Category Archives: Lesley Schooler

Redesigning Algebra

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The math department has been rethinking our math classes and
how we can personalize the learning for our students.  Inspired by what we’ve
learned from Jo Boaler’s How to Learn Math forTeachers online course, we’ve decided to remove tracking
in our Algebra classes.  We want to show
students that mathematics is creative and open ended.  It’s
about identifying problems and working toward finding a solution.  It’s
collaborative learning, real life problem solving, and sharing this information
with others.  We’ve had the opportunity to spend time in a small group discussing
what we want Algebra (with the intention of expanding out to other classes) to
look like next year.  Our work has just
begun but I thought it might be helpful to others to share our progress so far.
We really want to encourage our students to develop a growth
mindset.  We believe that all students
can do math and we want them to believe this about themselves as well.  
“When I asked over 800 teacher leaders in the
US recently which educational
practices develop and maintain fixed mindset
ideas in students the number one reason given was ability grouping. I agree, it
is hard to give a stronger fixed mindset message to students than by putting
them into groups and telling them they have a certain ability.  In a
recent study Romero (2013) found that significantly more students developed
growth mindsets after they were placed into high track groups. Students who
develop fixed mindsets will often do anything they can to maintain the idea
that they are ‘smart’ which can make them vulnerable to unproductive learning
behaviors and the avoidance of challenging work or higher-level math courses.
 It is extremely important that schools communicate growth mindset
messages to students, and don’t limit students’ achievement by giving fixed
mindset messages through grouping and other practices. This is important for
equity, it is important for students of all levels, and it may be the key to
unlocking the potential of millions of students in mathematics.”

We’ve decided that our Algebra classes
will all be of mixed abilities.  Instead
of having Algebra with Math Lab, Algebra, and Algebra Honors, we will mix in all
of the students together.  We will have 3
sections of Algebra during one period with 4 teachers team teaching these
students.  The curriculum will be broken
up into units.  We are moving away from
chapters and sections and instead we will be presenting the concepts in an
interconnected way so students see how one concept relates to another (we are
thinking of having the girls create their own concept maps and continue to fill
them in as we progress through the curriculum). 
Each unit students will self-pace through the following items:

  • Presentation of concept – this can be through a video or a discovery activity
  • Practice Problems – this is where students demonstrate mastery on the basic idea of the
    concept (can they solve an equation in one variable, for example)
  • Topic Challenge – these
    are application problems where students work collaboratively in small groups to
    apply the concept they learned.  Many
    problems will be presented as an open ended idea/problem and students will
    develop the plan to solve it.
  • Unit Challenge – this is
    a larger project that will connect all or most of the concepts from the
    unit.  This will also be completed
    collaboratively.  Some unit challenges
    will be worked on throughout the unit while others will be completed at the end
    of the unit.  Here is where students can
    really see how mathematics is used, how it connects big ideas, and how it
    applies across disciplines.  During the
    topic and unit challenges students will be working collaboratively to solve
    these challenges with the teacher acting as a coach to help guide them along
    the process.
  • Unit Assessment –
    Students demonstrate mastery on these short, application based
    assessments. 
  • Honors Challenge – If a
    student wishes to have the honors designation on their transcript at the end of
    the year then they need to complete this challenge.  These are what we like to call the     “wicked problems” where students really need to
    persist and make connections in the data and apply it to concepts they may not
    have initially been taught.      In addition,
    students will have a peer tutoring requirement and need to create instructional
    videos for their peers.     

We are envisioning using 3 classrooms where the students will move
fluidly among each one based on the needs of that class period (or a portion of
that class).  The 4 teachers will be
moving among each room too each day (which means we will need to touch base at
the end of every day to determine who will be facilitating each room the next
day).
Room 1: “Traditional,”
direct instruction
Topic challenges
Practice problems, collaboration
Room 2:  Teacher coaching/guiding, student-centered learning
Unit challenge
Honors wicked problem
Room 3:  Teacher monitoring, no direct instruction
Assessment
Practice problems for mastery
We have outlined the units for the Algebra curriculum and are now
beginning to determine which concepts will go under each unit and create the
assignments.  There is still a lot of
work left to do but we are excited to continue moving forward!

Scatter Plots

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I was really excited to teach my Algebra Honors students about scatter plots and lines of best fit today.  I have been looking forward to this lesson because it allows me to teach statistics, which I love, to my students but also because we were going to use for the first time the HP Prime graphing calculator app on their iPads.  I knew I wanted to make this lesson interactive working with data they collected that would be interesting to them.  I found a PowerPoint that had 20 pictures of celebrities and students were supposed to guess their ages.  The students loved seeing pictures of Justin Bieber, Kim Kardashian, Nick Jonas, etc. and guessing their ages.  It definitely grabbed their interest!  I was feeling really confident about this lesson.  I then gave students the actual ages of the celebrities.  Students now had two rows of data and it was time to have some fun with the HP Prime.

