Math - A culmination of thoughts and experiences

Over the past weeks this quarter, I've blogged about exercises and ideas that could be used in the classroom and I've also blogged about how I might (and did) try to use these ideas in my actual main placement.  What I have learned over time is that I am still learning!

In some respect, it looks like I've thought of our weekly class sessions as workshops with really great ideas that could be implemented in our classrooms.  Sometimes I didn't think ideas were ELL sensitive, but overall, I wanted to take these ideas to my main placement.  I always complained that my main placement teacher hardly ever conducts group work projects.  I loved how we learned about students working together in groups and  through inquiry, they taught themselves through exploration.  What a great way to teach a lesson!  Many of my students hate math, and I thought that these types of group work lessons would be a way to grab their attention and interest.

Little did I know, my main placement teacher was not on board with my ideas.  Though I was hurt by the lack of room to experiment with different ways of teaching, I understood that this is ultimately her classroom and she is responsible for their learning.  What I have learned is that whatever we students take from our sessions should be taken into consideration before implementing.  We are not expected to change the world as student teachers. For me, it feels as if I'm just learning how to be adequate!  Having the math guidebooks might be more of a blessing than what I used to think of it:  something that hindered me from teaching with creativity and sensitivity to special needs students.  The ideas and exercises that we learned about in class are things we keep in our arsenal and one day, when we are comfortable and accomplished as working teachers, then there will be a place for these ideas.

Math Identities

It was interesting to read from the article "Complex Identities" that some students think they need to be creative to be good at math and some students think they need to be obedient to be good at math.  It was also very interesting that when asked to place a classmate on a number line (from good at math to not good at math) it was comparatively different to where that actual student placed himself/herself.

I thought about my classroom, given this information.  Then I thought about the time my master teacher told me that I shouldn't spend so much time guiding a particular student.  "He gets it, he's just not a focused student most of the time.  You don't need to pay so much attention to him."  As soon as she said that to me, I had a hard time dealing with that.  How could I just let him go without aid?  I could see on his paper that he was not giving the right answer to the math problem.  I know she doesn't want me to lose time (she feels pressured in math to stick to a timeline) and to make sure that if I have the majority getting "it" then I have to keep moving on.  But after reading this article, I still maintain that I can't, in good conscience, leave a student behind like that.  What if, to her, he "gets it." But in reality, he is playing a really good act and fooling her?  It's something to think about...                             

GeoSketch

The geometry game we played in class was a worthwhile tool.  I was very fascinated with it!  So fascinated that I sometimes found myself placing more importance in finishing my puzzle rather than listening to the lecture!  Whoops!  I suppose that is good enough evidence that GeoSketch is a powerful tool.  If adults are so entranced with this tool/puzzle, I can imagine that students would be interested in these puzzles.

I really like the puzzles because you really do have to know shapes and the definition of those shapes.  For example, I did not remember what makes a rhombus a rhombus.  In consequence, the puzzle would not be right and I had to remove all of my shapes.  I had to start all over again because the rule of the rhombus would not allow me to get the right angle I needed to fill up the overall shape.  Hopefully though, as a teacher you are not giving a lesson while you allow the students to experiment with the GeoSketch.  Otherwise, the students may not pay attention to you while the work on their puzzles!

Math Playground

I was just wandering around the internet and came across this site, mathplayground.com.  I found it to be really helpful - a really good resource for math teachers.  If you have computers in your room (and you are one of those teachers that actually turns them on and let's students use the computers), this would be a nice tool to use for those students who finish early or if you have free time (in my class, the teacher implements a "Friday Free Time" reward in which the students get about a half hour or so to play leggos, draw, play make-believe with stuffed animals.  Being able to play math games would, in my mind, be more productive).  It has games for kids, manipulatives, math work sheets for teachers, and math videos.  I tried the manipulatives (thinking blocks) and it was really interesting.  There are side notes to help tutor the student (if help is necessary).  And it's okay to get the answer wrong!  In fact, it's a safe place to mess up because the "tutor" helps you to see your error.  It doesn't hurt your grade or embarrass you in front of other classmates during an actual lesson.

