Show, Don't Tell

I now realize how important it is to make writing a daily part of work in the classroom. Many of the students in my fifth grade dyad placement were struggling the other day, when asked to write an “I Am From” poem.  The poem was scripted, each line containing a prompt, yet the students still had difficulty.  Many almost seemed afraid to write, in fear of “getting it wrong”.  Several of them approached me, individually for assistance.  Generally, I helped the students by asking them a series of questions.  If the line said, “I am from (name something you like to do)” I’d start by asking, “Do you play any sports?  Do you like to dance?  Do you like to bake?  Ride bikes? etc.”  Sometimes it took awhile, but I was eventually able to find a question that “sparked” the students into action (writing).  This made me realize how important it would have been to “brainstorm” with them before sending them "off on their own".  It would have been helpful if I had gone through the poem instructions, line by line, and had the students “brainstorm” together.  This, I believe, would have made the assignment much easier.  I could have, for example, asked a series of questions (the prompts in the poem) to help them come up with ideas.  I know, from personal experience that I also write much better after doing this. 

I also realized the importance of “showing” students rather than merely “telling” them how to do an assignment.  I believe the fifth graders in my dyad would have benefited greatly if I had shown them an “I AM From” poem that I had written myself.  But, Regie Routman actually takes this idea of modeling one step further.  She writes in her book, Writing Essentials, page 47, “Many teachers do their demonstration writing behind the scenes.  They want to do their modeled writing ahead of time, to be prepared.  Then, they show students the finished writing as part of their demonstration.  This robs students of the opportunity to see real-life writing in process and diminishes the learning possibilities.”  She makes the point that students need to see the work being modeled.  They need to see the process of writing an assignment on demand, within a set time frame.   Both of these strategies, brainstorming and “real time” modeling would have, I believe, helped these fifth graders write their poems. 

IPods in the Classroom - An Update

Is it practical to use the iPod Touch in the classroom as an educational tool? 

I’m still struggling with the practicality of giving every student in the classroom their own iTouch.   My main concern is monitoring their usage by students.  How can a teacher ensure that 20+ students are staying “on task” while using an iTouch?  Can a first grader (or 10^th grader, for that matter) really be expected to ignore its other features during class time?   Won’t they be distracted by its other apps?  Is there a way for a teacher to restrict its use? 

Now that I’ve had the opportunity to review several applications I can see their usefulness as a learning tool, BUT, how do I, as a teacher, make sure my students ONLY use the applications they’re assigned to use?   A teacher cannot “see” what his or her students are doing, while working on an iTouch, because  its screen size is so small. 

In my earlier post, I also talked, in particular, about the appropriateness of iTouches for the younger grades.  It still makes me a little uneasy to put such expensive devices in the hands of a five or six year old.  I know the key is setting up expectations for their use, but I’m still leaning toward offering them to students in the upper grades (and possibly on more of an individual basis for the younger ones).  I know iTouches  are somewhat durable, but there is still the issue of whether a child is developmentally ready to use one.  For example, does a six year old understand that the screen could be scratched if placed next to a sharp object?  Do they have the dexterity to plug in the earphones?  Again, my concerns center on whether it’s appropriate to give an iTouch to a young child, without close supervision.

I have no doubt that an iPod Touch is an amazing learning tool; I’m just not sure they have a place in the hand of every student in every classroom, as least not until a system is in place to monitor student use.   

A Roll of the Dice

What did I learn?

I learned a great way to teach about probability in our math class this week.  Instead of merely going through a step by step lesson on probability, students can learn by “experiencing” it for themselves, when playing a dice game.  If two players are awarded chips, based on a certain roll, each player will want to know if they have an equal chance of winning.  Each student playing the game will want it to be fair, so this is a great way to introduce them to probability.  They have a “stake” in whether or not it’s a fair game, because they’re playing it!

At first glance at the rules of the game presented in class, it looked like Player 1 had an advantage over player 2 because he or she was given 7 “sums” compared to player 2, who was given only 4.   But, after closer scrutiny, it became apparent that the “sums” given to player 2 had a greater probability of being rolled. This could be shown mathematically by creating a chart that showed the 36 different combinations of rolled dice.  As it turned out, a sum of 6, 7, 8, or 9 had a 10% greater chance of being rolled than a 2, 3, 4, 5, 10, 11, or 12. This “increased chance” of winning became apparent in our class when player 2 won almost every game (by collecting 5 counters before player 1.) This type of problem will show students the value of being able to solve a probability problem, even if this knowledge is only used to evaluate whether the rules of a card game are fair.  It empowers them to learn to evaluate the various probabilities in their everyday lives.

What do I have questions about? 

