Maryland Common Core Summer Institute for Algebra

Continuing my professional learning July, I had the privilege of attending a week long institute devoted to learning more about instructional strategies for better teaching Common Core Algebra. The session was led by two professors at Towson University, and the insights they shared, especially pertaining to instructional tasks, was invaluable.

To start the first day we were paired with another attendee and instructed to place yarn handcuffs on our wrists so that the respected yarn strands crossed one another. We were then tasked with figuring out a way to uncross our yard without cutting or removing the cuffs. This served as a nice awkward ice breaker, as my partner and I tried everything that we could think of, including stepping inside of each other's yarn to see if that would allow us to get uncrossed. This was a nice problem solving exercise as it had a solution, but it was far from obvious and required some outside of the box thinking to solve. After a while, the instructors started providing hints and support. This was very much needed, and it helped the groups to be able to support each other. As one group figured out how to do it, we could then support other groups who were still trying to figure things out.

The yarn handcuffs exercise taught me two main lessons.  1) It is important to balance when to provide support, so as to maintain student sovereignty of their solving process, while preventing frustration and shut down, and 2) utilizing student ambassadors to help support other groups in the classroom is a valuable technique to make sure that support is more widely spread throughout the class while allowing students to have the opportunity to teach others, which solidifies their own understanding.

After the handcuff activity we watched a video about Austin's Butterfly. It was about a third grader who was tasked to draw a picture of a butterfly as a scientist would. He drew the first picture, and while it was clearly a butterfly it was not precise. From his first attempt his classmates gave him specific and focused feedback on how he could improve his drawing. The emphasis here was for the students to kindly provide constructive feedback with the goal of Austin drawing the most accurate depiction of the butterfly. He continued to adjust his drawings, completing four drafts before adding color, and through the process using the feedback to improve from one draft to the next, Austin was able to produce a much more scientific drawing of the butterfly.

The lessons learned from Austin's Butterfly that were emphasized throughout the week were to create an environment where students are comfortable giving a receiving feedback, for feedback to be constructive and focused, and begin with a focus on what is going right, keep in mind the goal of any project, and attempts should be thought more of as drafts that are meant to be constantly improved.

The next opportunity to problem solve with my peers came in the form of a sort of puzzle. The set up is there is a sheep named Eric waiting in a line to get shorn. There are 50 sheep in front of Eric, and he is very impatient. Each time that a sheep is shorn, Eric skips ahead of two sheep. If this continues, how many sheep will Eric need to wait for before he is shorn?

Working through this puzzle was a terrific experience. Not only was the puzzle interesting, especially the extensions available if he skips more sheep or if more sheep are shorn at a time, it was great to be able to work through a problem with other teachers. It was very rewarding to be able to bounce ideas off of one another, and I think that as teachers we take that for granted too often. Another great lesson from this task was the availability of having manipulatives to work with. Being able to model the scenario using chips proved invaluable. While getting students to act out the situation is engaging and helps to introduce the problem, it is not efficient for them to work through multiple cases. I also learned about floor functions, as well as alternate scenarios for the problem such as a lunch line or traffic setting for the problem. The big question remaining after working through the problem, is there a function that would represent the relationship between the number of sheep Eric would have to wait for given n sheep shorn and k sheep skipped.

The remainder of day one was spent working through developing a task within groups. While working to develop a task we focused on trying to come up with a puzzle or trick that the students were trying to figure out, and trying to make sure that there was a need for students to work through the math. For instance, if I wanted students to use a table or come up with an equation, I need to provide a need for those strategies to be useful.

On the second day we spent time talking about exponents, fractions, and ratios. The goal in it all was to work to get to the why behind certain properties that have traditionally been overlooked or taken for granted. Students need to see why things are as a means to build their conceptual understanding. In this way math will no longer seem to be a sort of magic to students, and they can be active participants in the process, rather than passive observers of a mystic power in the hands of experts. The theorem we tried to prove was that a/b < (a+c)/(b+d) < c/d . A good endeavor that any teacher of math should be able to execute.

