5. Using a Planning Rubric: Higher Order Thinking, Instruction and Assessment, Media and Technology, and Communication

5. Using a Rubric to think about Instruction and Assessment

This we believe (NMSA, 2010).

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·       *Varied and ongoing assessments advance learning as well as measure it. Varied Assessments

A few summers ago, I was working with educators at the University of Arizona on a project (Teaching Foundations Project) that provided a rubric designed to help teachers create powerful learning experiences. The rubric was designed by multiple stakeholders who were engaged in training future teachers at the university and community colleges in Arizona. The rubric focuses on tools of best practice. There are four parts to the rubric and I believe they capture the essence of how teachers should think about planning. The four categories of planning are: higher order thinking, instruction and assessment, media and technology, and communication.

The categories are generic to all areas of instruction. They could be used to create interdisciplinary instruction; but in planning, the rubrics can help us think about balance and integration of multiple instructional tools and strategies.

If we look at each of these through the lens of National Council of Teachers of Mathematics’ Principles to Actions: Ensuring Mathematical Success for All, it is possible to see the multiple layers that can be woven together within lessons and/or within weekly structures.

The first is a connection to Higher Order Thinking. Helping students learn how to think is a challenge for middle school students. Very often they are quick to give an opinion (No offense, but I often see this more in boys than girls – although, girls can do this too, and often it may not be based on any thinking. So, our job is to help them slow down and begin to analyze what they do see and what they are thinking. (:

Figure 1. Higher Order Thinking

TFP design descriptor	Targets	NCTM Eight Instructional Practices (2014)
Higher-Order Thinking Skills (1) Reading/ Thinking/Acting	Throughout the course, students are challenged to think and act intentionally Assess the credibility, accuracy and value of information; Identify audience to whom the information is addressed. Analyze and evaluate information; Make reasoned decisions; Take purposeful action; Identify problems; Think through solutions and alternatives;  Question, Use evidence to formulate explanations;  Justify;  Argue, Debate; Predict; Make Estimates, Form hypotheses	Implement tasks that promote reasoning and problem solving, Facilitate meaningful mathematical discourse Pose purposeful questions Build procedural fluency
Higher-Order Thinking Skills (2) Connections/ Multidisciplinary/Interdisciplinary	The course is rich in connections, within and outside the content area of the course Topics are introduced with integration in mind. Connections among topics within a given discipline are explicitly established. Connection between topics within one given discipline and other disciplines are explored and established, preferably through applied situations. Make pairwise connections (e.g., math-science; science-history, etc), and larger clusters (e.g., art-history-science; art-math-science etc) : explore connections, interactions, influences, that run between different ways of seeing and thinking about the world.	Use and connect mathematical representations Support productive struggle in learning mathematics
Higher-Order Thinking Skills (3) Authentic Learning Experiences	The course is highly relevant to students and other stakeholders because of the authentic and creative application of academic learning to important day-to-day realities Proposing academically-driven solutions or advancements to a real audience; Accurately interpreting evidence; Assessing appropriate match of audience and message; Identify/formulating key questions; Identify the salient arguments; original data collection and display; sharing/publication of findings; Conducting extensive research, Ongoing communication with numerous stakeholders; Receiving substantial and ongoing formative feedback during development; Authentic and high-profile culminating presentations and summative assessment.	Implement tasks that promote reasoning and problem solving, Use and connect mathematical representations, Facilitate meaningful mathematical discourse

The following is an example of how to get students thinking about math. We are using Paideia Seminars. This classroom discussion tool is part of a national effort to engage students in thinking and reflecting. This week I used  an article about The History of Labor Day to engage my students in learning the process of Paideia. We sat in a circle. We talked about ground rules and norms for the group. We made an individual and a group goal (These relate to listening, sharing, and questioning). After reading the 25 line article, students were asked to re-read the article and make notes about how what they were reading related to math.

After the discussion students were asked to write a reflection of the experience, what they learned, what they questioned, and how their knowledge of mathematics was useful in this exercise.

Students need structured opportunities to share their thinking, to think about how they use math and how math is necessary. It was a beginning and I am hopeful for the next experience.

