Let The Journey Begin!


 This school year I embarked on a new adventure of teaching math to sixth through eighth grade students with disabilities.  I graduated in December with a Master’s Degree in Teaching Learning and Leadership with a concentration in K-8 Elementary Mathematics Specialist.  My new teaching assignment allows me to put all of my new-found knowledge and experiences into practice.  I have to admit that while I was bubbling over with excitement to have this opportunity, I started the year with a considerable amount of trepidation.  I have worked with students with disabilities throughout my teaching career, and I know that many of these students also come to school with social and family problems that further hinder their learning.  Add to that a long history of failing and struggling in math, and you have a student who usually would much rather be anyplace else other than any math class.  I realized that if I was not able to provide experiences that would change these attitudes learning would not happen no matter what I did.

With this in mind I spent a considerable amount of time over the summer researching, reading and preparing to start this school year.  It was my goal to begin the year by establishing norms and creating a community where members trust one another and are not afraid to take risks.  One of the books I read was Mathematical Mindsets by Jo Boaler.   The ideals and message in this book were the icing on the cake that I needed.   Growth Mindsets is the plaster that hold together all of the other teaching practices and principles that have now become such a part of me.  I literally have conversations about teaching and learning math with almost every person I meet every day!  Yes, I know this makes me a math nerd, I own it humbly yet proudly!  The last week leading up to the start of school found me in a fervor putting together a plan that I hoped would reach my students and get them excited about math.  I also knew from experience that it has taken years for these kiddos to develop the mindset that they bring, and I could not expect to change it without a considerable amount of time and investment.

Here is how the first few days of my school year have gone:

The Weeks before school began:

“I am part of all that I have met.” Alfred Lord Tennyson

Start the year believing: Relationships in life are paramount.  Without them connections cannot be made.

I wonder: Will sharing all that I have met create a pathway for connections?  Am I willing to be that vulnerable?  If I show I am willing to be vulnerable, will it inspire my students to also trust and be willing to take a risk and share themselves?

I notice: Students will not trust you if they believe that you are not willing to see past their struggles or life situations.  They crave to be seen for who they really are as a person.

I notice: It still takes more.  Students who struggle academically often bring a defeatist attitude with them to class.  They have developed a closed mindset towards math.


I wonder:  Can I convince them that: Anyone can learn to do math to high levels; Speed doesn’t matter; Mistakes Grow your brain; We are in this together; I’ve got you and you’ve got me.

I resolve:  I am going to see my students as the beautiful people they are.  I am going to look past all of the baggage they bring due to their disabilities and other life struggles.  I am going to introduce them to what I believe is the most promising and beautiful kind of learning I have known.  I am going to facilitate activities and learning experiences with them that will turn them into powerful problem solvers who notice and wonder at every opportunity.  I am going to continually remind them that they can grow their brain and change their mindset if they are willing to look for patterns, take their time, be willing to struggle and make mistakes.


First day of school –  “I am part of all that I have met.” Alfred Lord Tennyson

My story: I laid a lot out there –  my childhood, my fears, my likes, my dislikes and, my struggles.  I kept it age appropriate and left out some things, but I was honest and vulnerable.  I also shared my life now –  12 Things You May or May Not Know About Mrs. Naegele

Students also shared  things about themselves with the class:  Getting to Know You

Math Attitude Survey  This was eye-opening even though not surprising


School Required Review of Student Handbook (time-consuming, boring and necessary)

Math Is Snowball Activity

Math Is Wordle – our graphics were not very positive!


Go Ahead Break the Ice  – This activity was designed to introduce students to the problem solving process in a non-mathematical/non-threatening experience.  You may read about how it went here: Melting Ice on Day Three.


The GOAT video –  What did you notice and wonder about Michael Phelps?

Talk about what we do when things get hard – reference the video games discussed yesterday.

Spend more time on Four 4’s

Day Two: Brain Crossing Video – What did you notice and wonder? Number Visuals with Animation – What do you notice and wonder?


Day Three: Which One Doesn’t Belong Wednesday – We had some great justifications for our choices!

Speed Video followed by Modified Paper Folding Activity – What do you notice and wonder?  We wondered and then noticed that the denominator doubles when the paper is folded in half!


Have a reminder talk about what we do when things get hard – reference weight lifters and athletes.  Do they get better by lifting ten pound weights or only working out for a short time each day?  What does that tell us about the math we need to do to grow our minds?

Day Four: Patterns Video followed by – What do you notice and wonder about the patterns found here?

I honestly didn’t think life could get better after Thursday!  Here is my Facebook post: Today my class explored 2015’s day four of Week of Inspirational Math. (https://www.youcubed.org/ ) My students LOVED it! They were noticing and wondering about patterns left and right. They made conjectures and we tested them. They struggled and got frustrated. They agreed and disagreed with each other, and they completed the activity. I had students thanking me for pushing them to struggle. Some said, “This is the funnest and hardest math I have ever done, and I love it!”  I lost count of how many students requested to take a copy of what we did today home so they could do it again with their families! How stinking cool is that?

