Putting it All Together

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

As I am not one to lead in the area of math at this point, I'm not quite sure what my greatest challenge would be. If I were still at a school, I would say the greatest challenge would be getting teachers to use effective practices to ensure students are understanding the how and not just getting the "correct" answer.

B.  What obstacles do you anticipate?

With anything else....change is an uncomfortable concept for many to embrace. This is always an obstacle when getting your staff to move from good to great.

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

I feel most prepared for providing professional development to teachers and being a data-driven instructional leader.

Case Study

In reading this case study, I think about the instructional coaches that we have at our schools and how they have to divide their time up between so many schools that have different ideas on how to help students be successful. Meeting in PLCs is the most beneficial and effective way, that I see, of providing any type of professional development. At our schools, we follow the process of establishing norms for our PLCs, having defined roles, an agenda, minute taker and time keeper. This helps to keep the meeting moving in a positive direction that is solution oriented. This helps everyone feel like their time was well spent.

Professional Learning Communities (PLCs)

• Do you or have you worked in a school that implements PLCs?  If so, how are/were they structured? 

My whole school system currently implements PLCs at every school, although it is left up to the administrator at each school to carry out in a way that fits their school. At the high school I am based at, PLCs are scheduled every two weeks during the teachers 90 min planning block. These PLCs have a focused topic and administrators attend every one. After the PLC, teachers are given "assignments" to work on before the next PLC.

• How have PLCs been beneficial to you?  What are/were the drawbacks? 

Since I am in a different position, I do not attend PLC meetings. In the past, as an administrator of an elementary school, PLCs were beneficial in that we were able to look at data as a grade level and target students who needed to fill some learning gaps in order to be successful with grade level content and group students for enrichment purposes. Some of the drawbacks from teachers was having to "give up" planning time in order to meet.

• Please share any strategies or advice that you have for successfully implementing PLCs.  If you have not worked in or with PLCs before, what questions do you have?

One piece of advice I have is to make sure your PLCs are purposeful or they will turn into a complaining gripe session for teachers. That is not productive and it doesn't get us any closer to having students be successful in their classes.

Instructional Strategies

I have utilized KWL charts when I was in the classroom with students. KWL charts helped me to organize and helped the students see critical elements and vocabulary terms and the relationship between the two. Seeing what students already knew, helped me to differentiate for students who may have already mastered some concepts Having a list of items concerning what the students wanted to know, helped me determine what resources were needed to meet their needs. It was a very useful tool for me and my other students that were visual learners.

I can see where vocabulary strategies could play a key role in helping students understand math content. A lot of times when I talk to students and ask them why they believe they are struggling in a class, it’s because they do not understand what one word or a few words mean. This can make a big difference in being success and understanding math concepts and becoming frustrated. Incorporating a vocabulary strategy to pre-teach important math vocabulary terms would be helpful.

Accessibility Strategies

I also think PLCs would be the most effective way for this type of teamwork to occur. Because content teachers have common planning time, it’s a natural fit for them to talk about different strategies to include in their lessons for differentiation and to meet the needs of individual “pockets” of students. The most important piece I see is conducting the observation and collecting data, then coming back together for feedback.

Common Core Standards for Mathematical Practice

1- Make sense of problems and perseverance in solving them

D Anna thinks about another familiar type of problem that could help her solve the current one. She also monitors and evaluates her progress as she works through the problem, and makes adjustments along the way

2- Reason abstractly and quantitatively

H Ricky is making sense of the quantities and their relationship in order to solve the problem

3- Construct viable arguments and critique the reasoning of others

A Noah, Nick, Amy, and Maria are discussing triangles and each is arguing his/her point of view based on previously learned information

4- Model with mathematics

E Rachel created a model to help solve a real-world problem

5- Use appropriate tools strategically

B Mindy used the number line as a tool to solve her problem

6- Attend to precision

F Lin and Ben are discussing a rhombus to one another use precise terminology but Lin also goes back and adds more detail to his argument

7- Look for and make use of structure

C Zoe found a pattern and used it to help her solve the problem

8- Look for and express regularity in repeated reasoning

G Kelly notices a pattern/strategy (jumping to zero every time the signs are different) in her attempts to solve the integer problems which she uses to solve other problems.

