Frog, Log, and the Questions that Ensue...

Yep!  Tonight was one of those nights when I really needed to be pulling together my unit 1 plan for my algebra class, I found myself completely distracted.  I blame the orange flippy frog that was staring me at me on my desk and the empty toilet paper tube sitting next to it.  It was not my lack of self discipline! :) 

Anyway, I started playing with the flippy frog instead of working diligently.  I then started wondering if the frog could make it over the toilet paper tube.  I thought it was a solid experiment and worthy of exploring.  So, I did.

What I noticed was that sometimes, he didn't make it over the log.

Yet, other times he would make it.








Now, I realize that it doesn't take any great skill to know that this would happen.  It fact, a small child probably could have told me what would happen.  I started wondering if the frog was more likely to make it over the log (aka toilet paper tube) or not to make it.  I hypothesized that it would be an equally likely chance that the frog would make it over the log.  Well.. at least theoretically, it should.  The operator plays a huge role in changing the chance of the frog making it over the log.  My frog failed to make it over the log the majority of the time. 

I could use this idea for a demonstration of theoretical v. experimental probability, but I wanted more to the lesson.  So that led me to the question, at what distance is it improbable that the frog will make it over the log?  At what distance is it almost certain that the frog will make it over the log?  What then is everything in between those two distances?  Are they all capable of producing the same probability?  Where does it change?

Well, that led to another experiment.  I made a little "football" style field.  I marked lines at 1cm intervals and tried to find some answers to my questions, but I was left unsatisfied.

I feel like my students could determine a distance where it is improbable that the frog will make it over the log and where it was almost certain.  I'm not sure that the data in between those points can be determined as easily without quite a bit of experimentation and data collection.  There is nothing wrong with doing that, but I am wondering if it is an activity that will be valuable for the time that it would take.  I was playing for over an hour.  I know that we could do some group collection of data and analyze that.  There would be value in doing noticing and wondering. 

I am feeling unsatisfied by the results though, and it bothers me.  Maybe because it seems that there should be a simple answer.  However, maybe I am looking for a simple answer when their isn't one.  There is even the possibility that the experiment doesn't support what I want to know and I need to revise. I'll have to keep thinking.  Data and probability won't be until mid-year.  Plenty of time to develop, modify, or throw out this idea.

If anyone has any thoughts on any of the questions that I posed, I'd be open to hearing your thoughts.  I will be thinking about this some more.  If I develop this farther, I will post what I did and anything that I used to guide the students. 

A Final Thought on TMC...

Oh boy!  I have been reading a lot of blog posts about TMC.  The biggest discussion has centered around a post by MrKent800 entitled, "I'm a Fraud".  There is a lot of discussion about this and posts in response to it.  If you haven't read it, go and read it. 

I read the post by Mr. Kent and felt sorry for him.  I wanted to offer words to sure up his confidence, because I don't think that one conference makes you feel the way that he did.  Other things have to have been happening in his classroom and professional life.  I also empathized with him a great deal because even last year, there were times when I wanted to throw in the towel and quit teaching as well. 

The thing is, when teaching is a part of you, you cannot just turn your back on it.  Yes, you get tired – to the point of exhaustion.  But, even at exhaustion, I am willing to try one more thing.  Do one more thing.  This is because I haven't completely given up on myself.  I know that I can do better.  I can be better. 

I am striving to be the best that I can be.  I use other teachers who I work with or who I religiously read their blog, to help me define what the best is.  Each person that I was a bit star struck by at TMC has helped me to refine, shape, polish, destroy, and rebuild what my definition of best is. 

I know what my strengths are and what my weaknesses are.  After fifteen years in the classroom, I know what weaknesses probably aren't changing.  I need to find ways to counter my weakness so that it does not hold me down and keep me from changing, or at the very least, trying to change. 

As I think about TMC and consider the reflections of others, I am realizing that I can't change the world.  But, realistically I don't think I ever truly believed that I could.  I just want to help the people in my little corner of it embrace the possibility of what can be.  I don't believe that I am great at it.  I just keep talking about what I know, what I believe, what I want to create and hope to achieve by it's creation.  I don't expect miracles.  I don't even expect huge amazing changes because I have come to realize after working in many different situations that I am the only one who can change.  If others chose to follow my example, so be it.  As for me, I will continue to seek out people who inspire me, challenge me, and support me.    

