1. Task based learning focused on the learning cycle.

Task based learning is the rage right now with Common Core. Our state, Tennessee, put teachers through intensive training on how to teach math using tasks. The problem with this is teachers were left to create their own tasks or find random tasks. In order for task based learning to work, the tasks must be sequenced appropriately and build on the previous learning. MVP does this. They have different types of tasks for different purposes and they are sequenced to build on each other. The learning cycle involves Developing Understanding, Solidifying Understanding, and Practicing Understanding. When you look at the tasks in a unit, the tasks are labeled as one of these. This helps for both students and teachers to understand the purpose of the task. Some tasks only develop the understanding. Later, only after a teacher can guide a class discussion, are students expected to apply and practice the new learning. This idea of different types of tasks for different stages of learning is critical.

2. The have low threshold and high ceilings.

I was amazed with the multiple entry points for the tasks. It felt as if any level of student could do something. Often with tasks though, the mathematics is “dumbed down.” This is not true for MVP. The tasks are rich and have high ceilings. If you have a group of student who finish early, there is always something in the task to stretch the learning.

3. Story contexts throughout the module.

Take a look at Module 2 in Math 1. It starts with a rich task about two children starting a pet sitting business. The purpose of this first task is to start students down the pathway of thinking of multiple constraints on a variable (systems of equations). Students will use this context throughout the entire module adding a little more information with each task. Students should feel as if they are invested in a Problem Based Learning approach, broken into small, obtainable chunks.

4. Not just what to teach, but how to teach it.

Most curriculum contain what a teacher should teach, but little about the best methods for teaching. This is the first curriculum I have encountered that explicitly helps the teacher know how to teach the standards. Each problem or exercise has a purpose:

- Teach new knowledge
- Bring misconceptions to the surface
- Build skill of fluency
- Engage students in Math Practices

5. Meaning full homework and practice.

Practice is done by experts… Doctors practice medicine and Lawyers practice law. Why would we send home practice when our students have not mastered the material? This creates frustration and with Common Core, it leads to parents posting crazy math homework on Facebook. MVP has amazing, thought out homework assignments. They divide the homework into three categories:

- Ready: Things a student needs to review to be ready for upcoming work.
- Set: Things we did today in class that you need to practice to solidify understanding.
- Go: Things students should be “good to go on.” This is review material.

Each assignment also has links to online videos to help review concepts students may not remember. (I know in reality, that my students may not have done the homework, but I could use this as starters and exit tickets in my class.)

6. Flexible Curriculum

Since the MVP curriculum is online, it can be updated at any time. This means if something isn’t working or their are mistakes, they can easily be fixed. This is not true of traditional text books. The MVP team did hint that they are currently working to align the tasks and material to release them in a traditional math pathway. This means that if your district does not do Integrated Math, you will still be able to use the MVP curriculum.

Overall, MVP offers a great curriculum and fantastic professional development. I encourage you to attend an event and at the least, take some time to review the material.

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46^{th} 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.

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“The PARCC Educator Leader Cadres (ELCs) will help each state build and expand the number of educators who understand, support and feel ownership of the successful implementation of the Common Core State Standards (CCSS) and PARCC assessments.”

I found an activity on the site focusing on the Critical Areas in Mathematics. I printed out the cards on colored paper and asked the Instructional Coaches to place each critical area into the correct grade level. The cards are below:

Critical areas game K-5 A blue cards

Critical areas game 6-8 A and B green cards

Critical areas integrated A 9-11 pink cards

Critical areas traditional 9-11 A yellow cards

After teachers worked together, I gave them this page (2.2 Critical Area Activity Sheet ) and asked them to check their answers and record any discrepancies. It is important to note that this activity calls the topics the Critical Areas and this differs slightly from the “Major Work of the Grade” as laid out by PARCC. PARCC’s use of Major Work of the Grade is more specific and the Critical Areas activity creates fewer and broader categories that do incorporate the major work of the grade.