The following is an activity that was developed by one of the instructors of the Arizona Teaching Foundations Project. You can view the entire website at: https://pll.asu.edu/p/

True or False

 Consider the list of statements below.  Determine which ones are true and which are false.  Then choose one true statement and one false statement and prepare an “argument” to convince your classmates that the statement is true or false.

a)    The sum of two even numbers is always even.

b)   The sum of two odd numbers is always odd.

c)    The product of two odd numbers is always odd.

d)   For every even number, all multiples of the number are also even.

e)    If the difference between two numbers is odd then the two numbers must both be odd.

f)     If the sum of the digits of a number is divisible by 3 then the number is divisible by 3.

g)    A number is divisible by 7 only if its last two digits are divisible by 7.

h)   If the last three digits of a number are divisible by 8 then the whole number is divisible by 8

The second focus is on instruction and assessment. Most colleges of education look at these two areas as the most important elements of planning. Instructional strategies are the tools we use to build background knowledge, allow students to engage in content and how we know whether our students are gaining the knowledge, skills, and dispositions necessary to apply what they are learning to their own lives and to their world.

Figure 2. Instruction and Assessment

	Target	NCTM Guiding Principles
Instruction	Course instruction is highly student-engaging; students think, communicate, and participate at an uncommonly high level on topics that challenge them to apply knowledge, reason, perform skills, and/or create products Examples of ways such instruction is carried out / promoted/ evaluated; RTOP (Reformed Teaching Observation Protocol) Discourse in Inquiry Science, The Learning Cycle, Modeling, “Process Drama” History as debate and multiple perspectives, Cognitively Activating Instruction in Mathematics, Environmental Mode in Writing	implement tasks that promote reasoning and problem solving; use and connect mathematical representations; facilitate meaningful discourse; elicit and use evidence of student thinking
Assessment	Course assessments move beyond basic knowledge-level multiple-choice formats alone to measure students’ mastery of reasoning, skill performance, and/or the creation of products Open-ended written essays of reasoning; Research papers; Oral presentations of (individual & group) projects; Science experiment design, execution & reporting; Design a prototype of a sustainable, high-use product; Perform an activity

The RTOP provides four criteria with which student engagement can be measured. In their report (https://mathed.asu.edu/instruments/rtop/RTOP_Reference_Manual.pdf) five areas are looked at.

Table 1. Reliability Estimates of RTOP Subscales

Name of Subscale R-Squared

Subscale 1: Lesson Design and Implementation                                       0.915

Subscale 2: Content – Propositional Pedagogic Knowledge                     0.670

Subscale 3: Content – Procedural Pedagogic Knowledge                                    0.946

Subscale 4: Classroom Culture – Communicative Interactions                0.907

Subscale 5: Classroom Culture – Student/Teacher Relationships          0.872

One of the subscales, Subcale 3 (R2 = 0.946) had almost as high a reliability estimate as did the total score  (0.954).

I use a mastery learning approach. It was coined by Benjamin Bloom (yes, of Bloom’s taxonomies). I love using it! Look at the blog on instruction and assessment to see how to begin to implement a mastery learning approach. There will be more blogs about this process as the year progresses.

The third part of the rubric is on media and technology. Our schools are gaining new tools that allow teachers to set up systems and structures to engage students in independent and group learning. The tools that are available to teachers and to students are amazing. And the schools that teach students how to use these tools effectively and appropriately are providing a generation of learners who are able to navigate, communicate, and create knowledge in the classroom and beyond.

Figure 3. Media and Technology

	Target	NCTM Eight Instructional Practices (2014)
Technology-Enabled Strategies	TARGET: Course-embedded, just-in-time training on technology tools needed for meeting course outcomes	establish mathematical goals; implement tasks that promote reasoning and problem solving; use and connect mathematical representations; facilitate meaningful discourse; pose purposeful questions; build procedural fluency; support productive struggle in learning mathematics; elicit and use evidence of student thinking
Distance Collaboration	Use of digital tools and media to involve collaborators regardless of location Use of social networks, blogs, wikis, to enhance discussion, learning, and presentation; engage other teachers/students in local knowledge production (e.g., neighborhood GIS resource maps); local- and distance-peer-review & editing; Assignments designed with this aim in mind make collaboration an essential (rather than incidental) part of the implementation and learning goals.  (e.g., assignments facilitate social studies-based community building and social engagement at the neighborhood and family levels.)
Research & Information Fluency	Use of digital research tools to create find, organize, manipulate, analyze, and share information Use tools for: brainstorming, organizing, research reviews, analyze text, write collaboratively, share research reports, bookmarks and other project resources.
Enriched Communication	Use of digital tools to create products, enhance presentations and participate in Web 2.0 activities and communities Digital video, internet: variety of graphics, (data visualizations, models, maps, charts, graphs, etc), screenshots, and illustrations, wiki, blogs, social media