Math Lesson (Observation)

My lesson went really well!  I was a little bit surprised that it did because I was up all night worrying and fretting over how I might screw it all up.  The day before my master teacher suggested that I teach the lesson before my observed lesson, just so the kids get used to me teaching math with them.  That lesson didn't go well, so of course I was worried the observed lesson would flop as well.  I suppose the extra nerves was in my favor because I studied my lesson plan over and over again...until the wee hours.

However, when I gave my master teacher my proposed plan, she basically told me to change the lesson.  I had chosen not to go with the teacher's guidebook lesson and try a differentiated lesson (which is supplemented in that book) that involved a collaborative group project.  On one hand, I do understand the pressure she is undergoing with math.  I think she is a lesson or two behind schedule.  On the other hand, I was hoping an internship would allow me to try out different ways of teaching so that I may be able to find out what kind of a teacher I would like to be.  So far, I feel frustrated that I hardly ever get to try out new ways of teaching.  I understand that it is her classroom and that I am a guest in her classroom, but I also thought the understanding was that I would get a chance to "mess up" here and there and experiment, try out different teaching methods.

We are learning about all the great ways to get students to learn in a collaborative group setting in our courses, but I feel very frustrated that I never get to try these methods out in the field.  The students hardly ever get to do group projects or work together as teammates.  Maybe this'll have to be something I try out after I get my tenure.

Mira! Mira!

Look!  What a fascinating tool!  After discovering that this math tool has been around for decades, I've wondered if I would have looked at math differently when i was in elementary and junior high school.  I'm pretty sure I would have loved it!  Math was always so boring and mundane.  It wasn't until geometry that I (somewhat) enjoyed math.  Before learning rules and theories, we found evidence with our rulers and protractors.  All other math classes, math was just about memorizing formulas and plugging in numbers.  School is all about experiencing, discovering, and learning.  Tools like the mira make learning fun and interesting.  It's a little sad that there are so many math tools and manipulatives for students, but they are seldom used or seen.

It is difficult, though, when you are a realistic teacher, with a realistic budget, with a realistic time line, and with an instructor's math guide with play-by-play steps.  As a first year teacher, I am almost positive that I will do everything by the book.  I just hope that I don't get used to or comfortable with that routine.

Questioning Strategies

As I am counting the days to my first observed lesson (a math lesson), I am aware that I need to ask the right questions to engage my students, keep them interested, and help them to successfully organize their thoughts.  I never realized how much energy and thought goes into asking the right kind of questions.  The article, Never Say Anything a Kid Can Say! gives a plan to use specific questioning techniques when teaching math.

Of course, one of the techniques that I like is "Never say anything a kid can say."  I see that this goal sounds simple, but my master teacher hardly ever does this in her class.  It is very hard to find patience and time to let the students do all the thinking and questioning.  Especially when you are a few lessons behind or trying to finish up the lesson before transitioning to another subject.

I have tried this technique as I'm walking around the room while observing, though.  I really see how taking ownership in their own thought process, rather than listening to the teacher explain how to fix this and that, is more beneficial and rewarding for both teacher and students.

Keeping an Open Mind

I did have strong feelings about how that math session went -- the anxiety of being called upon, not having enough time to think a problem through, pretending to understand a problem for the sake of time or to save face.  But after observing my main placement's math sessions, I wish they did math differently (like the kind of sessions that I had once disapproved of).  This is what I witness every day:  a direct instruction from the teacher, the students working on their own white boards, the students instructed to work on practice sheets on their own.  I am pretty excited to try out this method that I've felt so uneasy about!  I want to put these kids into small groups so that they can talk to each other and support each other!  For the past few months, the kids have not been good friends to each other.  They hardly ever get a chance to be in groups in anything together during class.  I am interested to see if this beginning of splitting them into groups will help their relationships with each other.  If they can be put into groups for math, they can make sure each member understands the math problem (if they are unexpectedly called upon).  They are also responsible for supporting each team member if/when a member is called upon.  I am very glad I am opening up my mind to this method of teaching.  For this class, I think they would really benefit from working together.

