IMAGINE... classroom teachers directing their own professional development, conducting their own research in their own classrooms. Having access to leading North American researchers and staff developers. Having time to support each other. Having funding to make it possible. Imagine . . . nine teachers in Thunder Bay are doing just that.
THE CHALLENGE: Learning a new way of teaching math
Over the past 20 years, methods of teaching mathematics have shifted, from keeping students busy with the rote learning of disconnected facts and procedures to teaching for automaticity and flexibility and for a deep understanding of mathematical concepts. 1 Today, communication and community are critical in teaching and learning math. Classroom experiences are structured so that students will develop mathematical strategies and ideas as they work toward making sense of problems. Students also learn to collaborate, responding directly to the ideas of others that may conflict with their own. In such a community, students learn to articulate their perceptions, listen to each other, and analyze each other’s ideas.
As classroom teachers at Agnew H. Johnston Public School in Thunder Bay, we wanted to provide our students with the most appropriate and progressive learning experiences. We knew that every year there are students who “just don’t get it,” we were aware that we needed to do things differently. We wanted to teach math in a manner that ensured allstudents learned. Some of us simply weren’t comfortable with math ourselves and didn’t have the confidence to know where to begin.
The reform movement in mathematics education is something we hadn’t experienced ourselves or seen in practice. We didn’t have the background knowledge, and the expertise wasn’t available in our school community. Trying to squeeze one more thing into an already packed instructional day was also a daunting task. As Jacqueline Watts, a Junior teacher, pointed out, “There is so much in the math curriculum in grades 4 and 5. Trying to tackle all of that and do it in a new way was pretty intimidating.”
THE SOLUTION: Designing our own learning
To put challenging instructional theory into practice we turned to each other – kindergarten to grade 5 teachers, English and French Immersion teachers.
Our story goes back a few years. Nicole Walter Rowan’s professional relationship with Dr. Alex Lawson began when Lawson was a graduate student and spent time in Walter Row- an’s classroom. Lawson, now an associate professor at Lakehead University’s Faculty of Education, urged her to attend workshops offered through the Mathematics in the City program at City College in New York. 2 Thanks to a small MISA grant, she was able to do that and it was there she met Antonia (Toni) Cameron, the facilitator of her first workshop.
At the end of the 2006–2007 school year, the Lakehead board’s elementary and student success coordinators agreed to fund a two-day workshop that introduced members of our teaching team to Dr. Lawson and Toni Cameron. The workshop took place in July and it increased teachers’ enthusiasm for additional learning.
Subsequently, ETFO’s Teachers Learning Together (TLT) project made it possible for some teachers at our school to conduct a small action research project in their classrooms. Diane Scocchia, a French resource support teacher, was among them: “We started with the ‘Five Productive Talk Moves’ identified in the book Classroom Discussions.3 We quickly realized there was much more to learn.” Developing this type of thinking seems straightforward at first glance, but genuinely embedding it in the classroom culture takes skill, practice, and professional support.
ETFO staff also made Nicole Walter Rowan aware of the Ministry of Education’s Teacher Learning and Leadership Program (TLLP). The teaching team applied for and received a grant of just over $100,000. This funding made possible Toni Cameron’s visits to Thunder Bay. It allowed two team members to travel to New York City to observe and participate in collaborative learning community meetings led by Cameron. The grant also paid for release time so that the team could work together.
LAYERS OF LEARNING
The team built its project around coaching and research. Lawson’s leadership ensured research components of the project were grounded in sound practice, and Cameron’s guidance provided the team with an effective model for coaching and co-teaching.
Teachers played a variety of roles in the team’s loosely structured grade-level groups. We planned focus lessons together and observed each other teaching, shared and celebrated successful lessons, and problem-solved when things did not go as planned. Finding a credible and manageable means to track our professional learning was a priority.
Ultimately, with the help of Lawson and Cameron, the team decided to analyze a video. 4 We watched and made notes about teacher actions and student behaviours that provided evidence of the classroom culture. This exercise allowed us to document the baseline of our understanding.
Having spent a year scrutinizing our lessons, analyzing student work, examining our questions, and exploring the role of student talk, we believed that we had a fairly deep understanding of how teachers’ actions impact student learning in a successful reform classroom. We were surprised by what we saw.
When he first viewed the video, Gaetan Roy, a grade 5 French Immersion teacher, was taken aback. “The teacher was so skilled at facilitating the class discussion. And the level of dialogue among the children supporting their reasoning and explaining their process, questioning and defending. In grade 3!”
BUILDING CLASSROOM COMMUNITIES
We focused on the “Five Talk Moves” (see sidebar) to build communities of learners in our classrooms. All of the social structures appeared to be in place. Students were looking at the speaker, they could restate someone else’s reasoning, and they sometimes even politely disagreed with each other’s ideas. But Cameron’s first visit to our school exposed a problem.
What was missing? There was social accountability in our classrooms: everyone had the right to solve the problem in their own way and all ideas about process were accepted. Students talked about their solutions and took turns explaining their thinking. It was a safe place to learn; but students did not challenge solutions they did not understand. They did not defend their opinions if someone disagreed. They were not motivated to express their ideas with a clarity that would ensure others understood their thinking. They weren’t really talking to each other as young mathematicians. Academic accountability was not yet an expectation within our classrooms.
As teachers, we struggled with this process among ourselves. Being rigorous in critiquing each other was a huge challenge. One team member remarked recently how much she has grown in this respect. At the beginning, she took feedback personally, feeling that it was a criticism of her students and of her skills as a teacher.
