The Garden in My Mind, a new picture book by Stephie McCumbee

Module 5

A.  What do you think will be your greatest challenge as you lead in the area of mathematics?

My greatest challenge as I lead in the area of mathematics will be overcoming my own fears off not being great at math. I know that I am a great fourth grade math teacher, but I fear that adult learners may ask me questions that I do not have the answer to. Leading adults is very challenging, and I fear that I will not be able to provide them with the resources or answers that they need.

B.  What obstacles do you anticipate?

I anticipate that older teachers may think that they do not need my help and that they know more than I do. I worry that older teachers will be difficult to get on board with new strategies. I also anticipate that I will struggle to find all the resources I need to be an effective leader. Thankfully, I work at a school who always tries to provide teachers with everything they need.

C.  What aspect of leadership do you feel most prepared for?

I feel most prepared to lead others through the use of motivation. I believe that I am a charismatic leader who is able to help others see my vision and mission. I feel most confident knowing that I can get others on board with my plan. I am much stronger in the area of curriculum and instruction in literacy, therefore I know this will not be an issue for me.

I feel that this class has helped prepare me for a future in the area of mathematics leadership and I look forward to what the next few years hold. 

Module 4

Collaborative Learning Communities

      I really enjoyed reading the case study for this week. As a teacher and a instructional coach, I found the norms that these leaders set to be very beneficial. As I read the case study, I reflected on all of my PLC meetings thus far. I work with an amazing group of teachers who are naturally very reflective. I know that my team is probably not the norm but we have found PLC meetings to be less than beneficial. 
     While reading, I tried to note any information that could help us have more successful PLC meetings. One thing that I really liked about this case study was the emphasis placed on setting group norms. As a leader,  I would probably be a little aggravated that it took three meetings to establish norms but I believe that this is helps future meetings be more successful  I also liked the theme of being a reflective practitioner. I know that I am naturally very reflective. In fact, I am almost annoyed by how reflective I am. I did not however think about teaching my students to be reflective. I have moments in which I have asked my students to stop and reflect, but I do not think that I have provided them with adequate time to do so. In the future this is an area I would like to work on.
     Several ways that I have had students reflect in the past is by having them take math notes on the right side of their paper and after the lesson, have them reflect on the left side. I started off being consistent with this practice however, overtime I began to stop having students do this. 
     One way that reflection is a part of my own practice is through the use of notes. I always try to write on my lesson plans things that went well and how to alter the lesson in the future. This allows me to better meet the needs of my students the following year. I also meet with my team members to discuss what I could have done differently in my lessons.

How can mathematics leaders help operationalize reflective practice for teachers?

     One way that mathematics leaders can operationalize reflective practices with their teachers is to have them reflect often. I like the idea of having teachers write quietly during their PLC time. This allows teachers to record their thoughts and to look back at them over time. I would suggest asking teacher leaders to come to each meeting with a journal. This way they can refer to their journal over time. I even suggest collecting the journals and writing notes to teachers in them.

Supporting Teachers of Mathematics

Common Core Standards for Mathematics

1. Make sense of the problems and persevered in solving them:
H- Because the student in this vignette looked for entry points and and thought about what he already knew about the topic.
B, C & E- in these examples the students worked hard to apply strategies that would help them tackle hard situations. They made sense of them by apply real world information and persevered to finish them.

2. Reason abstractly and quantitatively:
B- in this vignette the students were able to reason abstractly that this addition problem could be represented on a number line and that the first fraction is equivalent to 6/8.

3. Construct viable arguments and critique the reasoning of others:
A- In this example the student stated his understanding and then the other students built on what he said and constructed an argument

4. Model with mathematics:
E- In this vignette the student uses a real world situation and applies it to what she knows about equations. She then solves this problem by solving the equation

5. Use appropriate tools strategically:
D- In this example the student uses her pencil to create partitions in the garden so that she is able to solve the problem.

6. Attend to precision:
F- In this vignette these students explicitly discussed the qualifications of a rhombus and together clarified any weaknesses in their original definition.

7. Look for and make use of the structure:
A, G, H- In these examples the students uses a pattern or structure they knew to help them approach the problem.

8. Look for and express regularity in repeated reasoning:
C- in this example the student realizes that either way she solves the problem she will get the same answer.


Accessibility Strategies:

      I would love to see my teachers use accessibility strategies when planning lessons. I can see this occurring during their PLC's each week. In order to begin facilitating this type of planning in my school, I would start by asking teachers to bring with them an upcoming lesson that they will be teaching in a few weeks. Then, together we will discuss potential pit falls to the lesson, areas where students may need additional support or areas where many students have struggled in the past. Then, I would have teachers discuss how they have combated these issues successfully. We would record the best responses as a plan of action. So in a math class, where a teacher is teaching decimals, she may already know that typically students struggle with understanding that .5 is greater than .05. To help with this issue, I would suggest teaching students decimals through the use of money and actually have them shop for things.

