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.