From there the focus turned to the eight standards of mathematical practices. The two main tasks that we had worked through encompassed all eight math practices, and they gave us the opportunity to experience what it means to persevere, to reason, to construct arguments, to model, to use tools, to be precise, to look for structure, and to look for patterns. Seeing and doing those things in a focused and targeted way, helped us as teachers to realize what it is that we want our students to do, use, and think about as they become proficient in making use of the math practices. It was also emphasized that the practices to not take a back seat to content standards, as they go hand in hand in developing mathematically literate problem solvers.

We were given a presentation regarding the new PARCC assessments. This was informative as it provided us with details regarding the format and layout of the new tests. I like how the new tests will provide students with a way to show their thinking, and I like that the rigor of the test is meant to match the rigor that should be taking place in the classroom. There will definitely be an adjustment for teachers and students to get used to the different types of questions and the new technology meant to assess students' proficiency, but I hope that teachers will focus more on the content standards and standards of math practice more than they will on the format of the assessment tool.

Another problem solving task that we worked through was about two lines of people. Two lines of three people on their own block with a center block between the two lines, and the two lines facing each other. The rules of the game are that people can only move through a slide or a jump. A slide can be done one block at a time, and a person can only jump over one person at a time. Each move requires that the people are still facing the same direction, and the goal is for the two respective groups of three people to be on the opposite side of the center block in as few moves as possible.

This was an interesting puzzle, and it allowed for the group to work through a multitude of problem solving strategies. We tried to work out a simpler problem, starting with one person, then two, and so on. We modeled the problem working with chips instead of continuing to move people around. We made sure to record our findings, and we looked for patterns that we noticed that might help lead to a solution. Once we found the correct order in which to execute the jumps and slides, we worked to find a function that might represent the relationship. This was a nice exercise as it yielded a non-linear function, and with the shift in common core Algebra, non-linear functions are going to be emphasized more.

The other puzzle that we worked through dealt with the famous Tower of Hanoi problem. we tried to find the relationship between the number of moves as a function of the number of puzzle pieces. This was another nice problem because it dealt nicely with recursion, as well as exponential relationships. Both of which are also focused heavily in the common core standards.

The major lesson learned from a lot of the tasks and other demonstrations we had was to try to provide as many visual representations of concepts as possible. A great example of utilizing visual and tactile representations of concepts was the use of algebra tiles to demonstrate factoring and completing the square. The presentations make me want to invest in Algebra Tiles, and the entire institute makes me want to get chips and other items that students can make use of as they work through problems.

The final day of the institute was spent presenting our tasks that we developed in our respective groups. This was a terrific experience as there were six products that were presented that I am planning on using with my students. Most everyone tried to make use of the similar puzzles and problems that nicely incorporated multiple solution paths and techniques. There was a dice trick, systems stations, the locker problem, an outbreak of Algebritis, a field trip, and profit comparison all of which provided me with ideas that I can take back to my classroom.

The entire week served to invigorate my creative flow, and it makes me very excited to try out different approaches while working to hone my execution of the approaches that already know and use. I am excited for the next institute pertaining to the Common Core Number and Quantity standards, and I can't wait to see the new ideas and tasks that I can bring back to share with my colleagues.


 

Conference Day 2: STEMnet

As a part of my reflection process from the sessions I attended at the Maryland College and Career Readiness, this is my final eighth session reflection. The final reflection is from the session devoted to resources from STEM net. 

The main goal of the site is to ensure that teachers have a direct line to resources for providing students with valuable opportunities to engage in real world problem solving. One example of these resources is in the Scholars Speakers Bureau that is available. Students and professionals in STEM fields can come to schools and speak to students as a means to increase interest in science technology engineering and mathematics. 

Another similar resource is for STEM specialists to visit and cooperatively work with teachers n schools to enhance the STEM experiences being delivered to students. The main emphasis is to help students connect the fields of study to possible careers of interest. 

