Ms. Menard and the Very Blustery Day: #DITL November 21, 2016


This post comes to you at 6:22 AM on the first very cold and blustery day of the season.  It’s the start of the short pre- Thanksgiving week, and I am looking forward to the 4 day weekend probably as much as my students.  The harsh chill wind feels appropriate after the morning news; stories which contrast some Jewish support for Donald Trump with his anti-Muslim rhetoric and views are particularly upsetting this morning.  After a lifetime of holding up the Holocaust and saying, “never forget, never again,” it appears that some of my cultural compatriots are doing exactly that.  The fear my Muslim students expressed to me on November 9 stays with me, and I am wondering how I can make them feel safe, at least in my classroom.  I’ve spent a lot of time thinking about privilege the last few weeks, and I can thank the upset in the election for this – perhaps the only benefit I can see right now.

On the agenda today: In my three sections of Algebra 2, the students will be working in groups on tomorrow’s exam.  This is the first time I have tried this strategy, but, bolstered by input from Jonathan Claydon, Amy Hogan and my office mate, I’m hoping the communal efforts will boost student understanding of the content, and their independent demonstrations of mastery.  My concerns include making sure no exams (or photos of them) leave the classroom, and students not making good use of their time together.  In Discrete Math, we will beginning our unit on Problem Solving strategies, which is a distillation of the course I taught last fall.  I will still be using problem sets from Crossing the River with Dogs, but I’ve come up with several different versions of each set to use for assessment.  The summative project in this unit will involve the students creating problem sets of their own; again, I am trying to counter any inclination to over-collaborate (how’s that for a euphemism?).

It’s not even 7:30 AM and I volunteered to go on the spring trip to Quebec with the foreign language department. I don’t speak any French, but I’d love to visit Canada, and maybe screen-shot-2016-11-21-at-3-56-38-pmthey need a math teacher!? The sound of the wind is a howl in my office, which is located on a corner of the school building on the top floor.  Here we go, Monday morning.

9:51 am
Two sections of Algebra 2 worked on the ‘practice exam’; many students commented that they found it a helpful exercise.  From my view, the group review surfaced the topics that need the most study, and I was able to reiterate these areas to the entire class.  For me, it was an opportunity to observe, deflect questions and refer the students back to one another for support. At the end of each class, the students were puzzled that there would be no answer key provided for this review, and that they needed to leave the papers with me.  But I provided a review and practice sheet for them last week, complete with an answer key, as well as an assignment on with many practice questions.  I think it may have dawned on some of the students that they were looking at the actual exam, and this will be the only time I can use this element of surprise.  Hopefully, I will see better results and more work that evidences understanding tomorrow.

1:27 PM
My teaching day is over, although I’ve got two meetings left to go, and a private student.  My Discrete Math classes both went well (yay!!); the introduction to problem-solving was met with both interest and cooperation, some of which is a vestige of last week’s Parent Teacher Conferences.
Our first problem-solving strategy is Draw a Diagram, and we began with Virtual Basketball League:

 A new basketball league was formed in which each of the teams will play three games against each of the other teams. There are seven teams: the Antelopes, the Bears, the basketballCubs, the Dusters, the Eagles, the Foxes, and the Goats. How many games will be played in all? 

The range of approaches was impressive, although very few students attempted to draw a picture for a solution.  I saw charts, lists, tree diagrams, and on some papers, a simple but erroneous 7 x 3 = 21.  Many students who realized that the Antelopes needed to play 18 games assumed that each of the other 6 teams would play 18 different games as well. But in each class, there was at least one student who understood that the number of games each team would play when calculated this way was double the actual amount.  It was a clear learning moment for those students who had made the error – I hope. (Come to think of it, the student work on this problem would make good fodder for!) I drew a network sketch on the board to show how I calculated the answer, but it looked complicated to many of the students – I’m not sure I disagreed.

We moved on to Model Train Set:

