Mathematical Practices and Mathematics Common Ground

Finding common ground when talking about the new Common Core standards for math has not been easy.  The ODE is still in the process of completing the Content Elaborations for the Ohio Math Standards. PARCC has released their own suggested framework. Teachers are trying to come to terms with a shift to teaching more about less, especially in the elementary grades.  Traditional math programs, existing integrated math programs and secondary course offerings don't neatly align to the new content. There are significant shifts in content from one grade level to another.  Textbook publishers are playing catch up to the new curriculum.

Eight.  No, it is not my lucky number or how many pieces of chocolate I ate as I sat down to plan for my upcoming math team meetings. (that was only 3)  Eight is the number of mathematical practices that serve as a single thread across all grade and ability levels.  Eight is the common ground.  The Mathematical Practices don't describe what math facts a student should know or the order that they should acquire knowledge of geometric concepts.  The 8 Mathematical Practices define how a student should be able to act and think as a mathematician, whether they are doing basic addition or Calculus BC.  These are not just good mathematical skills, in many cases they are good for science, social studies and language arts thinking as well.  As teachers sit down together to work on creating lessons that will begin to transition their math curriculum to the new Common Core model curriculum, they need to start on common ground, framing each lesson within the concepts of the 8 mathematical practices.

The 8 Mathematical Practices 

1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning

Learn more about the 8 Mathematical Practices
Resources

• Engage NY - Instructional Shifts for Common Core Math
• Carroll County Public Schools - Mathematical Practices Resources Mini posters - 8 mathematical Practices, template for evaluating lessons based on mathematical practices, lesson plan template.
• Inside Mathematics  Good explanations of mathematical practices with example lesson videos. (various grade levels spans elementary, middle and high school)
• Mathematics Assessment Project ( University of California Berkeley)  example lessons for each mathematical practice (MS and HS)  The  MAP also has formative assessment lessons for HS and MS math.  Also great are the performance tasks, aligned to the 8 mathematical practices, written for experts, novice and beginner level students that can be used for summative assessment http://map.mathshell.org/materials/tasks.php   Finally, professional development articles and activities http://map.mathshell.org/materials/pd.php including handouts, examples, videos and interactives.
• Teaching Number Sense - how number sense is similar to phonemic awareness. ( Reading Rockets.org)
• Thinkmath.org  K-5 version of the 8 Mathematical Practices
• Chittenden East Supervisory Union - good summaries and discussions of the 8 mathematical practices.
• Teaching Problem Solving Skills  (Waterloo University Centre for Teaching Excellence)
• Understanding the 8 Mathematical Practices   a K-4 Progression created by Mesa Public Schools

What's In A Grade...How Does Grading Change With Common Core?

Consistency is one of the benefits of the Common Core Standards.  Consistency in what content will be taught at each grade level. Consistency in how students will be assessed by the state on their content mastery. Consistency in how each student is graded on their work...well, hmmm, maybe not so much.

Our district is working on transferring to a new gradebook/reporting system.  It is a great chance to spend time revisiting grading scales and grading practices across our different grade levels. What I have found is that there is no consensus among my staff on what grading system really is the best for reflecting student academic mastery - letter grades, percentages, checks and minuses, 1 2 3 and maybe 4 or rubric categories.  Each group has valid reasoning for why they support one over the other.  Venturing into a discussion on how to delineate academic progress from "good studentness" is even more heated.  Add to this mix the fact that even within a subject area or grade level, teachers teaching the same content may have different interpretations of what each grade category "looks like" in terms of student work and you wind up with a grading system that is anything but consistent... and a reason to avoid the conversation all together unless you have an hour or two to spend in debate.

Where to start the conversation?  I think everyone involved needs to have a clear understanding of why we assign grades to begin with.  Grading is a very emotional, personal issue for teachers. This is because down deep teachers take grading, to some degree "personally".  I think that sometimes we think that grades are a way to justify a our success or failure. We use them to delegate responsibility for lack of learning back onto the student as evidence to prove that students "could have done better if only they had -fill in the blank_____." Sometimes, we may even take a low grade to heart, as if the student is saying " I don't like you or this class".    As teachers, we need to take a step back and reflect on what grading REALLY should be.  Grades are a way to help teachers, students and parents monitor the student's progress and eventual mastery in learning and applying content for a course or grade level.  Grades cover to two types of work, formative and summative.  In order for grades to be an effective tool to communicate this learning progress and mastery, teachers all need to be in agreement about what mastery or developing work looks like.  And, teachers need to be using a grading system  that  will allow students and parents to compare progress from year to year.