And then came Friday.


Day 5: Mistakes Video    Growing Shapes Lesson Plan   How Do You See The Shape Growing?

On Friday we explored 2015’s Day Five Week of Inspirational Math.  My students came in still excited about Thursday.  Many asked if we were going to watch another “Jo” video, and were happy to hear that we were.  Our bell-ringer was a problem that gave mathematical clues that the students were supposed to use to find each place value in a five digit number.  I admitted to them that I had to read the clues more than one time to be able to find a solution.  I asked if they were ready to notice and wonder and beat that problem.  They were ready!  The last clue was; the sum of the ones, tens and hundreds place is fifteen, and the tens place is four times the hundreds place.  They were stumped.  I asked them what strategy they could use to figure it out.  They were not sure.  I said, “Well can you guess and check and come up with something?”  I kid you not when I tell you they were stunned to be given permission to guess!  I reminded them of the check part and they were off!  When they collectively found the solution I asked what they noticed and wondered about the process of finding the solution.  They still wanted to talk about being given permission to guess and check.  We talked about it and decided if you have no idea where to start in a problem, guessing and checking is a pretty good place to start.  I followed that with this question: “If you guess and check, what is the worst thing that can happen?”  I then showed the Mistakes video for day five.   As usual we followed the video with a notice and wonder talk.  Everyone was amazed to learn that mistakes make your brain grow.  I have a Thomas Edison poster hanging on my wall with the quote, “I have not failed, I have just found 10,000 ways that won’t work.”  We talked about what this meant and how it applied to what is shared about Michael Jordan in the video.  In one of my classes a sixth grade boy felt safe enough to share how promising the message in the video was to him.  He was moved to tears by the message that mistakes are not bad, and it is through them you learn.  He expressed how happy that made him because he has always felt like a failure because things are hard for him.  Every student respected that moment, and this teacher’s eyes were brimming with tears as well!   Every class on Friday had a plethora of noticings and wonderings about how the shape grows.  They noticed physical patterns as well as numerical patterns.  They connected this day’s patterns to the patterns explored in Pascal’s Triangle and commented how doing that activity helped them understand this one even more. I asked them to work in small groups to find the fourth, fifth and sixth pattern.  We moved fluidly from whole group to small group back to whole group and each class was able to take the task to their highest level of understanding.

how do you see the pattern growing

In each final large group discussion I recorded the class observations into an empty table.  Every class observed all of the information in the table below.  I was thrilled that they had gotten to this point!  I challenged each group to see if they could look at the table to come up with a rule that would tell what number of squares was in any case. They worked together thinking and drawing, talking and comparing ideas, but the bell rang before they could solidify a rule.  But wait, there is more!


Case # or c # of Squares Increase Relationship


1 4


2 9 5



3 16 7



4 25 9



5 36 11


+1 6 49 13


At the end of the day, I challenged my eighth grade students to look at the table and notice and wonder about what they observed.  I was beyond ecstatic that they not only noticed the increases, and relationships, but also that “If you multiply 3×3 you can see the number of squares in the case above that case, and it is the same for the others.”   They then wondered about that relationship and came up with the plus one.  I challenged them to think about that plus one.  I also asked them to see if they could come up with a rule for the number in any case.  They talked among themselves, and one student stood up excitedly and said, “I don’t know if this is right, but I think if you add one to the case number and then multiply that number by itself you will get the number of squares.”  I asked the group to talk to their shoulder partner to see what they thought.  They worked together, tried the idea, drew some more cases, and came to the consensus that the rule: (c+1)∙(c+1) would give you the number of squares to any case. I wrote their rule on the board and showed them you could also write it (c+1)².  When I turned around to ask them to use their rule to tell me what the hundredth case would be they were sitting in stunned silence, and a few mouths were hanging open.  I couldn’t resist, I said, “And that my friends is how you do Algebra.”  I mic dropped my dry erase marker and walked away from the board.  There were a few whispers about my  mic drop, and then an eruption of excited chatter about how smart they were filled the room.  I let them live in the moment, and truth be told, I don’t know if I could have talked without crying anyway!

These kids, now my kids, in a weeks’ time went from believing that they were failures who hated math to excited mathematicians celebrating their victory!  I don’t think I have ever witnessed a more beautiful educational moment in my life!

I know we still have an uphill battle to climb.  I realize that those nagging negative thoughts may return when we encounter problems that cause them to struggle a little too hard.  For now though, I too am going to live in this moment.  I am going to cherish it as the first step, just as I cherished my own children’s milestones.  I have more resolves now.  I promise that I am going to continue to provide positive experiences for my students that challenge and stretch them.  I am going to continue to teach them about developing a growth mindset.  I am going to strive to make every week better than the last, and not let this be the only mountain top experience we have this year.  Because I saw so much happiness, so much confidence, so much love of math on that mountain top that I cannot bear the thought of it being their last.  They deserve the chance to climb those mountains and reach the top, and I resolve I will bring the mountains to them.



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