The most exciting resource that is available through the STEM net are STEM Challenges. Businesses are contacted to provide current problems they are facing that students could tackle. From there the problems are connected to content that is being taught in schools. Then students can submit their ideas and solutions, and get recognized for their efforts with an opportunity for internships with the companies. 

In addition to these resources, there are also lessons and project ideas that are aligned to common core content standards. All of these resources in conjunction with the network of educators, energize me to begin incorporating STEM projects regularly in my teaching. 

My main goals after attending this session are to make effective use of the resources including the STEM Challenge, and I want to continue promoting true STEM for all experiences for all students in my district instead of a select few. 

Conference Day 2: Facilitation Skills for Leaders

The second session on the second day of the Maryland College and Career Readiness Conference was targeted to improving the skill of facilitation in leaders. 

Facilitators serve three main roles in their work with groups of professionals. They are designers who develop an agenda and a vision for the group. From designing facilitators then become pilots who lead the course of discussion and brainstorming, as well as landing the productive plane with an action plan that brings everyone to a common purpose. Continuing the group's travels the facilitator becomes a guide if the group through the action plan. As an expert, the facilitator uncorporates the valued opinions of the entire group in the discussion and execution of the process. 

This metaphor was very helpful in connecting the many differ bet hats of the facilitator as a leader of others. The main skills that stuck with me were as follows; listening and responding effectively, guiding others, attending to the conten and process keeping the group focused, being in service of the group, and creating conditions that bring people together. 

When working with a divers group of people towards a common purpose it important for the facilitator to maintain a sense ofcommunity and goal oriented focus. I connected this to how we as teachers organize our students  in the work toward a common goal. 

My goals after attending this session are to engage in facilitation with a group of professionals, and to improve the facilitation of my students in their problem solving. 

Conference Day 2: Integrating STEM

Continuing my reflection from the sessions I attended at the Maryland College and Career Readiness Conference, I am beginning to look back on day two. The first session I attended was about integrating STEM standards into middle school. I was very interested in this session because a major goal of mine is to provide STEM experiences for all students instead if te select few who get those opportunities through the STEM academy. 

The main emphasis of STEM centric teaching is to connect to careers, incorporate STEM standards, connect to the real world, and have the work be a natural fit in the disciplines. Projects and problems shouldn't feel out of place or disconnected, and there should be a connection to at least two of the STEM fields as often as possible. 

The process of designing a STEM centric lesson starts with the content and STEM practices. What is the content being taught? 

From there the task shifts to finding a real world connection to the content. What is a problem or projects that professionals in the field are tackling that connects to the content?

Once the project idea is put together, a connect to at least two of the Science Technology Engineering and Math standards. What science connects, technology uses, engineering opportunities, and mathematical thinking will students be doing? 

An abbreviation to which I was unfamiliar was the "5Es"; engagement, evaluation, exploration, entension, and explanation. The idea is for all five to be incorporated, so that students are working through all five skills throughout the process of the project. 

The connections and the resources presented in the session were very informative, and I left very excited to start preparing lessons through a STEM lenses on a continuous basis for all of my classes. This leads me to the main goals after attendng this session. I want to develop STEM lessons and projects for my 8th grade math class specifically, I want to incorporate hands on projects for students to work on often in all of my classes, and I want to promote the ideal that every student should have the STEM opportunities on a regular basis at the county level. 

Conference Day 2: PLC

Looking back on the Maryland College and Career Readiness Conference, I have been reflecting on the sessions. The third sessions from the second day of the conference was one I was very interested as it pertains to goals that I have for my department, Keeping the Learning in PLC. 

This session focused on keeping PLCs as a tool for ongoing rigorous growth for improving student achievement. The key features of a PLC include research, examining student work, enhance pedagogy, and providing time for reflection. All of there can be present in any Professional Learning Community. 

One of the key components needed for any development to take place is to ask why. Why are we doing research, why are we looking at student work, why are we trying to enhance instruction, why are we reflecting, why are we doing anything to grow professionally? The why is the key, for without a satisfying understanding of the why, we will have trouble defining an action plan or vision forward. 

