Pre-teaching

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

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

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

The concept seems sound, though.  

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

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

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

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







 

SBG in a non-SBG world

My school uses PowerSchool and a grading scale which is required by the school board.  I have spoken to both the vice principal and department chair and they are interested in Standards Based Grading, but they also seem hesitant to allow a single member of a department to deviate significantly from what other members of the department teaching the same class are doing with regard to grading. I've been told that I can make changes within the approved structure, but I cannot just throw it away.

Currently grades in the math department are calculated by using the following system:
20% final exam
40% Tests (and these are common assessments, given by all members of the department teaching a particular class)
20% quizzes (there is some wiggle-room here as these assessments are not necessarily common assessments)
10% homework
10% teacher's discretion  (traditionally I've used this as a participation grade based upon warm-up compliance and general participation.)

The first 3 listed above are pretty much written in stone.  These are the ones I really cannot change.  With regard to the 40% test category, we already do give students the opportunity to reassess the complete test (which covers either half or full units).

The common assessment tests are how I will either show that my attempt to implement Standards Based Grading is having an effect or is not.  I like the fact that these assessments will require retention from my students, which I see is a possible pitfall of most SBG systems I've encountered.  I will need to take the "common assessments" we have created and cluster the questions in such a way that I can more easily evaluate student comprehension across the standards, but otherwise these tests will likely be the same as those given in other Algebra 2 classes in my school.  Reassessment will be Standards based rather than whole assessment based as the department currently does things.

I will be modifying quizzes to be standard (or skills) based so that I can more easily determine where a student would need to reassess.  This would allow me to reassess particular skills rather than reassess a complete quiz. Also, my students will be assessed more frequently than other students in Algebra 2.  Students who will need to reassess will not receive a percentage grade, instead they will get strategies for reassessment.  The 10% teacher discretion points will factor in here. 

I want to add an additional kind of quiz as well.  I want to implement what I am calling "Mastery Quizzes". These quizzes will be focused on skills from Algebra 1 (or previous semesters in Algebra 2) in which students should be computationally proficient.  For the first trimester the "mastery quizzes" will focus on solving equations (probably 2 of them) and working with exponents(most likely 1).  These quizzes will contain 10 questions, and students will have to perform at the 90-100% level in order to not have to reassess. In later trimesters these quizzes will include factoring, completing the square and other topics I have noticed that students struggle with when we reach later units (ie, rational expressions and conic sections).  My teacher discretion 10% will factor in here as well. 

Homework:  Here's my thoughts on homework.  I have basically been told homework needs to a component of my grade scale.  So, I am leaving it as 10% (department policy) but I am grading each homework assignment as 1 point (which means first trimester should include approximately 35 - 40 points here). Another component of this 10% will be the Interactive Student Notebook.  The ISN will be worth 100 points.  Lastly, any student getting Mastery level on any standard (skill) will receive full credit (whether completed or not) on the homework related to that standard (skill).  So, potentially it is possible for a student to receive full homework credit and not have completed a single homework assignment.  

What does this look like?  Good question.  Here's a snapshot of my changes:

20% Final Exam
40% Tests (with reassessment on any major standard which is below proficient)
10% Homework (ISN and homework as described above)
30% for quizzes:  Mastery Quizzes will only count toward the 10%.  Standard (skills) assessments will count towards the 20% (department mandated) and the 10% as well.

My original thought were to make the quizzes worth a total of 40% and tests 30%, but it was pointed out to me that if what I am doing works then the 10% shift really wouldn't greatly affect the grades.  Making such a shift, would potentially make comparing my scores with the scores of other classes teaching Algebra 2 difficult and such a shift would also require school board approval which might be difficult given that no one else has tried using such a grading system previously in my district.  

Twitter Math Camp 2013

Ok, I didn't get to go.  Wish I could have, but it would have required more planning than I was able to pull off this year (and my wife had foot surgery 2 weeks ago and has been couch-ridden ever since).

I followed as best I could on twitter and by reading blogs, and now that it is over I can't wait to see what great kinds of collaboration have occurred and what kinds of ideas people have taken home with them.  If you haven't seen the program list then (look here).  Reading through this course list alone gave me ideas on ways to think about what I am trying to accomplish with my own students.  It has also given me a list of things which I really want to see someone, preferably both a presenter and a observer, post a blog regarding. 

I don't know much about GeoGebra, I've heard of it but that is about it.  Looks like something I might want to learn more about.  As I'm looking to use Interactive Notebooks, Megan Hayes-Golding's presentation would have been a great one.  I saw David Wees name in the listing after Megan's presentation, and then saw him on twitter. Next thing I knew I had spent 2.5 hours reading his blog.  Hedge, I'll drop and give you 20 if you share your presentation on your blog.

