Category Archives: Math

Supplemental Material

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I like to have as many resources as possible available to my
students to help address their differing learning styles. For several years I
have posted pdfs of my class notes on Schoology. Originally this was intended
to be used by students who had been absent. However, my students soon realized
that if they were having trouble keeping up in class, they would either print
my notes out or pull them up on their iPads to follow along and annotate during
class. Over time, more and more students have been automatically obtaining the
notes ahead of time so that they can spend more time listening in class and
less time scribbling down the notes that are on the board.

Last year, after many of my Algebra 2 students started
subscribing to Mary Beth’s YouTube channel so they could watch her videos, I
recognized a need for my advanced math students to have access to video lessons
too. While there are many quality video lessons available on YouTube for
Algebra and Geometry, I couldn’t find good lessons that were
specifically tied to my textbooks, so I decided to make them myself.  Any student of mine can now go onto Schoology
and when they look in a lesson folder they will find a pdf of the notes, a
video lesson and the homework assignment. 
Creating the videos is a lot of work
and at first I was disappointed by how few “views” my lessons were getting.
However, as the quarter has progressed, absences have started and quizzes and
tests are becoming more challenging. Now when I check out my YouTube channel I
can see that more and more students are making use of the videos. I think that
the extra effort is paying off.

Designing a Probability Game

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My Probability & Statistics students have been studying probability.  I wanted to plan a lesson that would help them review what we’ve learned this chapter but that would also let them be creative.  I asked them to work in groups of 3 to design a probability game of their choice.  The only parameters I gave them was that it must include at least 3 probability events (for example you couldn’t just roll a die once and have the game be over) and they need to have clearly written instructions for how to play the game.  I provided students with dice, spinners, or pawns if they wanted to use them in their games.

At first many students were frustrated to have such open ended instructions.  When students asked for help I would ask them some questions about games they enjoy playing to get them thinking about different possibilities.  Students had two class periods to create their game.  On the third day they set up their game and instructions and students walked around playing all of the games.


I was amazed at what my students came up with for this lesson!  Some students reimagined classic board games while others created their own game all on their own.  Mathland was similar to Candyland. 

We had a game modeled after Guess Who? but the pictures were all students in our class.

As students were playing the games they were commenting on how some games were very complex while others were much simpler but still a lot of fun to play.

 
Groups were required to turn in a write up of their game which included instructions for how to play the game as well as calculating the probability for winning the game.  Students were also required to write an individual reflection on this project.  Here are some of their comments:


“Projects that require creativity and give me the freedom to create something of my choice are very interesting for me. This project allowed me to see probability in the real world while also allowing me to be creative and have fun.”  

“I have not done a group project in math before and I enjoyed this project because it allowed me the opportunity to listen to other people’s opinions and take into consideration different ways of assembling things.  This was a fun hands on approach to practicing probability.”


“After completing this project, I am able to understand the concept or probability more clearly with the different methods of determining it.”


“This project provided a great opportunity for us to apply the information we learned about probability towards building a game.  I really enjoyed all aspects of this project.  I never really thought we would have the opportunity to be this creative in math class.  It was fun to create a probability based game, and it was very interesting to be tasked with finding the details of the math behind winning the game.”  


We had a few minutes after students played the games to discuss their take aways from this assignment.  Many students said they enjoyed seeing how math can be creative (one of my goals of this project!) and liked thinking about probability in a different way.  The class made the connection between what we are learning in an abstract way and how probability is applied in many situations.  They also said they never realized how probability is used in designing games.  Some students also said that after playing a game once and not doing well, they began to think about the probability behind each move and played it again taking this into consideration and did much better.  I loved that!  I hope through this project my students will see the connection of math, and more specifically probability, in their every day lives and that they continue to see that math is open ended and creative.

Finding Slope

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So I thought it would be really clever to insert a picture of Nemo here (Finding Slope – Finding Nemo), but I doubt it’s in Creative Commons and didn’t want Joan upset with me!

Last week I realized that my Algebra 1 students weren’t understanding slope as “rise over run” and therefore couldn’t find the slope of a line graphed on the coordinate plane.  So, armed with 50 cent brightly colored rulers purchased at a dollar store, I sent them out to find slope around campus.

