Book Review: Writing to Learn Mathematics by Joan Countryman


One of the main reasons I love Writing to Learn Mathematics by Joan Countryman is because the strategies she offers provide meaningful learning opportunities for my students and myself.  I often find myself dreading to grade tests or to correct homework.  When I hand back corrected work, I see students crumple it into a ball and shoot it into the trash can.  Why do I dread correcting?  Why do students not care about their work?  These observations lead me to believe that when work is not meaningful, it feels like a chore, as though it is unimportant.  When students and teachers are allowed to be creative, to think deeply, to give and receive feedback on original thoughts, to have ongoing written conversations, then work becomes meaningful.  I love reading the learning logs of my students.  When I collect them, I go around the classroom exclaiming, “I can’t wait to read these!”  Students find me before school and ask to turn in their log early, “Miss, wait till you read this!”  What’s more, I feel like I understand and know my students on a deeper level.  The learning logs, autobiographies, and formal writings of students that Countryman described have provided me a view into the mind and thoughts of my students; into the silent world of written text.  

Screen Shot 2015-12-07 at 9.28.54 PMLast summer, while combing through math books online, I came across Writing to Learn Mathematics by Joan Countryman.  I ordered the book and when it arrived, immediately began reading it.  Writing to Learn Mathematics is a short read that is packed with practical strategies for integrating writing into math class.  Each strategy that Countryman outlines is accompanied by numerous student work samples.  I didn’t read the book once, but multiple times!  December is now upon us and I have had the pleasure of trying out Countryman’s strategies in my 8th grade math classes.  We began the year with math autobiographies and are currently wrapped up in learning logs and formal writing in mathematics. 

Countryman provides a compelling argument for why we should integrate more writing into math class, she explains that writing enables students to become aware of what they do and don’t know about math.  Students are able to connect prior knowledge to new knowledge while writing, summarize their understanding and give teachers insights into that understanding, raise questions about new ideas, reflect on what they know, and construct mathematics for themselves.  Countryman thoroughly outlines how to integrate various writing activities into math class including freewriting, learning logs, autobiographies, journals, word problems and problems with words, formal writing, and lastly, how to use writing for evaluation and testing.

A love hate relationship with math

I was able to easily adapt and modify all Countryman’s strategies for my classroom.  In general I would not say that the strategies that Countryman outlines need to be modified.  However, I teach math to 8th graders in a full inclusion setting.  What that means is that I have students that are on grade level, above grade level, below grade level, with minor learning disabilities, with major learning disabilities, with autism, that speak English as a first language, and that do not speak English as a first language, and so on.  Therefore, any activity that I do in the classroom needs to be accessible to all learners.  When introducing the mathematics autobiography to my class during the first week of school, I broke it into three sections, each section taking one day.  The first section was titled About Me, the second section was titled, My Family, and the third section was titled, My History of Doing Math.  Just as Countryman suggested, the first section is designed to be the easiest, since all students can write about what they know best, themselves!  I offered sentence stems and questions if students felt like they did not have anything to write about.  Most students easily accomplished part 1 of their mathematics autobiographies.

In the second section, students were also writing about what they know, their family.  I had to push students to include details, examples, and to use proper spelling, punctuation, and grammar.

The last section was the most difficult.  I used the language of Countryman, “Tell me about your triumphs and disasters (in math).  Go back as far as you can remember.  What do you like about learning math?  What do you not like?”  For some students, that was enough of a prompt.  Yet for others, I had to ask more specific questions, “Remember when you were in Mr. Shapinsky’s 7th grade math class?  Remember how you learned about proportional relationships?  What do you remember about that?”  Many students struggled to provide details and examples in this section and had to write three to four drafts before I gave them the beautiful paper to write their final draft on.

20151207_095623Once a student had written the final drafts of all three sections, we glued them to colorful paper and posted them around the room.  This created a culture in our classroom and set the tone for our 8th grade math class.  So far this year I have not heard the complaint, “but this is math, why do we have to write?!”

The mathematics autobiographies will decorate our walls for the entire year.  Parents have enjoyed them during open house and parent teacher conferences.  Teachers have remarked, “I have never seen so much writing in a math classroom, this is amazing!”  Even the Superintendent of Boston Public Schools, Tommy Chang, visited my classroom and took the time to read a mathematics autobiography.

I would recommend Writing to Learn Mathematics by Joan Countryman to all teachers, not just math teachers!  This is a great read with very practical and meaningful writing strategies for content learning.  And what’s more, my students and I are doing meaningful work together that we care about, getting to know each other more, and constructing math knowledge together.



Writing Is Thinking Empowers Students to Wield the Power Tools

The following is Katy Ramón’s elaborated speech for the Leadership Lab hosted by Teach to Leadthe US Department of Education, and the National Board for Professional Teaching Standards on Friday, June 26th, 2015. 

