Math – Winter Quarter Reflections

As I approach the beginning of my full-time student teaching, I am excited and a bit anxious.  I have taught more whole class math lessons than any other subject, so I should be most comfortable there, right?  In my 5^th grade class, we use the Envision curriculum and it moves quickly with each lesson following the gradual release model (OLM) with demonstration, guided practice and independent practice.  Reflecting back over our intermediate math methods class, I know that I need to start doing more to augment the curriculum.  The frightening truth is the quote from the Lotan article on Group Worthy tasks that "one dimensional tasks require the same skills and the result is uniform success for some students and uniform failure for others."  The curriculum (at least how I have been using it), feels one dimensional and I need to focus attention on how to add to that.

This quarter, we have talked a lot about different ways to be “good at math” and the necessity of having multiple entry points into a math topic for our diverse populations of learners.  We talked about the importance of leveling the playing field so that socioeconomic, language and ability levels are blurred.  I want to be able to randomly group students so that they benefit from working with a variety of different students.  I am constantly trying to remember who I can put together and who I can’t.  Random groupings make a lot of sense and will simplify the process.

Manipulatives, virtual and real played an important role in our readings, class discussions and video reflections.  We have some manipulatives with the Envision curriculum, but they are mostly used for “games” at the end of the units.  I want to start integrating their use throughout the lessons to help get more of our students engaged in the learning.  I also found out that there are virtual manipulatives embedded into the on-line textbook.  We are all so busy getting familiar with the new curriculum and “getting through” the material that we are not using all the different modes we have to connect with our students.

I tend to be a planner, but I need to continue to get comfortable with the reality that sometimes things do not go as planned.  I need to be more flexible in my lessons, more flexible in my approaches and more flexible in my math thinking.  Our cohort has shown me that we all have different ways to approach math problems and now my students are showing me the same thing.  I need to get comfortable in being able to go where they lead and then bring them back as needed.  That journey can be uncomfortable but is how students create their own meaning.

Finding the ZPD for our students is one of the most important challenges that we have as teachers.  That continuum from boredom to anxiety is one that I see in my students faces everyday.  My own experience over the last two quarters tells me that I can be in a different place along the continuum on different days depending on the lesson, my background knowledge and a variety of other factors.  I know that some days, I was in the ZPD and that is what we want for our own students.  It won’t happen for every student everyday, but we need to be close enough to know that if not today, tomorrow.   

The more I know, the more I realize what I don’t know and that can feel frustrating.  I am going to try and relax and enjoy my student teaching experience.  This is what I have been waiting for!

ipod touch - final thoughts

     Perhaps the fact that I am not too broken up about giving back my ipod touch tells the story.  Quite frankly, it has not lived up the potential that I anticipated this quarter. I know that part of the issue is that I have been busy and rushed and I have not devoted as much time to trying to find ways to incorporate this tool into the school day as I would have liked.  Another issue is that the wireless in my classroom was not always fast or reliable (when I finally figured out how to use it).  A related issue is that the classroom computer usually could be used to check out google and with greater ease and visibility. However, for most of the quarter I have been hard pressed to incorporate using one ipod touch.



I have liked the audio recording device and wish I had a smart phone that could do that for me.  There are so many opportunities to use this feature that I might have to consider some alternatives.  The dictation and dictionary.com and google translate saw only "testing" in my hands.  I did use the Merriam Webster dictionary  (no internet required) last week and it worked well.  I used it to look up the Latin roots of equilateral, isosceles and scalene triangles.  It helped me give my students a way to help them remember what these mean and augmented my lesson on triangles. 


I am still very intrigued about the possibility of the touch just on sheer engagement alone.  My daughter thought it was the coolest thing that I was using a touch to help my teaching.  She is NEVER without it and as I have said before it is THE accessory of choice in her tween crowd.  I have also found that even in lower socioeconomic circumstances, it is something that kids own.  This device is powerful and I suspect as the price comes down and the availability goes up, access will not be an issue.  I think it is a tool to continue to think about in the classroom if everyone had one.  Only now, I will have to wrestle my kids to use theirs.