Inline image 1

This simple problem got them all drawing pictures – those students that resisted struggled a bit.  Many drew circles, but there was at least one solution that resulted in a triangle inside a circle, and then my personal favorite: Inline image 2
Of course – six poles – the vertices of a hexagon!  Brilliant, Itrain-track-clipart-clipart-panda-free-clipart-images-mfqqqk-clipartthought – this solution appealed to the geometer in me.
In both sections, particularly the troublesome 7th period, the unit launch went well.  I’m looking forward to more of the students’ work as we proceed through the different strategies.  The big lesson I learned from teaching this last year was the need to have problems with multiple solutions.  I  haven’t gotten to that yet, but I have created several versions of the problem sets I want the students to complete for each problem-solving strategy, and the unit project will provide differentiation in its open-ended nature.
The third section of Algebra 2 went as well as the morning sections, although, perhaps predictably, the student need was more evident – predictably because the quiz and exam results of this class have been markedly lower than the other two, much to my mystification.  While working on the practice exam, entire tables would become stumped by a question.  My first usual response to questions – “Have you asked your tablemates?” was as often as not met with “yes, and none of us know how to do it.”  I gave hints and tried to point them in a direction without giving a direct answer.  I began a list on the board entitled “What I Am Noticing”, to which I added items like “You need to practice f-d-a980615eb303ee117b66698aaabc2cc0696220683ce883a23ab7311eimageimagesolving quadratic inequalities,” or “Everyone should review Focus Directrix form of the equation of a parabola”.  I hope they take my suggestion to heart.  I’ve got 4 girls in my office at the moment, practicing those two topics (and others) until this afternoons basket ball game, and I’m hoping that their efforts are indicative of those of their fellow classmates.  I’d really love to see some improvement in the exam scores.  I can’t wait to see their faces, and hear their comments, when they realize they had been working on the exam all along.  Will they be happy? Peeved that I dissembled today?  Will I see work that truly evidences understanding rather than mere recall from the practice?
My first meeting was a bust – we have bi-monthly professional development at the end of the day on Monday; we are supposed to be engaged in one of two inquiry cycles to be completed during the school year.  We’ve been given little direction from our facilitators, but fortunately I am pairing with a teacher who understand the process, as do I.  She lives with the consequences of students not fully understanding how to manipulate and simplify rational expressions, a topic that I will be teaching in January, so we’ve come up with the strategy of having students look at incorrectly solved problems in order to hone their skills.  Today, however, our meeting never took shape.  The facilitators did not appear, nor did the other department we are working with on this assignment (science).  Calls to our assistant principal’s and principal’s office did nothing to enlighten the situation. The attending teachers, thus, spent the time reviewing [sort of] the inquiry cycle, among other professional (ahem) issues.  I’m not normally one to ignore an assignment, but this inquiry effort, launched by our administration with little framing and preparation for the staff, feels, if not misguided, then perhaps mismanaged, and just plain missed as an opportunity.  Tomorrow, the Instructional Cabinet (another committee I sit on) will be discussing just this issue at an open meeting tomorrow afternoon.  Hopefully some progress will be made towards a more constructive use of our professional development time.
I’m off to Manhattan for a meeting at Math for America to pre-plan for a summer conference, spearheaded by Matt Baker and Brian Palacios!  The wind is still howling outside, so talking about a summer conference sounds very nice indeed.
9:21 PM
Home at last – and almost time for bed.  The meeting at Math for America was great, and I was sorry that I couldn’t stay for the whole thing – the opportunity to be involved at the very beginning of the planning process is envigorating, even as my teacher energy is hitting that dip before winter holiday build-up begins (does that even make sense?).  I’m looking forward to continued participation in that effort.
I left early to meet with a private student – a girl I have been working with since she was in 7th grade; we no longer meet regularly (she is in high school), but she is insecure prior to exams and always wants a tutoring ‘booster’.  And anyone who knows me at all knows Picture 019that I never turn down an opportunity to talk geometry.  I turned her on to my favorite compass – always fun to see how excited someone becomes when they realize there is an alternative to the typical pointy hard-to-control tools.  I love having these long term relationships with students – watching them grow, and helping them learn to appreciate math – even if it means an extra-long Monday.
Finally at home, I get a snuggle from Ollie, and have a quick FaceTime conversation with Izzy, my friend’s daughter.  I’ve known this child since she was five; she’s now a freshmanphoto-on-11-21-16-at-9-17-pm at one of New York’s specialized high schools.  She texted me earlier this evening while studying for a geometry exam (seems to be going around tonight..), and not only am I sucker for geometry, but I’m a sucker for this kid as well.  It was my pleasure to discuss negation, triangle centers, and congruence shortcuts with her.
I’ve got two days to go to Thanksgiving break.  In those two days, I’ve got an exam to give, projects to grade, a meeting of my Professional Learning Team on Racially Relevant Pedagogy and a medical appointment.  Thursday’s lazy morning beckons tantalizingly.  But I’ve got to go to bed tonight before I can begin to get there.


1) Teachers make a lot of decisions throughout the day.  Sometimes we make so many it feels overwhelming.  When you think about today, what is a decision/teacher move you made that you are proud of?  What is one you are worried wasn’t ideal?

I was very proud of my deflecting all student questions during the exam review today.  I redirected the children back to each other, and answered their questions with more questions.  And I think I managed to keep them from being furious with me while I was doing it.

Conversely, I think I could have pushed my Discrete Math students with some questioning a little more during the problem solving activity.  I’m going to work on that in the lessons to come.

2) Every person’s life is full of highs and lows.  Share with us some of what that is like for a teacher.  What are you looking forward to?  What has been a challenge for you lately?

3) We are reminded constantly of how relational teaching is.  As teachers we work to build relationships with our coworkers and students.  Describe a relational moment you had with someone recently.

I am feeling more confident in the relationships I am developing with people at Math for America.  I’ve come a long way to get there, but that’s another story for another post (maybe).

4) Teachers are always working on improving, and often have specific goals for things to work on throughout a year.  What have you been doing to work toward your goal?  How do you feel you are doing?

I had four students come see me for extra help today in preparation for tomorrow’s exam – they came bustling in with their snacks in between classes and the school basketball game.  They asked questions, helped each other, and worked away.  I love when the kids are that comfortable in my office, and it lets me know I am creating safe spaces for them in which to be themselves.

5) What else happened this month that you would like to share?

Saturday night was Nerd Prom aka the Math for America Fall Function, complete with aerial entertainment, decagonal menus, and a mayoral speech.  I said in my last post that November 2016 has not been my favorite month ever, but Saturday evening helped.  Thanks, Math for America!


#DITL Day in the Life: Parent Teacher Conferences

treeautumnredandgrleaves900Today is the Autumnal Education Equinox – the longest day of the teacher’s year: Parent Teacher Conferences.  Arriving at school at 6:45 am, I will be leaving at 8:45 pm, and arrive back at school tomorrow at the same time for round two.  I don’t mind conferences at all, except for this intense two day period.  Tomorrow is a half-day; school is open to parents from 12:15 to 2:15, and the six class periods being held in the morning are shortened to 33 minutes each.  The classes meet earlier than their normal times because of this schedule, so absenteeism is high. I’m not happy to lose the day of instruction, especially with my Algebra 2 kids.

img_9684In Discrete Math, the kids have been working hard on their probability games, creating (among other things) some great artwork for the classroom.  I’ve gotten in touch with a number of parents in those classes in recent weeks (behavior issues, unfortunately), and I’m hoping some of them will come up to school.  Traditionally, however, my elective img_9682classes bring in fewer parent/guardians than my core classes.  In Algebra 2, I just returned an exam on which many students did poorly.  This is a ‘gifted’ track class, so I am expecting a big turnout.

