Twelve-Twelve-Twelve

My colleague (Thanks, JH!) shared these activities with me when we had a 20th anniversary celebration for a student group.  I decided to adapt them for today and spend about 12 minutes of math class on these 12 questions.

Twelve     

1. 12 could be...  12 could never be...
2. When is 12 a small number?  When is 12 a large number?
3. Write a number sentence that equals 12.  (use fractions or mixed numbers)
4. The answer is 12.  What is the question?  (not a number sentence)
5. List things that come in 12.
6. Find as many words as you can hidden in:  DECEMBER TWELFTH
7. 12 is to dozen as ____ is to ____.
8. Roll six dice (dodecahedrons!) and use the numbers and any combination of operations to equal 12.
9. If the product of two integers is 12, we know that....
10. What are items shorter than 12 cm?  Exactly 12 cm?  Longer than 12 cm?
11. List ways to use 12 cups of water.
12. List titles or common sayings with "12" in them.

Happy Thanksgiving

Two days off... I'm not complaining!



Mirror, mirror, on the wall...

I read in a book on teaching middle school that narcissistic adolescents like to look in the mirror.  (No surprise)  Several of the students (usually girls) have frequently asked to use the bathroom over the past couple months.  One student told me, "You know, they just go so they can look in the mirror and fix their hair."  The book suggested putting a mirror in the classroom.  I was shopping over the weekend and bought a mirror.  I put it up today at the students' height...  Sure enough!  I caught one of the girls who often asked to go to the bathroom admiring herself in the mirror.  She smoothed her hair, smiled at herself, and bounced away.  Perhaps there will be benefits!

Report Card Pick-up

Today was report card pickup (parent-teacher conferences).  No students!  We went from 11am to 6pm with 10 mins/student scheduled.  Parents of all but 3 of my 36 students attended.  I spoke to some through a Polish or Spanish interpreter while the rest of the parents spoke in English.  The principal told me participation in report card pick-up is well over 90% for the school.  This is a definite strength of the school! 

Do we have to do this one?

This was a question from a student today.  She was referring to a "word problem."  Actually, it was more of an exercise posed with a few words.  With the student asking this question, it showed how deficient our textbook is with respect to any sort of contextual exercises or problems.  It also showed that I must not be assigning enough of the few quality problems so that she expected that would be something she would not have to do. 

One Student Missing

Sad to say, but it is nice when "that one student" is gone.  Today two students who are both "that one" was gone from two of the classes.  It made for such a relaxed day!  Not only did I not have to keep my eye on those students, but they also weren't there to distract the students around them.  Wouldn't it be nice to teach only the students who wanted to be there?  (Wait, that's kinda what I do when I teach college students!)  A solution would be to remove all students who distract from classroom learning... but then how do these students learn?  Are there resources for this?  It is unfair that a few students demand and require (and, unfortunately, often get) more than their share of the teacher's attention even though they don't often put forth the necessary effort toward learning.

National Anthem

Every day the US national anthem is played over the school PA.  Students are expected to sing along.  As you might expect, after mindlessly repeating the words for several years, they have morphed into something different...

The correct lyrics:

Oh, say can you see by the dawn's early light
What so proudly we hailed at the twilight's last gleaming?
Whose broad stripes and bright stars thru the perilous fight,
O'er the ramparts we watched were so gallantly streaming?
And the rocket's red glare, the bombs bursting in air,
Gave proof through the night that our flag was still there.
Oh, say does that star-spangled banner yet wave
O'er the land of the free and the home of the brave?

The lyrics according to students:

Oh, say can you see by the dawn's early light
What so proudly we hail by the twilight last gleaming?
Who brought stripes and bright stars thru the perilous night,
Oh the ramparts we watch are so gallantly singing?
And the rocket's red glare, the bombs bursting in air,
Gave proof through the fight that our flag was still there.
Oh, say does that star-spangled banner yet sway
O'er the land of the free and the home of the brave?

I'm thinking I will have the students write out the lyrics sometime... I'm sure I'm missing many things!

Number Theory Games

This week:  Number Theory Games!  It has been a good change for the students and me.  These are part of "Prime Time" and "Accentuate the Positive" (CMP).  I wish this school had CMP as the adopted text.  We can do the class activities but without photocopying many pages (probably against copyright law) we can't do the homework followup.  I was surprised at the positive reaction of the students to the games.  In addition to the change of pace, it showed (at least to me) how a more problem-based classroom diffuses some of the behavior issues.