How will I be able to constantly think of new and exciting ways to present the different concepts in math to my students, to keep them engaged?  How do I make my students realize that they will encounter math in their everyday lives?

What are the implications for classroom practice?

This exercise, of playing a dice game, clearly shows the value of giving problems to kids that they’ll care about.  If students are given a game to play they’ll want to know if its rules are fair so they’ll spend time evaluating them.   Math becomes fun when students are allowed to creatively solve problems, like determining whether the rules in a card game are fair.  Making math fun can be as simple as having a competition among students in the classroom.  I witnessed this first hand in my dyad placement last week.  The students were working on double digit multiplication math problems.  In past classes, I had watched the students do their “daily check” problems at their desk with limited enthusiasm.  They all seemed to know the various steps, but at times, made careless errors.  Many couldn’t even get through the assigned problems in the allotted time during class.  This all changed on the day they were given the “Turkey Team Challenge”.  Four teams were formed, each competing to construct a turkey on the active board.  The rules were simple.  The correct solution of each problem was worth a particular body part on their turkey; the head, body, right wing, left wing, right leg, left leg, face, and various colored feathers.  To earn the privilege of placing a body part on their turkey, however, each member of the team had to solve a particular problem correctly.   The room was “a buzz” with excitement.  Every member of every group was “on task” as the competed to complete the turkey.   This was an excellent way to keep the students focused on math.  It was educational, as well as fun.  This is a game I will definitely play in my future classroom

What is your Mathematical Identity?

What did I learn?

I learned about a geometric tool called a Mira.  I had never seen or heard of one before.  A Mira has a reflective quality much like a mirror.  By placing it on any shape, children will be able to grasp the concepts of symmetry and congruence more easily.  The exercise we were given in class, to trace a child on a swing, using a Mira, would be one that school children would enjoy.  Making math fun is one of the best ways to ensure that what is being taught is actually learned.

Using pattern blocks for fraction addition and subtraction is also something I learned.  When teaching math classes in my son’s elementary school I had often used pattern blocks to teach about geometric shapes and patterns, but I had never thought to use them in this way.   This was a great lesson and I plan to use these manipulatives to teach fractions in the future.

I also learned, from the assigned reading by Leatham and Hill, that we all have a mathematical identity.   The authors’ assert that everyone has a system of dispositions about math that have nothing to do with their ability to understand it.  For example, if someone views math as a subject where they must be an avid “rule follower,” which has a negative connotation,  the person embracing this idea will be less likely to want to continue on in math, even if they had been successful in their classes in the past.    

What do I have questions about? 

How can we, as teachers, prevent our students from saying they’re “just not good at math”?  How can we show them that everyone encounters math in their everyday lives (when they draw maps, place tiles, solve a scheduling problem, etc.) and that they’re most probably good at it?

What are the implications for classroom practice?

The challenge in the classroom will be to determine the relationship my future students have with math.    It will be my job as a teacher to help them become more aware of their mathematical identities to help them realize that one bad experience in math shouldn’t warrant discarding the entire subject.  I will need to learn how to broaden their views about the nature of math, to help them see its value in many different activities and professions.

Many Approaches to Problem Solving

What did I learn?

In class on October 27^th, I learned that there are multiple ways to approach a problem.  I was truly amazed at the number of ways that the members of our cohort came up with when we were given the task of determining which park location would have the largest blacktop area.  I also learned how useful diagrams can be when solving these types of problems.   After hearing about the two possible park locations on the video presented, I immediately set up a math formula to determine which one would have the largest blacktop area.  It never occurred to me to draw a picture of the two options and then compare them visually. These pictures, however, brought clarity to the solution because, as it turned out, both locations ended up having the same area of blacktop.   When I first looked at my answers, I thought I must have made a mistake.  It took me a minute to realize that taking a smaller fraction (2/5) of a larger area (3/4) of Carroll Park was the same as taking a larger fraction (3/4) of a smaller area (2/5) of Flatbed Park, even though I knew the commutative property of multiplication.

What do I have questions about?  To ensure the success of this type of problem solving session with our future students would it be wise to select groups based on math ability or possibly set up roles within the group to ensure that each member understands the various ways to approach the problem?   

What are the implications for classroom practice?

I see the value of ordering the solutions that are presented to a class of various student groups during a problem-solving exercise.  By doing this strategically, I can advance the students’ understanding of the mathematical ideas presented.  As I teacher, I must take on the role of a facilitator.   It’s important that I monitor the student groups, listen to their strategies and then decide which groups will share with the class and in which order.

Another important implication is the importance of having students solve real problems, ones that they will care about, similar to the one in the video, about two local parks.  If this is done, the students will be more engaged in finding solutions.