in February and exponential laws and quadratics have filled their brain so they have forgotten how to graph a line, they can whip this sucker out and reteach themselves.  That's the plan anyway.

I was in a hurry to get this on the blog.  I needed something that stated vocab words or what the other variables meant...  m = slope, etc.  I am not liking VARIABLES on the left side of the page, but I don't know what to put there.  Any suggestions would be nice.

I like how you can see the tab on this picture.  The other tabs get increasingly longer, so the vertical lines tab doesn't need any cutting at all.  And of course, it would be stapled in the center.

Well I have an electronic copy of this document.  But I'm not sure how to post it here.

Monday, August 20, 2012

Quick. Think. Fail. Ish.

Today I attempted to use a mind map with my Algebra 2 class.  We went through the notes.  The students worked through the assessment.  We discussed the assessment to fix misconceptions.  I gave them one more assessment question to help distinguish a function and non-function.  Then... well... the thing I was so excited about last night.. the mind map of functions. 

"Draw a circle in the middle of the paper.  Write functions in it.  Then draw four squares.  The upper left is your definition of a function.  The lower left is where you write some examples.  The lower right is where you write non-examples.  And the upper right...."  Well, crap.  Ever draw a blank?  Quick.  Think.  Think.  Think more quickly.  Grab my phone and attempt to find the picture on pinterest?  Where did I put my original?  Think.  Think.  Oh no, three seconds has gone by.  Say something.  "Okay, and in the upper right corner... What does a function look like?  Take two minutes and fill this out silently.  Then we will share within our groups.  Then I'm going to collect this before you leave."    ... I hang my head for those two minutes.  I blew it.  I tried to salvage it.  I had missed the facts/characteristics in the upper right corner.  Que sera, sera. 

I wasn't really expecting these to be stellar since I couldn't remember the first quadrant piece.  But I got some awesome feedback none the less.  I saw which kids really understood it, which kids just copied/regurgitated the notes right back at me, and which kids still had some misconceptions.  I was able to give feedback directly on it.  In short, I will do this activity again.  But next time, I will have the correct information in front of me!  And next time, I will stress the fact it was supposed to be in YOUR OWN WORDS.

Now, to have some sort of activity for the three different forms of graphing a line...

Sunday, August 12, 2012

Full with three minutes to go

School started this past Wednesday.  For the first time ever in my career, all of my students in my first hour were in their desks, eager, and ready to learn THREE MINUTES before the tardy bell rang.  What the heck!?!?!  It's Sunday night and I am still freaking on this.  I actually asked my students if they were pulling a practical joke on me.  Unbelievable. 

Then we talked pancakes.  It went well.  Very well in fact.  They were talking, looking up information on the web, estimating all sorts of numbers and living in the moment of where we entertained a plethora of random questions.  They left class on a quest to discover if the human stomach can actually hold those 62 6 inch diameter and 3/8 inch pancakes.  As a bonus, what is the radius of one pancake with the same volume?

What's on the agenda for this week... laying the ground work for the remainder of the course, finding out what they know, and where holes must be filled.  It's all capped off with an assembly on Friday.

I've got some blogs to read and explore.  I need to prepare a presentation and submit my request to present. I am thinking it will have to do with Twitter, blogging, and essential PD.  Or something like it.

Three minutes early!!!!  I told you I am still freaking on this.

Tuesday, August 7, 2012

A good night's sleep

For the first time in, well, EVER, I will actually sleep well the night before school starts!  I can't believe it either.  I have been stressing out so much these last 4 days.  The endless list of stupid, time consuming, frustrating and just plain pissing me off situations that have occurred would have typically left me in a foul mood.  It's not worth it.  School is starting tomorrow in 8 hours.  And you know what, every one of those stupid, time consuming, frustrating, and just plain pissing me off situations have all worked out.  But that is NOT was this post is about.  Hooray!  This post is a celebration!!  Double hooray!!

With all that happened, I still needed to plan for my first day.  And when I say plan, I really mean dust off the first day of crap I have for the last 8 or so years, refresh my memory on how many trips it takes to transport A number of adults and C number of children across a fictional river with a boat that only holds one adult or two children.  This boat doesn't exist.  Nor, would any of those children subject themselves to rowing across the river 38 times to bring the lazy adults over.  There are child labor laws, you know.  So why am I forcing my students to dive into this abyss of "fun" math problems just to get them in the mind set of doing math in August?   Well, I decided at 4:30pm, I refuse to cross that river one more time.  PANIC.

I have 15 hours to come up with something else, something more engaging.  So, what do I do at 6pm?  I return to my classroom to straighten up my room and hang the many posters on the bare walls.  There is something very therapeutic about mindlessly hanging posters willy nilly on the walls to allow my brain to grapple with finding a new lesson.  And around 9:15pm after updating my course syllabi, it hit me.   We are talking pancakes tomorrow.  This may cause me to fall flat on my face.  Flat as a pancake on my face.

