Archive for the ‘General’ Category

NCSM Reflection

April 11, 2014 1 comment

I recently attended the National Council of Supervisors of Mathematics Conference in New Orleans.  I was honored to receive the Iris Carl Grant.  This grant pays for your travel expenses to attend.  If you have not attended a NCSM conference in the last three years, you ought to consider applying.  It was an invaluable experience.  I wrote a reflection of the conference to submit to NCSM.  I am including it below.

46th Annual NCSM Conference, New Orleans, LA

Reflection by Amber Caldwell, Recipient of the 2014 Iris Carl Grant

K-12 Mathematics Coordinator, Bradley County Schools, Cleveland, TN

All of my classroom experience did not prepare me to serve in the role as K-12 Mathematics Coordinator for my district.  After fourteen years in the classroom, I thought I was equipped and had the skills to serve the teachers in my district.  After a few months in this newly created role, I realized that enacting change in my classroom or at the school level was easier than trying to inspire an entire district consisting of 16 schools.  I enrolled in an online class with Jo Boaler offered free though Stanford University.  I was introduced to concepts and ideas that amazed and humbled me.  I realized after the course, that I needed more.  I am grateful to NCSM and the Iris Carl Travel grant for allowing me the opportunity to attend what I hope will be the first of many NCSM Conferences.

Mike Schmoker, in the opening session, reminded me that as educators and leaders, that less is often more and we need to focus on the basics of a great lesson.  He stressed the importance of clarifying, practicing, and mastering first things.  The most effective strategies that a teacher and school can implement are curriculum, cold calling, and 90-120 minutes of purposeful reading and writing.  This session reminded me to encourage and maintain the basics while trying to implement the CCSSM.

Cynthia Callard, Jane LaVoie, and Stephanie Martin offered a session on using the Progressions of Common Core State Standards to Deepen Teachers’ Content Knowledge.  While I have read the Progressions and used them while developing curriculum maps, I had not considered using them in a professional development setting with teachers.  One of my goals in my new position is to create Professional Development modules to be utilized in Professional Learning Communities to introduce units of study to teachers and initiate the planning stage.  Through this process, I would like to help teachers solidify and deepen their content knowledge.  After this session, I will incorporate the Progressions into this planning.

I had the honor of hearing Cathy Seeley speak and was very excited to receive her new book upon arriving at NCSM.  She reminded the attendees that all math students need to understand, do, and use mathematics.  The understanding is making sense of mathematics, while the doing consists of facts, skills, and procedures.  When a student uses mathematics, they are modeling, reasoning, and thinking.  The mathematical habits of mind require students to perform thought experiments.  While the habits of mind were not new to me, the reminder to focus on them was much needed.

One of the highlights of my time in New Orleans consisted of hearing Marilyn Burns speak on Linking Formative Assessments to the CCSSM.  While I had been exposed to the Mathematics Reasoning Inventory site before, to have her explain the process and anecdotes around building this project was invaluable.  I am excited about bringing this resource back to the teachers in my district.  I see how important it is to incorporate Math Talk into our daily routines and to ask students to explain their reasoning.  According to Marilyn Burns, students who lack understanding of a topic may rely on procedures too heavily.  True understanding comes from explaining and critiquing the reasoning of others.

The moment that inspired me the most was hearing Jo Boaler speak on Erasing Math Inequality.  Dr. Boaler’s work in the field of mathematics education is motivational and encouraging.  She presented five barriers to high and equitable math achievement.  I am sad to admit that I and my district are guilty of creating some of these barriers for children, and one of my missions is to remove these obstacle so all students can achieve.  Dr. Boaler encouraged us to change our beliefs regarding students and their ability to do mathematics.  She stressed that we are harming our students by placing them in ability groups and creating a fixed mindset.    I also see the need to encourage our teachers to look beyond one dimensional mathematics and to teach math and not calculation.  We can do this by encouraging sense making in mathematics.  I was convicted to try and remove timed mathematics testing from our district.  Dr. Boaler’s research shows that timed tests create math anxiety at an early age.  Math should not be associated with speed.  Jo Boaler speaks with such conviction while offering encouragement.  I left her session with a clear mission, determination, and a desire to enact change.