Even without being there I've been thinking, growing and planning.  There is a whole bunch of us out here who didn't get the opportunity to go, but in a way impossible a few short years ago we were participating. We're teaching during an era where things are changing at an incredible pace.  I'm not sure what changes will come to our profession in the next decade, I do know many of the people who will be helping to make and understand those changes

This post is dedicated to all the teachers who participated in Twitter Math Camp 2013, in person or from their own homes.  

Make-Over Monday ~ Postage

Dan Meyer's Make-Over Monday task for this week is about an example of a piecewise function.  It relates to the cost of postage since 1995.  The original problem gives the students a table, labeled with years and cost in $ (presumably per ounce) to ship a letter to a domestic destination.  (I tried pasting the picture into the blog, but the scale was all wrong...so here's a link instead)

http://blog.mrmeyer.com/wp-content/uploads/130715_4hi.jpg

I submitted a suggestion on twitter on how to improve this question.  First off by posing the question, without taking the fun of finding out the information from the students. I know that doing this would help avoid a pitfall my students seem to always fall into, how to deal with the independent variable. (should you look at 1995, 1999, 2001, 2002, etc OR should you consider years since 1995?)

Secondly, I suggested that the students could also look at how costs for postage have changed in other countries (Canada, the European Union, or its member-states).  Lastly, I suggested that the students could also look at how shipping costs using UPS and FedEx have changed in that same time-frame.

I think this question has another good extension which could be done.  Looking at how the postage costs have changed (since 1995) could be compared to either the inflation rate (another piecewise function) OR the costs of various different products (during that same timeframe).  The natural extension for each of these explorations would be to predict when the next price increase would occur, or how much that next increase would be.  

Of course, the best case scenario would be if you could introduce the original problem (but not how the original problem was given) to the students and if they were able to come up with the extension activities out of their own curiosity on their own. 

Sequences and Series Unit

For me, the sequence and series unit is the third unit we will cover this year in Algebra 2.  I like this unit, because ideally students should be pretty comfortable with linear and exponential equations already (from Algebra 1).  Because of this, my assumption last year was that I didn't need to spend much time reviewing explicit (or as I called them, "function"-al equations).  This was a mistake, I figured out after the unit was done. I'm making changes to prevent the mistake and timing of figuring it out.  

As I am going to be trying to create and use an interactive notebook system with the students in Algebra 2 this year, I figured it would be nice to create a set of cards which I could use with this unit.  My thoughts progressed and as of now I am planning on using 3 different sets of cards, one of which is a set I made for Algebra 1 + 2 last year that only includes graphs. 

One of the other sets will be one in which tables and equations are to be sorted by whether they are linear, exponential or other.  In this way I can get the students looking at 3 of the different representations linear and exponential equations can have. 

The last set includes finite and infinite sequences.  There are 40 cards and most of them are arithmatic or geometric sequences.  (I debated including some non-arithmatic, non-geometric sequences and decided that an other category is a good thing because it allows me to more easily differentiate the instruction for students who need a challenge).  I figure this same set of cards can be used for series as well as sequences, with 2 dice used to identify the upper and lower values for summation. 

I haven't actually written the interactive notebook pages to go along with these card activities, though I do have an idea about what they will likely look like.  I am hoping to get to those pages sometime in the next 2 weeks, though.

sequence and series cards

Feel free to look at them, criticize them, use them.  If you have suggestions, please let me know.  

How do they know how to do something we never show them...

Random thought...actually I was reading a blog on someone who I wish I knew better's site. Research in Practice - Ben Blum-Smith   If you've not seen it, take a look.  Just come back here when you're done.


............

I've seen some D. Ball videos.  I was forced to watch the same one 4-5 times and the little kids are cute, but they're not high school students.  My kids are a little more, um, real.  I've taught from 5th grade right through 12th.  Elementary school kids are much easier, molded.  (I sometimes wonder why I moved up)  She's still a master.

I live in Michigan, and though D. Ball is at Michigan State I still think she rocks, but my wife doesn't (really, just on general principle.  If you lived in Mi you'd understand)

I'm calling this the "Case for Co-teaching" 

Its so frustrating being the only person, in most classes, asking the questions.  Lets face it, at times we're like chess masters playing high-school neophytes.  I hate this.  I've once, in the past 5 years, had a student really surprise me, mathematically.  If only we did a better job modelling having a good mathematical discussion, then maybe they would know what one looks like (and how much fun it can be).

Our choices are to model this behavior in some way... Or, hope that mathematical discussions will just spontaneously begin and allow us to be witnesses of it.  (or you can become known as the weird math teacher with all the puppets and strange voices..)