“The human condition is the heart of it all.” 
-Juan Felipé Herrera


Recently, Juan Felipé Herrera was nominated to be the first Latino U.S. Poet Laureate.  My heart burst when I read this news.  Juan Felipé Herrera is the embodiment of the vision I have for my students.  Mr. Herrera’s story is a humble beginning, much like many of my students.  He learned to wield power tools: a pencil and piece of paper.  And from that, he became a master of poetry, the U.S. Poet Laureate.  I want this for my students.  It is with this inspiration that I wrote this poem.

Part One

Put at a disadvantage
Not disadvantaged
Starving to make a change
Teach the power tools
Make that difference

She has a way to make money
Before school she goes to Stop and Shop
Self serve check out bays
In the shadows standing shyly
Fidgeting, gazing away
They always forget their change
Run after them, try to give it back
Well thank you!
But keep it child

Baseball air inflates his lungs
Heart beat base hits
Boy from the projects
The team is too expensive
Internet and a computer at home?
Pfft, jokes

Put at a disadvantage
Not disadvantaged
Starving to make a change
Teach the power tools
Make that difference

Part Two

I’m a numbers girl
Proudly taking after grandpa Dallas
Known for hiring two accountants
Even though he’d do the math himself
He didn’t make mistakes, but he sure found theirs

Writing wasn’t my thing, not at all
They asked me, so what’s your point?
In college, hours at the writing center
They thought I didn’t know what I was talking about
Because they couldn’t look at the calculations
And just understand

I knew math
Couldn't write
Nobody listened

My sister
Her writing a fine calligraphy pen
Everybody remarks on her brilliant intellect  
She knows nothing of factoring trinomials  
Or analyzing correlation with a best fit line
But when she writes about math
Everyone nods, agrees
As if Truth had finally arrived

She didn't know math
But she could write
So people listened

Write well to get your point across
Respected, educated opinion
Be a part of the decision-making process
The conversation

Write well for a clear math mind
Deepened, nuanced understanding
Break through the shallow ice
Enter the expansive depth  
Of knowledge

Put at a disadvantage
Not disadvantaged
Starving to make a change
Teach the power tools
Make that difference

Students Helping Students: Peer Evaluation and Feedback in the Classroom

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In middle school, students care about what their classmates say and think about them.  Often students pay more attention to what peers say and do than to what the teacher says and does.  I wanted to harness our classroom culture of helping and learning from each other with the social influence of peers.  I did this by creating a writing activity that we can use with any piece of student work.  The objective of this activity is for students to evaluate the work of their classmates and provide meaningful student-to-student feedback through writing.  By synthesizing a protocol from the National School Reform Faculty called Making Meaning with Accountable Talk sentence starters, I created a Peer Evaluation Protocol for our middle school students.  My colleagues who teach K-5 at the Gardner Pilot Academy adapted the Peer Evaluation Protocol to make an elementary friendly Peer Evaluation Protocol.

There are a number of underlying beliefs that support this activity.  Some beliefs are backed up by research, and others are grounded in personal observations from my classroom.  First, I believe that math teachers are also writing teachers and math students are writers.  Writing activities must be deliberately planned in math because writing is not a skill that is built in to the curriculum.  Writing in math deepens mathematical understanding and students must be able to communicate their math knowledge through speaking and writing.  They can only do this if we teach them how to and give them plenty of opportunities to practice.

Second, students improve their math skills by evaluating peer work.  There are enormous benefits in making students active participants in the evaluation process.  There are two parts to this:  when a student looks at a peer’s work and learns something new, and when a student’s work is looked at by a peer, given feedback, and the student learns something new.  Indeed, since I began this process, I have noticed students caring more about their work.  I have asked my students, “Are you excited to read what others wrote about your work?”  The answer is always an overwhelming “YES!”

Third, students improve their math skills by receiving feedback from other students.  Giving high quality feedback is challenging for teachers, imagine for students!  However, given the tools, students are capable giving effective feedback and of asking quality questions.  The challenge for teachers, then, is to teach students how to give high quality feedback.  I believe that this includes the skill of students asking quality questions to their peers that will push mathematical reasoning skills.

Fourth, students improve their math skills by engaging in Mathematical Practice Standard 3: Construct viable arguments and critique the reasoning of others.  This writing activity is rich in critiquing the reasoning of others.  The last two parts of the protocol require the evaluator to conclude what the student should continue to do and discontinue doing.  Students will read the math strategies of their peers and decide whether it makes sense, ask clarifying questions, and make suggestions for improvement.

In step one, a student looks at the work of another student and writes about what they see.  They are only writing about what they observe, all judgment and opinions are left out of this step.  The sentence starter “I notice…” is suggested for this step.

Step two asks, “What questions does this work raise for you?”  The sentence starter that students can use is “I wonder…” I have found that asking questions about math work is not easy.  We want the questions to be cognitively complex and push students mathematical reasoning skills.  It may be helpful to provide students with question stems.  Here are Depth Of Knowledge questions stems that I have found useful.

