Building Relationships

I’ve already found that one of the most challenging aspects of teaching middle school is that the kids are so, so reluctant to open up.  I’m aware that it may take WEEKS to feel true connections with the majority of my students.  One of the major roadblocks is that almost 100% of my students have had one or more teachers quit partway through their journey together or simply not show up at all.  As a young, white, fresh-out-of-college teacher that hasn’t even lived in this city for longer than four months, my appearance and (lack of) background makes it tough for my kids to believe I’ll be any different.  Thus I’ve spent an ENORMOUS amount of extra time trying to put structures in place that show that I’m dedicated to forming strong relationships with them as individuals.

On the first day I gave out a lengthy student survey for each one of my kids to complete.  I took them home on Monday night and wrote comments, notes, and extra questions.  On Tuesday in class and for homework my students finished them and then wrote ME two questions.

I also wrote a parent letter that included my classroom vision and the goals I have for my students academically.  On the back was a parent survey.

I re-typed all of the student and parent responses into a 9-page spreadsheet that includes my rosters, parent contact information, and extensive notes about each child from the student responses AND their parents responses.  I keep all of the information on the clipboard I carry while I teach.  So far the comments have been extremely helpful in the way I approach interactions with individuals and they way I chose to re-direct students when they make decisions that aren’t in their best interest.  There are also some parents who specified exactly what they’d like me to do in order to be the best teacher I can possibly be for their child– for example, texting them weekly about progress, arranging seating in a particular way, and ensuring that their child has physical, emotional, and psychological accommodations that might not be listed elsewhere.

In my third block, my toughest, this has already made a HUGE difference.  Instead of calling children out by name when they need to redirect, I write them a sticky note with a reminder.  I also write note to the students who are role modeling superb decision making and who are on their way to accomplishing their goals.  Since public redirection is sometimes unavoidable, I also try to write notes as a way to repair the relationship, to tell the child that I was firm with them because I believe in their potential and I want to help them accomplish the goals they listed on their surveys.  It takes an enormous amount of time.  But I am SO confident that it will transform some of the negative behaviors I’m beginning to see transpire and also help me forge strong bonds between students and their parents.  We’re in this together.

Math is Colorful: Classroom Setup and Organization

I start teaching for REAL on Monday.  That is an extremely daunting, terrifying, and wonderful thought all at once.  I haven’t been able to stop thinking about the coming week for the past month– there are just so, so, so many details that need to be precisely prepared and thought out before my 90+ students walk into room 135E on Monday.  Nonetheless, it has been rather fun setting up a classroom with a clear theme: Math is Colorful.  Math is a subject that so many consider black-and-white and correct or incorrect, but in reality its intricacies, patterns, and thought-provoking ideas are worthy of a full spectrum of color.  I THINK I conveyed this in my setup 🙂 It also became a challenge to see how many items I could create using paint swatches.

My door (we can’t have anything bigger due to fire code 😦 )

Seating and Job Charts (each desk is labeled with a matching number)

Instead of tennis balls, I cut felt sheets into sixths and then wrapped a rubber band around them.

An Absent Station where students can collect the notes and assignments they missed:

The Daily Unit Plan: Standard, Essential Question, Activating Strategies, Teachings Strategies, and Summarizers (a school-wide requirement for teachers)

I framed (1.99 at Ikea!) cardstock to use as mini-whiteboards to keep track of Class Points (each group earns one when they complete a procedure or meet an expectation fully)

My classroom “Vision” is twofold with year-long personal growth and academic growth goals.

Personal: Growth Mindset, Respect, Effort, Accountability, and Togetherness (GREAT)

Academic:  at least 80% mastery on all assignments/assessments, at least 1.3 years of mathematical growth as measured by MAP data, and a 3, 4, or 5 on the End-of-Grade test.  I included WHY each of these goals is important.  (Really and truly, though, it’s not about the data in the end.  If my children “fail” the EOG, they are STILL the same people.  It’s when they make outstanding growth and show incredible increases in proficiency that they set themselves on a new learning path).

My bulletin board: the right is to celebrate students for excellent performance and mastery (“Wall of Champions”) and the left is to recognize students who clearly showed one or more of the GREAT traits throughout the week.  Each student writes three trait-based compliments every Friday in order to applaud their peers.

I used fabric instead of butcher paper– apparently the kids WILL tear paper down if given the chance.

The other side will become a Student Learning Map that outlines each unit beginning with a broad essential question and then narrowing down to daily lessons.  In other words, students will be able to see exactly what they’re learning each day as compared to the skills they learned in the days before and in preparation for the ones ahead.

For tracking our mastery and growth as a class (I’m going to use a similar system for tracking homework completion).  Students have personal/individual trackers that only they can see.

The rules and consequences are school-wide and MUST be common across all classrooms in order to ensure consistency for the kids.

A number line, Golden Ratio-based decor, and drawings of fractals from an old calendar I cut up and laminated.

Each student has a folder, color-coded by class (all 1st-Block items are yellow, all 2nd-Block items are green, and all 3rd-Block items are blue).  The turn-in drawers and Class Point frames are in the same colors.

To ensure that EVERYONE participates, I used a classic popsicle-sticks-in-a-cup system where the numbers correspond to seat numbers.

The bigger picture:

I’d like to thank Home Depot for minimal strange looks as I took more paint swatches than is socially acceptable for any one person and my boyfriend for flipping over heavy furniture so I could color-code with felt.

