## Thursday, August 21, 2014

### So, a Polish exchange student walks into a math class...

First and foremost, I am having the time of my life in my math classroom right now.  I am teaching 4 sections of Algebra 2, one section of AP Calculus, and one section of AP Stats.  I am being spoiled with having nearly all juniors and seniors, which make for much more mature discussions.  It's not all easy, though.  There is still the undercurrent of students who trip daily over understanding that going from -1 on the number line to 8 is 9, not 7.

This is not going to stop me from being overjoyed with what is happening in my room.

I am a few days ahead of some of the other teachers and needed to slow down and needed to catch some students up.  We just finished a lesson yesterday on writing an equation of a line in a slight variation of the point slope form (y = m(x - x1) +y1).  Some kids have fallen through the cracks and needed attention.  Today, instead of pressing forward into our next lesson, we stayed put and focused on the homework that I was collecting.  Today, they presented the problems in groups from the front of the room with the document camera.  The students had the first 10 minutes of class to work in their groups to look over the entire worksheet and fill in the gaps with each other.  In the past, this has been a classroom management nightmare for me.  The kids, in the past, would just copy the one person's paper and zero to little conversation extended past, "hey, let me copy what you have for number 6."  Today, that was NOT the case.

In one class, Jimmy says to his group, "I just started and I am behind.  I don't remember any of this, but I am willing to try.  Can anyone explain the first one to me and let me try the next to see if I get it correct?"  One of his groupmates responded, "Sure, we will all help you.  It wasn't easy at first for any of us, but we are finally getting it when we work together."  HOLY FREAKING COW!!!!

In another hour, a group that sat in the back noticed a girl in the front was alone today due to the absences of her groupmates.  They asked if for today, they could have the other girl with them so she could have someone to discuss the math with.  BAM!!

Other things I heard from allowing them to work together:

• You mean, that is all I have to do?  Oh, man this is easy now.  Thanks for helping me.
• Dude, look!  The constant rate of change is always delta y over delta x.  You know, the change in y divided by the change in x?
• So, if we want to find the length of the candle at 5 hours, plug 5 into the x spot here and do the numbers.

Then, came time for them to explain it to the class.  After first class's miserable experience, I adjusted the rules for the remainder of the day.
1.  All group members go to the front and everyone must share an explanation.
2.  Mistakes are okay.  In fact, I am praying for some mistakes to be made so we can talk about them.
3.  All explanations must be of quality.  I don't want, "I took this and put it here and got that" (arm motions involved).  Use complete thoughts.  I took the constant rate of change and plugged into the formula for m...

I was floored by the kids!!!  They were awesome.  We celebrated the easy right answers and found mistakes and shared how to fix them.  We even helped a group get through a problem on which they didn't have a clue.  The struggling students starting catching on to the content.  The middle of the road kids gained confidence.  And the eagle readers of the group shared their knowledge with the others.   They left a little bit more confident in their understandings of a linear function.

But the best part.... during the last class of the day... I inherited a foreign exchange student from Poland who was finding the Honors Algebra 2 class too difficult with the language barrier and joined me sometime last week. Allie pulled me aside and said, "Mrs. Berg, I know I know how to do this problem and that it is right.  I just don't know if I can explain it all in English."  My response, "Well, do you want to say it all in Polish?  I think that would be REALLY cool!!"  Allie, "Really?  Okay.  I will.  Thank you."

Even though I could barely understand exactly what she was saying (let's be honest... I only understand when she said 'delta'), her explanation with pointing and her work was dead on!  And the kids were so involved with what she was saying, they too understood what she was doing!!  So, a polish exchange student walks into a math class and teaches the problem in her native tongue and students could still understand it!

Is it Friday?!?!?!  Because it sure feels like my weekend arrived early!

## Sunday, November 17, 2013

### Statistically speaking...

Ever teach a class blind?