Thursday Night

I was very busy the first night, which is good, and had a fair mix of visitors from both of my courses – Discrete Math and Algebra 2.  As predicted, there were a fair number of Algebra 2 parents who were concerned about their children’s last test grade, and I spelled out for each of them the steps I was taking to support the children in their preparation for the upcoming exam – detailed review sheet mirroring the exam with an answer key,gradecreating weekend study partnerships, and group review of the exam the day before it is to be given – and what their children could do to help themselves – review class notes and problems, ASK questions in class, seek extra help, work through the review. (I felt a little like a broken record, but the truth is that most students need to do all of these things.)  I love being able to share details about their children’s classroom aspect with parents; I remember how important that was when i was on the other side of the table (nothing worse than feeling like your child is not much more than a line in a teacher’s gradebook).

I also had several parents who I had contacted regarding lack of work or challenging behavior on the part of their children; I was very glad to be able to have those conversations face to face, particularly if the student was there.  Some meetings were difficult, however; a student who I cannot engage in one of my Discrete Math classes laughed at his parents as they tried to find out why he refused to participate in any way in my class.  At the very end of the evening, after parents were theoretically no longer to be in the building, I had the opportunity to speak with the mother of a student who has pushed my tolerance to the limit this term – taunting others, copying work, and when submitting work, drawing pornographic pictures on it (don’t ask). Denying his culpability to the last moment, this boy finally agreed to make up some missing work over the long Thanksgiving weekend.  We’ll see.

Friday Afternoon

The half day of classes went very quickly – when periods are a wee bit longer than a half hour, they fly by.  But most of my Algebra 2 kids were in attendance, and dove into screen-shot-2016-11-18-at-6-13-20-pmcorrecting the aforementioned exam. But when conferences began, the afternoon moved much more slowly – I had only 6 visitors.  In fact, I wrote most of the recap of Thursday night while I waiting for parents.  I had a meeting with one more mother of a student who chooses not to do work but rather to argue with and bait me in Discrete Math; this mother is relying on faith to help her son as her other strategies have failed.  She thanked me for my patience, but I wish we could have come up with a better plan.  I’ll keep trying in class.  And so another season’s Parent Teacher Conferences have ended.



1) Teachers make a lot of decisions throughout the day.  Sometimes we make so many it feels overwhelming.  When you think about today, what is a decision/teacher move you made that you are proud of?  What is one you are worried wasn’t ideal?

I was proud of my launching of the ‘Weekend Study Buddies’ initiative in my Algebra 2 classes; enough students signed up in each class to indicate that it could be a worthwhile effort.  Maybe I can be even more structured about this in the future.

I had a few parents who weren’t satisfied with hearing that ‘many students didn’t do well on the last exam’ and I don’t blame them.  This doesn’t address their child’s specific needs, and I am certain that many of them say to their kids (as I said to mine), “I don’t care what other children do, I only care what YOU do”.  I wish I could have given them more specific information about their child’s performance on the exam, but honestly, with 102 students in Algebra 2, I just didn’t have the data.

2) Every person’s life is full of highs and lows.  Share with us some of what that is like for a teacher.  What are you looking forward to?  What has been a challenge for you lately?

I am looking forward to my first attempt at a group exam process next week.  I hope it improves the results and the students’ level of preparation when it comes to working on their own. A challenge? The flip side of the previous sentence – trying to figure out how to promote deeper understanding of ideas that I think have been clearly presented, how to formatively assess more frequently and effectively so I am not blindsided by clear evidence that deep understanding has not been achieved.

3) We are reminded constantly of how relational teaching is.  As teachers we work to build relationships with our coworkers and students.  Describe a relational moment you had with someone recently.

I had a lovely moment with some of the boys in an Algebra 2 class today.  Our school won the New York City PSAL Baseball Championship last year; apparently we have a number of young superstars, and the winning pitcher is in my 3rd period class.  These boys are already being recruited by colleges; some commit to an institution as early as their sophomore year, only to find out that ‘better’ schools might want them enough to provide full scholarships later on. We discussed the pros and cons of making an early decision, and they made me promise that ‘when’ they were in the Championship series again this year, I would attend the game (I sadly could not last June).

4) Teachers are always working on improving, and often have specific goals for things to work on throughout a year.  What have you been doing to work toward your goal?  How do you feel you are doing?

The attainment of my goal of building better relationships with my students is progressing in many cases, but not all.  I am working towards seeking more educational opportunity for all of them, and looking honestly at myself and my behaviors that may or may not promote that.  As I faced the parents of my black and Muslim students, I thought about the racism and prejudice they face, and their fears in light of the presidential election result.  I want to be an ‘ally’ in the true sense of the word.  I am trying to use my empathy and privilege to create safe spaces.  I don’t know if I am succeeding, although I have made it clear that equity is a theme in my classroom.

5) What else happened this month that you would like to share?

November 2016 has not been my favorite month.  The world is changing in a way that I cannot predict.  I don’t want to live in fear, but rather channel my grief and outrage into action, as mentioned in the previous paragraph.  I’m hoping to find co-conspirators in this effort, and to hold myself accountable to that goal.

And I hope my Algebra 2 kids do better on the next exam…. ; )



Grieving with my students


Last night, my stamina ran out at 1 am, after watching the count in Pennsylvania move from a 3,000 vote margin to a 2,000 vote margin back to a 35,000 margin.  I slept fitfully, and when my husband came to bed without waking me (presumably to share good news), I knew even in my sleep, that Hillary, and the rest of us, lost the election.   I somehow got myself out of the house on time – 6:10 am – but  once on the bus, felt the tears welling up.  When I got to school, I made it to my office and broke down.  How would I get through the day?  I went to twitter for support and help.  screen-shot-2016-11-09-at-10-11-56-am

It helped to hear warm voices, even virtually.

I took my cue from the wonderful Heather Kohn.screen-shot-2016-11-09-at-10-13-23-am

I already had a Desmos activity planned (thank you Mary Bourassa!), so I began each of my classes by telling students that I wanted to open the floor for conversation, but if they didn’t want to talk, they had the option of working through a Quadratic Transformations activity.  Laying out a few ground rules (one mic, safe space), I opened the floor.  And they talked.  Sadly.  Intelligently.  Asked questions of me.  Before I started the discussion, I had to step out into the hallway, because although I wanted my students to understand how deeply upset I was, I felt that crying in front of them at the outset would not set the needed tone.  I want to create a space for them share and ask safely, but ultimately to realize that we are not completely disenfranchised (despite appearances to the contrary) – that we have the power to speak up, to use any privilege we have to fight racism, Islamophobia, and other forms of discrimination, to make sure all voices are heard.