Twitter Math Camp 2014 (TMC14)

Last summer, I had been blogging for about 4 months when I read about Twitter Math Camp (TMC).  I had read a wrap up post or two (OK, maybe more than that) about TMC and thought it sounded like a really cool experience.  So, I wanted to make sure that I was able to attend this year and check it out.  As a first time attendee of TMC, I wasn't totally ready for this experience and this is why:

1) No Lurking Allowed!  It's Time to Share and Collaborate!
I am such a wall flower in new situations and I like to sit back and just observe.  Well, I tried that and within the first 5 minutes of the whole event starting, one of the organizers, Shelly I believe, approached me and asked why I was standing against the wall all alone.  I was shocked by this!  I fumbled through a nervous answer.  I had never been to any other conference where people had been concerned that I was alone.  I had been to a lot of events where I could just blend into the background and not be noticed.  I knew networking and meeting people was a huge part of the TMC experience, but I had planned to ease my way into it.  Didn't happen that way and that was a good thing!  I shook more hands, exchanged more smiles, and met more people than anywhere else that I have ever gone. 

Also, I have never been to a conference where I spent three morning session blocks with the same people all three days.  This is the hidden gem in TMC for me!  This was what changed the TMC from being a conference to being a collaboration.  Teachers were creating, asking questions, defining, debating, reshaping, and collaborating everywhere.  This is how community is built – in the exchange of ideas and rallying around a common cause.  Everyone at TMC was there to learn something from each other and to support each other in making mathematics education better.  It was hard not to start talking to someone about something.  Also, it was a room full of 150 passionate math teachers and where else you sit and talk with any person in the room about math?!

2) Star-Struck and Finding New Stars!
I wanted to go to TMC partially because I had been reading the blogs of many absolutely amazing teachers.  I wanted to be able to sit and chat with them and glean their knowledge for next year.  Well, it took all of my courage to tell Sarah, from Math=Love, that I loved, loved her blog.  I have stolen, I mean borrowed, so much from her.  I sat one person away from Julie, who writes I Speak Math, at a session and couldn't tell her at all how much I enjoyed reading her blog.  Then, I had an entire session with Katheryn, from i is a number, and said nothing!  I was NOT expecting to be so tongue tied!  So disappointed that I failed to introduce myself to the people I admire and strive to emulate in my own way.  But then, you meet all of these other great people.  People that you can't believe you never knew existed and are amazing!  I know that my blog reading list has just lengthened and I am really going to have to get better at Twitter.

3) The Hotel is Like Vegas!
I didn't stay at the hotel that almost everyone else stayed.  I was traveling with my dog, so I needed to stay in a pet friendly hotel.  I didn't realize until the end of TMC, how much interaction and sharing happened in the hotel after the sessions were over.  I wish that I had know this as a first timer to TMC.  I also wish I could tell you all that went on at the hotel, but I believe the saying was "What happens at the hotel from five to midnight, stays at the hotel", so I am not any help!  Although... there are some pictures floating around that show the Twitter math campers sitting in circles sharing interactive notebooks with each other! :)

So this year, as a newbie, I wasn't ready for everything.  My biggest take-away from TMC14 is that there is a huge support system on Twitter.  These teachers are totally awesome and are collaborating to make their classrooms better.  There is no need to worry about if you are a good enough teacher or even think that you have nothing to contribute.  Besides being able to put faces to Twitter handles, I left TMC14 feeling like my classroom is moving in the right direction.  I haven't fully processed the entire experience yet.  There are speakers, sessions, and games that I want to share, but they will have to wait for another post. 

Daily Mantra

Photo credit: www.hark.com

Does anyone remember Stuart Smalley from Saturday Night Live?  He had a little mantra that he said in every skit: "I'm good enough.  I'm smart enough.  And dog gone it, people like me." I know someone read that line out loud to their computer as they read this! :)

I have been reading a lot about growth v. fixed mindset in different blogs and tweets.  The other day I was thinking about how to increase my students' growth mindset when they come in with a fixed one.  I started thinking about self affirmations.  Would having a daily mantra that affirms their ability to succeed help change students views of math and their ability to do it?