Assessing Cogitive Demand of Mathematical Tasks

After reviewing the reading and re-evaluating the tasks, I would move Task C, I and J to high- level cognitive demand since these tasks either require an explanation, involve multiple steps or are abstract. These require higher levels of comprehension and application. .

Three of Ten Principles

Make Good Relationships with Teachers a Priority: As a leader, it is very important to have good relationships with the people you are working with. I am a relationship person and stress the importance of teachers having a positive relationship with students, so I have to model that in my relationships with teachers. Once that relationship is established, trust will be there and when it’s time to initiate change, you will have more people moving forward with you instead of setting you back.

Begin working with Teachers who are Interested, Curious, or Open to Change about a different way to teach math: Whenever I wanted to initiate change in my school, I would always start with the teachers who were interested and open to change. This way, you are not mandating the change and teachers are more open to take risks with support. Once these teachers are trained, begin implementing and most importantly see results, as they are communicating in their PLCs, their success will peek the interest of the others teachers and it basically becomes a domino effect of others that want to try something new.

Provide teachers with ongoing chances to meet with other teachers to be learners of mathematics and to reflect on their instruction: In my schools teachers either taught Math/Science or English/Social Studies on teams. I made the master schedule so teachers in the same grade teaching the same content had common planning time every day. One of those days had to be dedicated to content discussion, where teachers had the chance to discuss and reflect on their instruction within the classroom. They would often look at data and if one teacher’s kids were performing better on a certain concept than their kids, they were able to get suggestions on how to teach the concept so their kids could grasp as well. Teachers were very grateful to have this time built into the school day and were very productive with it.

Getting Started in Leadership

What issues did you face as a leader?  If you are not currently working in a leadership position, what issues/challenges do you anticipate?

            One of the leadership positions I held was that of Safe Schools Healthy Students Coordinator. In this position, I was to oversee the positions and activities throughout the county associated with a $4.5 million dollar grant. The positions that reported to me were graduation coaches in the middle schools, our GREAT officer, school psychologists, and nurses that were paid using grant funding. One of my responsibilities was to conduct evaluations, so that I could have data for grant purposes. One of the issues I faced was the concern and resistance I faced from the graduation coaches. As Rapacki and Cross Francis (2014) point out, that when you’re in a leadership position that is not clearly defined or understood by everyone, individuals turn on their defense mechanisms and fear of appearing incompetent kicks in. Another issue was trust. A few of the people in these graduation coach positions were previously our school social workers and because of funding, the county was not able to sustain the social worker position, so they were put in these grant funded to positions to “save” their jobs. Not having familiarity with me caused them not to trust me in this leadership position. Building that trust and rapport spoken about in the Rapacki and Cross Francis (2014) article was crucial in helping us have a working relationship that school year. I built trust by visiting them during the school day and in their afterschool programs before scheduling any observations, so they would be comfortable with me and learn more about me in a non-evaluative setting and even going over the evaluation instrument with them so they knew exactly what I would be looking for.

Getting Started in Leadership (continued)

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

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

What would you expect from the principal in this situation?

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

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

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

I think the first step in getting “organized” would be to review and disaggregate the school’s data. By looking at data, this person should be able to pinpoint areas of strength in the school and areas needing improvement. Trends will emerge which will help them narrow down their focus on specific topics/concepts for specific grades or even for specific teachers. They should let the data drive their planning as the Math Instructional Leader (MIL).

The MIL will need the support of the administration and “lead math teachers” within the school. They will have to build rapport with these teachers and administrators by becoming immersed in their daily activities. This includes attending PLC meetings, doing some informal observations in classrooms, attending staff meetings, eating lunch in the lounge with teachers, and having regular communication (Rapacki & Cross Francis, 2014).