Mistake #1:  I had thought that the HP Prime app was automatically downloaded on all freshmen iPads but I never checked with the students prior to class if this actually was the case.  Some students had it but many did not.  I thought this was easily fixed, the app was free, the students could just download it.  For the majority of students this worked but there were 3 students that were unable to download any apps. They unfortunately had to just watch on with a partner.

Mistake #2:  The HP Prime calculator is very different from the TI-84 calculator and there is a learning curve.  I had budgeted some time to play around with the basic functions of the calculator before we started the activity.  I was thinking of the first time I used the HP Prime at a conference last summer and how I was intimidated to push buttons randomly so I waited for the instructor to walk me through step by step initially.  What I didn’t anticipate was students feeling much more comfortable with new technology and have them start pushing all the buttons and not paying much attention to my tutorial.  This resulted in many students asking me how to do the same things over and over.

Mistake #3:  Once I got everyone back on track and stressed the importance of staying with me while we entered data we started creating our scatter plot.  Students did great entering their two columns of data but as soon as I showed them how to graph the points they immediately got excited about the touch screen of the graph and started going off in a bunch of different directions.  This resulted in a similar replay of mistake #2.  It was fine at first that they were playing around with zooming in on their window but when it became time to sketch a graph with their finger many instinctively hit OK which then saved their line – even if it was a line they didn’t feel represented their data well.  Rather than ask for help they continued to draw multiple lines which I had to walk around and delete.

While we did finish the lesson and I think I demonstrated to my students that the HP Prime calculator is superior to the TI-84, the lesson did not go at all how I envisioned or wanted.  In hindsight I think it might have worked out better if I gave students written step-by-step instructions for how to enter the data and do the functions working in their groups.  I then could have circulated around the room to see how things were going and troubleshoot if needed.  The girls are way more comfortable with technology than I gave them credit for and I think they could have figured out what I wanted them to do working together.  We then could have had a class discussion on the different lines of fit each student created and discussed the similarities of them.  Overall I would do things differently but I am glad that we approached scatter plots this way rather than just completing problems in the textbook in a more traditional sense.

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.

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. 

We Will Rise

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I recently watched CNN’s We Will Rise video.  (You can watch the trailer by clickinghere).  

In the video First Lady Michelle Obama, Meryl Streep, Freida
Pinto, and Isha Sesay travel to Morocco and Liberia where they meet young women
who are overcoming various obstacles to get an education and improve their
lives.  These young women are fighting
for the right to an education so they can have the opportunity to better
themselves and their communities.  The
video highlights the stories of a few young women including Raphina in Liberia
who wakes up every morning at 5am to clean the house, bathe her little
brothers, prepare food for the household and go to market all before attending
her first classes of the day.  The only
time she has to study is at night with a flashlight from 9-11pm.  The video also talks about Fouzya in Morocco
who is the first girl from her village to obtain a college degree.  She discusses how in her community there is a
lot of gender discrimination and girls are not thought of as needing an
education.  The role of girls is to be in
the home and many parents do not prioritize their daughter’s education.

Despite the obstacles these young girls face, they
prioritize their education.  They embody the
growth mindset and are well aware that they need to continue with school in
order to have the opportunity to change the trajectory of their life.  They are passionate about learning and do not
want anything to keep them back from achieving their dreams.       
While many aspects of this video inspired me what really
left an impact was toward the end of the video when one of the girls asked
Meryl Streep what advice she had for the girls. 
This is what Meryl responded with:
“I’m not sure I have advice for the girls here. I think within each
one of them, the young women that I have met, have such strength of purpose. It
all exists within each of you. It is already there. And you just have to reach
in and access it. Because in my own life, I know that losing heart is the most
dangerous thing. You can put any obstacle in front of me and I’ll jump over it.
But when I lose heart, you lose everything. And so, you take your strength from
your friends, from that one person in your life who has said you are capable…You
only need one.”

Meryl’s words reminded me how powerful our words are to our
students.  I thought about how important
it is to share with our girls that we do believe in them.  We know they are capable.  We are setting the bar high for them because
we know they can achieve it.  As
educators we need to show our students that they have a strength of purpose
within themselves and they do not have to struggle alone.  We are here to support them.