Final Days of Summer School: The Big Picture

Twenty-four rising sixth graders have now been set free for summer vacation.  And I’ve been set free for two weeks of my own summer vacation (most of which will be spent reading because I now know more about what I don’t know– so Socrates).

In total, my kids learned 15 different Common-Core aligned objectives in four weeks (and only 12 instructional days!).  To look at evidence-based growth, all teachers in my program gave an initial assessment (standardized and Common-Core aligned) on the first day and gave the same assessment on the last day.  The data tracking program calculated a high but realistic growth goal (based on the growth of the top 25% of all students in summer school for the previous year) for each child.  On average, my class accomplished 104% of their growth goals with a range from 47% to 166% accomplishment.  ALL children grew at least 25 points from their initial to summative tests and the most outstanding growth was 88 points from start to finish.

A second data system– exit ticket scoring– was used to track daily mastery of objectives.  As you can see, the students continuously increased the mastery over the course of the four weeks:

Honestly, this is all very frustrating and heartbreaking for me.  Even though my class did fairly well on paper, there were some who did not accomplish their data-based growth goals but who made outstanding, permanent personal growth.  There were others who walked through the door hating math (and who weren’t afraid to admit that!) but who left feeling inspired and confident.  That growth is what I really wanted to capture.  I tried two activities on the last day to assess my students’ enjoyment of the material.

The first activity:  Math Maps

Math Maps

This activity allows students to map their overall knowledge.  The idea is not to include every single detail, but to connect and synthesize the overarching takeaways.  I took down all of my anchor charts, recycled leftover handouts, and had them take home their notes, so all they got was the sheet shown above.  I was astounded at the quality of their products!  Most of the class worked in groups of four students each, but some individuals chose to work alone.

When they were finished with their Math Maps, I asked each student to write me a letter about math.  It could include the parts they loved, the parts they hated, how their mindsets about math changed, which parts they anticipate using in sixth grade, or just about anything else they wanted to mention.  These were also wonderful, erring on the straight up honest side.

Note: the “Crazy One” is a way of remembering to multiply the numerator and the denominator by the same factor when finding fractions with a common denominator.  Also, I stressed that the resulting fractions would be equivalent because multiplying by one– even a “Crazy One” or a one in disguise– produces the same number. To practice identifying “Crazy Ones,” the kids had to come up with a ridiculous dance move whenever one appeared on the Promethean or white board.  This happened A LOT.  There were more crazy kids than “Crazy Ones.”

“I liked math class because Ms. Y was fun but I didn’t like working because I’m lazy and don’t like to work very much.” (I don’t make these things up, I swear).

“What I didn’t enjoy: you making us do the explanations (for) our work.  Our work explains our work.”  This is super funny because we worked SO hard on those explanations.  Common Core is all about explanations because articulating your thinking is a critical skill for academic success.

This child showed the most personal growth in collaborating with others, thus the “Go Teme.”  (Team).I told them that “equivalent fractions” was a big long vocabulary word that sounds like it should be said by the Queen of England.  So they got up out of their chairs and used a shrill English accent to say it every single time.  Some of the kids talked themselves through the summative assessment in a shrill English accent.

“I love math because I learned new things.  I love math now I learned sooo much with the best teacher.”

Finally, I had one student who spoke no English at all but seemed to take away more than anyone else.  In her letter she basically writes that she learned so many things she didn’t know before the summer.  She hopes that she can see her teacher someday again when she knows English better and can tell her everything without translating.

I will miss my kids so much!  This happened in four exhausting and wonderful weeks.  What can happen in a year?  One month until I start to find out!

Second Week of Summer School

I haven’t figured teaching out yet.  I’m most certainly still a learner. Even so, this week brought a LOT of growth in the classroom, both for my students and me.

It’s important to be honest about the truly aggravating, stressful, heartbreaking aspects of this work because you have a lot of them before the first triumph.  So I’ll start with those:

• Last weekend I spent nearly 12 hours each day writing lesson plans.  I finished four of them in 24 hours– about twice as fast as when I began.  But on Monday I realized that the way I had written my plans and the structure of the handouts wasn’t conducive to my students’ learning styles.  Even after editing everything and trying new engagement strategies, they still only mastered the daily standard on one of the five days.
• I have one child who works so, so, SO incredibly hard despite a learning disability.  He spends HOURS on the daily homework assignments and writes me long notes about where he got stuck and/or the topics with which he still needs help.  He can usually remember the first step, but all of his arithmetic is incorrect.  Thus despite his effort, perseverance, participation in class, and willingness to help others in the class, he is still technically “failing” math.
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• Another student rarely speaks and NEVER writes anything on his paper.  I suspect he has difficulty processing, because it takes him a long time to answer any question– even yes or no ones.  During the year he has an aid, but summer school sites don’t provide these kinds of resources.
• I also have a child who is off-the-charts intelligent but SO hyper (he runs and runs and runs around the classroom unless you explicitly tell him to slow down, take a seat, and breathe), two students who consistently score 100% on their exit tickets even when everyone else needs more review, a student who speaks no English, and several students who still haven’t learned how to multiply.