Professional Development:

     I have presented so much PD in my time as an educator and I really enjoy doing so. Every year, I present at the NC Reading Conference as well as several other conferences. I also present locally, and regionally. I was glad to see that we would be learning about how to present great PD, because my research shows that this is a large issue for teachers. I currently really believe that the best form of PD is Co-teaching and this comes from my own personal research interest. When reading the assigned articles, I evaluated myself on how my sessions are. Overall, I felt like I was doing a great job. I tried to not give one- shot sessions, I liked them to the standards and the interests of teachers. I do not require that all teachers attend my session and have meaningful follow up (Steiner, 2004).

     One area that I have not helped others use is action research. I use this all the time in my own classroom, but have never helped another teacher do this in her classroom. I know the power of action research and am surprised I have never used it to help me help others.

     In many of my classes, we are talking about the power of active learning and this something that I feel I am good at but will continue to work harder to ensure in my classroom. Active learning is wonderful because it is meaningful and helps students feel like they are having fun but really they are learning as well. So teachers struggle with this and then their students become bored.

What is Leadership?

I Am a Math Coach Now What?

I really enjoyed reading this article as it brought me back to my first experiences as a literacy coach at my school. It can be very challenging to get teachers to trust you and to believe that you are knowledgeable. Like the writer, I was only 28 years old when I became a literacy coach at my school. This can be very difficult for older more mature teachers to accept. They often felt that they did not need my helped since they had more experience than I did. It was very hard to build a relationship of mutual respect and support.

As a new leader, many of the teachers at my school did not want to ask me for help. It was very hard for me to even offer advice because they took it as condescending. I felt like I was constantly walking on egg shells. After a rough first year, I came back and the atmosphere had changed. I am not sure what happened or how the changed occurred, but it seemed like being a veteran team member afforded me with new privileges. Now, I was able to offer advice and it was received well. I was able to co teach with teachers and present PD without feeling some sort of tension. I am happy that now teachers feel confident calling on me for help and know that I am not here to evaluate them.


A Tale of Three Teachers

I really enjoyed this article as well. It was interesting to see how the three leaders were connected in some fashion. My favorite part about this article was the concept of the superhub. A superhub is a teacher who leads in her field informally. This teacher is often sought after by the other teachers and is highly respected among her peers. I have worked with many superhub teachers and can attest to the impact that these leaders have. They are so charismatic and others truly do gravitate toward them.

Case Study

What is this person’s first step or steps in getting “organized” for this new role?

• Look at the School's Improvement Plan to get an idea of the overall goals for the school
• Look at the County's Strategic Plan to get an idea of where the county is heading
• Meet with grade levels during their planning time to listen in on their issues and provide assistance
• Offer to present any Back to School PD in the area of math
• Communicate with peers by eating lunch with them, emailing them and offering to help plan lessons with them
• Offering your support with struggling students (remediation strategies)
• Send out surveys to ask teachers what areas they would like help in
• Find the superhub of each grade level and begin infiltrating the grade level by gaining their trust 
• Let the word of mouth do its work, eventually superhub teachers will spread the good word

What supports does she need and how could these be acquired?

A new teacher leader needs support from the administration and from the county leaders. This is very important in assuring that resources needed are available and that she is able to seek guidance from other leads in the county. This can be acquired by attending monthly meetings. For example in my district, we have monthly instructional coaches meetings. This is where these leaders get together to talk about common goals and needs. This would be a great place to start. Also, as mentioned earlier if you can get lead teachers to see the value in you, then do it.

What would you expect from the principal in this situation?

My previous experiences tell me that the principal is very busy and part of being a good leader is being able to assess where there is need and to be self directed. I would expect that the principal would hear your concerns and help you to create a schedule.

Note that the supervisor is barely mentioned, what is the supervisor’s role here?

The supervisor's role is to make sure that the new math coach has all the resources she needs to be successful at her job. If they do not have the resources then the instructor should work with the coach to figure out how to procure funds so that these resources are obtained. Additionally, the supervisor should be responsible for welcoming the math coach into the school and setting an example for how she should be treated. She should introduce the math coach at the first Back to School meeting and should continuously call on her for guidance. If the supervisor supports the coach then the teachers will likely follow her lead.

What should our newly minted MIL do about the across grade level mathematics gaps she may have?

Find leaders in the areas that you may not be experienced in. Observe their classes and ofter to co-teach with them. Part of being a good leader is realizing that other people may be more knowledgeable in certain areas and realizing that you should call on them.