I jotted this down on the back of an index card.  I kind of like it and am seriously considering using this to start my math classes this school year. 

Today is a great day to do math!
I am a mathematician.  
I know that being fast is not the same as being smart.
I know that I am smart enough to do all of the math that comes before me.
When I struggle, I know that I have the support of my peers and teacher to work through the frustration and succeed.
I know that success is not given; it is earned through hard work and dedication.
Today is a great day to do math!

Does anyone use a daily mantra or self affirmations in their classroom?  What have you observed?  I would be very interested to hear from you!

Out With The Old...

Well, I finally decided that I am going to remove the problem solving category from my grade book.  That isn't as horrifying as it sounds.  For many, many years, I have been giving students problems that would stretch them and get them to think a bit more creatively.  This was to be done independently of class time.  Some years, it has worked brilliantly and other years it hasn't been as successful.  I just feel like this has run it's course and is time to try something new.

As my classroom transitions next year to a blended and then flipped classroom, I am realizing that I will need to differentiate much more than I am currently doing.  I also need established tasks for independent work time or for fast finishers.   What I have done in the past just won't cut it for next year.  I have also been reading a lot about standards based grading and I am realizing that I have a great opportunity to replace something that needs to be gone with something that can tell me more about my students understanding.

The one hurdle I kept running into was the book.  Saxon isn't totally designed for how my train of thought was going.  As I was flipping through the teacher pages, that I've never really read, I found a list of lesson by topic.  As I examined the list, I decided to go rogue and not follow Saxon lesson by lesson.  I know it isn't recommended, and yes, I may regret this, but it is worth a shot right now.  So I am offering my apologies to all of the Saxon Algebra I users who are yelling at me as they read this.

The beauty of freeing myself from following lesson by lesson was that I was able to create.  I started looking through an old Transition Math and CPM Foundations of Algebra, Year I textbook that I had and found some inspiration.  I put some twists on a few of the ideas to match the standards I was teaching.  Once the creative juices were flowing, I was getting more and more excited about what was appearing on the paper before me.

Here is what I created.  I am excited to use these in place of the problem solving I have been doing.  I am hoping for a richer experience for my students and myself!

Hot Topic Thursday...

My head has been spinning the last few days.  I have been trying to start organizing units for next year for my algebra class.  It has been a lot of work especially if I want to continue making strides with standards based grading and holding my students accountable for mastering the standards.  I have so many directions that I want to go and I am still working to prioritize in addition to deciding what I can actually manage.

One decision that I made about next year is that I really want to structure some specific extra help time after school.  I am thinking to resurrect "Hot Topic Thursday".  Every Thursday there was a specific topic that students were struggling to master.  I started this because I noticed that students would come for help and have no idea what to ask, even with prompting, and couldn't advocate for themselves.  I also noticed that some students were simply shy, uncomfortable, or reluctant.

"Hot Topic Thursdays" started as a way to make coming for help more comfortable for the students I described previously.  With each Thursday having a specific topic, students were able to identify topics that needed more clarification.  It helped them to be able to advocate for themselves by simply walking in the room.  I also encouraged students to bring someone with them which reduced the anxiety of being the only one.  I also told them what we were going to do, but kept it loose enough to make changes if needed, when they came.  Students knew that they weren't going to do worksheets.  We usually used manipulatives to clarify topics.

I found that more students came and brought someone else with this structure.  I was able to work with them more intensely than when we were in class and the students asked more questions.  There was a lot of piggy backing off of other students questions.  The conversation was good and students made progress.

If you are interested, here is the flyer that I sent home with students:



What structures do you use to encourage students to come in for extra help?

What's My Function?

The bottom x value is a 3.  It isn't very clear.

A few years I switched schools and in that move, lots of stuff ended up in my office area at home while it waited to go to it's new home in my new classroom.  Well, some of it never made it and after looking at it for the past 3 summers, I finally decided that it was time to dig through what was in the boxes and start organizing or throwing.

Here is a little gem that I came across in the files.  Writing the function rule from a table was a challenge for this particular class, so I had them make these cards.  Everyday, a new student posted their function table and the class worked to figure out the rule.  We then posted it for students to use for review on their own.  It was great practice, but it took a lot of time!  I think that is why is is still sitting in the file because it would impossible that I just forgot about   it! : )

I started thinking about this because I liked the premise of what I did.  So I came up with two alternatives to use instead.