But my classroom is not an anomaly– it’s a typical public school class in any high-poverty area of the United States.  Student differences are what make teaching stressful, challenging, and heartbreaking, but also extremely fun, engaging, and important.  These are children who may not have had a teacher say, “I believe in you” every time they give an assignment.  These are children who haven’t been told WHY it’s important to practice, WHY mistakes are critical for success, WHY effort is more important than correct answers, and WHY it’s important to learn about and value each other.  With every consequence I give for behavior, I say, “This is because I’ve seen your potential and I’ve seen your best work.  You need to think about how (running/refusing to do work/talking while I’m talking) prevents you from being your best self.”  And every class begins with the words, “We are on an urgent mission to learn: we need to make as much growth as possible for you to be successful in sixth grade and beyond.”  I say this over and over and over again.

But amidst the long, long hours, exhaustion, sleeplessness, and stress there are the beautiful triumphs– the reasons that I LOVE what I do even after a mere two weeks.

• The Compliment Wall: for three days, Mr. Joe and I had the kids play “Compliment Ball” as a way to greet each other in the morning– one person would start with a compliment for another person and toss the ball to them.  That person would compliment someone else in the class, and so on. The problem was that no matter how many times we said, “Think about something to say about someone else’s PERSONALITY,” 20 out of the 25 kids would defer to, “I like your shirt.”  Kind, but not about to make the world a better place.  On Thursday, we gave each table a stack of sticky notes.  Each person had to write one compliment per person at their team table.  It had to be about their personality or something awesome they had done, but the note itself was anonymous.  Our kids wrote some beautiful things to one another, and they keep checking the wall to see what people wrote about their classmates and if new ones have been added since they last checked.  Joe and I even got some compliments!
• Fraction Frenzy, the Game Show: also on Thursday, the kids entered the room as contestants on Fraction Frenzy: the Game Show.  I split them into 6 teams (with evenly distributed Exit Ticket success rates), and each team had a designated spot on the whiteboard.  When I flipped to the next slide, they had to run up to the board and write down as many equivalent fractions as possible for the target fraction in 2 minutes.  The problems got slightly harder and harder, and the group work transitioned into partner work.  They LOVED it and begged to play again on Friday.  I promised we will on Monday for a different topic 🙂
• One of the girls who always writes, “I hate school, math, reading, and writing” on every survey we give told me yesterday, “Ms. Y, I like math now.  I just wanted to tell you that.”
• The student who has trouble processing worked ALL through class yesterday on a personal whiteboard.  He was also invested in his partner work task, and I caught him smiling.  He also answered a question in front of the whole class, which I know gives him a lot of anxiety.
• I’ve been asking the kids who score less than 75% on their Exit Tickets to do a quick review of yesterday’s material while they eat breakfast.  Then I give back their Exit Tickets and tell them that if they can find and correct ALL of mistakes, they’ll get 100%.  That brought our class average for “Finding Equivalent Fractions” up from 74% to 88%!  (The goal is AT LEAST 85%).
• I get the kids to practice these crazy hand motions I made up to go with all of our vocabulary words.  They have a hard time expressing in words HOW they find solutions, so we run through examples using the motions.  I asked for two volunteers to perform one of the explanations in front of the whole class.  If they did it alone, they’d get a Personal Point (long story).  The two students who are LEAST likely to focus on doing their work in class got up and performed! (Note: I’m really, really, really hyper when I teach.  This is just one of the techniques I use to prevent sleepers.  I’ve also thought about tap dancing, confetti, and backup singers.  Just kidding).
• The people I work with are SO awesome.  I love riding the bus in the morning because everyone will talk about how they plan to execute their lessons– and then we all take snippets of each others’ ideas and adapt them for our own classes that same day.  Also, Mr. Joe is pretty much the greatest and works tirelessly for the sake of our students.  This is how he operates in a nutshell:
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• Finally, there are the laughs I get when I sit down to grade.

Start of Summer School: A Photo Summary

I’m now two weeks into intensive training and one week into teaching summer school math.  I wanted to SHOW you a few of the structures and activities we’ve (my ELA co-teacher and I) have learned and implemented in the classroom.

I wake up at 5am and am on the bus to school at 6:05.  We begin setting up our classrooms at 6:45, and the kids start to trickle in from 7am through 7:30.  School (morning meeting, academic intervention, reading, writing, math, and lunch) lasts until 12:30.  All children have left the campus by 1pm.  We (teachers-in-training) continue to attend workshops and seminars until 4:30 and are back at the University (where we’re staying) by 5pm.  After eating dinner, I plan, grade, and organize materials until 11pm or midnight.

To be honest, these have been two of the most stressful weeks of my life.  Working 18 hours a day, though, is necessary when the learning curve looks like Mt. Everest.  And I FINALLY feel like I’m starting to get into my groove as far as planning and executing lessons go.

Here’s a tiny illustration:

The Ride to School/ the City Landscape

Behavior Management and Reasons to Grow

Day 1 Math Problem Response

(Explain your answer: “I know it because I did the math.”)

Response to Homework

(*Note: not all of the kids were this positive*)

An End-of-the-Week Teacher Evaluation

(Ranging from overwhelming positive to deeply honest)

Also, to clarify my summer school students are entering 6th grade.  AND I just found out a week ago that I’ll be teaching 6th grade year-round when I get back to my city!

The Language of Math

I’m so sorry I haven’t written in over a week: from moving, a four-day orientation with the teaching program, settling into my new apartment, and driving across the American South, it’s been hard to write (and the wifi inconsistent!).

One of the mornings of orientation was spent doing classroom visits across the city.  Along with one other incoming teacher, I visited a sixth-grade math class.  Each section of students had 31 students: the teacher (Ms. S) noted that there used to be 25 to a class, but another teacher went on maternity leave last month and there wasn’t enough in the budget to hire a long-term substitute.