If you are currently serving in a leadership role, discuss What challenges you faced as a new leader. What worked for you? 

As mentioned above, I had my share of issues as a new leader. I think what worked for me was that I built relationships with teachers and met with anyone who would allow me to work with them. Eventually, word spread that I was helpful and other teachers allowed me to enter into their classrooms.

Being a Successful Math Coach: Ten Guiding Principles

When reading this chapter three of the ten principles really stood out.

1.Work alongside teachers as a co-teacher not an evaluator:

This is huge! If you can not learn to do this, teachers will never trust you. You are hired to be a support system not an evaluator. I have been to schools where they have the literacy and math coaches performing walk throughs.  This should not occur. I believe that teachers should know that you are there to help them and that you will never use any of their weaknesses against them. In order to be a good leader, teachers are going to need to be vulnerable with you. If you are evaluating them, they will never open up. Explain that you are there to learn alongside them and to build a better school together as a team.

2. Encourage teachers to share with others what they are learning about mathematics.

This is important for two reasons: one, it makes the teacher feel like they have something to offer the school. Most teachers enjoy sharing what they know and feel empowered when called upon to share their expertise. Secondly, sharing what you have learned can help other teachers learn as well. I always ask my peers to literally show me how they have taught lessons. I have sat on the floor of my own classroom during planning time and asked teachers to reteach me how to teach the lesson. We can all learn from each other and sharing is a big part of a school's success.

3.Remember that parents are an untapped resource

I can't say this enough. Parents are one of the best resources that teachers have. Inviting them into the school is important but asking them to share what they know is even more powerful. This year I am planning on having a parent workshop in math. This way I can help parents understand how to use Singapore math therefore they can help their children learn the concepts more seamlessly. Having parents on your side and opening up a line of communication is powerful. In my school we have a math area for parents. This area has games that parents can bring home and play with their children. Many of the parents actually use this resource and so do I.

Condominium Problem

After viewing the power point, I found that seeing all three methods worked best for me and gave me a complete picture. Method A had me very confused to start with, seeing Method B helped to clarify some of my misconceptions but it wasn't until Method C that I saw all of my mistakes and was able to solve the problem. This is why I think that students need multiple exposures to skills and should be taught to attack problems in many different ways. In my class, I start off with method C (Yikes). I would like to start off with Method A and then move just like the power point did. I think then students with different learning styles will all be able to understand the problem better. For example, my husband is very good at math and he would have preferred Method C. For myself Method C alone would give me a very superficial understanding of the concepts.

Assessing Cognitive Demand Task

Lower Level Tasks: 

Memorization: E, L

Procedures without connections: A, D, G, O

Higher Level Tasks:

Procedures with connections: F , I,  J, K, M

Doing mathematics: B, C, H,N, P

When looking back at my initial work, I had four of the activities marked as lower level when they were actually hirer level activities. 

Task B- I missed Task B, because I thought it was just a calculator activity when it actually asked you to assess the problem and assess whether 375 could be one of the products. 
Task C- When looking at Task C, I understood that it abstract but I was thinking that a student could create a problem and not necessarily understand the problem. I was wrong though after looking closer at the cognitive demands explanations.
Task H & M- At first I thought these tasks were a higher level task but after looking at the problems I thought all the incorrect answers could quickly be eliminated or that the answers were obvious. After looking closer, it does have real world application and requires the student to know how to use a diagram

Ranking Tasks

When ranking the levels of tasks, I grouped them in the following categories:

Lower level:
A, B, C, D, E, G, H, L, M, O

Higher Level:
H, I, J, F, K, N, P

Lower level tasks indicates very little application and mainly memory of formulas or answers.

Higher level tasks require students to problem solve, use manipulatives and explain their thinking. Additionally, some ask students to think about multiple answers.

Fencing Task

I love this fencing task much better than the first fencing task. This one really has the learner thinking deeply about the different options. I am going to use this task next year during my lessons. If there are any more tasks like these I would love to know about them.

1. The first thing I thought about this is that all squares are rectangles but not all rectangles are squares. Therefore a 6 by 6 pen equals 36 sq. ft.

2. Once again, if we are going with the above note then a 4 by 4 rectangle will equal 16 sq. ft

3. This question is very hard to articulate but what I did was take the number given and divide by two. Then I guessed and checked so for number 2 when it asked about a rectangular fence using 16 feet of fence, I dived 16 by 2 and got 8. Then checked its area which would be 20 sq. feet. Then, I looked for other combinations that equal 16 feet.

I use Marcy Cook math tiles in my class which are similar to this type of activity.