It is a great activity for teachers to see the vertical progression of topics in mathematics with the CCSS. The PARCC.nms.org site went a step further and created this great one page document ( 2.3 Summary Critical areas summary) over viewing the critical areas from kindergarten to high school mathematics. The site also included a one page overview of the fluency standards (Key Fluency Expectations Recommendations and Examples of Culminating Standards). I encourage coaches to print these pages out and laminate them for every teacher.

The PARCC.nms.org site offers great activities on math practices, examining coherence in one domain, and text complexity. I strongly encourage coaches, administrators, and department chairs to visit the site and utilize some of the great resources.

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But now we have the CCSS and that means there should be a lot of great resources out there. Be careful! I have come across a lot of resources labeled CCSS and PARCC, only to find weak content and revamped activities. Not everything has to be new, but everything should be aligned. I wanted to share one of my new favorite sites for finding great resources for CCSS in mathematics. It has become my ‘one stop shop’.

Here is why I love this site:

- This site take the best resources and organizes them in one location.
- It is easy to search by standards to find tasks.
- You will find links to all the curriculum maps released by states.
- There is no password or login required!!

Here is part of the mission statement from the site:

“There is so much that has been created by so many and it is out there free to the public via the internet. However, it remains difficult to sift through it all to find the best things for our children to use. This site will hopefully allow teachers to spend more time teaching and give kids more of an opportunity to learn both at school and at home.”

You will find resources from

- Khan Academy
- Learn Zillion
- Mathematics Assessment Project (MAP)
- NCES.ED.gov
- NCTM Illuminations
- Science Net
- Texas Instruments
- Dan Meyer
- Hot Math
- and many more…

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PARCC recently released sample questions in their intended environment. This means the computer-based tools such as drag-and-drop, multiple select, text highlighting, and an equation builder are all active. It is a great opportunity for teachers to see what computer skills are necessary and how students will navigate the assessment. This sample assessment does not reflect a complete PARCC assessment. The questions on the online assessment are all previously released sample items. The one frustration that I have is that the questions are separated by grade bands and not grade levels. In my experience, teachers want to focus on their grade level, although I think it is important to be aware of what comes before your course and where students are heading. To help teachers and administrators, I have created the following documents to support teachers while they are looking at the online PARCC environment. The documents address each questions content standard(s), grade level (course), and math practice. Detailed scoring guides and explanations of the questions can be found on the PARCC website under the respective grade band. Please feel free to provide feedback in the comments.

PARCC Computer Based Samples Grades 3-5

PARCC Computer Based Samples Grades 6-8

PARCC Computer Based Samples High School

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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.

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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.

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(These cards are attached to a ribbon and have the definition on one side and word on the other)

All teacher are required to have academic vocabulary (Tier 3) posted on the wall. Every teacher has a unique twist to their word wall. The definition is always included and students are encouraged to get up and use the wall during class if they need to refresh their memory. One teacher even moved words to the “Mastered” wall after the class demonstrated a thorough knowledge and understanding of the word. The teachers would cycle the words according to the unit of study. I absolutely loved that the words had the definitions hidden, but accessible to students. If I was still in the classroom, I would find space for this on my wall.

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When I was in the classroom, I was guilty of reducing mathematics to an algorithm. I taught cute tricks like “Outers over Inners” to simplify complex fractions. I think all teachers are guilty of this at some point. I came across this video in an elementary classroom that testified to this:

http://www.teachertube.com/viewVideo.php?video_id=77588

The teacher was teaching students how to multiply a two digit number by a two digit number. I had heard from several teachers how great this “new” method was for students. It is so cute! I had to bite my tongue. If you watch the video, my questions are “Why does the turtle drop an egg?” and “Why do we draw a collar on the turtle?” I need students to understand this. What happens if I have a three digit times a two digit? Does turtle multiplication still work? I need conceptual understanding that transcends to problems of varying types.

Here is how I would love to see multiplication by two digit numbers taught:

http://www.teachertube.com/viewVideo.php?video_id=154703

What are your thoughts? Are we hurting students by teaching cute algorithms in isolation? Is procedure really what matters? What other “tricks” do we teach that hinder conceptual understanding?

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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.

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