1) Students would find a new partner each day and practice finding the function rule of their partner's card.  It would allow the opportunity for the students to practice coaching.  Also, it gives them an opportunity to explain their thinking and get clarification from a peer if needed.

2) Students could put the same information onto an index card.  They could do a mix 'n' match with them.  I could collect the cards and redistribute everyday and do a quick 5 minute review.  The index cards could also go into a station activity at a later time.

There are probably more ways to use this that my summer brain isn't coming up with yet.  Does anyone else have an idea of how to use this in the classroom?

What the Newbie Learned about Standard Based Grading...

So last year, I made my first attempt at moving towards a standards based classroom.  I began very small by listing the learning goals (standards) at the top of each test and then breaking the test into sections.  Each section contained only questions relating to that standard.  This is nothing new to me, but not something that I put into practice very often.  I heard about doing it years ago from my guru, Rick Wormeli, at an AMLE conference or SDE conference. (I love hearing Rick present!  He energizes and challenges me.  Go see him if you haven't!  I'll stop gushing now.)  Here is an example of what I was doing:

 

After a year of doing this consistently on every test and quiz, I learned the following three thing:

1) The test really wasn't enough to demonstrate mastery. 
In all honesty, there was a part of me that was hoping the test would be enough and I could say that standards based grading was a breeze.  Ha-ha-ha! That was a nice wish.  Next year, I have to focus on the assignments that I am giving and how they help me see what my students know.  I do a variety of activities, but I need to reexamine how I use them and why I am using them.   I am also thinking that less may be more when it comes to what goes in the grade book. 

2) My scale of 3, 4, and 5 was just renaming the traditional grades of 60-100%. 
I began to realize as the year went on that I was bringing awareness to the standards being learned, but not really standards based grading.  I need to keep working on a rubric that reflects the students' journey towards mastery.  This has been tougher to develop than I thought it would be.

3) It is hard to do standards based grading in a traditional, on-line grade book.  
I managed better than I expected, but I didn't feel a traditional grade book let me record the up and downs of working towards mastery.  I need to track this outside of the on-line grade book.  Just not sure what will work for me yet.

I am at the very beginning of standards based grading.  I plan to take what I learned and improve upon it.  Thankfully, since standards based grading isn't mandatory, I have time to develop standards based grading in my classroom.  That is a luxury I am not taking for granted. 

Algebra Zoo

It's hard to see on the picture, but the fish are Cs.

As I was cleaning out files today, I came across some pictures of the "Algebra Zoo" that students had made a couple of years ago.  I use the "Algebra Zoo" to give students a visual of why we can't combine two different variables.

The "Algebra Zoo" goes back to my eighth grade algebra teacher, Mrs. Ryan.  Mrs. Ryan was from Ireland and she had red hair, an Irish accent, and told fabulous stories.  I really liked her because she had silly stories that helped me remember important ideas in math.

Mrs. Ryan asked us one day, "What is a zoo like?" and we said the normal things like a lion, bear, giraffe, cages, animal shows, etc.  She then asked "What animals are put in each cage?"  She then went on to ask something like, "Why wouldn't you put the lions and gazelles together?" and the obvious answer was that the lion would kill the gazelle.

The dolphin forms a U!

Mrs Ryan used her metaphor to explain that trying to combine 4x and 5y was like putting the lions and gazelles together.  It would never work and wouldn't end pleasantly.  They were different creatures and they couldn't live peacefully together in the same cage.

She did stress that x and 5x were the same creature, but they looked different.  They were special and lived peacefully in the same cage.

I love that the monkeys are Gs!

That idea has stuck with me since 8th grade and I have told that story, or at least some version of it, to many students.  I have only been having students make pictures that we display as a reminder for the past few years.  It is silly but it really does help some students.

When I give this assignment, I ask the students to be creative.  I ask them to try and make their animals look like the variable they represent.  I expect that it is colored and neatly finished.



I also tell them that although x and x^2 look the similar, they are not the same creature and cannot be in the same cage together.  It is always interesting to see what they can come up with in their pictures.