Factor Game - this game allows students to practice finding factors to numbers through 30.  It also requires students to think about the relationships of the numbers and encourages faster recall of basic multiplication facts.
Online version:   http://illuminations.nctm.org/ActivityDetail.aspx?ID=12
Paper version:   http://illuminations.nctm.org/lessons/6-8/factor/handouts.htm

Product Game -  This game encourages students to develop a better understanding of the relationships between factors and multiples. 
Online version:  http://illuminations.nctm.org/ActivityDetail.aspx?ID=29
Paper version: http://illuminations.nctm.org/LessonDetail.aspx?ID=L272

Integer Product Game - This game extends the product game (above) to include work with integers. 
Online version:  http://connectedmath.msu.edu/CD/Grade7/IntProdGame/IntProdGame.html
Paper version:   http://blog.wsd.net/anholtry/files/2012/09/Integer-Product-Game.pdf

Why do we need to know this?

After a week of following the traditional textbook examples/exercises for operations with integers, I heard "Why do we need to know this?" for the first time.  I took this as a cue to change things up next week.  If I don't see the point and the students don't see the point, what is the point??  I'm going to abandon the textbook and do some things that are more interactive.

PEDMSA (or is it PEMDAS?)

30 - 15 + 12 / 3 x 2

It's no surprise, but order of operations poses difficulty for the students.  I asked the students to simplify the expression shown above.  As you might expect, the answers included 13, 18, 23, and an assortment of others resulting from incorrect calculations. 

My students have been 'drilled' to know "Please excuse my dear aunt Sally."  I told them it could be as easily called "Please excuse dear my sally aunt" but they didn't seem to believe something they had been told for years could possibly be wrong (or inadequate).  I don't think the two class days had much impact on the students...

CCSS - Standards for Mathematical Practice

The Standards for Mathematical Practice from the Common Core State Standards were mentioned at the workshop held this past weekend.  A file was distributed that appears to be potentially useful for a math methods course.  To "unpack" each math practice standard, participants were asked:

What does this math practice standard mean?

What would this math practice standard look like/sound like in the classroom?

Students will be saying or doing (words and actions)… The teacher will be saying or doing (words and actions)… High-level questions students or teachers might hear/say…

Let me know if you'd like to see the file with a list of suggestions for each heading in the table.

The website Illustrative Mathematics was also mentioned.

No Nonsense Nurturer

I attended a "new teacher" workshop this past weekend at the New Teacher Center.  Many topics were discussed including classroom management.  The model promoted by the facilitators was "No Nonsense Nurturer."  In my most difficult class I tried the"MVP" and "narration" aspects of the program and found them quite effective at getting students on track and quiet. Honestly, I was quite surprised!   MVP is an acronym indicating that instructions should include directions for Movement (e.g., stand, sit, walk), Voice (e.g., silently, in a low voice), and Participation (What should the students be doing?). The narration element is different from "I like how Susie is sitting quietly" in that it narrates (describes), but doesn't praise the students.  As a program, I think it is organized in a way to help a new teacher who might be starting in a difficult situation.  Looking back, I think something like this would have been useful for a couple of the alt cert teachers I supervised several years ago.  It seems to me to be an "in the moment" solution (i.e., with practicing teachers) rather than something to share with future teachers.  The video below shows the implementation of aspects of the program in a coaching situation.  This document also outlines the elements of the program. 

Simplify, Evaluate, Solve

Simplify 2 + 5 * 2 - 3

Simplify 6(2 + 2n) + 3n

Evaluate 7 + y for y = -7

Solve 9y = 900

I'm sure it has been noticed by plenty of teachers, but the three words - simplify, evaluate, solve - do not seem obvious to students.  (Are they even obvious to teachers?)  Students seem to want everything to end with a "number answer" so to simplify an algebraic expression (so there are fewer terms) baffles many of them.  Just when they begin to think that simplify means "write in fewer terms" they are asked to simplify a numerical expression.  "Do you mean solve it?" they ask.  But solve, at least as it is used in our textbook, means "find the value of the unknown."  I think one reason there is a confusion is that these exercises are addressing skills in isolation.  If there was a context to reason in, I don't think there would be an issue.

Credit Card Payments

While this post does not relate to anything from my classroom, it seems like there is a lesson in consumer mathematics involved!

I received a bill for some of the things I purchased when I moved to my new apartment.  The following table was included with the statement:

It seems they fail to mention that you can "save" more than $700 by paying the bill in full.  But who, in their right mind, would spend 20 years paying for some household items that won't even be useable in 20 years?!

What about context?