Our school is getting Chromebooks for all the students. Many of the teachers are already using Google Classroom to set up classes, provide assignments, and set up learning circles within their classrooms so that students can communicate and collaborate with one another. Other teachers are using videos and cartoons as tools for helping students think about what they are seeing. Teachers are recording and putting directions in writing so that students who need to hear directions as well as see them are being served. Technology is being used in all areas of the school. A future blog will explore this more.

The fourth focus is on communication. The “writing process” has always included “publishing” as the final element of the process. In any subject whether it be academic or performance based, the publication of information provides students with the opportunity to share their knowledge and allows teachers to assess student learning.

Figure 4. Communication

	Target	NCTM Eight Instructional Practices (2014)
Writing-to-learn	Extensive writing for learning, reflection and demonstration of understanding Authentic writing tasks, writing as inquiry, discovery, meaning-making; pre-writing, peer-review & rewrites; high expectations for the use of discipline-specific language and clarity of scientific ideas; evidence-based reasoning; position papers; notebooks as personal learning records; reflective writing and self-evaluation	Establish mathematical goals; Implement tasks that promote reasoning and problem solving; Use and connect mathematical representations; Facilitate meaningful discourse; Pose purposeful questions; Build procedural fluency; Support productive struggle in learning mathematics; Elicit and use evidence of student thinking
Oral Presentation	Elaborate and ongoing oral communication of knowledge, reasoning, skill, process Formative (e.g., progress report) and summative (culminating formal presentation); individual & group; structured & informal; questioning, debating, planning; held to modeling discipline-specific structures and vocabulary, creation of a “podcast,” delivering the local news, artistic performance, exhibitions, teaching others

The following is an example of how to allow students to publish their ideas, their thinking, and their world.  This 9 weeks my students are going to create a project called “The Mathematics of Me”. It includes choosing their favorite number and analyzing it based on mathematical vocabulary, creating a timeline that looks at the year 2000 and three decades before and after the year 2000, when they were born and events that have taken place that are important in their lives as well as in the world. They will also create a graph of how they spend their week and plan a trip to a country they would like to visit.

I was at a technology workshop before school started. One of my former students shared how her students actually created a web 2.0 online book. The website is

The plan is to create a story: “The Mathematics of Us”, as we will be able to publish students’ stories, their words, their images.

By considering each of these components: higher order thinking skills, instruction and assessment, media and technology, and communication we can begin to plan lessons that provide our students with multiple layers of thinking, multiple opportunities to engage in content, and multiple ways to share their thinking and their learning.

7. What if You only had 36 Weeks?

This we believe (NMSA, 2010).

*Leaders are committed to and knowledgeable about this age group, educational research, and best practices.



Every morning I drive over the southern end of the Black Mountains and am treated to beautiful sunrises, as well as a 6% grade downhill. (This means that for every 100 feet, the mountain descends 6 feet) that opens to the east into a beautiful county. Our kids came Tuesday. I have known them as students for four days. They have already changed my life. They are our future and the future looks bright!

What if you only had 36 weeks?
I do wonder. What really matters?

I am thinking that there are two things that matter to me. First, students matter. I have taught them (the students) for four days. Yes, my feet are tired; yes, I did not sleep much the first week; and yes, I love them. They are magical, tireless, and willing; they are respectful, and silly, and make some fabulous and some poor decisions; they are gentle, and mean, and insightful, and worried; they are compassionate, and insensitive and then sensitive, and precious. They need teachers who care about them, as they are, and who want to help them be better people! There is a sense among the teachers at our school that this group should be designated as our "Students to Watch". Overall, they have come to us with a reputation of being a wonderful group of students!
Secondly, we must embrace those who make up our school community: children, teachers, administrators, support personnel, parents, and community partners. By embracing I mean get to know them, work with them, and honor the gifts they bring.