Complex Identities

OK, I admit it, I like 1970s worksheets.  I am comfortable with them anyway because it is what I grew up using in math classes.  It is good to come full circle and realize that our students will be at an advantage because we can give them a variety of options for learning and understanding geometry.  They can “play” with shapes on the computer or make drawings with a pencil on a piece of paper.  We can provide the definitions of the concepts first, or let them do some discovering before labeling the shapes.  We have more tools at our disposal and we need to get familiar with all of them and make them available to our students so there are as many entry points to math as possible.

The measuring activity was enjoyable too.  It was great to use a variety of everyday objects to “measure” the rectangle.  I appreciated hearing the different thoughts about why the graph of the measurements was linear.  It was a great way for me to deepen my own understanding of measurement, graphing, algebra and slope.  Nothing fancy required here, so it is very accessible.  This helps me as I have been concerned with the availability of some of the math software in our schools.

I really like the idea in the complex identities article where “helping our students become aware of their mathematical identifies can empower them to make that relationship more meaningful”.  My school is having a math week later this month and there was a staff planning meeting about it this week.  I proposed to my master teacher that our class have a math community building activity.  We would we talk about all sort of different mathematically related activities (the table in the article).  We then have an opportunity to have our students consider and talk about the activities that they are good at doing.

I will be reviewing some other math activities that we might include.  Some pictures of  the Fibonacci sequence and connections to nature are floating through my mind…..

ZPD and Engagement

It is good to have some practical examples of what the ZPD might look in a math class.  Boredom on one end when math is too easy and anxiety on the other end when math is too difficult.  The ZPD looks like a pretty narrow target and I believe it is going to take some practice to hit the bull’s-eye and engagement is critical!

Going to the computer lab was a good example of how we might engage some of our students in different ways.  Geometers sketch pad was a lot of fun and would allow some of our students a different entry point for geometry. I need to review my geometry vocabulary as I had my kite and rombus a bit confused.  Using DASL in conjunction with  Fathom 2 was a great combination for engagement for statistics and graphing.  We have already talked about how using real data can allow students to connect and create meaning in ways that “made up” data sets does not allow.  I think analyzing data is lot more important that being able to graph data and this is a brilliant way to enable that to be easy.

I did ask my high school senior and he has never used any of these tools.  He attends a pretty resource rich high school (Issaquah), so it does give me pause about the cost or feasibility of schools using these to engage students.  He does have the same TI graphing calculator that he has used since middle school.  Although he has never hooked it up to a probe to do motion analysis, he has done something similar with Loggerpro that he tells me is pretty cool.  My understanding Loggerpro allows a variety of sensors (thermometer, ph, etc)  to plug into hardware that connects to a computer for graphing.  So maybe it will eventually be at our fingertips, or smart phones.

He was good at math.....

I have been struggling to focus on math (and school) this week.  But today I realized that Tyler’s story is full of math connections.  Tyler struggled academically but was a passionate and successful lacrosse player.  His desire to play at the college level resulted in a switch to a small private school this year.  He had recently been accepted at a Division II school in California where he was going to play lacrosse.  Last week a car accident took his life and ended those dreams.

I remember the first time I met Tyler’s mom, it was at the parent meeting for lacrosse when our boys were high school freshmen.  We met in the coach’s classroom, he used to split his time teaching math and phys ed.  The coach was pretty intense and I remember he spit out a lot of statistics about his team.  Patty whispered to me that Tyler was not good at math and maybe the coach would be able to help him out.  I remember telling her to have Tyler check in with my son Aidan, he was a “math kid”.  That was before I knew all the ways you could be good at math.

Tyler had an amazing ability to see the entire lacrosse field and know where all his teammates and opponents were located.  He was a defender (like my son), but his talent for always being where the action was earned him a spot on the varsity as a freshman.  In addition, he was the guy to go to when you needed to restring your lacrosse head.  This is an art that requires patience, hand eye coordination and 3 dimensional visioning – a kind of puzzle.  This week, I learned that Tyler also knew all the starting NBA line-ups and their jersey numbers. 