The opportunities for networking and collaborating were invaluable.  Being outside of the classroom and in a leadership role can be isolating at times.  I am so thankful to NCSM and the Iris Carl Travel Grant for this opportunity to attend such a valuable conference.  I am returning to my district renewed and impassioned to be a catalyst of change and a resource to the teachers and students whom I serve.


Categories: Common Core, General

Why My Son Needs Common Core

February 3, 2014 7 comments

I know that there is a debate regarding the “new” math common core state standards.  I understand parents are frustrated with children having to learn “new” ways to add, subtract, multiply, or divide.  I understand that parents are frustrated with children having to show work and defend an answer, even when the answer is correct.  I understand your frustration as a parent.  I have a child who is off the charts in math.  He consistently scores in the 90th percentile and above on all standardized assessments.   He just “gets” math.  (His mom is a math educator.)  He is always frustrated when I ask him to defend his answer.  His typical response is, “because I know it’s right.”  I used to think common core was not written for children like him.  He does not need to draw a picture or learn a “new” way to divide.  I was wrong!  My son needs common core.

A few weeks ago we sat down and worked several TCAP (Tennesse State Assessment) type problems for math homework.  They were all division problems similar to the one below:

John has 12 apples.  He wants to share them with 3 friends.  How many apples does each person receive if John gets the same amount as all his friends?

My son was flying through these problems.  After a few moments of watching him, I realized he wasn’t even reading them.  I stopped him and asked him what he was doing.  This was his explanation:

“Mom, the lesson is on problems with division.  I just divide.  The bigger number always comes first, so I take the bigger number divided by the smaller number.”

Something inside my math teacher heart died.  I wanted to scream, “The bigger number doesn’t always come first!” and “What if the problem was multiplication and you assumed wrong?” and then I realized that our curriculum and check list standards have reduced real life mathematics to this.

A week later my son’s need for Common Core became evident.  We were at Publix grocery shopping and we came to the juice aisle.  Orange juice was on sale, 3 for $6.00.  At Publix, you do not have to buy all 3 to receive the sale price.  My son started to put three juice cartons in the cart.  I stopped him and explained we only had to buy one.  I then asked him, “If they are on sale for 3 for $6.00, how much is one carton of juice?”  Remember, my son was in the 98th percentile last year in math and he “gets” it.  His response, “$2.50? $3.00?”  What?!  We stopped in the grocery store and got out paper and pencil and I made him show me how he arrived at his answer.  He drew a picture.  Through this process, he realized his mistake.  He told me he didn’t realize it was a division problem.  He said, “Mom, I know 6 divided by 3 is 2, but I didn’t realize this was a division problem.”  So yes, my third grade son sometimes needs to draw pictures.  Memorizing his math facts is not enough.  He needs to understand the situations that necessitate the memorized facts.  He needs to be taught strategies to solve problems when they seem unfamiliar.  He needs Common Core.

Categories: Common Core, General

Why I Blog… for @k8nowak

December 3, 2013 1 comment

I took some time last week to scroll through my own blog and could not believe some of my old posts.  I hardly recognized my own words.  I am definitely not the same educator or the same person I was when I started this blog over three years ago.  I have changed.  My job has changed.  Education has changed.  Kate Nowak played such an integral role in starting me on the path to blogging so I wanted to respond to her request:

1. What hooked you on reading the blogs? Was it a particular post or person? Was it an initiative by the nice MTBoS folks? A colleague in your building got you into it? Desperation?

Dan Meyer.  I found Dan Meyer one summer through desperation.  My principal asked me to serve as department chair and I felt so unworthy.  I had a 25% failure rate in my classroom.  I had students who hated my class and did not see the purpose in being there.  From Dan’s blog I found Kate’s and Sam’s.  All of these blogs showed a passion for teaching I had never seen or experienced before.  I wanted to be a part.

2. What keeps you coming back? What’s the biggest thing you get out of reading and/or commenting?

Teaching is hard.  It is rewarding, but hard.  I see teachers everyday struggle and cry.  I see teachers leave their rooms in joy with the desire to share their successes and I see them hang their heads and want to hide from their failures.  I see how overwhelmed some of them are with all of the changes Common Core is bringing.  It is more necessary now to build a free community of resources and support for teachers.  We can not and should not do this alone.  If what I write or say can help even one teacher, then it is worth my time.