Despite the full classroom and other challenges, the teacher was effective in getting her students engaged and working immediately.  I noticed that one boy in the back was sitting perfectly still and upright, facing the board silently with his hands clasped in front of him.  I walked up to him and asked if he had a pencil and piece of paper so he could get started on the 5-minute warmup.  Before he could respond, Ms. S took me aside: “Sweetheart, he doesn’t speak a single word of English.  He just moved here from Vietnam and I got him last Monday: I have no idea how to help him without a translator and with 30 other children in the room.”  The boy continued to sit still, intently peering at the screen in the front.

It hurt to see all of the other children working so hard and this young boy falling further behind with each passing second.  One of my values as a teacher is that every child matters, and every moment matters in giving ALL children the education they deserve.

I sat next to him and pointed to his notebook and pencil case.  I removed a sheet of paper and pencil, understanding my gestures.  I gave him a smile (facial expressions are universal!) to indicate that he had interpreted correctly.

I decided to see if he would understand the questions if I wrote them out completely in numbers.  Instead of, “What is the value of 2.17 plus 1.86?” I wrote, “2.17 + 1.86=?”. He nodded in understanding and proceeded to solve it correctly. Encouraged, I continued to the next problems, a review of what the class had practiced two days before: adding and subtracting both negative and positive integers.  The boy easily grasped equations such as “6 + -8= ?”

Ms. S returned and was astounded at his correct answers.  She brought the full practice sheet that the rest of the class had completed the day before.  Again, he solved the first few immediately and precisely, but each successive problem became more difficult.  I thought about how I might teach the concept visually without using a spoken explanation.  To do so, I asked him to take out a sheet of notebook paper and made up a few of the easier equations again.  For every negative integer, I drew the value in “-” signs, and for every positive integer I drew the value in “+” signs directly underneath.  When a “-” and “+” aligned, I crossed out the pair.  The remaining drawing was a representation of the overall sum or difference:

He quickly caught on to the method, and began to draw the “+” and “-” symbols himself.  I left him to work independently for a few minutes so as not to single him out amongst the others in the class.  When I returned, I realized that all of his absolute values were correct, but he had begun to confuse when to draw a “-” versus when to draw a “+”: in other words, he knew to cross off pairs of signs but not when he should use one sign instead of another.  We returned to his sheet of notes, where I wrote a few more points:

1= +1 (2= +2, 3= +3, ….)

-1= -1 (-2= -2, -3= -3, ….)

Then I circled each of the preceding signs and drew a direct arrow to the visual representation, so “-7–> – – – – – – – ” and “6 –> + + + + + +”.

He nodded and got back to work, solving more correctly than incorrectly (but still confusing symbols from time to time).

The next problem was problems such as “-5 – -7”, which require the subtraction of a negative number. This was extremely challenging to represent visually, as it’s tough to explain in pictures why sets of “-” symbols are crossed off in pairs when the original rule represented was that pairs of opposite symbols are eliminated.  I found myself changing the way the problems on the worksheet were written.  Instead of the original equation, I wrote “-5 + + 7”.  This was a reminder of the way I had been taught math myself: I knew to switch double “-” signs to “+”s, but it was an automatic step rather than true understanding.

The boy turned in his completed worksheet at the end of the period with 80% of the problems correct.  Ms. S was so excited that I had gotten through to him, and I think the boy was truly proud that he had completed so much work.  I was happy too, but only because I felt that he had taken something away in those 45 minutes.  That’s not enough for me, and I left with some deeply challenging questions.

• If I were Ms. S (a sole adult without additional aides or translators) and had to ensure that 30 other children were engaged and challenged, how would I simultaneously work with a student like the young boy?
• How would I represent progressively more challenging problems with the visual technique?  What would happen when he got to equations like “78 – 114= ?” or “-10.56 + 8.08”?
• How could I ensure that he had a true sense of mathematical understanding, and not an automatic formulaic response to certain types of problems?

I have so, so much to learn.

Making Math Relevant

I think relevancy is something all teachers think about– after all, an extremely common question is, “So when am I going to use this in real life?” (As far as math goes, my answer is, “You might not use this exact formula/concept, but learning about all aspects of math gives you the ability to be a more logical, creative, and reasonable thinker– math is a different way of seeing the world”).  Nonetheless, many concepts provide opportunity for a more satisfying answer to such a question before it’s even asked. Here are some examples.

While Mrs. D had a planning period on Tuesday, I snuck in to observe another teacher’s “fundamental” section.  They were focused on the aspects of central tendency: mean, median, mode, and range.  Mrs. B (the other teacher) used arbitrary numbers for her examples of data sets until she noticed some of the students losing their focus.  She noted, “In fact, I actually use mean when calculating your homework scores.  They’re a weekly average: I add up the grades for all of the homework given in the week, and divide by the number of assignments.”  A few ears perked up, glad to finally have some insight on the mysterious formula that produced their scores.  “Who wouldn’t mind if I shared their homework scores anonymously to show you the process?”  Nearly every hand went up, excited to be the subject of attention.

The example went as follows.  A student was given five homework assignments in the previous week.  He had received an 82, an 85, a 93, a 90, and a 0 because he didn’t turn in Friday’s homework.  (Here Mrs. B asked a student to calculate the mean).  The result was a 70.  Looking at the average of just the four days when he DID turn in his assignment, his score was 87.5 (rounded to 88).  By skipping a single night of homework, his weekly grade went from a B+ to a C-.  The students glanced at each other with a slightly worried and awed look.