Their first instinct was to make the ruler the slanted/diagonal line.  So I had to explain (and they had to demonstrate!) that the vertical (up/down) is the rise and the horizontal (left/right) is the run.  I then had them measure and calculate the slope, and document it with a photo.  After about twenty minutes of wandering around campus, we came back to the classroom and shared photos.

Their calculation weren’t always correct, but that wasn’t the point.  I wanted them to be able to visualize and have a “hands-on” experience of slope.

Maybe they’ll look at the Inner Court stairs differently now!

Where are the Girls?

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I showed this short video clip from the CBS nightly news to my Algebra 2 classes.  It’s only 3 minutes but if you don’t have time to watch, here’s the synopsis:


Four exceptional Kansas high school students who are smart, politically active and forward-thinking are running for governor of Kansas. The state’s constitution has no age — or other requirements — to run.  


What struck me about this clip was WHO these “smart, politically active and forward-thinking” students were:  all boys.  And so, I decided to show it in my classes as a way to continue to remind our girls that they have been socialized to be perfect while boys have been socialized to be brave.  


Something unexpected happened when I showed the video and the Sociology Major inside me is freaking out about it.  After showing the clip, I asked the students whey they thought I chose to show it to them.  I received many responses such as, “You want us to take chances.” and “You want us to reach for the stars” and “You want us to try new things.”  I pushed them more.  Why else might I have showed this to you?  More and more of the same but not one comment on the fact that they were all boys.  I couldn’t believe it!  They were so socialized to expect boys to take these types of risks, they didn’t even see it.  



When I told them I showed this to them because they were boys, there were many a-ha moments, like when you look at a magic-eye puzzle and the hidden image suddenly appears.  I told them that this clip made me mad, because I believed that girls are just as smart and innovative as boys (if not more so!).  I (again) encouraged them to go big, take risks, and that now is the time when they have a safety net under them to catch them when they fall.  None of those boys is going to win the governorship.  But, each of them will experience incredible growth throughout the process, not to mention a killer college essay.  

Women of Heart, Courage, Faith, and GRIT!

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Before you begin reading, predict the numbers that complete this equation.

        Intelligence =_____% effort vs.  _____% ability*



Consider this quote from Michael Jordan: “I’ve missed more than 9,000 shots in my career. I’ve lost almost 300 games. Twenty-six times I’ve been trusted to take the game-winning shot. . .and missed. I’ve failed over and over again in my life. And that is why I succeed.”
Michael Jordan (1997 Nike commercial)

     What are mindsets and how do they affect our classrooms? What are ways we can build a growth mindset within our classroom? What are some ways to help students adopt a growth mindset? As I continue to research and read, these questions appear to urgently be in need of answers and more importantly transformed into daily classroom practice in every classroom beginning in preschool.  As I write this blog, I think about how the world watched an entire global celebration of grit and growth mindset during the summer Olympics in Rio. Bring it on!

The growth mindset confirms that intelligence can be developed, and expertise can be built by 
means of deliberate practice.

      Back in August I read about teachers allowing their students to struggle to help them understand that learning often times involves struggle and failure; however, with continued effort and perseverance the likelihood of success increases. One of our own teachers, Amanda Jain, actually experimented with this idea during one of her exams. The problem I see is, if one teacher focuses on grit, the students will be influenced while in that particular teacher’s classroom. For a genuine shift to occur, the students need consistency over time and within different contexts. The idea of a school-wide campaign on grit appeals to me and what the mission of the CSJ’s represents. 


       In August, our department started a “How to Learn Math For Teachers” course constructed by Jo Boaler, a Stanford University Maths professor. Through the continuing discussions we have about the growth mindset, the idea of grit was also apparent. It led many of us to a TED talk video from Angela Duckworth about grit and her findings of how it was such a key factor in student success. As a department we have discussed what grit means to us and how we could apply that in our classroom to help make our students more successful. 

Have you used the idea of grit in your classroom this year yet?

       My focus for grit in the classroom is on building their stamina and confidence in their own abilities, as well as building cognition. My job is to give them tools and skill sets to do the very best they can and to not feel overwhelmed/ready to quit before they even begin. I model grit as often as possible for my students, and have found myself on many occasions using it myself. Often times, I find myself overwhelmed with all of the things I have to do that have nothing to do with planning quality lessons. I also am overwhelmed with continuously trying to differentiate my craft so that I meet all of the individual needs of every student. I to feel like giving up some days due to the fear that I will fail the monumental task entrusted to me, but know that I need to push on and push through (use grit) because the job I have is so very important. 

