One view of a "hook".

I know I am not supposed to do this but I delivered a lesson on Friday.  I showed the class how to calculate residuals and root mean square error.  I did it at my cooperating teacher’s request and we both knew for the sake of the class I could turn to him at any point.  Basically the department had a worksheet that the Algebra 2 classes were going to work on during class and I was going to walk them through it augmenting it with the residuals and RMSE.  Between periods my CT gave me pointers and the lesson got better and better but the real lesson for me was when my CT gave the exact same lesson to the AP stats class (weird coincidence but a gift for me).  He was able to walk the seniors through it in 20 minutes with a super smooth delivery.  He admitted that it would have taken him a whole period with Algebra 2.  The beauty of his delivery was that he wasn’t really talking about residuals and errors rather he related how lazy he was and how he just wanted some way to calculate some values and know how accurate they would be.  This was his hook, I did not have a hook; I just gave the facts to the students.  His hook was not some inviting, senior in high school approved hook but it put the whole concept in such straight forward language I think it just eased everyone into the lesson.  This is a skill I need to be aware of and develop.

Ideas for interactive whiteboard uses.

Sometimes technology can offer you a lot, but how do you learn to use technology beyond the obvious ways you think of using it?  An example I love is using a microwave oven to boil water.  I would never have thought of that application of a microwave but in the absence of a heating element it is a brilliant application of a microwave oven.  How do you discover applications of interactive white boards to metaphorically boil water?  When I posed this question to my cooperating middle school teacher she immediately lead me to iTunes and various podcasts including a category called activtips and general searches on “Smart board” and “interactive whiteboards”.  This is a great way to start to get a sense of all the creative things teachers are doing on interactive whiteboards.  I think podcasts are going to be my starting point for creativity in my active whiteboard use.

Writing Story Problems

If you think solving word problems is difficult, try writing them in a way that is appropriate to the lessons you are teaching.  We tried to engage the students by having them write “silly stories” where they invented their own word problems based on an equation.  Many satisfied the “silly” requirement but few wrote a story that actually fit the equation.  I was charged with editing some of the best stories, changing the numbers into a worksheet to create equations from the stories.  I struggled with the stories.  Given a story I can easily build an equation but creating a story from an equation is harder.  I think fundamentally I think symbolically and I need to practice more non symbolic ways of representing mathematics.

Creating Meaning

I saw two similar manipulatives for creating meaning from symbolic manipulation.  The non technology manipulative uses integer chips which are manipulated as positive and negative 1’s to add and subtract positive and negative numbers.  The technology analogue to the chips is the virtual use of integer chips on an interactive white board.
I struggled to understand the balancing of an equation through the use of the virtual chips on the interactive white board. I think that is because I learned to balance equations in a pure purely procedural way.  Clearly I have some meaning attached to my knowledge of mathematical balancing procedures but this meaning leans heavily toward a symbolic meaning.  The chips, both real and technological, are creating a different meaning.  This meaning is a bit visual and easily translated into something real; the chips can be put in your pocket while the symbolic representation cannot.  I think there must be more manipulatives that offer other non symbolic ways to build meaning for different learners.
The translation between the manipulative and the symbolic can be rough for some learners.  One boy was struggling to apply balancing to the equation -24 = 8y. He really wanted to divide the 8y by 24.  The teacher kept bringing it back to positive and negative chips in boxes but I was not sure that way of considering it was helping him. I just wanted to tell him: “You want to get the y by itself on one side of the equal sign.”  I am conflicted: is that the “easy way out” for both the teacher and the learner?  Does the more difficult reference to chips really build meaning or is it possible it just creates confusion?

Public Records "aha"

Public records.  One day during my September experience the principal of Hale came to observe our class with her district boss.  It was a short visit, perhaps ten minutes, but the one thing they wanted addressed as lacking in the classroom were “Public Records”.  The use of Public Records is one of eight “High Leverage Teaching Moves” outlined by Seattle Public Schools.  As the intern I got the assignment to maintain the Public Records in the classroom.  The stated purpose of Public Records is to: “Provide students with a resource- an opportunity to reconnect to skills and processes they’ve learned or to apply learning in a new way”. In my middle school experience Public Records are used in the classroom.  I learned some basic guidelines governing Public Records.
Create Public Records with the classes they apply to, the last class period to cover the material in the record is a good time to finalize the record, this does not require separate prep time for the records.  Do not create too many records; this clutters the walls making them less powerful.  Segregate records into classes on the walls.  Remove public records from past units that are no longer pertinent.  When I  return to my high school classes I will master making Public Record Posters on a printer, expanding 8 ½ by 11 inch sheets to larger poster sizes, because I think my writing is sloppy.  By using the Smart board I can get input from the classes on the actual Public Record by editing the file with which we create it.  This is important, it gives the students ownership and fluency of the records.

Checking homework "aha"

A small, “checking homework ‘aha’”.  When my cooperating middle school teacher checks homework she has several tricks that shave off time from the task.  First she uses a Palm pda to enter anything she wants into Easy Grade Pro, this is a big improvement over printing a roster, carrying it around, and then entering the grades into a computer.  With the Palm she simply uploads the grades.  The possibility for making mistakes is greatly reduced.  Second, she only grades as “unsatisfactory”, which is to say if the homework is complete she does not have to enter a grade, it is automatically graded as satisfactory.  When there is a missing or unsatisfactory homework she can record it on the Palm.  Even if half the class does not have a satisfactory assignment she has cut her effort in half, freeing up more time for the class and herself.  Third she uses rubber stamps to mark satisfactory assignments.  This is the only real record of the satisfactory grade and if the student later claims that a satisfactory assignment was not marked appropriately they have the evidence to prove it.  The students have to be organized to make this work but of course that is a skill we hope we are fostering in school.

Smart board "aha"

Technology is a little overwhelming in my classroom at Nathan Hale.  It is not the technology itself it is just the new applications of it and the disparate manner all the technologies work together.  There is the Smart board, the doc cam, and the desktop computer.  The Smart board is something of a blank slate as it is new this year to Hale so everyone is getting up to speed and  I am as proficient as almost anyone.  In my alternate middle school experience I was assigned a teacher who uses technology similar to Smart boards: Active board.  There have been multiple “aha” moments while watching my middle school cooperating teacher, who has fully integrated the Active board into her lesson plans.
One involved the warm-up.  She presents the warm up on the Active board rather than the doc cam.  This may seem small but it has advantages.  First, there is no paper involved and this is big because at the end of the day we are swimming in paper in my Nathan Hale classes.  Second the use of the Active board allows you to post the problem and create a markup layer when you go over it.  When the next class starts you simply delete the mark ups and start again.  With the doc cam you need a fresh copy of the problem for each time you go over it.  I lean toward working out a problem on the board, rather than the doc cam; perhaps this reveals a traditional style of teaching in my approach.  A  real traditionalist might point out that you can just post the problem on the white board, work it out on the white board (erasing each solution), and achieve the same results as all the technology.  The time savings of keystrokes over writing and erasing may be small but I think they add up.  Another advantage of the technology over a more traditional approach is that you can save your problems and solutions to build into your curriculum the next year and you are not swimming in paper.  The bigger promise however is the potential to work in any number of other supporting media to the problem, be it a TI-84 emulator to an internet based applet.  This is an “aha” moment I want to develop.