The story has a happy ending, though.  The student in question brought in his homework on Monday.  The maximum points he could receive was 80 because the policy entails a 20% deduction for each day late.  He got the maximum score– 80.  A second student calculated his new weekly homework average: an 86, or a B. There were three morals to this story:

1. Missing your homework means that your grades diminish quickly.
2. Late homework is far better than no homework.
3. “Mean” is used in real life by real, familiar people.

Later that afternoon, Mrs. D’s students practiced multiplying whole numbers by percents/decimals/fractions (they have been developing fluency in interpreting each of the forms and moving between them).  Mrs. D first asked her students to turn to a partner and brainstorm situations where they would have to multiply by a percentage.  When they reconvened a minute or so later, there was a long list that included figuring out how much an item cost during a sale, tipping a waiter or waitress, and sales tax.

After a brief review of what sales tax is and the current rate for this state (6%), the students were asked to solve the first problem on their whiteboards.  Mrs. D knew one of her students had bought a skateboard the week before.  She asked him how much it was at the store ($79.95).  The students were then asked to calculate the price he paid at the register.  They quickly realized it was a multi-step problem.  They had to convert 6% into decimal form (which was fairly automatic for many).  After multiplying 79.95 by .06, they recognized that the answer was only ~4.80: in other words, it was only the sales tax itself, and needed to be added to the original price. Mrs. D asked volunteers to share an item they had recently bought or planned on purchasing for a few more practice problems.  As in Mrs. B’s class, the students were eager to share a personally relevant item.

Finally, one boy raised his hand and said, “My dad lives in another state where there is NO sales tax.  Why don’t all states just make it that easy?  Wouldn’t people be more likely to make purchases?” This led to a really great discussion on different types of taxes, why they’re implemented by the state and country, and how different states set different tax rates in each particular category.

Mrs. D slightly shifted the focus towards interest and the similarities and differences with taxes.  She asked how many students had a savings account at the bank– about half raised their hand– and by multiplying a reasonable amount ($100) by a hypothetical rate (8%: high, but with a purpose), they discovered that leaving saving money in an account ultimately meant that interest worked in their favor.

After a few more examples, Mrs. D asked a child she knew was really into cars what type of vehicle he wanted to purchase and to give an estimate of the cost.  His only guidelines were that it had to be appropriate for a high schooler to drive and similarly affordable.  He picked a Honda Civic, estimating that an older used one would cost around $6000.  Mrs. D explained that when most people purchase a car, they take out a loan for the price of the car and then pay it back with interest over a few years.  She asked the students to work in pairs to figure out what the actual cost of the Civic would be if the student took out a $6000 loan with an 8% rate over 3 years. The caveat was discovering that the result of 6000*.08 had to be multiplied by 3 to account for each year of payment.  The students were astounded to discover that in order to purchase a reasonable $6000 car, they would have to pay an additional $1440 in interest alone.  Other students pointed out that this was just a foundational cost, too: there was still car insurance, gas, and repairs to consider. *Note: technically this isn’t the precise formula for finding the accumulation of interest on a loan, but Mrs. D’s version gave a fairly accurate estimate of the responsibility for taking out a loan.*

The period ended with further points about how banks might offer you various rates depending on your credit score (and that this in itself was calculated based on how well you managed your finances) and how a second option might be to finance directly with the dealer, though the rate would probably be higher than that of a bank.  I was also able to share that the lesson was extremely relevant to my situation, as I’m about to purchase and finance a reasonably priced car.

It was a rich economic discussion that allowed the students to practice the content in a meaningful way, consider how relevant the material was to their everyday lives, and begin to think about how important their financial decisions would be in the near future.

These lessons reminded me of a phenomenal workshop I attended at the National Council of Teachers of Mathematics conference in April.  Two educators from New Jersey created a database of Common Core-aligned word problems related to topics of social justice called Socially Conscious Math.  The questions are meant to invoke thoughtful conversations surrounding issues such as gender and racial inequalities, the impact of poverty, environmental conservation, public health, historical context and more– all through the lens of mathematics.  Here’s a sample:

6. Equality: The entire world has a population of 7 billion people.  The US has a population of 314 million people.

6a. Find the percentage of the world that lives in the US.

6b. The entire world has a population of 9 million in jail.  The US has 2.2 million people in jail.  Find the percentage of the world’s prisoners that are in the US.

6c. Compare your two figures, the US population to the whole world population and the US prison population to the whole world prison population.  What are your thoughts about these two ratios and why they differ?

http://www.worldmeters.info

In their presentation, the founders Deborah Gordon-Goodrich and Gary Kaufman shared guidelines for using their problems (and similar socially-applicable ones) most effectively in the classroom.

• Clearly convey that these are the numbers, not your opinions.
• Encourage students to recognize that their viewpoints are relative: for example, “cheap” and “expensive” are subjective adjectives for monetary values.
• Allow 20 or more minutes per problem in order to structure time for the accompanying conversation.  (If a problem takes significantly less time, you may need to challenge your students to think more deeply and more critically).

Additionally, the classroom culture needs to be such that the students can easily have a meaningful and respectful conversation on a topic that may not be freely discussed in many settings.  This requires that students feel safe to express their thoughts and opinions to you (as their teacher) and to their peers.  Thus these problems should be implemented only after strong routines and expectations are in place.