I would expect the principal and supervisor to have a vision for what they would like the MIL to work towards and for the principal to communicate that vision with the staff. A lot of times I have seen administrators get “new” positions within the building, but never communicate why that person is there or how they are to be used. It’s often left up to the person in this coaching position to fumble their way through and do what they think is best to increase student achievement. When the principal communicates why the position is needed, the teachers are more willing to work with the person and help them. I think the supervisor continues to be a support and resource to the MIL and will conduct their observations throughout the school year.

Again, meeting with PLCs in different grade levels can begin to give the MIL a foundation of the math skills needed in each grade, sitting in math classes during instruction, and even reviewing the curriculum standards for each grade level will help fill in the gaps. Also attending professional development offered by the school or the district would be very beneficial to the MIL.

Reference

Rapacki, L.J. & Cross Francis, D. I. (2014, May). I Am a Math Coach: Now What? Teaching children            Mathematics, 20(9), 556-563. doi: 10.5951/teacchilmath.20.9.0556

High Cognitive Demand - Sorting Task

Martha's Carpeting Task

 In this problem, I drew a picture and labeled the length 15 and the width 10. I then used the A=l x w formula and plugged in the numbers to get 150 sq. feet as the answer.


Fencing Task

With this problem, there was a little more work involved:

1- To get the greatest area, you would have to try all of the combinations that would give you 24 ft on the perimeter: 7x5, 6x6, 9x3, 8x4, and 10x2. Using the area formula for each one, you find that a pen that is 6x6 on each side gives you 36 sq. feet which is the most room.

2- Again, you have to look at all of the combinations that would give you 16 ft on the perimeter: 5x3, 6x2, 7x1, and 4x4. In this case the largest are is 16 sq ft, meaning each side would be 4 ft. long.

3- In both problems, the perfect squares yielded the greatest area in the pen. If you have an amount of fencing that you can not use a perfect square with, you can always draw a picture to figure it out.

Similarities: both problems are area problems, both require a prior knowledge of area and how to find it

Differences: the amount of thinking/reasoning required for each problem, the number of ways in which the problem can be solved, and the need to generalize, 



Elementary Tasks

High Level Cognitive Demand	Low Level Cognitive Demand
Task A: interpret unit of measure	Task C: real life situation and solve
Task B: continuing patterns	Task D: respond to graph questions
Task F: fractions	Task E: place value
Task H: use graph to make predictions	Task G: solve division with calculator
Task M: interpret average (application)	Task I: multiplication
Task N: analysis	Task J: comprehension (explain)
Task P: application	Task K: comprehension (explain)

High levels of cognitive demand include: making connections, analyzing information, drawing conclusions, abstract thinking, and completing procedures (tasks) with connections to meaning

Low levels of cognitive demand include: stating facts, following procedures, solving routine problems, having single cognitive answers to a problem, and memorization with connections  to meaning

Discussion

A. Does a particular feature (e.g., writing an explanation as part of your answer, drawing a picture to explain what you did, using manipulatives to solve the task) indicate that the task has a certain level of cognitive demand?

While I do not think because a task has a particular feature that it indicates a certain level of cognitive demand, high cognitive demand tasks requires students to make sense of them. They have to read, determine what the questions is and how to use the information provided in the task. There are often multiple ways of finding the correct answer(s) to the task. High cognitive demand questions invites students to explain their thinking, make new connections, describe their process of figuring out the answer, and/or critique other's ideas.  Low level cognitive demand generally focuses on correct answers.

B. Is there a difference between "level of cognitive demand" and "difficulty"?

Yes. The level of cognitive demand describes the type of thinking required by a task, not whether the task is "difficult".

C. What effect does context (e.g., setting in which the task is used, students' prior experience, grade level) have on the level of cognitive demand required by a task?

The tasks in which students engage provide the contexts in which they learn to think about subject matter and different tasks may place differing cognitive demands on students. There is a connection with how the question is written, how it is presented and how it is implemented that will have an effect on the cognitive demand.