As you know, I attended the "bestest eva" professional development last week.  And you even ordered the book (see the previous post).  Well in Steve Leinwand's powerpoint slides, he talks about the world record holder for eating pancakes.  Tomorrow my plan is to talk about it.  I'm giving them the details and the details only.  Act 1.  They generate a list of things they want to know.  Then, they somehow arrive at an answer to those questions.  Act 2.  They will then share their answers with the class and how they get those answers.  I hope to see at least 3 different approaches for each question like I hoped for the Barbie Dreamhouse on Christmas when I was a girl.  Act 3.  Homework...  I have a couple of questions in my back pocket I want to know the answer on.  They will answer these for homework provided they didn't come up with those questions on their own.  Sequel.  Bam!  What a way to incorporate my two favorite people into my lesson.  Thanks again Steve Leinwand and Dan Meyer.  ((Has anyone every asked if the the two of you are related?))

I'm going to do this with both my classes.  What?!?!  I will do this with my Algebra 2 students and with my Pre-calculus students.  I don't care these two classes are two years apart in ability.  The two ability levels of the classes may or may not create different answers.  We'll see.  I'm willing to take this risk.  I'm willing to lead my students down an alley way just to see what is there.

At 10pm tonight I had my new lesson plans settled.  I was celebrating.  I had my iPod on loud on the speaker phone with "Oh Yeah" playing.  I couldn't help but dance down the hall as the music echoed in its emptiness.  No more stressing.  Time to go home and get a good night's sleep for the first time ever the night before school starts (right after I blog about my night).

Sunday, August 5, 2012

Because it is what's right for kids

This summer has been the busiest and yet the most productive for me, professionally.  In a department of 22 members, 11 have been hired in 2012 (9 just this summer).  I have gone to some AH-mazing professional development this past week.  I have been asked to present to the other 20 some department chairs just what I learned tomorrow in a meeting.  Nothing like waiting until the last minute, right?  Didn't I just say it was the busiest summer for me?

Monday, I attended a district supported session on grading practices.  Five others from my school attended with me.  Steve Ventura presented material from the Elements of Grading by Douglas Reeves.  Oh, how I wish this was more than one day of training!  So much to digest, so little time.

I realize how much of a disadvantage we put our struggling students in when we assign a zero to a grade.  Even the traditional 90 - 80 - 70 - 60 scale isn't fair, if you think about it.  A student has 50 points to show you how miserable they are at math, and just ten points each to show you mediocre, average, above average, and excellent work.  When you give a student a zero for a behavior issue (didn't turn in the assignment, ditched class, etc.), it can impact their grades in such a way that their final semester grade is not an accurate assessment of what they really know.  Or in the case of the student who might need longer to show you mastery of a topic, a low grade isn't showing you the potential they have.  To counteract this, Steve talked about the 4 point scale or even assigning a 50 instead of a 0 to level the playing field.  A few hours was not enough to settle this issue for me.  I need more!  Lots more dialogue with my teachers and experts in the field.  I can easily see now that I should really begin Standards Based Grading.   This however, will have to sit on the back burner and simmer for awhile.  I don't think my department is ready to move on this, not while instruction needs to improve.

However, I am going to ask my department to do several things this year regarding grading practices:

  1. Allow late work.  Allow the student the chance to demonstrate their knowledge.  And if the teacher is having difficulty getting students to turn in their work, then we need to have a hard conversation about ways to either get them to or ways to get around it and still get the data needed.  A zero should only be given if it is the very last resort.
  2. Each subject area will need to agree upon the weighted percentages for homework and tests.  The homework assigned is practice of the material to be assessed.  All Algebra students should have the same opportunity despite which of the 9 teachers they may have.  
  3. Homework (academic practice) should no longer be graded just on completion.  Students need feedback on it.  It can come from teachers or other students.  And showing the answers on the board and asking "Any questions?" is not proper feedback.  (I feel I need an I'M JUST SAYING right about here.)
From the sticky notes left in my binder:
  • All children can learn because of what I do in my classroom.
  • Ineffective teaching and grading practices are like chipping away at granite with a spoon.
  • It's not what the students need to do in my class, it's showing me what they have learned.
And more books/authors I need to research and digest:
  • Beyond Monet
  • Dylan Wiliam
  • John Hattie

And now on to Tuesday...  drum roll please....