It was also hard for teachers to give feedback: we didn’t want to criticize. Sometimes we didn’t even see what was missing or know what we should be focusing on, and when we did, we sometimes lacked the vocabulary or clarity to discuss it.
OUR LEARNING HAS AN IMPACT
All of the teachers testified to changes in their practice, their beliefs about student learning, and many positive outcomes in both teacher and student learning. “It challenged my thinking about what’s important in math instruction. There needed to be less emphasis on the final product and more value given to the process,” Lynn Crookham, a grade 1/2 teacher, said.
Susan Momot, a kindergarten French Immersion teacher, admitted she initially had reservations about the language barrier. “The children were already good listeners and considerate of their peers but now there are significant changes. For example, I have a little boy who will start out by saying, ‘(Name) has a good point, but . . . And they are very adept at using the phrase parce que now. This approach works in French Immersion as well.”
Jennifer McGuire, also a Primary French Immersion teacher, described how her practice has changed: “I now prompt further student participation with carefully planned questions, use wait time more deliberately, and am comfortable with the silence that sometimes follows. The students must know it’s their responsibility, not to just listen, but to understand each other’s reasoning rather than waiting for the teacher to jump in and clarify.” “I now see that students are very capable of doing more challenging math than I expected and they are really enjoying it,” said kindergarten teacher, Tasha Vlotaros. “They are counting and adding by 10s, 5s, and combinations of the two. They are interested in how their classmates are finding solutions and excited to express their own ideas!” “I’m beginning to see strong thinking in students who I originally thought were not strong in math,” said Sarah Gerry, a grade 1 French Immersion teacher. She found that learning to listen for students’ thinking provided valuable insight.
TEACHERS WORK TOGETHER
Lawson and Cameron’s influence on the depth of learning was irrefutable; however, we credited a great deal of our growth to collegial support. The collaboration was both planned and incidental.
We had lofty goals – to increase our content and pedagogical knowledge and improve assessment practices in mathematics in one school year. We did it through co-teaching and coaching, observing students, collegial discussions and sharing our experiences.
Cristine Sillen, a JK/SK teacher at École Gron Morgan Public School, was the only team member not at Agnew. “Being involved in the pre-planning, the hatching of thoughts and ideas, and then watching another teacher facilitate the lesson has been a wonderful growth opportunity,” she said. However, Sillen found working alone challenging: “Having the opportunity to quickly bounce ideas off other participating teachers would have had a huge impact.”
Our approach made a difference in the culture of our school, according to Principal Joy Petrick: “It has contributed to a new level of professional openness. Teachers have taken huge risks professionally, and have done so with all of their colleagues watching and giving them feedback. The professional accountability and collegial support crosses divisional boundaries. In our schoolwide literacy PLCs, it has changed the way we talk about our practice and its impact on student learning.”
Judith Sowder, a renowned researcher of mathematics education, wrote that teachers engaged in changing how they teach math need to be dedicated to becoming “serious learners of practice rather than learners of strategies and activities.”5 It was not enough to read about, try, and discuss new lessons, or to implement a new list of activities to do with students. We had to become a learning community committed to “lateral accountability” and examining our practice to see how it could be improved. 6
We have taken our practice public. Early on we partnered with a TLLP team from the Rainy River District School Board. We have opened our classrooms to LDSB central resource teachers, Lakehead University master’s students, and student teachers. We had visits from teachers from the Superior Greenstone District School Board and members of the Literacy and Numeracy Secretariat. At times working in a fishbowl has been a little overwhelming; but everyone who took part insists we would invite another hundred people in to observe before giving up this remarkable experience.
THE FIVE PRODUCTIVE TALK MOVES
- Revoicing (“So you’re saying that . . . ?”)
- Asking a student to restate someone else’s reasoning (“Can you repeat what he just said in your own words?”)
- Asking students to apply their own reasoning to someone else’s reasoning (“Do you agree or disagree and why?”)
- Prompting students for further participation (“Would someone like to add on to what she said?”)
- Using wait time (“Take your time; we’ll wait . . .”)
(from Classroom Discussions)
RESOURCES / NOTES
1 M. Battista, “The Mathematical Miseducation of America’s Youth,” Phi Delta Kappan, 80(6), 425-433.
2 Mathematics in the City, established in 1995, is a collaboration between City College of New York and the Freudenthal Institute in the Netherlands. It is both a think tank and a national centre of inservice for K-8 mathematics education. For more information visit the website:mic3217.addr.com.
3 Suzanne Chapin, Catherine O’Connor, and Nancy C. Anderson, Classroom Discussions: Using Math Talk to Help Students Learn, Grades 1–6. (Sausalito, CA: Math Solutions Publications, 2003).
4 Maarten Dolk and Catherine Fosnot, Turkey Investigations, Grades 3-5: A Context for Multiplication, in the Young Mathematicians at Work series (Portsmouth, NH: Heinemann, 2005).
5 Judith Sowder, “The Mathematical Education and Development of Teachers” in Second Handbook of Research on Mathematics Teaching and Learning, F. Lester, ed (Reston: National Council of Teachers of Mathematics, 2007), pp. 157-224. Also see: D. L. Ball and D. K. Cohen, “Developing Practice, Developing Practitioners: Toward a Practice-Based Theory of Professional Education” in Teaching as the Learning Profession: Handbook of Policy and Practice, L. Darling-Hammond and G. Sykes, eds. (San Francisco: Jossey-Bass, 1999), pp. 3-32.
6 B. Lord, “Teachers’ Professional Development: Critical Colleagueship and the Role of Professional Communities” in The Future of Education: Perspectives on National Standards in America, N. Cobb, ed. (New York: College Board, 1994), pp. 175-204.