3. If you write, why do you write? What’s the biggest thing you get out of it?

I started writing as a window into my classroom.  I wanted to share what worked and what failed.  I now work at the district level and have access to hundreds of classrooms.  This is a huge responsibility and honor.  I feel like writing about these experiences gives me the opportunity to share to a larger audience.  I write to push myself.  Right now, I found myself going off on a tangent (I deleted it) and started writing an I wish I would have when I was in the class room list…  That will be a later blog post.  This just goes to show that blog writing forces me to reflect and push myself to improve.  It really is a selfish exercise.

4. If you chose to enter a room where I was going to talk about blogging for an hour (or however long you could stand it), what would you hope to be hearing from me? MTBoS cheerleading and/or tourism? How-to’s? Stories?

I would love to hear the nuts and bolts of how to start a blog.  Also, how to handle reading blogs and not get overwhelmed.  I remember a time when I wanted to just shut down because I could never get caught up with my blog reading or what I wanted to write about.  Baby steps…  Oh yeah, and twitter.  Twitter and blogging go hand in hand.

Categories: General

Differentiation: Not Another Buzz Word

October 3, 2013 Leave a comment

Oh the buzz words in education!  I love that we dissect great instruction into definable strategies, but I hate how quickly these ideas become buzz words.  When teachers hear these key phrases repeated and diluted, they lose their power, and there is power in this one.  One of our targets this year as a district is to focus on differentiation in the classroom.  As a teacher, it is easy to focus on the students in the middle.  We often fail to provide support for the struggling students.  It is easy to overlook the higher achieving students.  On the other end of the spectrum, it is tempting to pour all of our efforts into the struggling students and fail to push the higher achieving students to reach their potential.

As a teacher, I was guilty of reactionary differentiation.  I would have a few students who would finish a test early and think, “Oh no, I have to find something for them to work on now.”  If a student struggled in my class, I would encourage them to come to after school tutoring or try to modify the assignment with fewer problems.  My “go to” method in differentiation was having a strong student sit and help a struggling student.  All of my strategies were reactionary.  I never planned my differentiation in my lessons.  To be honest, my strategies and methods were not solid differentiation practices.
I then found intentional differentiation.  I did not create this wheel.  I can not claim responsibility for this brilliance.  I only did a lot of research to arrive at my conclusions.  Here is what I have learned about this buzz word:
1.  Differentiation needs to be planned as a part of my lessons.  It must be intentional.
I need to consider all of my students when planning my lessons.  I need to make sure I have an entry point for all students.  I need to create opportunities to extend the learning for some students.
2.  Differentiation is not more or less work.
By giving more work to students who are ahead, I am communicating that more work is the same as rigor.  This is not true.  Modifying assignments by giving struggling students less work only tells them that I do not believe they are capable of doing the same work as the rest of the class.
3.  Differentiation is not creating multiple assignments or assessments.
All students must take the same PARCC or Smarter Balanced assessment in 2014-2015 and the number of accommodations will be limited.  All students must take the same ACT or SAT to enroll in college.  If we are creating separate assessments for students, we are creating a false sense of success for them.
4.  Differentiation can be embedded into my lessons easily.
My favorite way to differentiate in my math class is with these graphics:
I created posters of these for my classroom.  When a student (advanced or struggling) is working on a task in my classroom, they normally select one path to a solution. It was easy for me to say, “That is great, now can you take that equation and draw a graph, make a table, or put the equation into a context?”  For elementary school, teachers can use the diagram in blue.  If a student is struggling with a math concept, the teacher can ask them to approach it from another area in the chart.  For example, if a student can not write an equation for a given problem, the teacher could ask them to use a manipulative (Uni-fix Cubes) or draw a picture.
5.  Differentiation is necessary for all students.
I tried to limit my whole group instruction in my classroom.  There was seldom a time in my class where all students needed the exact same thing from me.  All 35 of my students were at different places in their learning.  It is my job to meet them where they are at and help them grow.  Differentiation provides a way to do that.
A great resource to learn more about differentiation is Differentiation Central.
Categories: Common Core, General

Number Sense and Math Reasoning Inventory

January 4, 2013 2 comments

I have two children of my own. Often, they end up becoming guinea pigs when it comes to math instruction (or just about anything). As a secondary teacher, I feel qualified to teach integration, quadratic functions, or any other topic beyond Algebra 1. When my son brought home his first set of flash cards from school, I was at a loss. The only tool up my sleeve was memorization by repetition. Needless to say, we spent many hours drilling and crying (ok, I was the one crying). My younger son watched and didn’t speak, but he was absorbing. Little ones are like sponges and sometimes that is not good.