The session took a step towards distinguishing between dialogue and discussion. Dialogue is meant to provide a means for a group to talk while reserving judgement, promote inquiry and examination, and listening. Discussion is meant to advocate for a position, convince others of an idea, and solutions are not necessary. This was an interesting day crib to make, and we discussed that both forms of communication are appropriate depending on the situation. 

The main goal that I have moving forward frm this session are to effectively organize and participate a PLC in my department. I have noticed that meetings among colleagues tend to be too focused on administrative details and not focused enough on learning and improving practice. I would like for meetings to be regular and to address a goal of the collective department. 

Conference Day 1: Aligning Tasks to Standards

As part of my reflection process from the Maryland College and Career Readiness Conference, I am recording my thoughts and goals following each session. This session focused on using four main protocols meant to aid instructors, publishers, and curriculum specialists in determining how well curriculum materials are aligned to math and language arts common core standards. 

The tool that I worked on dissecting was the EQuIP tool. This process was structured as a rubric meant t measure the enxtent to which lessons and units effectively incorporate appropriate depth, conherence, rigor, differentiation, and assessment. The main goals are to make sure that materials are aligned with an emphasis on performance based assessment as evidence if effective lesson design. 

The five steps of the protocol are to review the materials, analyze the purpose as determined solely by the directions presented, compare the content to the standards, diagnose student work looking for patterns, and making suggestions on how to improve the materials. Through those five steps the EQuIP has a nice overall evaluative tool for units and lessons. 

The other tools discussed were primarily mean for entire assessments, individual assessment items, and supplementary materials. I am very glad that I was given access to the entire toolkit, a hefty phone book sized document. 

My goals after attending this session are to use the tools to evaluate materials that I am using in my own instruction, and I want to make administrators and supervisors aware of the tools  in case they are not already, so that they can a way of making sure materials are appropriately aligned. 

Conference Day 1: Coaching Skills

Following the Maryland College and Career Readiness Conference, and am continuing to try reflect on the eight sessions that I attended. 

Staring the session, there was a distinction established between being a mentor and being a coach. The main separation between the two roles is that an instructional coach primarily asks prompting questions that are meant to empower teachers to solve their own problems, while mentors primarily consult teachers and work to problem solve for a mentee. 

This was an important distinction, as most of the participants serve as coaches meaning to empower teachers. There are three stages of coaching that shift the approach of the coach. The first stage is a standard coaching relationship where the teaching is the main actor in the problem solving process. The second stage, which may be utilized depending on the level of capability of the teacher, is a collaborative relationship where the coach and teacher are working together to get through a problem. The third stage is meant to be a last resort where the coach takes on a consulting relationship with the teacher. This third stage is very similar to serving as a mentor. 

The idea behind the distinction in the three stages of coaching is to provide a structure for coaching that is flexible based on the teacher's needs. 

The most important skill that effective caches possess is being able to listen well. This took the session into a focus on determining what time of listener we are, so that we can better listen to teachers in order to better attend to their concerns. The key focus was to make sure that full attention and effective listening takes place no matter who the speaker is. In order for us to be effective coaches, the teachers need t know that we are listening fully, and devoting undivided attention to their needs in the moment. 

From being an effective listener, the focus went towards being able to paraphrase effectively so that the teacher knows that you have accurately listened and understood their problem. The main ways to paraphrase depend on how well you as the listener understood what was said. The coach can either acknowledge and ask for clarification, summarize and organize the information, or shift the conceptual focus appropriaty to a productive way forward. The important feature of each method is to affirm for the teacher that their concerns have been heard and you are ready to help them work out a solution. 

We had the opportunity to practice our coaching on a hypothetical dramatization of a teacher. This was a great exercise as it put us in the shoes of a coach trying to help possibly difficult clientels.  After engaging in this practice I realized that, just as with students, if teachers do not see the need for change and growth none of your suggestions will really help them. They need to own the process. 

After attending this session, my goals moving forward Into this year are to build trust from my colleagues and to improve my listening skills to better support teachers in ourcollective shift to new curriculum, strategies, and technologies.