       Teaching reeks stress and havoc as a result of juggling so many priorities, and yes, they all are priorities that all need our time and attention. Right now. And faster is better. The reality is that our accelerated pace truly does not serve anyone (teachers and/or students). It is not how fast students master learning but rather their persistence, grit, and effort they put forth along with the right menu of teaching strategies. The growth mindset of a teacher contributes greatly to his or her responsiveness to the needs of students. Let us all step back, take a deep breath, be reminded that teaching is the most noble of all professions. We are truly the fortunate who can call themselves teachers. Thanks for stopping by and strengthening some neurons.


* Depending on your mindset:  
Fixed mindset = 35% effort vs. 65% ability
Growth mindset = 65% effort vs. 35% ability





A Week of Inspirational Math

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After almost six weeks of slogging through the first two
chapters of the textbook, I decided to take a break with my Algebra 1 with Math
Lab class and do a Week of Inspirational Math. 
I wanted to apply and share with my students some of what the Math Department
is learning in Jo Boaler’s How to Learn Math for Teachers class.  The resources are on her website www.youcubed.org.  Each day we watched a short video and followed
it up with a discussion.  Then we did a
hands-on activity to illustrate the video’s message.  The topics included:

  • how our brains grow and change
  • how we see numbers and patterns differently
  • how our brains grow when we make mistakes
  • the importance of having confidence in your ability
  • the importance of visualizing math
  • that speed is not important, but deep thinking is

For me, this was an important activity to do with this
particular class.  These are our students
who struggle with math.  It has never
come easy to them and often they don’t feel very smart.  At the end of the week, I asked for their
input.  I found their comments very
encouraging:

Through the week of
inspirational math I learned a lot about myself and that my brain is ever
growing and changing and I can always improve my brain, and it is important and
ok to make mistakes because it helps my brain to grow and change.
It made sense that
they said that making mistakes is a learning opportunity because it gives our
brain a chance to grow. I learned that I should always take my time and get the
better grade, instead of rushing & making careless mistakes and getting
points taken off. I feel now that when I make a mistake, it grows my brain
more, which makes me more happy.
I feel like now that
I’ve watched those videos that I can have a better attitude towards math and
try my best at doing it as well.
I learned that I like
to visualize or draw things, more than just doing all of the math in my head.
It helps me understand what’s happening.
I guess I didn’t know what to expect heading into the
week.  But now seeing the impact it has
made on several of the students, there will definitely be more Weeks of
Inspirational Math in our future!

Shadowing Kenzie, Junior

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First period, Spanish
4
As I walked into class with Kenzie all of the students were
talking about the oral exam they had this morning.  Students were frantically reading their notes
and reviewing their vocabulary.  When
class began it was conducted entirely in Spanish.  The teacher went around the class and asked students
questions about the vocabulary and the reading. 
The anxiousness and anticipation of what question the teacher would ask
was evident in the room.  I found myself
feeling nervous that I was going to be called on which made me nervous because I was unlike the students and hadn’t prepared for class.  While I understood what the teacher was saying in
Spanish I had no idea what their reading was about and felt that pit in my
stomach of being unprepared for class. 
Students were very encouraging to each other and cheering when students
got questions right or saying, “you know it, come on!” when a student struggled
to come up with an answer.  
Second period, AP
Language
After prayer the teacher reviewed with the class what they
needed for class on Monday.  Then there
was a short discussion from an article students read about Freedom High
School.  The teacher asked the class what
struck them about the piece of writing. 
Students shared their thoughts on the reading (how students weren’t
given the opportunity to take any AP classes, students were told that since
their parents worked in a factory that was what they were destined for).  The teacher also asked the class what they should
do with this information, what is their take away?  Students then spent the rest of the class
working on their outside reading assignment. 
The students quietly began their reading.  It struck me that students didn’t need to be
in class today.  This lesson could have
been completed online in a blended model. 
Most students worked on their outside reading assignment but I did
notice a few students around me studying for other classes.  I asked a student near me what she thought of
the bell schedule.  She said that she
enjoys the blocks for some classes where the teacher has the students do
activities or projects.  The blocks are
awful when a teacher lectures the entire time. 
I was grateful for break as I found myself not used to
sitting and not being as active.  I got a
cup of coffee to wake myself up before heading to third period. 