First, come to an agreement of what grading system will accurately communicate student learning progress and mastery of content.  Make this decision at least at the building level. There are some districts nationally that have moved toward adopting district wide grading.   Distinguish between academic grades and reflections of "student habits of mind" which can be reported to parents, but should not be included in academic grades.  Habits of mind include classroom skills like collaboration, communication, preparedness, critical thinking, quality of work etc.  Talk about how to report formative assessments and summative assessments and what might be included in a final grade.

Then, the best way to come to a common understanding of what "A" or "4" work, "B" or "3" work etc. looks like is to sit down together and look at samples of student work.  Have conversations within grade levels, building and subject areas about what learning is expected in the Common Core or the Model Curriculum and what mastery student work would look like.  Build a portfolio of "exemplar" work for each grading category that everyone has access to.  Show this exemplar work to the students so they can see what is expected of them.  Communicate these expectations to the parents so they understand what a grade actually represents.  Share student progress regularly with parents and students.  Make students accountable for their own learning by helping them monitor their own progress.

Grades should never be a surprise, a gift or a consequence.  Grades for content mastery should not be determined by behavior, personality or attitude.  Grades ARE a communication tool. Grades are a way to help teachers AND students monitor the student's academic strengths and weaknesses as they work toward mastering content.

Resources

• EdLeadership Study Guide - Effective Grading Practices   Guiding questions to help focus discussions on grading policies and practices. (Teresa Preston, Nov. 2011)
• At Some Schools, Failure Goes From Zero to 50 ( Steve Friess, USA TODAY,  May 2008)
• Courageous Conversation - Formative Assessment and Grading (Andrew Miller, Edutopia Blog, Dec 2011)
• Grading Practices (Barbara Gross Davis, UC Berkeley )  Good insights for College Readiness
• The Case of Illogical Grades (Lissa Pijanowski, EdLeadership, Nov 2011)
• Grading Exceptional Learners (Lee Ann Jung and Thomas R. Guskey, EdLeadership, Feb 2010)

  

Is There Room For Poetry In A Informational Text World?

I become liquid

Conforming to any shape

I flow, I shift, change.

C.S.

April is National Poetry Month. I challenge all of you to tie poetry into one lesson this month. One lesson. What, you say, you are not an ELA teacher? That's ok. Poetry is about taking content knowledge and interpreting it in a new way that someone hasn't thought of before. Take a look at my Haiku, is it about liquid as one of the 3 states of matter - science content OR is it about how I feel about what is being expected of teachers as they transition to the Common Core? Poetry is a way to condense key ideas, vocabulary, concepts down into something that is approachable or memorable. Poetry can be very structured and mathematically precise or it can wander and roam across a page mapping out thoughts and ideas. Poetry can be a bridge between fiction and non-fiction. Poetry requires the readers to really work at understanding the meaning of the poem - looking closely at what words the poet chose to create an impression or provoke an emotion.


But wait, the Common Core focus is very much on reading Informational Text and not poetry. Do the writers of the Common Core really expect the math department or the history department to teach reading? No, not directly. The writers do expect that all teachers will take responsibility for ensuring that students in their classrooms have the background knowledge experiences they will need to be successful readers of a wide variety of materials as they become adults. Don't you as teachers already teach them how to be thinkers? Stretch that thinking just a bit and you will realize that in order to be thinkers in your classroom, students must be able to read primary source information and draw their own conclusions. Readers need to spend time deciding what the author of a primary source document was trying to accomplish with the writing. What information did they choose to include or not include? What impression or emotion were they trying to elicit? What was going on in society at the time the piece was written? This is a shift away from the traditional textbook based content area reading assignment where the student reads p16-23, taking notes on bold faced words and answering the questions at the end of the section. It will require department and grade level teams to spend time reading the primary source material they will be using in their classrooms and having their own discussions. Lunch room conversations could become a lot more interesting!  


Are you up to this challenge... can you figure out how to add a little poetry to your classroom? And more importantly, can you help students to unlock the meaning of primary source materials that are relevant to your class?