I've done the "special-ed" co-teaching thing.  Generally with a teacher who is also teaching history and another math class as well.  I love the Special Education Dept at my school, so let me get that out into the open and honestly had I done things differently then I'd be one of them as well.  That being said, they are either stretched too thin,  pulled from the class or honestly ill-prepared and sadly the kids get an opinion about them that unfortunately is true.

I want a teacher, someone who the kids know is in the classroom to come by and visit.  I want 5, maybe 10 minutes of their time.  Just to come by and have a mathematical discussion.  It doesn't need to be scripted out, the visiting teacher would get to choose the topic (and would pre-warn me...seriously, if I've got to talk about the economic theories of Malthus or something I want a little notice).  I want to model a mathematical discussion.  I want the students to see two people work their way through a problem involving mathematics.  Imaging me coming to your class (for sake of argument, my part in any movies will be played by Johnny Depp as he is the teacher I most often get told I look like) and asking you to help me with proving Heron's formula the week before you start teaching proofs to Geometry students. (I promise I won't try and make you change all the "s"'s to "arrrrrrghs".)

I've contemplated the idea of doing this virtually.  Timezone issues make this problematic, though not necessarily too bad as I live in the Eastern Standard Zone.  For teachers in the West, sorry it is not fair. (math teachers will get that, probably no one else).  It does require two teachers willing to follow the same general curriculum timeline (hello CCSS... you've given us the same topics lets see what we do with it). Although in all honesty, it really doesn't.   Better yet imagine Skyping with my class; as students in my class help you introduce Logarithms.  In this way we first model the discussion, then we show students having the discussion with a teacher and perhaps, finally our kids could discuss mathematics with each other. Either IRL or virtually.

Liebster Award

Wow, I got an email saying I was nominated for the Liebster award (actually, now in my comments I have been twice nominated).

So what does this mean?  Well, first of all it means somebody out there is reading!!  Secondly, it means my next blog post is all about the requirements of this award.  Seems there are a bunch of questions and I have to go out and nominate a few blogs to receive the award as well.

The "Rules" to Accept the Award: 

•    Link back to the blog that nominated me 

•    Nominate 5-11 blogs with fewer than 200 followers 

•    Answer the questions posted for you by your nominator 

•    Share 11 random facts about yourself  

•    Create 11 questions for your nominees   

•    Contact your nominees and let them know you nominated them 

Lessons With Coffee (Jameson Michelle) questions: 

1.     What made you start writing a blog?

I've been reading blogs now for about 9 months.  Last year the MTBoS had a challenge for new bloggers.  I was hoping for one for this year and basically harassed Sam Shah one evening on twitter about when it would be and he challenged me to blog 3x a week for the summer.   

2.     What song do you most listen to when you are in need of a pick-me-up?

Lately I would have to say Get Lucky by Daft Punk

3.     Can you name a movie adaptation that was better than the book?

No, I cannot

4.     What children’s book describes the meaning of life best in your eyes? OR What book (children or adult) changed your life and why? 

I've always read so much and pieces of lots of books have helped shape my perspective.  There's a mnemonic device in Piers Anthony's On a Pale Horse involving 5 lines which I frequently find my mind returning to when I am stuck on a problem that has probably influenced me as much as anything.

5.     What obscure pieces of trivia are you most impressed with yourself for knowing?

That there are 8 letters which can act as vowels in the English Language.

6.     What are you thinking about doing for Open House this year?  

Stations.  Having parents do an activity like their kids are doing and getting as many of them signed up on the grade program as possible in one of the stations

7.     What are you thinking about doing for first day of school this year?

I just blogged about this one.  Feel free to go back up and read my last blog posting.

8.     If you had to pick another career what would it be?

Ombudsman.  Plant propagator.  Own my own restaurant.  

9.     Who is your celebrity crush?

Christina Ricci (but not from Casper, like from Sleepy Hollow) Though I would totally like Nicholas Cage to play me in a movie.(not that he looks like me)   My Math Crush is of course Fawn Nguyen

10.  What is your favorite thing about your mate or best friend?

She's very supportive.

11.  What is one piece of advice you would give a new teacher?

Find your own voice.  Each day should be used as an opportunity to challenge your students and yourself. 

 Radical Robin's Questions: (from Flip Learn Share)

1. What was your favorite subject in high school/college?

    In High School, my favorite class was Humanities. In college, it was Geometry (which is odd because I didn't like it at all in high school)

2. Where is your favorite vacation spot?

     In winter it is visiting my family in Florida. In summer it is Little Compton, Rhode Island.