Finally, Deborah and Gary note that their database is just a starting point.  They hope classroom teachers (and students) will begin to write their own problems based on the plethora of numbers represented in nearly all current topics.

I yearn to teach tolerance and acceptance in my classroom.  I want my students to be able to use what they learn (in math and in other subjects) to change their world.  All too often, I think that math is left out of this process as it’s not considered a subject where students can freely express their beliefs and ideas.  Socially Conscious Math– and even simpler applications like in Mrs. B and Mrs. D’s classes– are paving the way to change this.

Six More Hours in Sixth Grade

It was another fantastic day with Mrs. D and her students at the middle school!

Last week I asked the students what their favorite project, activity, or unit has been in math class.  ALL of them– every single one– said that they absolutely LOVED the “House Project” and I HAD to do it with my students next year.  After asking Mrs. D many, many questions about this mysterious and terrific academic attraction, I can give you a glimpse of it.

The goal of the project was to give students a hands-on, real-world platform for a comprehensive review of the scale factor and rates unit.  However, it also features elements of surface area, geometric figures, budgeting, architectural design, and most importantly, imagination.

In self-selected groups of two or three, the sixth graders were allotted a week of class time to complete the activity.  They began with a $250,000 budget and were asked to design their “dream” house.  As is true in real life, each type of material cost a unique price per square foot (note: application of unit rates!); as is also true in real life, the pool material was the most expensive (the ultimate way to crush a sixth grader’s heart– what 12-year-old hasn’t dreamed of owning a 3-floor house made of mostly pool?). In addition, the plan had to include a certain number of doors, windows, closets, bathrooms, hallways, bedrooms, lawn and driveway space, among other typical building components.

An initial sketch was done on normal printing paper with a grid of 1-cm boxes.  Each 1 cm would be equal to 3 sq. feet in actual size and 1 inch on the poster.

Another page was designated for totaling the cost of all materials and the overall space:

The final products were quite astonishing.  They are currently on display for all visitors and members of the sixth grade wing, and more importantly, allow the students to take pride in accomplishing such a weighty task.

Today the lesson with the “fundamental” (below grade level) group intrigued me the most.  Mrs. D introduced the concept of multiplying fractions.  I was really anxious to see a unit introduction because I imagine it must be one of the most challenging curriculum elements to plan and execute: after all, one must captivate students’ interest in order to engage them in the next several lessons, communicate the importance of the unit, provide a base for exploring Common Core sub-standards, and also ensure that there is understanding behind the relevant process.  Furthermore, multiplication of fractions is among the most difficult mathematical items to understand for kids: the student must have a strong conceptual understanding of fractions and recognize that the terminology “[x] [y]ths OF [z] [a]ths” is a multiplication problem (contrary to all terminology “shortcuts” often taught in previous grades). As a final challenge, most of the students in the section are not yet fluent with basic multiplication and division facts.

Mrs. D used a really interesting and effective visual to demonstrate fraction multiplication.  The sample problem was 1/3 * 1/2. First, she folded a piece of paper into thirds and shaded in the first third for a representation of 1/3.

Next, folding into halves using the opposite rotation, she shaded in the top half using another color.  This was a representation of 1/2.

Here she stopped for a moment to remind students of one conclusion they had reached in their carefully planned warm-up problem: as the denominator increases, the fraction represented gets smaller.  To one student who still seemed a bit confused, she asked, “Would you rather have 1/8 or 1/2 of a candy bar?”  That worked!  She noted that this would be important in a moment.

To visualize the physical multiplication of the fractions 1/3 and 1/2 together, she folded and shaded each of the portions on the same sheet of paper.  She noted that the answer to the problem was the overlapping area: that is, 1 of the 6 boxes was shaded in both colors.

She then asked, “If multiplication often creates a product GREATER than the numbers being multiplied, why does our answer seem so small?”  The students came to the conclusion that multiplying 1/2 and 1/3 together resulted in multiplication of the denominator– and a larger denominator indicates a smaller fraction.

During practice, Mrs. D encouraged the students to draw out the visual process for the first few problems.  This worked for a few students, but others tried to shade both segments with pencil (resulting in frustration when all of the boxes seemed to be the same color) or found that simply applying the formula– multiplying straight across– was faster and immediately dismissed the “understanding” portion of the lesson.  I might try the following techniques to help alleviate these difficulties:

• Have each student physically complete the visual process (folding the paper, shading with two different colors, and doing both processes on a final sheet of paper).  Doing a task results in better memory for it than simply seeing.
• Give other examples using everyday objects: “Say I went to our local pizza place and asked for 1/2 of a pie.  When I got home, three of my friends stopped by and asked for a taste.  How much of the original pizza did each of us get if I divided the half I bought equally?” (1/2 * 1/4, or 1/4 OF 1/2) [You could even act this scenario out, using a piece of paper to represent the pizza and folding/cutting/shading as needed].
• Have them represent each step of the process in extremely clear and explicit terms in an Interactive Notebook (a tool I want to use in order to teach effective note taking and organizational skills).  They can refer back to this page during warm-up, review, and homework practice problems.

A single idea lends itself to so many adaptions: depending on the teacher and the group of students, one or two may be far more effective than others.  The trick is discovering which that/those is/are– and that’s what I have to practice.

Six Hours in Sixth Grade: Ability Grouping

As part of our pre-work, my program requires that we spend at least 10 hours observing teachers in a similar grade level/subject area.  One of my mom’s former colleagues recently switched to the middle school level (the same junior high school I attended seven years ago) and I asked if I could spend three days in her classroom.  Here is the reflection from Day 1.