These were some of the fears – heartbreaking – that were surfaced.

  • From a Muslim girl: My mother told my brothers they had to shave.
  • From a Muslim boy: Can he make us wear identity badges?
  • Another male student: I’m Latino, and I can’t understand why 37% of Latinos voted for him. I’m angry at them.
  • A student whose parents were born in Mexico: I’m okay but my parents are undocumented.  I’m worried about them.
  • A boy from Trinidad: I’m going to be deported tomorrow.

I tried to allay fears where I could – I told the boy who feared id badges, that if he had to wear one, then we all could wear them in solidarity.  I wasn’t sure to say to the kids who are afraid of deportation, but I told them I was fairly certain that it wasn’t imminent.  I wanted to answer responsibly, but their pain and sadness was hard to see.

For the most part the conversations were thoughtful, heartfelt, and reasonable.  In one class, Planned Parenthood funding and reproductive rights came up and things quickly in another direction.  I explicitly steered the talk back to the election, not ready (or feeling sufficiently prepared) to engage with that topic.

There were students who were visibly shaken, had clearly been crying, and even when not participating, were taking in every word of what I hope was helpful in some sense.  I tried very hard to keep my own opinions moderately and infrequently voiced, which was not always easy.  One girl, even though unhappy with the outcome, said “Well, you know Hillary was a crook and should be in jail, so it’s not really a surprise that she lost.”  I pressed her for the nature of Hillary’s crimes, and was told “the Wall Street Journal says so, she stole a lot of money and she stole half the White House.”  I asked the student what that meant – to steal half the White House, but the girl couldn’t answer.   I told her I respected her right to her opinion, but she needed to make sure she had facts before accusing someone of a crime.

Kianna in my 5th period said “We can’t just give up.  We need to stand up for what’s right.  We’re not done for, and we need to keep protesting and speaking up.  Just being negative screen-shot-2016-11-09-at-10-10-20-amwon’t get us anywhere.”  I could’ve kissed her.  And I reminded the kids that 50% of the population didn’t vote for Trump.

In my last class, there were a few dicey moments – when two boys began baiting some of the students who expressed fears about being undocumented, or when another student told the boy sitting next to him “Go back to Mexico!”.  These last two were allegedly kidding around, but I wonder how much true feeling was in that jibe.  I hope not too much.

I’m almost ready to go home, still feeling like a truck hit me, physically and emotionally.  I just read the concession email that Hillary sent out, which put me back into the tears I began the day with.  But I’m proud of my students for discussing something so painful in such a respectful manner, and I’m proud that my classroom became a safe space for all of them.  And I’m going to try to keep what Kianna said in mind. Going to try.





Money Animals!

I have to confess that I have not always been comfortable teaching probability.  I’m fairly certain that I didn’t learn anything about it in high school (NYS Regents mathematics way back in the day BEFORE Sequential I, II and III), and I never took a course which included it in college.  My knowledge is self-acquired and taught – through preparing for certification exams, Praxis exams, and teaching.  In the 5 years I’ve been teaching the topic, I’ve worked and reworked my lessons in Algebra 2 to bring my own understanding to a conceptual level which is deep enough to communicate to my students, and have relished the loving addiction to Pascal’s Triangle I have thus created in many of them.

money-duckThis term in Discrete Math, I took the plunge and taught a unit (using lessons generously shared with me by a colleague at school) based on games of chance – dice, spinners, flipped quarters, etc.  After two weeks of playing and analyzing games, we spent several days learning about Expected Value, relatively simple to calculate (in our examples) but tricky to understand.  Once I was convinced that the students knew how to approach an expected value problem, we worked through the famous Money Duck lesson, developed by Dan Meyer.

Attendance is an issue in my Discrete Math classes, so over the course of the lesson and the task that followed (a total of three and half days), I replayed the video for students who screen-shot-2016-11-01-at-8-23-35-pmwere either absent physically or perhaps mentally.  I never anticipated how much 16 year old students would enjoy watching Dan Meyer wash his hands repeatedly.  The class came to a standstill every time I turned it on.  This enthusiasm for the video carried over to their analysis of the probability distributions.

My colleague designed an extension for the lesson, similar to Dan Anderson’s activity.  The students designed their own “Money Animals”, complete with a price, distribution, untitledand an expected value.  This was all done on one sheet; the design, price and distribution were visible to all, while the calculations were on the back.  After everyone had finished, we had our Money Animal Bonanza.

The students were allowed to purchase two Money Animals, based on the desirability of the product itself and its distribution.

At first, just a few students wandered over to the Money Animal Mart.  I was impressed with how thoughtfully these early shoppers examined their options.  And then EVERYONE rushed the board, eager to debate the pros and cons of design and potential gain.  The results were interesting, and in some ways predictable.

(1) There’s an artist in every class, waiting to draw a gorilla. univorngorilla

(2) Everyone loves unicorns.

(3) Marketing is everything, and frequently outweighs sensible decision-making.

The clock ran out, and I announced the ‘sales’ results and the concomitant expected values.  The potential earnings on the BAPE soap were pretty low with its steep price of $35, but the students unanimously supported its cachet. bape

I would like to have the students complete some sort of analysis which would make the relationship between the price, the distribution and expected value more concrete.  Maybe expand the Money Animal Mart idea, give them Monopoly money to shop with, and find a way to calculate everyone’s profit as a designer, and winnings as a shopper?  I’m looking forward to running this activity again with further refinement – because if I can get the students up, moving and this interested, there’s definitely a bigger future for this.



By the way, Happy Halloween!