Third period,
PreCalculus
I sat right in the front row of class and followed along
with the teacher’s lecture on polynomial functions and models.  The teacher wrote definitions on the board and
asked students questions about what she was writing.  She paused often to look at the class to see
if they were understanding what she was discussing.  As I looked around the room, all of the
students seemed to be engaged and taking notes. 
While I was enjoying the subject matter and refreshing my memory on
multiplicity I found myself tired.  The
temperature in the class was warm when we walked in and the passive nature of
sitting and taking notes made it hard to stay focused and engaged.  The lecture finished with about 8 minutes
left in class and students were given time to start their homework.  Most of the students used the time to chat with each
other.  It felt like a breath of fresh
air. I already felt like I have been sitting too much today and I’ve only observed 3 periods.  
Fourth period, Sports
Medicine
It felt good to get up and walk over to De La Salle.  As we walked over I asked Kenzie whether she
prefers blocks or 45 minute periods.  She
said she likes having blocks because it gives her an extra day to do
homework.  She plays a sport so doesn’t
get home from practice until close to 5 and a few days a week she works in the
evenings so the extra day is really nice. 
She did say that she doesn’t like block periods when the teacher
lectures the whole time though.  Once we
got in to class the teacher did a lecture on Caring for Skin Wounds.  While this was another lecture this
felt different.  I think it might have
been because there was a lot of natural light in the room with a whole wall of
windows and the overhead lights were off. 
In addition, the door to the classroom was open so there was a nice
breeze coming in the room.  The teacher was
engaging and moved around a lot as he talked and class went by quickly.  Class ended with about 6 minutes left.  I noticed a few students around me began
working on their My Math Lab assignment for PreCalculus.
I was happy lunch was next. 
I felt very disjointed moving from 4 different subject matters,
classrooms, and teaching styles this morning. 
There just seemed to be a lot of change and I felt out of sorts.  The day already felt very long and it was
hard to imagine having 3 more classes after lunch.
Fifth period, AP U.S.
History
As students walked into APUSH they were talking about the
reading quiz they had today.  I asked
Kenzie how she prepares for the quiz and she told me that she reads the chapter
twice, reviews her notes, and watches the Adam Norris videos yet she still will
probably fail.  Another student near me
said she watches the videos 5 times and just tries and memorize all of the
information.  The teacher gave me a quiz to take and I was quite impressed with myself for getting 1/15 considering I haven’t
taken a U.S. History class in over 20 years. 
I noticed that as students around me finished the quiz they took out
materials from another class to work on (My Math Lab was up on a few students’
computers).  After everyone finished the
quiz, the teacher showed two images and asked the students what they observed.  As students studied the video the classroom
next door kept playing the National Anthem multiple times which seemed quite
fitting considering we were studying U.S. History.  I did find it distracting though.  I thought there was a connection between
students studying these images and how math teachers ask students to study
graphs.  There could be a common language
history and math teachers use when analyzing graphs. 
Sixth period, Religions
Studies 3:  Symbols and Ethics
This class began with the teacher talking to the students about
the importance of speaking their heart and honoring their own truth.  When she spoke with the students about a
heavier subject matter she moved her chair to the middle of the class.  It felt intimate.  The class then transitioned to talking about
Saint Hildegard of Bingen.  After
reviewing some information on this woman with the class students were asked to
fill in some information on her on a paper they were working on during a
previous class.  I noticed, once again,
quite a few students around me finish this quickly then immediately take out
materials from another class to start working on it.  The class ended with an inside outside circle
activity which involved us sitting down in two circles on the ground.  It felt good to get out of the desk and move
around and to discuss something lighthearted. 
My brain was beginning to hurt from all of the information across disciplines
today. 
Seventh period,
Biology
As we walked to her 7th period class, Kenzie
stopped by her locker to pick up her history textbook.  She said she wanted to get started on her
homework if she finished her test early. 
I am going to be completely honest. 
I was done at this point.  I was
exhausted and felt like I had reached maximum capacity for what I could take
in.  While I was happy to learn there was
a test today and I wouldn’t need to stay the whole period I felt bad for the
students who still had to be “on” for this last period of the day.  Are they used to this frantic pace of
switching subject matters, taking in information, and constant sitting all day
so they are better equipped to handle this?  
I was surprised that despite changing classes every 45 minutes I felt
very sedentary today.  The passing
periods seemed short and not enough time to decompress from one class before
transitioning to the next.  I left this
day feeling exhausted but also grateful for the opportunity to experience what my
students go through.  It definitely has
made me more mindful of how I structure my classes and has given me a lot to
think about.  I think all teachers should
have this experience. 