THIS WAS BY FAR THE BEST PROFESSIONAL DEVELOPMENT I HAVE EVER BEEN TO IN MY ENTIRE LIFE.  THE.  BEST.  After a day of swimming or riding bikes, my oldest son will walk in the house and announce to the entire neighborhood from inside my living room, "This is the best day ever!!!"  Well, that is exactly how I feel about this training.  I think only winning the lottery could be better.  I'm not lying.

If you have not read Accessible Mathematics by Steven Leinwand, stop reading my post, open up Amazon and get you a copy!!!  No, seriously.  I'll wait...

I wasn't kidding.  Order yourself a copy.  112 pages of pure genius at work in this book.  I read this book this summer.  I found myself saying "NO FREAKING WAY" lots in this book.  It is an easy read, but you will want to pause to think about what he says.  With that said...  Steven himself was utterly amazing.  I felt like a Baptist in a tent revival waving my white 'kercheif around saying, "Hallelujah, preach it, brother!"

He completely gets it.  He gets why our math programs suck.  He gets why we are screwing our kids up.  And he is out there trying to tell us we have screwed up.  He is my superhero.  He could have worn a cape and flown around the room, and that would still not have been as great as the info he shared.  He writes about 10 instructional shifts that need to take place.  I have picked my three favorite. But I am not going to spoil the ending.  You should have ordered the book by now.  When it arrives in a few days, read it.  These are my three favorite:
  1. Make "Why?", "How do you know?", "Can you explain?" classroom mantras.  [By the way, let's throw in "Does anyone else have something different?" in here, too]
  2. Embed the mathematics in realistic problems and real-world contexts.
  3. Take every available opportunity to support the development of number-sense.
Side notes or sticky notes wisdom from this day:
  • We need to build a classroom environment where is safe for our kids to take risks.  If they don't feel safe, number one above will never be possible.  
  • Be deliberate about everything you do.
  • Four areas to start the desperately needed change:
    • Curriculum (cut what you don't need)
    • Instruction (get better at questioning, planning, etc.)
    • Assessments
    • Professional Culture
  • Google PISA released items
  • Google balance assessment library
  • Video tape yourself to give yourself feedback
  • Go visit other teachers while they teach.  Invite them to visit you
Next week sometime, I will be sharing this with my department.  I will ask them to start incorporating some of these changes because it is what is good for students.  It will take some time.  This will not be a sprint to the finish.  This will be a 1500 km race, not a 100 yard dash.  I will be there to model it and to support them.

Math classes today can no longer be taught in the "sit down, shut up, and learn this" method.  It is not effective.  Let me rephrase that.  It. Is. Not. Effective.  For those teachers who are ready, I will ask them to read a copy of the book.  For those who say they don't have enough time, I will ask them to watch someone who does and who is trying out the strategies in the book.  Being mediocre at teaching math is a battle.  I have suited up and am prepared to conquer the ineffectiveness in my own classroom, in my school, and in my district.  

My students have no idea what they are going to walk in on Wednesday when school starts.  May God have mercy on them.  And for the love all that is holy, order the darn book already!

Thursday, July 12, 2012

My advice to the new teacher

Advice for new teachers.  How will you survive your first year?

Where to begin?  Where to filter?  What worked for me, might not for you.  What will work for you, I may not have even thought about.  After thinking about this for a few solid days, the best piece of advice I can give is to get connected.  You have been hired because you know the content and you have been given some training.  But what seems to lack in the current education training world is how to apply the pedagogy.  You will not have the years of experience to tell you where students are going to make errors.  You will not have the experience to use this phrase instead of that phrase to clarify the meaning of a topic.  You will not enter the classroom with the experience of handling everyday situations that become second nature to most teachers.  Yet.  This will all come in time.  It has taken me years, well okay, almost decades to develop into the teacher I am today.  And, I am not finished yet.  There is always room for improvement. 

The one single thing that saved me from running out of the school building at the end of week one and not returning was my connection to others.  The internet was still using dial-up modems when I started teaching, so I didn't have social media to help me.  I had to go face to face with other teachers.  I learned from them.  I watched them on my prep.  I lacked the art of the HOW.  I constantly asked them what would be the best way to present this to where it seemed I was a thorn in their sides.  However, it was precious to me that first year.  It molded me, shaped me, and prepared me for future years.  Throughout my 17 years of teaching, I have always seemed to have someone to bounce my ideas on, to dialogue about the best approach, or to share a disaster of what not to do in class.  Other teachers have been like lighthouses to me, always there in calm weather and there when I needed guidance during the darkest, stormiest, crazy days of teaching.