Day in the Life: October 21, 2016

Friday, Friday!giphy

It’s hard to feel that joyous at 6:10 AM, waiting for the bus in the dark. This is the first full five day week in three weeks, so I’m a little tired. I am looking forward to the weekend, but I am attending a full day restorative justice training tomorrow (Saturday), so I  won’t be sleeping in for another day or two.  I’m also feeling the hint of a scratchy throat and post nasal drip, and hoping that the extra vitamins and Airborne I downed this morning keep the threatening cold at bay; hopefully the momentum and energy of the day will push me past it.

The nice thing about commuting this early in the morning is that it’s quiet and quick. (I’m actually the only one on the bus for the first few stops.)I see the same group of 4 women taking their daily walk around the park at 6:15 AM; I’ve seen them every day for the last 5 years, and know the bus is right behind them.  I sort of envy their ritual and imagine how much of each other’s lives they’ve shared in this early morning trek.  Then again, they’re getting up before 6 am when they don’t have to, so maybe envy isn’t the right feeling. 😜

I’m always amazed at how much is already happening at school when I arrive at 6:45.  I eat breakfast at my desk and open up my lesson for algebra two. I’m introducing quadratic inequalities today, and I am nervous. My department tends to teach this topic in a completely procedural manner, and I am determined to get the children some conceptual understanding before we go into procedure. I’m borrowing an idea from Sam Shah, but I don’t really have the time to go through his entire excellent exploration. I decide to use a demonstration on Desmos; the students can open the calculator on their phones, and do the exploration along with me. First we have to review compound linear inequalities, and I know from experience, that even though they have seen these in middle school and Algebra 1, for many children, it will be as if this is a brand new topic this morning. Knowing that they need to understand linear any qualities before we even approach quadratic inequalities makes me nervous; given our departmental pacing calendar, I don’t have time to spend a whole period on this introduction. I also know, that if I don’t make sure everyone is familiar with linear inequalities, that I will lose one third of the class when we move onto quadratics. This push-pull between the pacing calendar and the realities of my students’ proficiency informs most of my instruction. It’s 30 minutes to showtime, so I’m off to set up my classroom.


My first 2 classes were back-to-back sections of Algebra 2, ‘gifted’ track; I was spontaneouslyuntitled observed during the first class, which of course meant that the SmartBoard wasn’t working properly.  The display was functional, however, so all was not lost.  We began with this warm-up, and things went as I predicted.  Most of the students were comfortable with the first two problems, many were not with the second pair.  As they worked and conferred with one another, Iuntitled asked students to put some correct and incorrect work on the board (I thanked the students who were putting incorrect work on the board, and told them that they were giving the class the opportunity to look at a common error).  We did a lot of noticing and wondering, and then moved on to some purely algebraic examples, which served to surface further questions, such as ‘Does the variable always need to be on the left?’ and ‘Do we read the inequality from left to right or right to left?’.  All great questions which reflect conceptual misunderstandings that should be corrected before we go further.

By the time we worked through the Do Now and the three examples above, and reviewed how to express the solutions in Interval and Set Builder Notation, there was barely time for independent practice, and quadratics?  Hopefully on Monday.  I spoke to my AP during the observation; she also teaches a section of Algebra 2 and agreed that the pacing needed to be adjusted to make sure the students were recalling all that prior knowledge we were assuming they had.

I have a break after these two classes which is supposed to be my lunch period (it’s from 9:45 to 10:30); I have a student monitor during that time who is great at sorting through paperwork, checking in homework, and running errands that would eat up the free period. Two Algebra 2 students from different sections stopped by for help with the previous night’s homework.  I am always very glad to see kids with questions, and wish there were more who had the time or inclination to come ask.  Quite frequently this makes the difference between moving forward with the class or getting left further behind.

After ‘lunch’ comes my daily challenge – three classes in a row: another section of Algebra 2 sandwiched in between two sections of Discrete Math.  The character of the two Discrete Math sections is very different.  In the first section, the attendance is healthy, as is the percentage of work submitted by students, and participation.  We are in the middle of a unit on probability, and after a week of spinners and dice, we have moved on to Expected Value.  It’s the first time I’ve taught this topic, and I’m enjoying it, as are the students who are allowing 140426_1themselves to stay involved.  Yesterday we spent the period flipping marbles2quarters and manipulating game score structures to change the expected value for each player.  Today, I proposed a marble game to the students (they would pick a marble from a bag, and I would pay them a certain amount of money depending on the color), and asked the kids how much they would pay to play.  (By the way, my students are very wary and kind of cheap! No gamblers here.) The kids are intrigued because the math is accessible, the topic is not hugely remote, and in fact, entertaining.  Next week, we are moving on to Money Duck, which will be followed by students will be designing their own money animals.  The final assessment for the unit will be a group (optional) project in which the kids design carnival games.  This is not my project, and I’m not sure who created it – a quick Google search reveals the same pdf file on several websites.  Here’s the version I am using (many thanks to its originator):

I am really looking forward to seeing these games.

The afternoon Algebra 2 class ran similarly to the morning sections, and my teaching day finished with my second, and more challenging, Discrete Math class.   This class has lower and varying attendance; I have a group of boys who come to class intermittently, and sometimes all together. The class has five current or former English Language Learners, six students with IEPs, and many of the students (ELL/IEP or not) are not on track for graduation.  There are twenty seven students on the roster, but I rarely have more than sixteen in class (except for the day I was observed, natch – how do the kids know??).  Although I’m not dealing with the type of hostility I encountered last fall, there is a smarmy and somewhat sexist lack of respect coming from some of the young men which I have not yet found an effective way to counter.  The content is engaging (games of chance, logic puzzles, tossing dice, flipping coins and collecting data).  I’ve tried private conversations, reaching out to guidance counselors, and some phone calls home.  I am avoiding involving the Dean’s office unless absolutely necessary.  I realize that the problematic students are outnumbered by those who are working and engaged, but the off-task behavior seems to control the class.  I’m frustrated; it’s the end of the first marking period, and we’ve got a long way to go this term.  I’m contemplating individual goal-setting and contracts to start the second marking period, but have a feeling that this may not be the best strategy with 17 year olds who have not found anything worthwhile in a math classroom in quite a while.  If you’ve got any ideas, I’d love to hear them.