Does a problem situation or context matter?  Can it be used to engage (or disengage) students?  A recent example comes to mind where students seemed to be more interested in one problem situation than another.  While students responded differently, there is no way to know whether it is the students or the context that caused the resulted in the different responses.  I tend to think it was the context that did matter.

Textbook example:  Domingo decided to save $0.03 the first day and to triple the amount he saves each day.  How much will he save on the seventh day?

Variation:  Would you work for someone if they paid you $0.03 on the first day and tripled the amount for each additional day you worked?  Would you work for them for a week?  For two weeks? 

In the textbook example, there is a single answer:  $21.87.  Students calculated the amount and it seemed to end the discussion.  It is realistic for someone (or, if they personalize the situation, themselves) to have about twenty bucks to stash away at the end of a week.  Extending the problem into the second week becomes unrealistic because it is very unlikely anyone could continue saving at that rate.

When I varied the problem, however, it provided a lot of discussion.  While the context is unrealistic (no one would ever hire someone with this scheme), it did provide a connection to the students.  They had to decide whether they would work for this employer...  if so, how long?  Clearly, it would not be advantageous to work for only a few days.  However, someone would would continue to work would be rewarded generously.  This seemed to really illustrate the point of exponential growth!

Open House

Parents (and some students) attended an open house for 1.5 hours tonight.  I did not do an exact count, but I would guess about 20 of the approximately 140 students were represented tonight.  It is always interesting to meet parents - sometimes it is the clear the apple doesn't fall far from the tree!  Everyone was nice and asked about their student.  It was hard to provide many details as it is still early in the school year and we don't have many grades yet.  One mother overspent her time and wanted to report on several (minor) occurences her daughter had experienced already this year.  (I found out the other seventh grade teachers got to hear the same stories!)  Fortunately there wasn't enough time to do a full conference with her.  I don't know, but I may be hearing from her later.

Shakeup

Without the other teacher in the classroom, it seems the kids have tried to see what they can get away with!  Seventh graders are seventh graders so they like to be social... but failing to do homework, talking out of turn, and distracting others doesn't make for a productive class.  At the beginning of the year I seated the students somewhat arbitrarily.  Now that I have gotten to know the students (and they have shown their level of responsibility in the classroom), I have rearranged each of the classes - separating some students, moving others to the front or back as needed, and wishing I had more corners!  These changes didn't make some of the students very happy - which I take to mean it was the right thing to do.  :-)  I may need to make a few more changes in the next few days if there are more students who can't handle their position in the classroom.  The downside to having 36-38 students in the class is that there are very few, if any, empty desks.  I did get two more desks so that I can create a buffer if needed.  But now there is even less room to move around the room!

Baby!

I was completely on my own for the first time today.  (Another first day!)  The teacher whose place I'm taking was planning to work another two weeks before giving birth.  This morning she texted me and said she didn't feel well.  During the day I heard she went to the hospital and tonight I heard she has a new baby boy!  Things don't always go as planned...  Fortunately, I did all of the procedures (collecting lunch money, taking attendance, etc.) yesterday on my own so I was able to manage today.  She had been coordinating the Language Arts lessons so I'm now responsible for those, too.

First Day... After Strike!

And yet another first day!  Today was the first day back after the strike.  Most of the kids looked familiar and I even remembered some of their names!  For the most part we were able to pick up where we left off.  Next week will be rough... a full week of class without any breaks!

Opportunities

One impetus for the strike was conditions of the "full school day" initiative.  What extra opportunities do the students get?  Although the school offers all of the "core" subjects (math, English, science, social studies), there is only limited time each day for additional experiences.  Students get one hour each week of gym, music, library, computer, and art.  There was no music teacher last year but a new one was hired for this year.  The music curriculum is a "general music" experience; there is no band or choir.  Some of the library and computer time is spent on testing (they take 3 "progress" tests each year and the state tests toward the end of the school year).  The library is usually scheduled with classes from the various grade levels so students do not have "free time" in the library.  Likewise, the computer lab is heavily scheduled so classes or students cannot go in there during the school day.  There are no student activities after school.  In prior years there were parent volunteer coaches for girls volleyball and boys basketball.  Those parents are no longer coaching the teams.  There is talk this year of a cross country team for both boys and girls if there is enough interest.  There are no programs for "gifted" students and no special interest groups for students in the older grades.  There may be a "student council" formed later in the year to organize two in-school dances and a few academic teams might form, too (e.g., book club, cinema club, and math club).  To me, the school day seems "basic."  I know I had more required or elective opportunties in the middle grades.  When I taught 8th grade, those students, too had more opportunities.  It is unfortunate that these students can't have more opportunities to study journalism, ecology, computers, band, choir, foreign language, etc. while they are in the middle grades.