That is how I feel I am teaching AP Stats this year.  It is a new prep for me, as well as a new class at our school.  I am the only one teaching it at my school.  There are only 10 students in the class.  I love it and I hate it.  I feel like I am just keeping up with the material.  This is not unexpected.  I knew going into this, it would be difficult.  I just never imagined the material would make any sense until I had to teach the Stats Unit for Algebra 1.
I am truly in awe of how the mathematics connect.  There are lessons I teach that teach me something more about the beauty behind the math.  I count on it every year.  It's a perk of teaching.  Well, last week it hit me while driving home.  Algebra to AP Stats.  Who knew?  I look forward to seeing what else I can connect this year.

## Wednesday, November 13, 2013

### Why do I blog? Why haven't I for almost a year?

Okay.  I have been motivated as previously posted to start blogging again.  Here is an excerpt from Kate Nowak's blog that has been rolling around in my brain since she posted it.  Damn you, Kate.  Well, okay, it should be more like "THANK YOU, KATE"!

From Kate's blog:
Ahem. If you would, comment on this post and share with me some things:
1. What hooked you on reading the blogs? Was it a particular post or person? Was it an initiative by the nice MTBoS folks? A colleague in your building got you into it? Desperation?
2. What keeps you coming back? What's the biggest thing you get out of reading and/or commenting?
3. If you write, why do you write? What's the biggest thing you get out of it?
4. If you chose to enter a room where I was going to talk about blogging for an hour (or however long you could stand it), what would you hope to be hearing from me? MTBoS cheerleading and/or tourism? How-to's? Stories?

1.  I started reading other people's blogs about math two summers ago right before they had their Twitter Math Camp.  I was jealous I couldn't go.  They seemed like so much fun and full of great ideas.  It really started with getting a twitter account and following Dan Meyer.  I saw who followed him and followed his followers.  That's where and when it all started.  Then, I was inspired to start a blog.  I had no intention of anyone reading it.  I still don't.  It is really for my own thoughts.  I hope to encourage myself with my successes and revamp my teaching through my failures.  Then there was the initiative to post on my blog once a week.  I made some good connections with others.

2.  Humor keeps me coming back.  Frankness of others keeps me coming back.  Success of others ideas and just reading what others are doing (because I am nosy like that) keep my eyes glued to the email box for when new posts are available to read.  I don't usually comment because usually has said it much better than I could and posted the comment 30 seconds before I could.  I know it's not a race to comment.  My 4 favorite bloggers in no particular order:  Kate Nowak, Dan Meyer, Matt Vaudrey, and Sarah Hagan.  By the way... Sarah Hagan rocks it!!!  She's a brand new freakin' teacher and has it going ON!!!  I would like to hire her for my school.  I would like to hire all the above people to teach at my school.  It would be my teaching fantasy line up!!!

3.  The biggest thing I get from blogging is relief.  I can empty my thoughts onto paper, well okay screen, and not have to have swirling around in my mind any longer.  The biggest reason I haven't continued blogging is time.  I am so freakin' busy.  That is not a valid excuse anymore.

4.  I would go into a room just to hear Kate read from the phone book.  I am not a stalker, I swear.  I might have a little math crush going on with her though.  Mostly because she reminds me of a dear teacher friend of mine who was so influential to me and my teaching.  I aspire to be a teacher like her.  I would love to sit down and have a cup of coffee or tea or a beer with her.  I have lots to still learn and lots I can still learn from her and her blog.

I have lots more to do tonight.  I at least have this done.  My evaluation by my new principal is tomorrow.  I am sure I will have some reflections to share.

### Almost a year

I would like to blame my lack of blogging on lots of things.  But, the blame is all on me.  I need to carve out the time.  And being inspired by Kate Nowak about just needing to get back to blogging.  I have been on the perimeter of the MboS looking in and wondering what it would be like to jump in feet first... Much like a little kid being prodded by their parents to jump into the pool.  Here I am again, testing the temperature with my toe.

Three, two, one...

And it's time to load up my children into the car, get them to school, and then get myself to school.  And alas, the firewall at school does not allow me to write there.  I shall continue this tonight.  I need to answer some questions that Kate posted on her website almost a week ago... but they keep spiraling in my mind.  And this is my first clue I need to start writing and get them out.

## 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.

WAIT A SECOND!?!?!

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
versus
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.