Advice

1) Structure. You will hear this in any and every education class. Structure is paramount and giving students clear expectations across every element of the class period is very important. We use the following format in our class:
*Practice
*Do
*Communicate
*Create
Our language function is ANALYZE.
I know, it is just another way to say warm-up, give notes, practice, and apply... but I like it.

The other structure I use is a modified CHAMP model of classroom management. It is part of the Safe and Civil Schools Network (safeandcivilschools.com). I use a quadrant approach to let students know if they are to work alone (quadrant 1), with a partner (quadrant 2), as a team (quadrant 3), or whole class (quadrant 4). For each of the categories associated with CHAMP, I let students know what my expectations are. If there is no conversation, I place a magnet on 1 next to Conversation; if they can communicate with a partner the magnet is on 2, if they can talk to anyone at their table, it is on 3, and if they can talk to anyone in the room, it is on 4. The same goes for asking for Help. Usually if there is a test, there is no talking; they are working alone, quadrant 1. The Activity indicates whether they are working alone (quadrant 1), with a partner (quadrant 2), as a team (quadrant 3), or as a whole class (quadrant 4). Pair and group activities give students opportunities to collaborate and communicate. Expectations related to Movement are always good to share. Quadrant 1 means, no movement; quadrant 2, only one of the members of the pair may move; quadrant 3, only one member of the team can move; and quadrant 4, the whole class can move. The last expectation I give has to do with the final Product. My approach differs from the actual CHAMP model. (CHAMP model explains the P as it relates to Participation.) I use product to indicate if they are turning in their own work (quadrant 1), work they have completed with a partner (quadrant 2), team work (quadrant 3), or whole class (quadrant 4).

 

So far all is good!!

2) Team Work! A second important thing you can do as a beginning teacher is to be a team player. I happen to be working with an amazing, caring, passionate team. Our personalities, to me, center on respect and trust for all members. We are all different and bring different, important elements to the team. In one week I have seen and been able to participate in collaboration, as well as the sharing of information about our students. (Today I did almost faint when the nurse was showing us how to use an Epi Pen and she shoved it into the leg of my team mate; it wasn't loaded; I didn't know that.) We have conversations before school, during lunch, and after school, conversations about our students that are constructive, that focus on their needs, that provide us with more insight in to how to help them be successful. My team mates have shared with me their knowledge, their tools, their insights that have made me feel welcome. I believe one of the most important things in teaming is valuing one another as individuals, as educators, whose focus is students.

3) Ask! The third piece of advice I have is to reach out. I have the gift of working with another math teacher who has shared her files with me. She is the vertical team leader. I have come with few resources. Her format and her approach to teaching math are proven to be successful. It is my hope to learn as much from her as I can so that all or students will be successful. To pre-service teachers, never think you know everything. There are those around you who are gifted educators; they are your resource... rely on them!

4) Celebrate. Next is the importance and value of celebrating!!! Yesterday we were told that, Friday is "Spirit Day" and teachers are invited to wear jeans and the school t-shirts to show pride. My team leader sent an email to the staff to encourage us to bring gifts/treats to our administrators. What a great idea!!! Only I didn't bring anything. So, I allowed our students to participate in this Spirit Day event. At the beginning of each class I had small strips of paper 8 1/2 x 1/2 for them to write appreciation notes to our administrators and our team mates. (It took ten minutes and was part of the practice.) We made "Spirit Chains" for these leaders. What an easy way to allow students to say thank you. (: And now we each have appreciation chains so that if we forget; we have evidence that our students appreciate us.