A few days after the flashcards disappeared, my then 6-year-old said, “Mom, I know why 3 x 5 is 15.” I was curious. His response shocked me. He explained that if he counted by three’s 5 times, he would end at 15. He also told me that he could do it the other way and count by five’s 3 times. Of course, I knew this, but in my pursuit to push my older son to memorize faster, I skipped the understanding. What my 6-year-old was developing was number sense.

One of the complaints I most often hear from high school teachers is that students do not have number sense. I’m not sure how you measure number sense or how to teach it, but you know it when you see it and you definitely know when it is lacking. I need students to understand that 3/4 – 1/4 is 1/2 without having to perform an algorithm. Sometimes I think we become too engrained in teaching algorithms without understanding. My hope is that the new common core assessments will force teachers to fix this.

Recently a colleague introduced me to a website, Math Reasoning Inventory, that encourages formative assessment for understanding and building number sense. Maybe some of you already use it and can offer feedback. I have not seen anything like it in mathematics before and am excited about how this could change elementary mathematics education. The site encourages teachers to conduct interviews with the students on mathematics problems. The focus is not only the correct answer, but how a student achieved that answer. For example, if a student is asked to calculate 7000 – 70, using a standard algorithm would be considered an inappropriate strategy. I have to say I love this! Students forget algorithms and cute tricks, but true number sense and understanding will always work. I encourage you to look at the website and provide feedback below. I would love to have students at the secondary level who had been evaluated with this method. 

Number sense is hard to define and harder to assess, but I believe that the Common Core will help us achieve what is so necessary for mathematical success.

Categories: Common Core, General

A Calculus Wedding

December 5, 2012 4 comments

We had a wedding in Calculus.  I gave the students a copy of an invitation the day before, asking them to come dressed in black and white to observe the occasion.  I purchased a cake for the event and provided a bouquet of flowers for the bride.  On the day of the wedding, students arrived in suits and dresses.  I was really surprised with the effort the students put into this event.  I thought they would think it was cheesy, but I guess they know me by now and expect nothing less.  One student went as far as to  borrow a wedding dress from the theater department.

Calculus Photo

I allowed the students to vote for a female student to represent Deriva, the Derivative and a male student to represent Integroom, the Integral.  Each person was allowed to select an attendant.  I played the wedding march and directed the ceremony, officially wedding the Integral and the Derivative using The Fundamental Theorem of Calculus.  The wedding was all the buzz of the school and several students in Pre Calculus came to ask me about it.

 This is my first year teaching Calculus and AP Calculus.  I think it is important for the class that we establish an identity in the school so other students see the importance of being in such a rigorous class.  My goal next semester is to order t-shirts for us.  Does anybody else have any good ideas for setting the AP Calculus class apart?

Categories: Calculus, General

Roller Coaster Fun

August 28, 2012 2 comments

The STEM academy at my school is starting a Science Olympiad team this year.  To recruit members, the engineering teacher and I collaborated for a roller coaster project during class.  We took our students to the auditorium and put them in groups of three or four.  We gave them a handout explaining the details of the activity.  The students were asked to create a mock roller coaster using the supplies they were given.  They were told the roller coaster would be evaluated using the following equation:

The students had to first discuss how each of the variables in the equation would affect the final score.  The goal was to achieve the highest score, while creating an aesthetically pleasing roller coaster.  After the student finished the roller coaster, they were asked to create their own equations that would give them a higher score.  They had to defend why they weighted each item as they did and why they put it in the numerator or denominator. 

We supplied each group with a piece of foam tube for track, four notecards, four straws, a styrofoam cup, and a roll of tape, and a razor blade.  The students were allowed to use items in the room as supports, but not as actual parts of the roller coaster.  The passengers were marbles of varying weights.  The students had a great time and it was amazing to see the differences in  each roller coaster.  I definitely see expansion ideas for this project.  Next time, the engineering teacher and I will create a store for the supplies and make the students purchase their supplies with a limited budget.