Rallies

 Saturday's rally at Union Park

 Thursday's Rally at Wacker & Michigan

Wednesday's Rally at Kelly High School



On Strike... until further notice

Downtown Rally

Big rally downtown on Monday afternoon!

First Day - Strike!

Another "first" day... teachers are on strike today!  An eighth grade teacher made some signs and brought them for us to carry on the picket line.  Our school was designated as a place for up to 3000 (or so I heard) students.  Fortunately, less than two dozen students showed up.  Some people reported there were more adults in the school than students.  Several parents and students came to support the teachers at our school this morning.  Many people also drove by to show their support. 

Exponents

A textbook was adopted and given to me.  What will I do with it?  (A question any teacher must asked her/himself!)  The textbook we have has a typical two-page spread with three (or more) worked examples followed by two pages of "Guided Practice," "Independent Practice", and "Practice and Problem Solving." 

For the section on Exponents, the stated goal is:  Represent numbers by using exponents.  This is not students' first experience with exponents, so the examples and exercises such as find 5^2 and 2^6, write 49 with a base of 7, and compare 15 and 4^2 did not seem very challenging.  Many students reach first for their calculators so these become even more trivial.

After examing the section and the teacher notes, I did find some tasks that I thought seemed a bit more interesting and encouraged students to think more about the meaning of exponents.  How would you characterize the cognitive demands of these tasks?

• Guess/Check/Revise:  Guess the missing exponent and use your calculator to check.
• 3^?=729; 2^?=4096; 9^?=4,782,969; 4^?=1024
• Explain how you can find the value of 2^11 if you know that 2^10=1024.
• Is 6^3 = 3^6?  Explain.
• In as many ways as you can, represent 64 using powers.

Note:  Of course the textbook does not use ^, but I didn't feel like taking the effort to format this entry.

Anonymity

I figured with nearly 3 million people in the city and 10 million people in the metro area, it would be unlikely to randomly run across people I know.

On Tuesday...  a former student who was in a club I advised started teaching in a classroom a few doors down the hall from me. 

On Wednesday...  a former student got on the train as I was heading home.  He is now working and going to school in the city.

On Thursday...  a girl on the bus asked where I taught.  After I told her she said her coach, who dropped her off at the bus stop when I got on, thought it was me.  I asked what her coach's name was and it turns out the coach had a been a student in one of my classes a few years ago.

Who from my past will I encounter tomorrow?

Uniforms and Routines

There are a few things quite different here from other schools where I have attended or worked.  Most noticeable, all of the students wear uniforms.  Top: Solid, light blue (powder blue) shirt or blouse w/collar (no prominent logos, words, pictures, stripes, or decorations).  Bottom:  Solid, navy blue pants, shorts, skirts or jumpers (no jeans, denim, nylon; no stripes, decorations, logos).  On gym days, students wear royal blue t-shirts and shorts or sweatpants. 

The students have been trained to be quite respectful.  During lunch count, for example, each student says "yes, please" or "no, thank you" when called.  During class they raise their hands and wait until being called on even when a chorus answer would be more appropriate.

Students always line up in two rows:  boys on one side and girls on the other.  They march down the hallway and stop at each turn until told to move on (e.g., top of the stairs, bottom of the stairs, end of the hallway).  Five are allowed in the bathroom at one time.  As one exits, another enters.  When entering a classroom or lunch room, the boys always wait and allow the girls to pass first.

First Day of School!

One day finished...  We shortened the length of each class period today and spent more time at the beginning and end of the day in order to get things arranged.  Students came in the morning with a big bag of supplies:  pencils, notebooks, binder, paper towel, etc.  We sorted things out, assigned desk and lockers, and established some rules and procedures.

There are 36 students in our homeroom and a similar number in each of the other three 7th grade classes.  I will be working with another teacher who will be leaving for maternity leave in approximately one month.  With 36 students, every classroom should have two teachers!  I will be teaching math to each of the four 7th grade classerooms and also language arts to the homeroom group.  Until she leaves, the other teacher will be leading the language arts class and I will take the math classes.

Day Two - with teachers

Meetings this afternoon focused on Teacher Evaluation.  The district is beginning to use a new evaluation system based on Charlotte Danielson's Framework for Teaching.  I'm impressed by the empahsis on Teaching Practice as part of the framework.  In particular portions of each domain (especially 1, 2, 3) of the framework seem relevant for working with future teachers.  (Rubrics to evaluate teachers have the potential to be adapted to evaluating peer teaching in a methods course.)  I think this would fit well with mathematics-specific frameworks for teaching developed by QUASAR and others.  The bottom line for the classroom environment seems to be to encouraging students to be independent and engaged learners.  Preparation, discussion, reflection, and feedback all seem part of the evaluation process as well.