Resources

Teaching Informational Text

• EngageNY  ELA Shift 2 Video (New York Dept of Ed) Informational Text, Knowledge in the Disciplines
• Appendix B - Common Core Curriculum ELA Exemplar Texts and Performance Tasks
• Teaching With Documents Lesson Plans - National Archives
• Teaching With Primary Sources - The Library of Congress
• Switching Gears - Helping Students Move Successfully From Reading Literature to Reading in the Content Area - Steve Peha (Teaching That Makes Sense)
• Simple Poems, Powerful Teaching: Experiencing Poetry in Content -Area Classrooms by Allison Baer (2007 Adlit InPerspective Magazine Ohio Resource Center)

Poetry Websites

• Ohio Resource Center - National Poetry Month Website
• British Poetry from Old English to the Modern Day  searchable by author view, first line view, timeline view, keyword view. Includes a section of literary criticism of poetry.
• The Academy for American Poets homepage  find text of poems along with a wide variety of lesson resources
• Poetry for Teens - poems about topics relevant to teenagers
• Popular Poems for teaching poetry
• World Poetry Sites  part of the National Poetry Month Initiative
• Poetry Foundation

Poetry Lesson

• Poems for Democracy
• Lessons to Teach the Power of Poetry
• In the Poet's Shoes

Spring Cleaning...Making Room for the Shift in Education

Feeling overwhelmed by it all?  I found myself sitting at my dining room table the other afternoon just staring at the laundry basket full of dirty clothes, the pile of papers to be sorted, the snowmen still on display on my mantle, the dust bunnies on the floor...I sat there a full 20 minutes doing absolutely nothing.  I didn't even know where to start.  I really just wanted to go up to my room, crawl into my bed and pull the blanket over my head.  But, I didn't. I had some chocolate. I prioritized. I started with the laundry. I still haven't gotten to the snowmen, but that's ok.  I am working my way through the tasks in my house, chipping away at them a little at a time.   I think that is the message that may be getting lost in the avalanche of information about Common Core Shifts, Formative Instruction, teacher evaluations, student growth measures, new grading systems, College and Career Readiness, technology integration, inquiry science, real world learning, authentic assessment....  Where to start?  How do we make room for all of this in our day, in our classroom, in our planning time?

As a curriculum director - I am looking at prioritizing my time and resources too.  I suggest starting with the Common Core and Formative Instruction. So many of the other "hot topics" in education are related to these two main initiatives.

Where to start...The Common Core

• If you haven't already, look at the model curriculum for your course, or if you are a teacher in a none core area (foreign language, art, music, phys ed, business, consumer science), revisit your current standards and think about how you might be able to embed more content area reading and writing into your class.
• Focus on content that will be similar in the new model curriculum to what is currently being taught in your classroom.  Spend time thinking about how to teach it more deeply, give students more time to practice a skill, ways to help students apply the content to prior knowledge and real world problems.
• Identify content material that will be "moving out" of your grade level or class and begin to cut away all but the basic lesson material around that content to make room for incoming content or more time to spend on content that will be similar but taught at greater depth.
• Look through your classroom materials, texts and lessons - find materials that you can share with colleagues at other grade levels who may now be teaching content you will no longer be teaching.
• Resources:
• PARCC Model Content Framework - math and English/Language Arts
• ODE k-8 Comparative Analysis - Math 
• ODE Comparative Analysis - Science
• ODE k-8 Comparative Analysis - Social Studies
• ODE  Language Comparative Analysis K-12
• ODE Reading Comparative Analysis K-12
• ODE Speaking and Listening Comparative Analysis K-12
• ODE Writing Comparative Analysis K-12
• Bay Village Common Core Resource Page

Where to start....Formative Instruction

• Write clear learning targets for your class based on the new Model Curriculum or your state standards.  Spend time thinking about what the underpinning learning targets will need to be - what will your students need to be able to do before they can master the ultimate learning target? How will you communicate these to your students? What will your plan be to do an initial assessment to see where they are in their learning? How might you differentiate lessons based on the underpinning targets?
• Choose one unit that you really like and already have learning targets for...and take an honest look at the assignments and assessments you include in that unit.  Do the assignments allow you to formatively assess student learning progress?  Are they differentiated? Is there opportunity for student self assessment or peer to peer feedback? Does the summative assessment for the unit accurately measure their mastery of the learning targets?
• Get out the "New Bloom's Verbs" chart and use it as you create a new unit that might align to the new content coming into your class...or revise a unit that you aren't so happy with. Develop learning and assessment activities that meet higher levels on Bloom's Taxonomy. 
• Resources:
• Classroom Assessment for Learning Chappuis and Stiggins (ASCD Sept. 2002)
• The Best Value in Formative Assessment By Stephen and Jan Chappuis (ASCD  Jan 2008)

I have a small picture I keep on a shelf in my office - it is a Chinese Proverb. " The person who removes a mountain begins by carrying away small stones"  I have a small pile of beach rocks by the picture to remind me that no matter how daunting or overwhelming a task, you must start one small piece at a time.   Stop staring at the mountain and find a stone to carry away.  Together we will accomplish what needs to be done, one stone at a time.