3. What is your favorite book/movie or play?

    There are so many books:  The Bible, Kafka's The Trial, On a Pale Horse, the Joy of Mathematics Series, too many to continue

4.  Why did you become a teacher?

June, July, August.  Just kidding.  I had a math teacher in high school who came in one day and said "I've not gotten this far in the book in too many years. I've forgotten how to do these problems.  We'll work out the first 20 and whomever gets the most correct gets to teach for the next 3 weeks" Lastly, I had a son young and the notion of being able to have a job which allowed me to be with him as much as I could was extremely appealing for a non-custodial father.

5. Do you follow your textbook from start to finish?

Heck, no.  In fact the kids complain that I make them bring it from time to time because I so infrequently actually use it for other than homework.

6. What is your favorite teaching resource?

how about top 3:  projector (sorry I remember chalk all too well), my Algeblocks and my gridded whiteboards

7. What is/was your favorite lesson to teach?

I've got a few.  I do one on scientific notation which is filled with really crude humor and its a lesson in which I have 100% of students on task the entire time, we laugh almost the whole period and scores are always very good on the assessment. (But I would never do it with witnesses present)  I do another one called "Is Mr. Hills Normal" relating to the distribution of heights and its another good one.  I'm short and according to the math I end up within 1 standard deviation of the mean (Normal) every year! (at least when the whole class is included)

8.  What kind of music do you like?

Everything.  Name a style and I'll name 2-3 groups/artists I like.  

9. What is the funniest joke you know?

I'm telling you, that Scientific notation lesson keeps 34 of us laughing and fooling around for 70+ minutes.  That's the funniest thing I can think of.  

10.  How did you choose the title of your blog?

I wanted something for my twitter handle that combined my teaching and gardening interests.  I kept the same name for my blog.

11. If you could live anywhere in the world, where would it be?

Somewhere where I could have 4 seasons, enough land to garden to my heart's content, a stream where I could fish.  Close enough to civilization that a trip into town doesn't feel tedious.  Far enough that I cannot see my neighbors. 

My 11 questions:  

1.  Is there anything you wish you could teach, but don't get the chance to?

2.  Did any teachers when you were in school particularly challenge you, and how did they do it?

3.  Do you worry about continued employment from year to year?

4.  What do you think is the greatest impediment to people becoming or staying teachers?

5.  If you could have your own child in one of the bloggers who you follow's class next year, who would it be?

6.  If you could take your class next year on a field trip, where would you take them and why?

7.  If you're in the middle of a lesson which is bombing, what do you do?

8.  In the past year, approximately how many hours of (real life) professional development have you done?  approx. how many hours of virtual PD?

9.  Are you a member of the national association relating to your subject matter (ie, NCTM)? If so, why. It not, why not?

10.  What is the opinion of your co-workers (about you and what you do) in your department at school?

11.  If you were made superintendent of your district for a day what would you change about how things are currently done?

11 Random facts about me:

1.  I'm short.  5' 5.5"  

2.  I'm the oldest math teacher in my department at school and you'd never know it.

3.  I've taught Science, History, Math, Grammar, Literature, Business and Sunday School.

4. Some people have gambling or drinking problems, I have a gardening problem.

5. I have a poem I recite before each quiz, test or final.  The kids expect it and "remind" me when they think I've forgotten it.

6.  I have 4 kids, an almost 20 year old boy, a 9 year old boy and 2 new children a 13 year old girl and a 10 year old girl.

7.  I cook well, well enough that I've been told I make the best grilled cheese in the world. (and honestly that's not the extent of my ability, I swear).

8.  I cannot eat cheese.

9.  My desk is always messy...  but I know where everything is

10. I never get as much one on one time with students as I would like.

11. I love it when ex-students come back to visit

Blogs I'm nominating: (in no particular order)

1.  Kathryn at Restructuring Algebra

   This Kathryn is a friend on twitter and she is giving a great perspective with regard to trying to apply CCSS standards to Algebra 1)

2.  Kathryn at i is a number

    This Kathryn is a new find for me, but I am very impressed with her energy and perspective on INB/ISN's

3.  Andrew at Social Studies and More

    Andrew is brand-new at blogging, but I follow him on twitter and he is well worth following)

4.  Druin at Stat Teacher Blogspot

    I really should know her real name, but @druinok is her Twitter handle.  this one undoubtedly breaks the rule regarding less than 200 followers, but she definitely deserves a mention!

5.  Jessica at Algebrainiac

        Generous with her creations, been doing SBG for a while, down to earth and easy to talk to.  Well worth a look!!

6.  Amy at Teach Reflect Repeat

    I love the fans!  I really have got to find a way to use these in my INB/ISN this next year!