Similar to many of the nation’s middle schools, this one is organized with three teams of teachers in each of the three grade levels: a science, math, language arts, and social studies teacher all share the same group of students.  Math is ability grouped, generally into three or four sections– one for students who are far behind grade level, one or two for students at grade level, and one for students beyond grade level.  This type of separation is among one of the most salient pedagogical debates:  should we ability group/ differentiate learners?  One on hand, doing so allows for more individually-paced instruction, easily promoting optimal challenge, and creating a “safe space” where students recognize that they are performing at about the same level as the rest of their peers in the class.  On the other hand, kids know exactly what level they’re grouped into, even if the teacher never explicitly labels them.  Although it can be done, it’s difficult to switch between groups, so some students ultimately recognize that with the exception of miraculous growth, they’ll be in the “low” section for the rest of their public school experience.  Finally, the ability group level determines the academic path the student takes in high school: those in the “high” group advance to the point where they can complete the calculus series before graduating high school, and those in the “low” group may barely (or never) reach the minimum level required to enter college.  As Mrs. D noted, “The rich get richer and the poor get poorer.”

In urban or rural settings, race and class have a profound impact on the grouping process.  Students of color and/or those coming from low-income households are disproportionately placed in the “lowest” levels while white and/or middle-class students are typically deemed more mathematically capable.  Behavior may also play a role in a student’s placement, so a hyperactive child who becomes distracting when bored may be improperly evaluated as belonging in the foundational level when in fact, he or she really needed heightened challenge.

Nonetheless, teachers have little power over whether or not the school groups students according to this structure.  However, I plan to buffer against some of the psychological and motivational effects with strategies I’ve derived from my college major, read about, or have seen in action:

• Encourage students to recognize that effort, persistence, and hard work are far more important than group placement.  It’s so easy for a child to arrive at the mentality that since they are in the “low” group, they are bad at math– and will ultimately stay bad at math.  Yet neuroscience research shows that the brain has infinite potential: it simply requires synaptic growth.  Synapses are created when correcting errors and when connecting concepts– ultimately, hard work pays off.
• Help students recognize that focusing on foundational mathematics is an important opportunity, not a punishment.  One child told me today, “This is so stupid.  I hate being in the low class.  I learned this stuff in fourth grade and the rest of the kids are doing so many other things.”  (Note:  this was not in Mrs. D’s class, but a separate section). I responded that the skills that were being taught in his section were so integral to later math.  Even though he might have seen the concepts in fourth grade, now was his chance to learn it better (the brain learns concepts faster and for a longer duration the second time the material is presented).  Once he internalized it and knew it cold, he’d be more than ready for the challenging advanced concepts.  Yet internalization and mastery takes hard work and persistence, so putting in as much effort as possible is imperative.
• Have high expectations for EVERY student.  Push them just beyond their current level, and expect no less than total engagement in the learning process.  When students are in class, they should be learning.  Outside of class, they should complete all assignments because practice is the path to mastery.  Have clear and consistent consequences for violations, and recognize the positive behaviors you emphasize– perseverance, hard work, focus, and participation.
• Make it fun, engaging, exciting, and worth their time.  Hands-on lessons, projects applicable to the real world, movement, videos, songs, and even just heightened enthusiasm/expression/energy are likely to get students focused on and engaged in the material.  Increasing motivation for the subject helps chance the “I’m bad at math so I hate math” mindset.  [Example: Mrs. D. showed this video on central tendency.  The students actually preferred this one which just goes to show how far humor can go in a room full of middle schoolers].
• Give students opportunities to be “experts.” For a review of mean, median, mode, and range, Mrs. D. asked a table group come up and be the “experts.”  Each chose one of the four concepts to present.  Individuals learn the most when they teach others a concept (versus listening to, writing, or reading the material), so it’s an incredible mastery opportunity for presenters.  In addition, peers are likely to be more interested when their fellow students are presenting an idea.  Finally, it supports students’ competence and mastery: ultimately, they can reach the conclusion “I’m so smart I can teach this!” This technique can also be reduced in size:  “experts” can teach in small groups or pairs, and each student can have the chance to take on the role.

Mrs. D. and I also had a fantastic discussion on the importance of making connections with students.  Ultimately, a child’s educational experience in a classroom is characterized by the strength of their relationship with the teacher. It’s clear that Mrs. D. does this using a “tough love” kind of approach.  The students know she’s a stickler for hard work, completed assignments, and respectful behavior but also that they can approach her at any time for extra help or just to chat.

During one of the classes, I had a chance to make a connection.  Mrs. D. was walking students through a practice performance task for an upcoming test.  It was complicated and had many steps, but almost all of the students were persevering, asking questions, and helping one another.  One student, however, had curled himself up in his chair and tucked his head into his sweatshirt.  His papers were blank.  I knelt down beside him and whispered, “Are you okay?”  Noticing that he was crying, I asked him if he’d like to talk.  He nodded and we snuck out into the hallway.