I Can and I Will — Why Carondelet Needs to Lead the Way

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As we grapple with this big Wicked problem that is education, sometimes may wonder why WE have to lead the way…

Kevin shared this three-minute video today which I believe summarizes why Carondelet, as a girl’s school, needs to lead the way.

I also like the shiny gadgets and use of virtual reality (there are resources out there to create virtual reality or use virtual reality resources that we could use right away in all sorts of subjects.

Yes! This is the way it should be done.

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Chapter 1 of Geometry has so many new terms and symbols. Students can do the algebra needed to find a value, but are not familiar enough with the geometry notation to express their work clearly. I emphasize that they have a reader for their work. (They realize this for other classes, but often not for math.) For now, I am the reader and perhaps a classmate they are trying to help, but later on it will be their client or a colleague in their research lab. When grading some of the first assignments, I noticed student work which was done as I had shown. I thought of my father-in-law who would exclaim, “That’s the way it should be done!” So I wrote Yes! and took an iPad photo of the problem. I did this in honors and regular classes. I showed these photos in class the next day. (I did not use names or use the same student’s work twice.) I said it was possible to earn full credit without the yes, but I knew they would want to see what was special about these solutions. I did this a few times and on the first quiz and test many more students than in the past used the approximately sign for a rounded number and identified the length by EF (for example) rather then just having the answer “floating”. More students also remembered units. (Note: I did take .25 point for no units, but not for the other notations.)

We’re ready to embrace a growth mindset, but our students might not be.

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Chapter 1 of the Algebra 2 curriculum is a review of very basic concepts from Algebra 1.  As such, I employed a self-paced “review and practice”-style for this chapter.  After a few work periods where students had time to get the minimal set of practice tasks done, we had a quiz.  When it came time for me to make the test, I was struggling with how to make it different than the quiz (which covered the exact same content).  Instead of making it a carbon copy of the quiz, I employed a different format.  The test had just four questions that were all real-life applications of the basic Algebra skills covered in the chapter (yes, they were word problems!).   Here is a copy of the test.

In an effort to boost their confidence, grit, and perseverance, right before handing out the test I told the students that the format was different, but that they knew the concepts required to solve these problems and that they just needed to apply them.  And most importantly, I told them that I made the decision to give such a test because I believed in them and that I knew they could do it.  And this last part was 100% true.  I did believe that they had it in them to do quite well on the test and I was excited to seem them rise to such a challenge.  Unfortunately, while I was emphasizing these uplifting comments, all they heard was “the test is different.”  Needless to say, there was a lot of drama that day; girls in tears, girls registering their complaints and the injustice to both me and Lesley.

This all happened on a Friday and I spent the weekend spending a lot of mental energy on what happened and what I was going to do about it.  Why were our girls so crippled by this test?  The questions actually weren’t terribly hard; had I sabotaged the experience by naming this as a “challenge”?   I quickly graded to see how they did and I rewarded perseverance in addition to correct calculations.   They actually did quite well, with several girls getting 100%.  Why was their reaction so negative to an experience where they were, for the most part, quite successful?

I decided it was worth a class period to talk about this experience and to try to convince them that Math is more than just calculations.  It is a subject full of beauty, complexity, and connections to the world around them.  And, that struggle is good for them and that we need to be brave and take risks to truly learn and grow.  I rearranged our previously scheduled material to talk about these ideas.  I started the class by giving them a short survey about how the test went for them.  I then showed them Reshma Saujani’s Ted talk, Teach Girls Bravery, Not Perfection.  They were captivated by this talk and the discussions after were positive and inspiring.  I then showed them Jo Boaler’s, Four Boosting Messages Video.  This video is a little cheesy, but the messages are important.  Finally, I shared with them this slide show that was recently discussed at a Math Department meeting which presents quotes from Jo Boaler and others.  I then gave them another survey.  Both surveys were anonymous.