Small Group Math Discussion

From this experience, I saw just how important it is to feel safe and welcomed with one another.  Our group completely forgot to make introductions, and I think it really threw our behaviors off.  For one, I did not feel comfortable probing the students further with their explanations because I did not feel a connection with them.  We hadn't put in the time to get to know each other, and we were kind of like strangers throughout the entire discussion.

One student did something very unusual.  When he gave us his thought process, as to how he counted the dots, he told us that he chose to group the chunks the way that he did (which was extremely random) because he knew no one else would count it out like he did.  I wondered why he would want to do that, be competitive like that?  I wondered what the class community was like in his classroom and if it was something that needed to be improved.  I know that our small group really needed to improve on community building.  I think it is really necessary to have a safe environment when we're talking about our ideas.  We need to know that our thoughts will not be rejected.

Lesson in Kindergarten Math

What a great lesson!  For my observed lesson, I combined a read-aloud with a math activity.  First, I read the book, Elmer, by David McKee.  It's a cute story about an elephant who looks very different from the rest of his herd.  Instead of regular elephant color (gray), he is patchwork colors.  Elmer does not like that he looks different, so he runs away.  When he comes across some gray-colored berries, he decides to cover its juices all over his body to make him look regular elephant color.  When he returns to the herd, the rest of the elephants didn't recognize Elmer.  When it rained, Elmer's identity was revealed, and the elephants were so happy to see him again and laughed because they all thought Elmer was playing the greatest joke of all time with them.  They decided to name that day the "Elmer's Day Parade" and celebrated by painted their bodies with beautiful patterns and designs.

For the math activity, I decided to review the concept of patterns.  The class had been introduced to patterns recently, so I knew they would be able to understand how to create a pattern.  We looked at the last page of the book and described all the patterns that they could see.  Then, on an elephant coloring page, the kids were instructed to create their own pattern, of their choice, using shapes and colors.  Together, we talked about AB patterns, ABB patterns, AABB, patterns, and so on.  It was pretty evident that they (or at least the majority) remembered how to make a pattern, so I handed out a blank elephant to each student and told them that we were going to have our own "Elmer's Day Parade," and they made such beautiful elephants!

 Of course, there were a few that did not show to me that they knew how to make a pattern.  With those kids, looking back on it now, it would have been a good idea to give them the option of working with blocks or some other types of manipulatives.  Perhaps they just did not care to color?  Perhaps the concept of patterns was not fully learned yet?  I am not sure, but I think it would have been worthwhile to give another option to those students.

Math Anxiety

For the first few sessions in our K-5 math class, I have been relatively comfortable.  I'm learning new ways of thinking, and actually realizing what exactly I'm doing when I do these unusual steps:  carry the one, borrow a ten.  It's been eye-opening.

Ever since last class, though, I have been extremely anxious.  We had middle school math, and though I've always been extremely comfortable with fractions, I did not enjoy what I was feeling at all in class that day.  We also had a new teacher who had a very different way of teaching than our elementary teacher.  I felt so nervous the way she'd randomly call on us to give her answers.  Though this is nothing new to me, I've seen this done in classrooms all the time, I felt nervous experiencing it for myself.  I kept thinking, "this isn't very ELL friendly."  As an adult, I actually felt like not coming to next session!  If I was in high school, I most likely would have skipped if I knew there wasn't a quiz or test planned.  I'd just study hard at home and avoid the uncomfortable spotlighting in class.

In a way, this was an eye opener, too.  For me, personally, learning these new ways of thinking requires me to think longer.  In this new class, I did not feel time was a necessity.  She spoke quickly, explained quickly, and went off on tangents quickly.  It was easy for me to drift off if I could not keep up with her.  That, also, made me nervous.  If I didn't listen to her, she would probably call on me (with my luck), and I wouldn't have an answer.  How unprepared and embarrassed would I feel?  Today's second session with her will be interesting.  I'm very anxious about it.  I hope I will keep up and think fast!