He was a fabulous lacrosse player and he was good at math.  He will be missed.

Comprehension - next steps

S. is a confident 4^th grader who enjoys and identifies with being a reader and a writer.  She reads and writes at home for pleasure and she is supported by a family of readers.  S. reads different genres including historical fiction and adventure.  S. is fond of animals and her cats inspired the Fuzzball the talking cat story.  She has been known to create books to give as gifts and last year she gave her Mom a book for Mother’s day.  Her love of plays and acting contribute to her love of language.

The testing we have done to date, confirms that S. is a skilled reader.  On 1/25, we did a running record while she read The Mouse and the Motorcycle (grade 4.4 on the AR scale).  S. had 98% accuracy (based on 6 errors/300 words) and none of the errors affected meaning.  In addition, the QRI testing on 2/1 showed that S. read 139 words/minute putting her at the 75 percentile for 4^th graders.  In that passage on Amelia Earhart, she scored in the instructional range based on 7/8 questions correct.  She was also a 4 on the NAEP fluency rubric for qualitative measure of fluency and expression.  In her retelling, I scored it as a partial retelling (3) based on the 7 phrases she included in the recap of the story.

Regarding a lesson, I would like to take a deeper look into a story with S.  As Routman says “most students do not read deeply” and I have had glimmers that this might be true based on some superficial retellings.  In addition to the Amelia Earhart piece, S. has given us another retelling of a fictional story (Mouse and the Motorcycle) that was event focused as opposed to character focused.  I might base a lesson on character development and determine if S. can really connect with the characters and understanding why they behave as they do.  I would focus on inference to uncover if S. can read between the lines to understand a character’s motivations.  I have no information in this area.

My thought is to use Tovani’s double entry diary as an easy tool.  I would have S. fold a piece of paper down the middle and make two columns.  On the left would be specific quotes from the text with page numbers (alternatively it could be a summary of a section.)  On the right would be where she would write I infer…..  I would model how to do this out so that my teaching is explicit.  We could then do one together before letting S. go back to her seat to do more on her own.

Ipod touch revisited

Well, things have not worked out quite like I had planned regarding using my ipod in the classroom.  I thought I might be able to use some kind of combination of Dictation and Google Translate for R, for translating modifications to his homework.  It has not really been needed.  R. just does the math computation and skips the word problems, his English has improved considerably in the time I have been gone.  It also took me a couple of weeks to be able to access the wireless network in my classroom.  My teacher does not use it, so I needed to seek help from another teacher.

I did get the opportunity to use my ipod with H.  He was struggling to complete a science assessment that consisted of two short answer questions about labs from the previous week.  H. was inside during recess to get that completed as he struggled to get it done during class time.  My MT was out of the classroom and he turned it in to me with virtually nothing on the page.  I tried to coax him into giving it some additional time and he could not.  I then asked him if he might be able to talk to me about questions from the lab and he agreed.  I did record his answers on my touch.  Unfortunately, my MT told me that he did not have “voice recording” as an approved accommodation (he has a 504) and in addition, she is trying to get him to write and does not give him alternatives!  I ended up transcribing his answers to the assessment so that she could determine how much he understood from the lab.  She gave him a 2.5 (just below benchmark) for the assessment and felt it was helpful.

I have not used the touch for C, to extend science in any meaningful way.   I did use Google to get a quick picture of a plateau to assist my MT while she was teaching.  The concept was confusing given the pictures we had and so I found a picture and put the ipod under the doc camera. 

I have used the ipod to record the six science interviews I have done in class.  All the students were engaged and intrigued that I had this device as part of my classes.  It has allowed me to focus on getting to know the students and not have to worry about taking notes.  I will continue to look for opportunities to use the ipod touch in my classroom as a means of differentiation.  I will look to my cohort peers to see how they are using the touch.