5) Advocate. My fifth piece of advice is to be an advocate for all stakeholders. There are several people in any school who are 'behind the scenes', yet provide such a gift. They are the administrative assistants who greet and meet everyone. On the first day of school our administrator patiently helped about twenty students find out what bus they rode. The custodians in our school are amazing. I asked the head custodian what I could do to help his staff. He said, "Put the chairs on top of the tables." I asked the custodian in our wing on Friday afternoon how the kids were doing keeping the restrooms clean. She shared, "Well, the boys had paper towel wads that had been saturated and thrown and there was some graffiti on the walls."  The administrative assistants (we have two) keep up with everything: logistics, supplies, discipline, student-schedules and have shown more patience than you can even imagine!   The guidance counselors, nurse, assistant principals, and principal, as well as others are amazing people. Our principal took a child to her office to call the little girl's mom to find out where she should get off the bus on the first day of school. Both assistant principals have been in my room, connecting with the students. One AP shared a math puzzler with my students that captured their thinking and made them smile. (He faced away from the board, asked the student to write a 3-digit number on the board so all could see, then asked them to reverse the numbers - 256 to 652. He then asked for one of the digits (tens, ones or hundreds) and told them the original number.)  (:

What I see in this school is that everyone is working so that our students are successful. As beginning teachers, my advice is to find a way to let those people know they are valued and that you appreciate them! No one should feel that they do not matter. Verbal acknowledgements of appreciation to your students, your administrative team, the support personnel, and your team mates must be shared openly!

6) Do your paperwork! Okay, next piece of advice is to get organized!! You have to sign in everyday! You have to call roll every day and our team recommends calling roll every period. The newest technologies allow for you to set up online grade books, online correspondence, and many teachers have their own websites. Use them. It is expected; it is needed. Communication is your friend.
In order to get class lists, set up homework lines, and to access information about our students, we have to complete many modules (okay, only four). On Thursday afternoon, I finally finished the correct modules and voila, the system crashed. It came back on for us around 1:30 Friday afternoon. Thank goodness for good old fashion folders and paper. Your team mates will have systems for organizing. All that being said, have a backup plan, a backup system!

7) Live it wide open! My final piece of advice today is to take care of yourself. Every day I take my lunch: a sandwich and an apple. Every day I drink water. Drink lots of water. Every day I go for a walk. I have to say, it would be so easy to lie down and take a nap, or unfold my lessons and lesson plans and student papers onto the table to begin working on the next day, but i don't. I took time to breathe, to unwind. You have to take care of yourself!

What if I only have 36 weeks? I hope I will give 110% every day to try to make a difference in the lives of those who are in our school community: students, teachers, administrators, support personnel, parents, and community. I hope I will embrace the experience. Friends, we only have 36 weeks to make a difference in the lives of these children, these colleagues, this community.

15. Parents and Guardians: The most important part of a team

This we believe (NMSA, 2010).

* The school actively involves families in the education of their children. Family Involvement

I describe teaming as a triangle. I believe the best teams are made up of students, parents and guardians, and teachers. When a middle school team balances responsibility, care, and advocacy on all three elements of a team, great things can happen. We all have a role in helping middle school students be successful. Parents are particularly important.

Last night was 'Meet the Teacher Night'. Parents and caseworkers, guardians, and grandparents came to our school. In the cafeteria, parents met the PTO leaders and the school nurse. We are a full-service middle school. Guardians were given the cafeteria procedures, waivers to sign, and were greeted by guidance counselors and administration. Once they left the cafeteria, each team welcomed parents, gave them a "supply list" and common lists of rules and behaviors.

About one-third of my parents showed up. I gave their child a math book to take home and shared procedures for homework and quizzes. However, my focus was to establish a connection with each parent and the families of these students. I spoke individually with about 35 parents. Parents want the following:
1) They want to know that you as their teacher want to work with them and their child;
2) They want to know there is a chance for their child to be successful and to know what you as a team will do to ensure their child has opportunities for remediation and/or enrichment; and
3) They want to know how they will know how their child is doing

Based on last night's conversations, I believe we need to think about how we can capitalize on this "event." The draw for this was that students received their schedules and supplies lists. I would recommend the following:

1) Make Meet the Teacher a spaghetti dinner. Highlight activities and events students can participate in. Treat it as a celebration of the school community. 4:45 - 5:30.
2) Have a speaker who encourages parent/student relationships and student motivation 5:30 - 5:42 - someone from the community or district or the Teacher of the Year from the school.
3) Give parents "tips for middle school success" 5:42 - 5:50.
4) Send parents to children's homeroom for an orientation to what students' days will be like, how the team will contact parents, and fill out forms. 5:50 - 6:15.
5) Rotate the parents, with their child through the child's schedule (5 minutes per period - including the change of class, ring the bell) 6:15, 6:20, 6:25, 6:30, 6:35 - 6:40.
6) At 6:40 come over the intercom, tell them about Spartan Time (advisory, remediation/enrichment, club time), they should be back at their homeroom; thank them for coming.