Problem Solving

In a particular condominium community 2/3 of all of the men are married to 3/5 of all of the women.  What fraction of the entire condominium community are married?

To find the fraction of the total population that are married, I found the lowest common numerator

3/5 of women: Multiply top and bottom by 2 to get 6/10

2/3 men: Multiply top and bottom by 3 to get 6/9

Add 6/10 + 6/9= 12/19 of the entire condominium community are married

Introduction

     Hello! Math has always been one of my FAVORITE subjects in school and I have always enjoyed teaching math to students. In this class, I hope to learn more about the math curriculum, instruction, and assessment so that I can help teachers deliver instruction in such a way that students are able to understand the concepts being taught. I received my undergraduate degree in Elementary Education (K-6) and my Master of School Administration degree from UNCW! This past spring makes 2 years that I have been taking classes in Educational Leadership with a focus on Curriculum and Instruction.

Stephanie Willis

About Me......
     I am a native of Wilmington, N.C. I graduated from E.A. Laney High School, where the FAMOUS (if you're into sports) Michael Jordan attended school. I lived in Raleigh for about 3 years while attending N.C. State University, before transferring to UNCW. Upon graduating (the first time) with my Elementary Education degree, I worked in Brunswick County as a Pre-K teacher for 3 years and then I moved to 1st grade for 3 years. I think I still would have been teaching, if not for my assistant principal (at the time) who pulled me aside one day and talked to me about applying for the Principal Fellow's Program because of what she saw in me as a classroom teacher. Nevertheless, I figured I would apply and if it was meant to be, I would get accepted into the program. I guess it was meant to be, because I found myself taking a leave of absence from work while completing the 2 year program. While taking classes, I worked on campus in the Education Building in King Hall and taught an EDL200 class and worked with different professors on projects. After my internships at a 3-5 school in Pender County and my high school, I was employed by Pender County Schools as an Assistant Principal at the same school where I was an intern. After a few years and transitions, I became principal at the same school. I then moved into a county role managing a 4.5 million dollar Safe Schools, Healthy Students grant and for the last 5 years I have been working as the Coordinator/Administrator of our Alternative Learning Program which I built from the ground up.

GO PANTHERS!

      My husband (who is also a Wilmington native) and I have been married for 18 years (will be 19 in September) and we have one son who is 16 years old and VERY active in school and in the community. I have been a soccer mom, t-ball mom, basketball mom, football mom, and lacrosse mom since he was 4 years old. Football and Lacrosse seem to be the sport of choice as he enters his junior year of high school.....at Laney. Our spare time consists of working in the community as I am
also the Co-Founder/Director of a girls mentoring group called GRITS (Girls Rocking in the South). We love to travel and are AVID fans of the Carolina Panthers! We try to attend at least 2-3 games each season at Bank of America Stadium.

     One thing that is unique about me is my ability to connect with students who are considered "at risk". I have a passion for helping student see the best in themselves when others have a hard time finding the best in them. Every student should have someone that can be their advocate even when they have pushed the limits and made the wrong decisions. I tend to be that person for a lot of the students that are assigned to our alternative program.

How I feel about mathematics............
     Math is very exciting to me! It's like taking the pieces of a puzzle and making it all fit together. I have always loved math in school (except for the proofs and theorems in Geometry) When it comes to learning mathematics, I feel eager. When it comes to teaching mathematics, I feel confident. School mathematics should be engaging and FUN! Being good at mathematics means being able to apply the concepts in a variety of ways.

What exemplary mathematics teachers do to help their students learn mathematics.....
     Since I have not been directly involved with the math curriculum in a few years, I would need some refreshing, but I feel confident in my ability to lead others in the area of math since I consider myself to be a quick learner. An exemplary leader is one who meets the learner where they are and builds a trusting relationship so the learner feels that they can take risks when asking questions and feel supported. Exemplary leaders in the area of mathematics make sure that they are teaching math in a way that meets the learning styles of all learners and is engaging for all students. They use data to drive their instruction, and they use a variety of assessment tools to check the pulse of their learners frequently.