This summer seems to be very similar to my first year of teaching. I have become connected with others outside my school and district.  I have become a social media nutter.  I have connected with other teachers who are pushing me to challenge what is happening in the classroom traditionally.  I have read, and read, and read books, blogs, and posts to make me a better teacher.  I would like to lead my department of 22 math teachers into a world where students are engaged and learning instead of being bored to sleep by lecture all the time.  I even started this blog to have a place to reflect on my journey.  Some posts I make available for all to read.  Some are hidden just for me.  It's that connection I needed to take my teaching to the next level.  Get connected, stay connected, find new ways to connect.

Friday, July 6, 2012

When is enough, enough?

So, I am sitting here pondering what new things I want to incorporate into my school year this August.  (And, just as a side note, this summer has flown by as fast as a desert storm hitting my house.  Hmm, maybe there is an analogy here somewhere.  I'll come back to that one later.)  I keep festering over the one or two things to pick this year to try or fine tune. My mind keeps coming back to homework.  I have followed a couple of blogs and have been inspired.  The thing is, I am getting in my own way. 

I can't seem to wrap around my stinking brain the part about kids don't need a thousand homework problems a night.  How much is enough?  If they only have 15 problems, is that enough to cement the learning?  Is 15 problems too many?  How do I find the balance of enough?  Can I instruct so well and assess before they leave class to give no assignment?  If I give no homework, how do I know they will retain it?  With all these questions, one thing I know for sure I must do is at least give the feedback to the student on homework.   It seems students painfully sit at home in front of their books, glassy eyed, and praying to a higher power for some divine intervention on how to solve this thing with numbers and variables.  As a math teacher, I don't really want it to be painful.  I would hope that I have clearly explained it that it should be a breeze.  However, for forever and a day, math teachers have always assigned daily homework, checked only for completion, and complained about how kids don't do their homework.  My charge this year is to break that cycle.  I will be flying in the face of my colleagues by challenging their beliefs.  I more than likely will be standing alone in my endeavor although my wish would be a unified front from my department.

Here are some blogs I have been following for the last few weeks.  They are shaping my thoughts on the idea.  Oswald, Nowak, Cornally, and Meyer   All are great ideas and have merit.  (If you have the time, check them out).  I just need to find something that will work for me.   Let me flesh out some thoughts in my head here, let it sit for a day or two, re-read it, re-think it, and revise it.

  • I feel the homework calendar my learning team wants to use has too many problems.  
  • I don't think the book we are using has enough problems for basic practice where there aren't a few weird problems thrown in that are the exception to the rule. 
  • Do I want to generate worksheets everyday for homework, with the exact problems I choose to be on it? 
  • If I do create my own worksheet, I can give feedback better and faster because the worksheet will force some organization.  Some. 
  • How can I change my instruction so that I can assess and re-asses each day how well the students have learned it?  And I think I may have just hit the nail on the head here. 
  • Balance.  
  • I want my students to learn it in class and go home a few hours later and still demonstrate their knowledge without much struggle.  Maybe a quick peek back into the notes. Maybe I allow students to complete as much as they need to have it mastered.  Susy may be need 8 problems and Robby may need 12 while Travis needs 1. 

Time to let it stew for a few more days.

Any feedback would be appreciated. I need to eat my breakfast anyway.

Tuesday, July 3, 2012

I have to start somewhere

I have been teaching math since 1995, but my students haven't really been learning math until 2009.  Quite a difference in time I might add here.  I used to be the typical stand in the front of the room, expect all my students to understand by the time the bell rang, grade homework with no feedback, and thought I had it all figured out high school math teacher.  Well, I did.  But I clearly didn't.

There are several people I really need to thank.  I won't mention them here to save their spouses from a summer of ultra-puffed egos.  But I genuinely and sincerely appreciate the push in the right direction and occasionally a shove or two.

I have learned so much in the past several years.  I have really learned a lot in the last year.  And to help me sort through all the info out there, I needed a place to put my thoughts.  I want to share my success and failures.  I want to grow as a teacher.  I want to make a difference in my school.

This summer I have been like a sponge.  My summer reading includes isn't filled with the fiction I so used to cling to, but rather to professional development.  And yes, I highlight in my books and write notes to myself in them.  I have followed multiple bloggers and flooded myself with following others on Twitter.  I now need a place to share what I am learning.  I am a math nerd and always will be.  I look for the math in everything, which may be annoying to my husband at times.  My seven year old may think we are playing "McDonald's" when he actually learning about place value and number comparison.

I am a mother of four boys.  Yup, God does have a sense of humor.  When asked if I will have any more children to try for a girl, I politely say no and give the following explanation.  I love math so much that I even have my children in a famous sequence.  1, 1, 2.  The next number is 3 and I don't want to risk having triplets right after having twins.  I mean when I have a 75% chance of having at least one girl when I was having twins only to have 2 more boys...  See, math nerd.

So.  It was time.  I needed to start my blog.  I have to start somewhere.  And here seemed like a pretty good place to start.