Advice

1) For open house or any time a parent comes by: Create a form that has a place for child's name, parent/guardian, phone, email. (My team leader shared a copy of this with me.)

2) As a team, create a welcome newsletter complete with your email information. (We sat down as a team and updated last year's.)

3) Determine structures that will be consistent across team members (scheduled tests, read thirty minutes every night, homework expectations).

4) Provide a supply list (we asked students to bring in a ream of paper as part of supplies) and don't be afraid to have a wish list (Our chorus teacher asked for a keyboard and has been given two!!).

5) Think about how you will communicate regularly with parents. With email it is possible to keep in touch with a percentage of parents. In addition, there are "Parent Portals" that provide parents with students' grades and behavior information. Think about how to ensure all parents receive information. I gave students weekly progress reports when I was teaching. Consider your non-English speaking parents and how you and your team will communicate with them.

16. The Essence of a Strong "Community" starts with Relationship

This we believe (NMSA, 2010).

*The school includes community and business partners. Community & Business

I have participated in three days of orientation at my new district. I was struck by the consistency with which we heard how deeply committed the district educational leaders, school board members, and community partners are to the children in this system. Even today when the research analyst was giving an overview of EVAAS (Educational Value-Added Assessment System), his first words were 'our children are more than a test score'. The spirit and energy and sheer joy and pleasure to be "in this together" permeated every speaker, every event, every exercise we participated in. I am reminded of the importance of starting the year in celebration and anticipation, in advocacy and joy, under the umbrella that teachers are valued at all levels. 

Superintendent Garrett welcoming the new teachers to the County.

I was also struck by how the district appears to not only "grow their own" teachers (about half of the new teachers grew up in this district), but also how open the entire community has been to welcoming new members, from outside the district, to their system. I was further inspired by the efforts taken by this district and their partners to ensure that their children's health and nutritional needs are taken care of. This full-service school system is truly addressing the needs of the whole child. And while we often hear people complaining about government cutbacks, the needs of these children, in this district, are being taken care of.

It appears that this system also takes their role of nurturing and advocating for new teachers very seriously. Every day we heard stories of how teachers make a difference. We heard from multiple stakeholders: The superintendent, instructional coaches, the president of the school board, the mayor, and the head of the Chamber of Commerce. Every one of them talked about the importance and value of relationships. Everyone spoke from the heart and inspired us to build relationships.

We rode on a school bus through the entire district taking in the diverse communities we serve; we participated in exercises to learn more about the demographics of this district, state laws, how community partners assist in supporting the children, and we learned ways to engage all learners.

The plethora of instructional coaches, who will look after us, are the former and current movers and shakers of the district. Their experiences are wide and deep; and their expertise collectively expands over a century of innovation, passion, and reflection on what it takes to meet the needs of the children in this district. Their enthusiasm and expertise were presented openly and held a "we can do this" spirit of support and dedication to helping new teachers be successful personally and professionally. One new teacher shared, "I feel like this district has a plan and I feel good about working with them." One of the coaches shared, "The leadership in this district is ripe to make a difference." You could feel the electricity of "we can do this; and we want you to help us" throughout the three days.

The orientation followed guidelines from the state and laid a foundation for beginning teachers.
I hope that all beginning teachers are given the support and inspiration that this district has given to us.

Advice

1) Start every year, regardless of whether it is your first or 30th year, whether you are a principal, assistant, custodian, administrative assistant, media specialist, guidance counselor, or teacher, in celebration and anticipation, in advocacy and joy, under the umbrella that together we can make a difference.

2) Nurture and advocate for beginning teachers. It cannot be a once and done experience. Support must be sustained, ongoing, intentional, and differentiated.

3) We must never forget that we truly do make a difference in the lives of children.

4) School districts must dig deeply into the depth veteran teachers bring and veteran teachers must dig deeply into the importance of advocating for and supporting those who are beginning their journey.

5) It's all about relationships to improve morale, take on challenges, risks, and make a difference.