Today is the end of the first marking period, so there was a flurry of late work submitted to my inbox.  I allowed corrections on DeltaMath for the last Algebra 2 quiz; many, MANY students took advantage of this opportunity, and I have decided to give back 50% of the points.  When students do corrections by retaking assessments in my presence, I usually return 100% of the points.  But after a lot of thought, I decided that working through examples on a website was great practice and progress toward mastery, but not necessarily evidence of independent proficiency.  It’s tricky, and not something I have done before.  We don’t do standards based grading at my school, but I am a firm believer in allowing students the opportunity to take the time they need to learn.  I don’t, however, have a complete structure in place, and occasionally worry that my foray into allowing corrections will backfire – it only takes one angry and vocal parent to create a problem.

It’s 3:46 P.M. – I’ve been at school for NINE HOURS.  I have a pile of grading which needs to get done in time for marking period grades to be submitted early next week, and I’m still fighting my body’s urge to succumb to the cold.  If I go home, get in bed, and rest for a day, I might avoid it.  But the restorative justice training tomorrow beckons….

img_9524I could continue this post for the rest of my day, but I can predict what the next six hours will look like:  me in pajamas, fending off kittens while I try to grade papers and sip tea.  Eventually I will crash with a crossword puzzle (and I predict that the training will have to happen another time; the thought of getting sick right now NOT ALLOWED).


Happy Halloween! from


1) Teachers make a lot of decisions throughout the day.  Sometimes we make so many it feels overwhelming.  When you think about today, what is a decision/teacher move you made that you are proud of?  What is one you are worried wasn’t ideal?


I think my decision to stay focused on linear inequalities and surface misconceptions was a good one; if I pushed ahead to quadratics, not only would I have lost some students content-wise, but their frustration might have farther reaching consequences beyond this lesson.  And when kids come to talk to me about their homework, I know that they trust me, and care enough about the class to make sure they are keeping up.

Not ideal – I can’t seem to strike the right note with the boys that are giving me some trouble in my last class.  I can feel my temperature rising with some of their rudeness, and have wished that I could say what I am thinking…not a good sign.

2) Every person’s life is full of highs and lows.  Share with us some of what that is like for a teacher.  What are you looking forward to?  What has been a challenge for you lately?


As we shift to the Common Core standards in Algebra 2, I am committed to moving beyond procedural teaching and investing the time in looking at bigger ideas; I know I have made some concrete steps in this direction in a number of lessons, and I’m looking forward to continuing with that work.  As far as challenges, I think I’ve described them pretty well in this post.  It’s ongoing.

3) We are reminded constantly of how relational teaching is.  As teachers we work to build relationships with our coworkers and students.  Describe a relational moment you had with someone recently.

A student came up to me the day before yesterday and asked me if he could still retake the first quiz.  Before I answered, he apologized for being out of it (which I hadn’t noticed; he had been participating in class), and said he had a lot going on at home.  I asked him if he was okay, and he told me that his parents were splitting up.  He choked up and had tears in his eyes.  I felt so badly, and we talked for a few minutes.  I think it’s hard for boys to be emotional like this in high school, and I’m glad he trusted me enough to reach out for help.  He’s been out for the last two days, and I am concerned.

4) Teachers are always working on improving, and often have specific goals for things to work on throughout a year.  What have you been doing to work toward your goal?  How do you feel you are doing?

I continually try to connect with the students as the term goes on.  My response to the students in my Discrete Math classes that are challenging me is more open and conciliatory than it has been in the past, despite my frustration with some of their behavior.  The conversation with Damon (previous question) shows me that there ‘s so much going on with our kids that we can’t see, especially in a math classroom.
5) What else happened this month that you would like to share?

Next week the Racially Relevant Pedagogy PLT I am facilitating with Jose Vilson meets for the first time – I am nervous and excited.  We had a great planning meeting last week, and I think we’re pretty good collaborators.  I was also proud to have my blog post in the Math for America Teacher Voices blog a week or so ago.



Enrich and Enhance Your Professionalism through Blogging

This was cross-posted in the Math for America Teacher Voices blog today (along with the headshot!).

Joining the online community of mathematics educators has had an indelible impact on my professional development. Through blogging, I explore and reflect on my teaching wendy-menardpractice, as well as contribute resources to a vast network of similarly inclined teachers. By writing honestly, I expose myself not only to critique, but also to support. And by raising my voice in response to inequities and injustice in education, I am stepping out of my classroom and comfort zone to engage in debate. The greater the number of teachers who challenge themselves to blog, the more vibrant the online community becomes, thus elevating the profession; consider taking this creative step to develop yourself.

The first teacher blog I ever read was Math Teacher Mambo by Shireen Dadmehr. As an early career teacher in a high need school, I was continually searching for high quality materials to engage students for whom math was at best a tolerated chore, and at worst, a subject to be avoided. That Shireen had a widget on her blog, which linked to all of her worksheets, freely available for borrowing, was a game changer for me. I visited her site regularly, downloading her content for current and future use.

Shortly thereafter, I came across Dan Meyer’s blog, and realized that the world of math education blogging was huge. Reading through comments on any of Dan’s posts, and clicking on the links therein, led me down a fascinating rabbit hole of blogs containing resources, reflections, policy debates, and humor.

I created my first blog, Math on the Blogosphere, in 2009. A combination of classroom reflection and student outreach, I envisioned my students checking my updates and following intriguing instructions nightly. Not successful in engaging them, I posted irregularly for a year or two, and stopped writing.

My blog reading, however, continued, and in 2013, I began writing anew at Her Mathness. My goal was no longer garnering student readership, but rather participating in and giving back to the online community – sharing resources, and having a voice in continually evolving conversation about math education. A long time ago, I earned a couple of degrees in English, and the opportunity to exercise my writing muscles was welcome.