He tearfully told me that in art class the period before, the teacher asked them to look up a famous artist on the iPads.  He accidentally hit “enter” for the wrong Google search term which resulted in something “inappropriate.”  The art teacher walked by and noticed, and told him he’d be subject to the consequences of inappropriate internet use. I first asked him to think about the art teacher’s perspective: that the school has clear rules regarding technology use which she has to follow and that making an exception for one child would undermine her authority. I told him that there wasn’t much I could do since I would only be in the room for three days, and that Mrs. D. had 80 others children to care for.  That meant that HE would have to work through the situation autonomously.  I helped him recognize that he had three options: 1) accept the consequences and move on, 2) visit the art teacher and explain his point of view when he wasn’t as emotional and could think through his words, or 3) talk to his guidance counselor during study hall.  He asked if he could visit the guidance counselor now, but I told him that he was in the middle of a really important mathematics lesson.  We had already missed a few minutes for a discussion in the hall, so it was imperative that he work really hard for the rest of class.  I acknowledged that it might be hard to concentrate, but I believed in him.  I would also be free during his study hall if he wanted to talk again.After taking a few minutes to wash his face, he came back into the classroom and finished the entire packet with everyone else.

It can be difficult to handle situations like these, especially if they are routine.  Later when discussing it with Mrs. D., she told me that he gets emotional nearly every day and asks to use the bathroom or go into the hallway.  He’s also missed numerous days of school.  She noted that he uses attention-seeking as a way to avoid work, especially when he’s overwhelmed by all he has to catch up on. I was glad I had allowed him the brief break in the hallway– if he had stayed and cried or continued to do nothing, the other students would become distracted– but recognized that emphasizing that he needed to be autonomous in his resolution of the conflict was really important.  Even though he was permitted to leave to take a deep breath and talk through the situation, he was still accountable for all of the work done in class.

I hope this was the right action to take.  I’m sure when I begin teaching it will help that I know my students really well and that in the face of patterns like this one, we can work together to establish individual goals and the steps it might take to reach them.  A final realization is that academic achievement and mental state are inextricably linked: as a teacher, you have to care deeply about both.

In just one day I learned so much from Mrs. D: I’m looking forward to two more visits next week!

The College Opportunity

I just graduated from college. Sitting in my cap and gown during the early morning ceremony made me realize that one weekend of culminating speeches, champagne toasts, hugs, and pictures cannot possibly encapsulate four years of growth, learning, love, heartbreak, and triumph. One cannot quantify how much an individual changes over these four critical years. But the most important realization I arrived at over the weekend is closely related to my philosophy of teaching.

Many schools and teaching programs (including mine) push the idea that all children should graduate from college. After spending a semester in Denmark, I subscribed less and less to this viewpoint. Children passionate about farming, machinery, early childhood development, culinary arts, music/dance/theater, and other fields are encouraged to follow their passions once they reach the American equivalent of tenth grade. Trade school is not seen as lesser than a university, and does not result in a significant income difference. At any point, a child on this “alternative” path can change their mind and go to university.

But the reality in American society is that if in tenth grade you stop encouraging or holding high expectations for a student who expresses interest in trade school and somehow make the prospect of high school graduation less imperative, you are closing off opportunities. It is so much harder to go to college if you dropped out or received less than great grades. It becomes easy to assume that students with other interests may not need information on how to attend university affordably or even how to apply. High school is the time when supports are ideally in place: trying to navigate this process at a later point in life is so difficult. Furthermore, many trade school degrees offer little financial security.

Ultimately, college is a path that should be encouraged. It shouldn’t be forced or pushed—because truthfully, it is not an environment where everyone flourishes or can reach their dreams—but it should be made a very real option. Every child should have an academic base that allows them to succeed should they chose to take that route. Every child should know how to apply to college, secure funding for it, and be vigorously prepared to enter such an institution. Even if they choose another option, this one remains open.

I remember how nervous I was listening to the entrance speech by our university’s President and other members of the college community. I didn’t imagine that within four years I’d have fallen in love with the handsome boy I spotted that afternoon in the crowd (now the man I’m moving in with in two weeks!). Psychology—a field I had never studied—would expand my mind, make me a more receptive, open, empathic, accepting, and curious person and remains profoundly applicable in nearly everything I do (most notably in how I approach teaching). I went from wanting to be an industrial-organizational psychologist, to an adoption and family lawyer, to a kindergarten teacher, and secured employment as a middle school math teacher. I formed a close relationship with a city so vastly different than my tiny childhood coastal town: a city marked by poverty, violence, racial tensions, biased law enforcement, and failing schools but also immense hope, incredible food, beautiful niches, tightly-knit neighborhoods, and a plethora of programs and people who envision positive change. I befriended people from all corners of the United States and numerous other countries; I studied abroad; and I became conversational in two other languages. I became a leader through heading a student organization, establishing and teaching a summer literacy program for local schoolchildren, and living as a freshman RA. I suffered an ineffable tragedy- one of my residents passed away in her sleep—and the strength and persistence that can result from a community that truly cares about one another. I became an extravert, drank too much coffee, learned I can fit in my laundry bag, forgot to save a final paper, put body wash on my toothbrush, and discovered that frat parties are exactly like they’re portrayed on TV. I got really sick and recovered, worried for my sister when an illness kept her out of school for six months, took an awful job at a coffee shop so I could pay for laundry and medicine, and learned to find ways to manage my stress. I did so, so many things I had never done before, didn’t think I could do, and/or didn’t imagine I’d ever WANT to do.

This is the kind of experience that cannot be replaced or replicated. I now have an insanely expensive piece of paper that attempts to memorialize my time, but it can’t do justice to how I’ve changed as a person. No one will have the same collection of thoughts and moments that made my college experience what it was, but everyone deserves the chance to create their own four-year story.