I will admit that this is cutesy, but sometimes, cutesy just works! :)

Kahoot! is a Hoot!

So, at the end of last year, I was reading through the posts on Edmodo that other math and social studies teachers had posted.  One that caught my eye was about Kahoot!  Several teachers commented and talked about the fact that their students loved it.  I was intrigued and looked into the site.  First off, I found out that it was free which fits perfectly into my teacher budget.  Next, I found that it was super easy to use and didn't take a lot of time or work to make a review/quiz which fit into the hectic end of year schedule that I had.  Finally, I discovered that my students loved it!  It surprised me, to be quite honest.  The first group I tried it with was my least math loving students.  They were totally into it and wanted to play more.  I decided that if it could motivate my students that didn't love math, maybe it was worth using more often.

Kahoot! can be played on a computer, a laptop, an iPad, or a cell phone.  As long as you have access to an internet connection and web browser, you can play from anything.  Here is a quick walk through of Kahoot!  I took a lot of screen shots so you get a feel for the game part of the site.  I was also in the preview mode, not the full game of the literal equations review/quiz that I had made.  The cell phone is only on the side when you play a preview of a review/quiz.

First of all, Kahoot! is full of reviews/quizzes that other teachers have made and shared.  If you didn't want to make your own, chances are you will find something that you can use.  This is a screen shot of a search that I did for equations through the public reviews/quizzes that are available from other teachers.  I found a lot of reviews/quizzes that are available and I do not even have to take the time to make them! : )

When a review/quiz starts, the students are shown the game pin.  For this game, it was 50964.  Students go to kahoot.it and they will be asked to enter the pin.  Also, the pins change each time you play, so you can't just write the pin on the board and use it for every class.  Yep, I tried that and it didn't work.

 

Students are then prompted to enter a username.  I know when I do this next year, I will assign the group names to the students.  This was the most time consuming part.  As students enter their username, it appears on the screen.  When all of the students are entered, push the start now button and the review/quiz will begin.

 

The question comes up without choices to give students time to read it before the choices appear.

Then the question with the choices comes up.  On the students screen they just see the 4 boxes (red, blue, gold, and green) with the shape in each colored box.  You can set the amount of time students have to answer the question.

Kahoot! shows how the class did.  If, I remember right, the students also see if they are correct after everyone has answered on their device screen.

This screen shot just shows what it would look like if the answer was wrong.  Since I was the only one playing this game, it looks a little funny.  I liked these screens at the end of the review/quiz because if I was using it for error analysis, I could see how many students/teams in the room were making a particular mistake.  It was a quick "dipstick test" to see where understanding was.

Another feature that I like is that 2 answers can be correct.  Actually, all 4 could be correct if you wanted it to be.  In this screenshot, I had E/R=I and I=E/R as correct answers.

After the correct answer is revealed, the scoreboard is revealed.  Students really loved this!  There was a lot of motivation to do the next problem if you came in 2nd, 3rd, etc. place on the last question.  I was surprised that even my struggling students were working to solve the problems and didn't give up.  Competition was motivating!

At the end of the game, the final scoreboard is shown and students can see how they did.  I just gave the first place team eternal bragging rights, but next year, I think I will have a prize of some sort.

After the final scoreboard, there is a feedback form that students can fill in about their experience with the review/quiz.

The final screen declares the winner.  I like that it says how many right and wrong the team/individual had.  I think it helps to see that no one is perfect all the time.  Speed usually causes even the best students to mess up.

I usually don't talk about a website to this extent, but this is actually one that I am excited about and think it will be useful next year to switch things up and do something different.  

Mathematical Conversations

Mathematical conversations are a technique that I learned over a year ago, but never put it into practice.  This year I am going to give it a go and I am hoping that it helps some students solidify vocabulary and procedures.

The technique is pretty simple.  The teacher writes a script that the students will read in partners or triads.  The students then put on their best acting abilities and read the script with each other.  The script should be read through at least twice and students should change roles.  The script does not have to be long, but should be focusing on key vocabulary, procedures, or concepts that students aren't understanding.

After students are comfortable with the way a mathematical conversation should be in the class, they can try their hand at writing their own for the class to read or acted out by the authors.  It is a great way to get writing happening in the math classroom!  Student written or teacher written scripts could make a possible activity for a station.  Several scripts as stations could be a review activity as well.