To say the results were fascinating is an understatement.  The statistician in me is still crunching the quantitative data but it is the qualitative data (selected responses below) that are so telling.  I’ve learned so much from this experience.  Let’s start with the good.  Some were on board with this style of learning:

I feel as though the test sparked a bit of inspiration after knowing more about the research. I already knew that women are raised to be perfect rather than brave because my dad would repeat that there is no learning without taking any risks. But, I like to see more in depth research about this problem. I happen to quite like this style because it gives you a chance to be rewarded for hard work!

I really like this style. At first before the test I was super nervous because I was worried that what I had studied would not be on the test, but to my surprise the test wasn’t too bad. Afterwards I felt accomplished and proud of myself. I feel like if you had not said that it was a challenging test, I may not have been as worried about it beforehand, but I did have a feeling of relief afterwards. Also, I REALLY liked the Ted talk and it empowered me to take on challenges and be more brave and willing to make mistakes.

Before taking the test I did not think I was prepared for it, but afterwards I felt more confident in my abilities because I was able to take on a challenge.

Some were negative and very resistant to this style of learning:

i don’t understand how the way math it taught can just change after we’ve been doing the same type of learning for the past 11 years.

The test was confusing for me becuase it was a format that none of us were aware that we would have to be tested on. Usually in math we are expected to have a test with problems and we solve those problems. I am not good at learning from project and I am not good at reading from the book. I do better when someone is up teaching it on the board.

Some were quite terrifying in their misperception of what Math is:

I think it is important for some subjects to have critical thinking skills and be able to do things without much direction; I do not think this is true for math. I think for math you need to be given the directions so you know how to do the problems. You can’t just figure it out for yourself. You have to be taught math and given instructions on how to do things. In english or history critical thinking is important, but math is much different. You can’t learn math yourself, you have to be taught math.

I do like the message and all that jazz about it but to start doing this now is unbelievable. Colleges aren’t going to give me a math problem to solve and see how well I can adapt to it, they’re going to look at my grades for junior year. The SATs and ACTs are the same way, I’m going to have to bubble in the correct answer to get the right answer and that will hopefully help me to get a scholarship that will get me into a good college that will hopefully set me up to live a good life. But I don’t believe it was fair to throw that type of test at us when you did. Not after that quiz since everyone expected the test to be like the quiz, just like last chapter. And we are already under a lot of pressure and stress and it’s not fun having something like that thrown at you. It was like standing in the dark and someone says “to your lefT” but instead drops a ton of bricks on you.

i agree with method but maybe in a different area. i think in math you have to practice and understand the problem you’re doing and if i just get a random problem thrown at me that i never practiced i don’t think would do well. and since this class is based on grades i don’t really think it’s the place to practice this method. maybe like one on a quiz or something.

Wow, we have a lot of work to do! But, most interesting for me from this experience were the messages from students that were conflicted:

I can see why the test was formatted like that after seeing the videos. However, because tests impact our grades significantly, I would appreciate if the questions like the one on the test were just classwork. I like the idea of this way of learning and agree with it, but sadly grades mean a lot for college.

So I did good on the test, but I still don’t like the format of the test. I’ve considered myself a math person, and I and always working as hard as I can on everything, but this format made me feel so dumb. I think having activities that challenge us and were me make mistakes is good, but getting good grades is so important to us. Like we hear over and over, “the grade don’t define us”, but they do determine our gpa, which is so important. The videos had really good messages, but our school world is just getting more and more competitive and harder and harder, and grades are becoming even more important. We already have so much stress in our lives and creating even more stress with a test felt really insulting.

Like I said in the previous survey, I enjoy these problems but I don’t feel challenged by them. I am all for trying new things and learning from mistakes but I don’t want to be making mistakes on the SAT/ACT. Are there ways to prepare us for the SAT/ACT while making us “braver?”

It is these last, conflicted, messages that I can’t stop thinking about. The girls understand they need to be brave, that challenge is productive, but they are burdened by the system, a system which requires them to be perfect, to get all As or as high of a GPA as possible. I don’t want to give up on challenging them, but I’m mindful of what they’re up against. And so I am brainstorming ways to measure and reward perseverance, determination, grit and innovation as much as (or maybe even more so) the right answer. It’s a really exciting time to be a new member at Carondelet and I’m riding the momentum of the school as I re-imagine what challenge (real, authentic, practical and productive, challenge) might look like in our math classrooms.