In 2013, I attended my first weeklong residential conference at Exeter and wrote a lengthy post about the classes, participants, and inspiring keynote speakers. One of these speakers was Dan Meyer, who noted my recaps in a post of his, and I was on the map (485 hits in one day!).  I also attended Twitter Math Camp that summer, and my commitment to blogging was permanently cemented. The community of math teachers who regularly share, reflect, and thoughtfully converse about their teaching experiences became real, welcoming, and inspiring.

I wrote more regularly, and ran a pictorial daily 180 blog for one year. I shared resources I developed, reflected publicly on my teaching – its weaknesses and strengths, wrote about injustices and frustrations, and shared personal posts. My blog became my online professional journal; the process of writing each post gave me the mental space to contemplate my classroom practice and my students’ concomitant participation. I now attend to the appearance as well as the writing of my blog, posting photographs, images and videos to enhance the content. And I always cite my sources and inspirations.

Diving into the math education corner of the internet is a rewarding and broadening experience which connects me with a diverse group of like-minded professionals, who prioritize student learning through open reflection – the MTBoS (Math Twitter Blogosphere) is my professional learning community.

Writing a blog is not without risk; the memory of the Internet is infinite, as is one’s exposure. This exposure forces me to be thoughtful, intentional, and as clear as possible when expressing opinions, or citing someone else’s. Last May, I wrote a post about the ‘Course Corrections’ event at Momath – a conversation between James Tanton and Andrew Hacker about who needs what type of math education. I was keenly aware that I was attributing words to the speakers based on a fallible recording (my handwritten notes). I issued disclaimers when I wasn’t entirely certain that quotes were accurate, and checked with others who had been at the event. My caution paid off, and the post was well received and heavily commented upon. In fact, four other Math for America teachers (James Cleveland, Amy Hogan, Patrick Honner, and Jose Vilson) have blogged about Andrew Hacker as well – each eloquently expressing their reaction to a perceived attack on math education.

Among the Math for America (MƒA) teacher community, there are almost thirty bloggers, seventeen of whom are actively blogging (with posts written in the past year). Their blogs, listed below, reflect the diversity of our schools, professional and personal experiences, and teaching areas. Each blog merits notice; in the interest of keeping your attention, I will try to summarize a few broad categories which describe them. (The blogs have been listed in alphabetical order by author in each category.)

Sharing Resources and Lesson Ideas

  • MƒA Master Teacher Evanthia Basias has just started her blog, Fun with Geogebra, which promises to be filled with tips for using Geogebra, Desmos, and other dynamic resources in the math classroom.
  • MƒA Master Teacher James Cleveland, in addition to writing reflectively about his classroom, conferences he’s attended, and LGBTQ issues in the classroom, shares instructions, resources and classroom action tips for using games to teach and practice math over at The Roots of the Equation.
  • At A World of Science, you can find detailed project-based curriculum guides, and technology-based how-to videos; additionally, MƒA Master Teacher John Derian also shares auxiliary documents he has created.
  • Steve Gallagher, an MƒA Master Teacher, has generously shared an entire course in Forensic Science over at Crime Scene, complete with lesson plans, photos, worksheets, and relevant links, available to anyone who stops by his website.
  • If you teach AP Statistics (or Algebra 2, or any math, for that matter), A Little Stats is a must-follow blog; Amy Hogan, an MƒA Master Teacher, shares thoughtful activities, data and technology sources, and detailed statistically related recommendations. Not limiting her writing to Statistics resources, Amy’s reaction to Andrew Hacker covered three posts.
  • Over at com, the mission is “to organize the world of Education, Science and Technology to improve lives!”  Towards that end, MƒA Master Teacher Parvez Jamal provides links to articles, videos, and tools; there is something for everyone at his website.
  • At MƒA Master Teacher Michael Zitolo’s wikispaces website, SOF Physics!, you can find physics, programming, and Arduino resources (including his tutorials).

Reflections on Teaching

  • MƒA Fellow Matt Baker, writing at Pythagoras Was a Nerd, questions his teaching and classroom persona publicly, sharing ideas and (bravely) soliciting feedback. He writes about his professional goals before the school year begins, reports on how well he did afterwards, and looks constructively forward, modeling truly reflective practice.
  • It is clear that Kit Golan, an MƒA Master Teacher, uses his blog, Those Who Teach Do More, as a space in which to think through some of the issues we all face – covering depth versus breadth, how to best start the school year, accountable talk in classrooms – as well as to share his personal growth as teacher.
  • Another blog that includes reflection – on classroom practice, relationships with students, graduate school, Pokémon Go and education – is Carl’s Teaching Blog, written by MƒA School Leader Fellow Carl Oliver.
  • Lazy Ocho, MƒA Master Teacher Brian Palacios’s blog, contains in-depth reflections on teaching, professional development, and education policy. Lazy Ocho also has a comprehensive page of online math education resources, categorized by both course and classroom use – thanks for doing the legwork for us!
  • If you want to see how a middle school science teacher ran an aquaponics project, from his Fund for Teachers research trip through a TED talk and visit to the White House, check out MƒA Master Teacher Michael Paoli’s Aquaponics from Europe to Kids in NYC Baby…
  • Howard Stern, an MƒA Master Teacher, reflects on teaching, professional development, technology and school politics at mathmtcs. His recaps of George Hart’s Geometric Constructions workshops include both experiences at MƒA and school.


  • MƒA Master Teacher Brian Cohen’s blog, under the Making the Grade Blog tab at com, primarily addresses both local and national education policy issues.
  • Math teacher, photographer and New York Times contributor, MƒA Master Teacher Patrick Honner shares his teaching reflections, mathematical photography, and policy opinions at Honner. His website is well organized, with links to a great collection of resources.
  • John McCrann, an MƒA Master Teacher, has a spot on Education Week’s Teacher Blogs page. His blog, Prove It! addresses a wide range of topics including experiential education, opting out, race, and privilege and assessment.
  • Author of This is Not a Test and founder of #educolor, MƒA Master Teacher Jose Vilson writes over at JLV. His posts are about race, class, and education; they are thought provoking, and full of relevant references. Jose also has guest writers presenting additional perspectives.