Domain 1: Planning and Preparation 1a Demonstrating Knowledge of Content and Pedagogy
1b Demonstrating Knowledge of Students
1c Setting Instructional Outcomes
1d Demonstrating Knowledge of Resources
1e Designing Coherent Instruction
1f Designing Student Assessments

Domain 2: Classroom Environment 2a Creating an Environment of Respect and Rapport
2b Establishing a Culture for Learning
2c Managing Classroom Procedures
2d Managing Student Behavior
2e Organizing Physical Space

Domain 3: Instruction 3a Communicating With Students
3b Using Questioning and Discussion Techniques
3c Engaging Students in Learning
3d Using Assessment in Instruction
3e Demonstrating Flexibility and Responsiveness

Domain 4: Professional Responsibilities 4a Reflecting on Teaching
4b Maintaining Accurate Records
4c Communicating with Families
4d Participating in a Professional Community
4e Growing and Developing Professionally
4f Showing Professionalism

First Day - with teachers

Today was the first day with all of the teachers present - lots of greetings and meetings!  Below is a list of topics/issues that came up through today's meetings.  Is a first year teacher prepared for these?

• Common Core State Standards - What should be taught/learned?  How should it be taught?  How will it be assessed?
• Teacher Evaluations - What counts as a "good job" of teaching?  What are the components of teacher evaluation?  Who will be doing the evaluation and when will it be done?  How will the evaluation help a teacher grow professionally?
• Students with Special Needs - IEP, 504, Special Education, etc.  How will instruction need to be modified/adapted for the various needs of students?
• Materials - What is available?  How do teachers get what they need?  Who pays for it?  (Incidently, I get very little - including white board markers - and must purchase what I need.  I do get a small stipend to reimburse for classroom materials.)
• Grading - What should be graded?  How much time will it take?  How are grades communicated to students and parents? 
• Teaching a New Subject - How can a teacher do to prepare for teaching a subject they are not "qualified" to teach?  What resources are available?  What are the expectations of the teachers/school/etc.  (I will be teaching writing - something for which I have no preparation.  Wish me luck!)

Second Day - no kids

Today was another "flex" day so most teachers were not present.  A few more did show up and I met several of them.  I worked on various small tasks and printed off some materials on common core.

I also discovered this poster hanging near a 4th grade classroom:



I thought it looked like a great opportunity for developing some notions of multiplication!  Cathy Fosnot and her crew have lessons with similar pictures.  For example, the meaning of multiplication is highlighted with the 3 ice cream sundaes (3x1) compared to the plate of 3 mini-cakes (1x3).  Many of the plates show arrays of items which has strong potential as a model for multiplication.  They can support an understanding of the commutative property of multiplication.  For example, with the red cakes on the bottom, students can verify that 4x2=2x4 (four groups of two is the same as two groups of four).  The three-tiered plate of candies can develop the associative property of multiplication:  3x(3x2)=(3x3)x2. 

Sadly, the teacher had no intention of using the poster for math. 

First Day - no kids

Not much going on today... most of the teachers are not in school today or tomorrow as these are both "flex" days.  In exchange for these days teachers could work two days during the summer.  I did a small, but tedius, project for the principal and also completed some new hire paperwork.

I walked around the school.  The building is two stories with an old (ca. 1920) wing and a new (ca. 2006) wing.  Many of the lower grades are in the newer wing; the upper grades are in the old wing.  There is an auditorium and small gymnasium in the old wing.

In the process of working on the principal's project, I learned that my classes will begin with 32-35 students.  I will have 4 math classes and 1 language arts class.  (I am waiting until Wednesday to find out what I will have to do with language arts!)  About 40% of the students prefer information sent home in English, 40% prefer information in Spanish, and 10% prefer Polish.

Some of the students' last names:  Flores, Hernandez, Kowalkowski, Martinez, Solisperez, Szczech, Chavez, Chodorowicz, Hajduk, Lesnicki, Lopez, Marusarz, Tomaszewski, Wojtasik, Diaz, Estrada, Ruentes, Garcia...  It is definitely a mix of Latino and Polish names!

I had lunch at the grocery store at the end of the street.  I heard people - young and old - speaking English, Spanish, and Polish.  The products were typical of any American grocery store; however, there was a huge display of sausages with Polish sounding names.  The bakery cases and shelves also had additional selections that appeared like Mexican goodies and Polish treats.