Step three asks, “Which math strategies are used?”  At this point, students describe the strategies they see and should be encouraged to use math vocabulary in their description.  Students own their description by starting with the sentence stem “I think…” In the past, I have put a minimum requirement of math vocabulary words that a student must use for this step.

Step four asks, “What should the student do differently next time?”  This is a chance for the evaluator to give some tips.  This step comes near the end of the protocol because students have had a chance to notice and describe, and now they need to develop an opinion and offer advice for how the author can improve.  Some students struggle to give advice to the more advanced students in the class.  However, I try to stress that our best can always get better and that even the most brilliant mathematicians are constantly seeking to improve.

Step five asks, “What should the students be sure to do next time?”  At this final step, the evaluator acknowledges the awesome things they saw.  This is a chance to praise and end on a positive note.

Peer evaluation and feedback is hard work.  The majority of the activity requires higher order thinking skills in the analyzing, generating, integrating, and evaluating categories.  Students are analyzing student work, reflecting on what they see, asking questions about student work, evaluating strategies for correctness and efficiency, summarizing strategies in their own words, and concluding with their opinion about what students should and should not do next time.  As students have more experience using the Peer Evaluation Protocol they develop their ability to ask critical questions and provide meaningful feedback to classmates.  This in turn positively affects everybody’s mathematical reasoning and critical thinking skills.

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After completing the Peer Evaluation Protocol, students were asked, “Do you care about your peer evaluation protocols?” Or alternately, “Are they meaningful to you?” Students overwhelmingly said, “Yes!”

Ideally, this activity will become a routine that is used throughout the school year. Students will improve their writing skills and engage in complex thinking through the peer evaluation protocol.  Students have reported feeling like this work is meaningful as evidenced by the sticky note collage pictured above.  I asked students if they care about their peer evaluations and if they are meaningful to them?  The feedback was powerful and has inspired me to continue this work of students helping students by evaluating each other’s work and giving feedback through writing.

Teacher Leadership In Action

Screen Shot 2015-04-04 at 9.09.01 AMThe Writing Is Thinking team is a group of dedicated teachers who deeply wish to help our students express their incredible ideas, thoughts, and opinions. We want our students to have a voice and to be heard through writing. When our team arrived at the 2015 Teach to Lead Summit at the Wharf Marriot in Boston, we only had a rough question: How can teachers systematically support English Language Learners and students with disabilities to express their understanding by thoughtfully implementing writing across the curriculum?

This question has transformed into an exciting project in which the middle school teachers at two schools in Boston Public Schools, representing multiple contents, are collaborating to design thoughtful Writing Across the Curriculum strategies and artifacts. In this way, we seek to accomplish two main goals: increase teacher capacity to implement WAC and increase the capacity of all students to express their understanding. Despite the fact that we represent different contents, we do share one common belief:

All teachers are writing teachers; all students are writers in all content areas. Writing experiences and opportunities must be deliberately planned in all content classes.

In addition to refining our idea, during the summit I had the opportunity to attend seminars focused on teacher leadership. It was during this time that I had a career changing realization: I need to aspire to be more than a great teacher; I need to aspire to be a great teacher leader. Not because I crave power or want to be in a leadership role. For me, teacher leadership is not done for power but for our students. Our collaboration with colleagues, quest to improve our practice, and influence on educational policy and instructional decisions are done, first and foremost, with our students’ best interests at heart. And who better to know the best interest of our students than us teachers?

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Our project is ultimately for our students but it is inherently teacher leadership in action. In the September 2007 issue of Educational Leadership: Teachers As Leaders, Cindy Harrison and Joellen Killion list and explain the “Ten Roles for Teacher Leaders.” The ten roles include:

  • Resource provider
  • Instructional specialist
  • Curriculum specialist
  • Classroom supporter
  • Learning facilitator
  • Mentor
  • School leader
  • Data coach
  • Catalyst for change
  • Learner

Screen Shot 2015-04-04 at 9.06.24 AMWhat I love most about this article is that teachers are providing these resources and services for teachers. These roles can occur organically, through the collaboration of colleagues or they can be formally implemented. We as teachers need to share the things we do and open our classroom doors; we need to make it a point to go into our colleagues’ classrooms, notice what they are doing, and learn something new. This action will help to shape our school and professional culture, it will positively affect student learning, and we will share practices among colleagues. is inextricably connected to teacher leadership. We are sharing resources with each other, colleagues, and the community by starting a blog. We are affecting instruction and curriculum by planning WAC in our classrooms and sharing our work at conferences. We are learning from each other by meeting once a month at each others houses, reading books together, looking at student work together, and video recording each others’ classes and practices. Most importantly, we are doing this to ignite student learning and expression in classrooms across Boston.