My first attempt at trying to write a mathematical conversation is below this paragraph.  I picked the topic of subtracting integers because it is reviewed in the text and I know that this was hard for the kiddos last year.  As Algebra students,
they have to be comfortable with the subtracting integers.  My conversation is longer than what it should be.  In reality, it should be less than a page.  I just wanted to try and bring in some conceptual understanding too.  I am also debating if I should go with the traditional rule of "add the opposite" or stick with the "keep, change, change" rule that I went with last year.  For consistency, "keep, change, change" really is the better choice.  If the conversation would be useful to you, you are welcome to it.

Reflection on Vocabulary

Tonight, I was trying to narrow down the 28 vocabulary words in the first section of my algebra text to a more manageable 13 or 14.  I was actually having a hard time because I know that all of these words will creep up again on my students on a test produced by the text or on a homework problem.  When I looked at the 28, I was having a hard time deciding which words should be cut.

Therefore, the mess above started.  I thought if I could draw out the connections and determine the words that would be connected together the most often, I could narrow it from there.  My mess of solid lines and dashed lines started to draw a very clear picture for me.  It confirmed something that my gut had been telling me the last couple of years.  The words that I think are the most important and vital to students future math classes doesn't agree with the publisher's opinion all the time.

After creating the mess of lines,  I took out my highlighters (because every teacher has more than one) and highlighted the words in yellow that had the most connections from/to them.  The orange are words I think my students really should know for the future and are part of a standard.  I realized that there are words, like closure, that I would stress to the students because it popped up in homework and on the tests produced by the publisher.  One reason the students always struggled was due to lack of connection with the other lessons in the first section.  Closure only connects to counterexample and there should be a line up to sets.  Other vocabulary can be connected to other terms in other contexts.

Looking at this mess of lines, I am realizing that this might actually be a really good activity to do with students.  I could start a flip chart on my interactive white board and we could revisit it after every lesson and add the new vocabulary and draw the connections on the board.  Students could also keep an ongoing chart in their INBs.  I am thinking through my keyboard right now, but I am starting to see some possibility here.

Does anyone have a good way of narrowing vocabulary?  Love to hear your ideas!

Definition Doctor

The first lessons of the text book are so heavily packed with vocabulary that I found myself going back to my bookshelf and looking for ways to practice, and not just memorize, the new vocabulary.  I found a strategy called "Definition Doctor" in a book entitled Style and Strategies for Teaching Middle School Mathematics by Edward J. Thomas and John R. Brunsting.

"Definition Doctor" piggybacks off of a technique called Vocabulary Knowledge Rating, or VKR.  In VKR, students rate their knowledge of the vocabulary on a scale of 1-4.  My sample is at the right and yes, there are a lot of vocabulary words in lesson one!  There are 28 vocabulary words in lessons 1 through 10.  I need to whittle the list down to an essential 13 or 14.  

For the "Definition Doctor" technique, students use the words that they rated in their VKR.  One student volunteers to be the "Definition Doctor" and another student chooses a vocabulary word from the list and asks the "Definition Doctor" to define and explain why the word is important to the lesson or unit of study.  If the "Definition Doctor" is stuck, they may ask another classmate for a "second opinion" to get some help.  After the definition and significance has been given, the student who chose the vocabulary word becomes the "Definition Doctor".  Practice continues like his until all the words have been reviewed.

When I read this techniques, I loved that it asked students to make connections and put a value on the vocabulary.  The word really is important to understanding the material!  I also liked that the activity has flexibility to be a large group, small group, or pairs activity. 

I wanted to make "Definition Doctor" feel more like a game, so my students would review all of the words.  I can totally see them reviewing 2 or 3 words and then chatting for awhile until I came to see what they were doing or listen to their group.  By putting the vocabulary onto cards, the technique had more of a game feel.  If it was a game, then there is a start and a finish.  The cards would need to be gone through before they could stop.  It's not perfect, but better than just choosing off of a list.  The cards also let me focus the practice to specific words because I can take out words I don't want my students to focus on.

The template that I used to make the cards is here.  As always, if it will be useful to you, you are welcome to it!