So, why blog? There are as many answers to that question as there are blogs – to make a statement, contribute to the educational community, to publicly journal your experiences. If you want to blog, jump in and give it a try – everyone started somewhere, often with an awkward introductory post! Remember, your blog is primarily for you, for your own professional (and perhaps personal) development. MƒA Master Teacher Brian Palacios (Lazy Ocho) says, “Write for yourself. Be selfish. Post privately if you have to. The act of writing about your teaching will transform your practice and improve it in ways you never thought of.”

Wendy Menard, blogging at Her Mathness, teaches math at Midwood High School at Brooklyn College, where she has been the math department technology coordinator and coach of the math club. She left a career in budgeting and finance to become a math teacher in 2006, inspired by the public school teachers she encountered through her children’s education.  Wendy became an MƒA Master Teacher in 2015, and will be co-facilitating the Racially Relevant Pedagogy PLT with Jose Vilson this fall. 



The Equalizer

My school – with its 4,000+ students – has a resource problem each term.  They need the right number of classes for the right number of students (no more than 34 per class per the UFT contract) with the right number of teachers during the right time of day (our school has 3 split sessions).  At the start of the term, particularly in September, every student is programmed into the classes they are supposed to be taking, and the overadministration has 10 days (I think?) to bring all class sizes down to 34.  Most classes are at maximum capacity.  This means the school needs to determine who the ‘no shows’ are – students who have moved away and not been removed from the roster by the Department of Education, or who have changed schools, or left for some other reason.  Some students appear to be no-shows, but actually arrive to school a week (or two or three) late due to family travel or circumstances, and need to be programmed into the mix.  At the end of approximately two weeks of school, a portion of the students receives new schedules as a result of this process, known as EQUALIZATION.  An interesting choice of word.

So here’s the thing.  I teach a Discrete Math course, which is written as a series of discrete (sorry, couldn’t resist) topics that fall under that mathematical umbrella, or if not, are topics that I deem engaging, relevant, useful and/or creative.  Those topics have included probability, voting theory, logic puzzles, personal finance (how to read a pay stub, taxes, managing a bank account, credit cards), problem-solving strategies, linear programming, and modular arithmetic.  I vary the curriculum from term to term based on the_equalizerprior successes and current class make-up.  I like the course because (a) it’s interesting and (b) we can set our own pace, not shackled by a Regents schedule.  This allows me to use multi-day activities and projects that time constraints do not permit in Algebra 2 or Geometry.

The students who are programmed for this class (and forgive me, regular readers, for being redundant) are students who have (a) failed Algebra 2 (b) passed Algebra 2, but not deemed Pre-Calculus material, (c) passed Geometry but not the Regents exam, and thus not deemed Algebra 2 material.  I have some seniors who are still trying to complete a 4-term Algebra 1 class, and need more math credits to graduate; these students take two math classes in an effort to graduate on time.  I also get a lot of English Language Learners in this class, and students with IEPs, who may have passed everything through Geometry but didn’t sit for the Regents exam.  This class, while serving a purpose for all of these children, is undeniably an off-track class.  Whether or not a student wants this, they are being taken off the higher math track.  This bothers some students, others are relieved that they don’t have to deal with challenging upper level courses.

But when equalization happens, I get a different set of students, who arrive bewildered and somewhat unhappy.  These children have been ‘bumped’ from Algebra 2 to Discrete Math due to class size.  It might just be the process, or perhaps some student arrived late to school, as previously described, and got their seat because it made the overall schedule feasible.  At least two of these children took a look at what we were doing – Number Talks and logic puzzles, and asked to see their guidance counselor.  One young man was particularly displeased told me that he didn’t understand why he was ‘kicked out’ of Algebra 2; he had been doing well for the first few weeks.  I sympathized with his plight, and told him that a parent call to the school might be the most effective means of moving him back.

Did I mention that the vast majority of students in these classes are people of color, and that most of that color is Black? Or perhaps from this story, you have already figured that out.

Please don’t misunderstand me.  I respect my students completely, and work very hard to design a course that will open them up to an appreciation of math that they may not have had before, and a sense that mathematics does not represent a door that is closed to them.  I also carefully consider means to differentiate for the wide range of academic readiness (I hate that term, but that’s the best one I can come up with at the moment); a bored and disgruntled student can either check out or become hostile, as happened last fall.

One of my goals this year has been to provide the greatest level of educational opportunity I can for all my students.


So how do I can I accomplish this given the programming constraints at my school, which I am pretty much completely powerless to change (voting with my feet would be my only option)?  I’ve thought about that a lot in the last week or two.  I don’t want to change the curriculum for this course (which I could because as long as there are no complaints or violations of regulations, there is little oversight of this class; I am counted upon to help as many students as possible earn a credit, by any means I deem appropriate).  It’s not supposed to be an Algebra, Geometry or Pre-Calculus class, and I don’t really want to teach it that way.  So I asked the kids on Friday.

I asked them to reflect on why they were in this class, and whether they were satisfied with that. I asked them to tell me what math class they thought they should be in, and what would their ideal math class look like (I did ask them to be more specific than fun/interesting, or no math class at all).  And I asked them to honestly give feedback on what we had done so far, admitting that the content had been questioned as lightweight and/or baby-ish by some.  I did this because I’m not sure how to move them along the spectrum above. I believe that if I can engage them, the content I am providing will prove useful and challenging.  But I wanted to hear their thoughts.  They didn’t all write, but these are some of the reflections I received:

It was good to hear that not only did students find the class challenging, but that, by engaging with the content, their initial impressions of the course were improved.  I’m still not sure I’m providing them with providing with the best possible access to educational opportunity I can.  My attendance in this class is poor, a reflection of many things, one being (I am sure) the seriousness with which the students view this class, given the seriousness with which the students themselves have been viewed by the power structure.   I’d love some constructive feedback.