OMCA Winterlude Retreat January 10-11, 2008 Connecting Research and Practice CIIM: Themes, results, implications Dr. Chris Suurtamm Dr. Barbara Graves

The iterative dynamic of connecting research, policy & practice

Focus Examine the context of math education in Ontario Share and discuss what the CIIM research is saying  Data from the CIIM report  New ways of looking at the data  New data Discuss what this means for OUR work

The plan Ontario math education & the CIIM report  Context of math education  Highlights of CIIM report  Research ideas emerging connected to CIIM report Who are the teachers and what are their practices?  What does this tell us?  What are the implications for our work? The critical role of the teacher  Challenges  Ways to help

Who is the audience? A. Math coordinator/consultant/resource B. Classroom teacher C. School board administrator D. Ministry of Education personnel E. Other

Who is the audience? A. Math coordinator/consultant/resource B. Classroom teacher C. School board administrator D. Ministry of Education personnel E. Other

Mathematics Education in Ontario Commitment and cooperation of mathematics educators Knowledge of math leaders about what is happening Evolution of curriculum in Ontario and other jurisdictions International standings

Where does Ontario rank in international assessments of math? A. At the international average B. Above the international average C. Below the international average

Performance on international assessments  TIMSS - Grade , 1999, Canada ranked in top 10 countries 1999, Ontario students scored significantly higher than the international average in all 5 content areas  PISA Ontario students performed significantly better than the international average, particularly in problem solving results just in

PISA 2006 Math results - countries with scores statistically significantly above OECD average Chinese Taipei 549 Finland 548 Hong Kong-China 547 Korea 547 Netherlands 531 Switzerland 530 Canada 527 Macao-China 525 Liechtenstein 525 Japan 523 New Zealand 522 Belgium 520 Australia 520 Estonia 515 Denmark 513 Czech Republic 510 Iceland 506 Austria 505 Slovenia 504 Source:

Not statistically different from OECD average Germany504 Sweden502 Ireland501 France496 United Kingdom495 Poland495

Statistically significantly below OECD average Slovak Republic492 Hungary491 Luxembourg490 Norway490 Lithuania486 Latvia486 Spain480 Azerbaijan476 Russian Federation476 United States474 Croatia467 Portugal466 Italy462 Greece459 Israel442 Serbia435 Uruguay427 Turkey424 Thailand417 Romania415 Bulgaria413 Chile411 Mexico406 Montenegro399 Indonesia391 Jordan384 Argentina381 Colombia370 Brazil370 Tunisia365 Qatar318 Kyrgyzstan311

But... we continue to work for improvement

Background of the research project

“So, is this curriculum working?” “I don’t know - are they doing it?”

Focus of the research To understand and describe the implementation of the current mathematics curriculum for Grades  "In the USA reform recommendations usually reach the classroom in the form of new curricula that teachers are expected to implement. However, teachers often transform such new materials in light of their own knowledge, beliefs, and familiar practices; as a result, the ‘enacted curriculum’ can be quite different from the ‘written curriculum’...” (Sherin, Mendez & Louis, 2004, p. 210)

Focus of the research  To determine how the current intermediate mathematics curriculum is understood and taught  To determine how teachers have been supported in the implementation of this curriculum  To describe environments where an alignment of the written and enacted curriculum is evident (or has been made possible)

Research Contributors Lead Researchers Dr. Barbara Graves, University of Ottawa Dr. Chris Suurtamm, University of Ottawa Consulting Researcher Dr. Geoff Roulet, Queen’s University Project Manager Suhong Pak Research Assistants University of Ottawa Emily Addison Ann Arden Nicola Benton Arlene Corrigan Adrian Jones Martha Koch Jennifer Hall Tom Hillman Queen’s University Steven Khan Jill Lazarus Kate Mackrell

Research Design Focus groups interviews with leaders in mathematics education (Winter 2006) Web-based questionnaire for math teachers in grades (Spring 2006) Teacher focus groups across the province (Fall 2006, Spring 2007, Fall 2007) Case studies in contexts where things appear to be working well (Spring 2007, Fall 2007, Winter 2008)

Sharing our results Ministry conference - February 2007 Regional conference in Guelph - Spring 2007 CIIM Research Report - September 2007

CIIM Report: Introduction & 5 chapters Minding the gap: Transition from Grade 8 to 9 mathematics The use of technology in math class The use of manipulatives in math class Assessment Professional development

Components of each chapter What does the research literature say? What do Ontario math education leaders say? What does the questionnaire data say? Connections, concluding comments

Assessment Teachers use a variety of assessments (Tables 1,2,3 - p. 118+) Paper-and-pencil tests and quizzes are the most frequently used forms of assessments There are differences in types of assessments used across the grades (Tables 4 & 5 - p. 121,2) The Achievement Chart is a concern (Table 9 - p. 126) Reporting by strands is a concern

Further research on assessment - teacher focus groups & case studies Published assessments that accompany textbooks are frequently used in Grades 7 & 8 Many, many assessment misconceptions  “They are only level 4 if they are beyond the grade expectations”  “Even if they get a 100 on a quiz it could only be level 3 because it is only testing knowledge”  “The Ministry requires that all marks be organized by the Achievement Chart categories”

The use of technology in math class Technology use is imbedded in the curriculum (Table 1, p. 59 Teachers could be more comfortable with use of technology in teaching math (Table 7, p. 64) Some technology is widely used - Graphing calculators used by % of Grade 9,10 teachers (Table 10, p. 67) Other technology use is emerging - GSP (Table 11, p. 67) Availability of computers is an issue (Table 13, p. 69)

The use of manipulatives in math class Manipulatives help to provide representation of a mathematical idea Use of manipulatives declines as students move through the grades (Table 7 - p. 95) Teachers’ perceptions  Only for some students  Help move from concrete to abstract Challenges  Connecting the mathematics  Knowing how to use the manipulatives effectively  Time

Further research on manipulative use - focused case study Secondary department using manipulatives  Collaborative effort  Systematic sequencing of manipulative use across grades  Focused professional development on manipulative use  Students are expected to represent mathematical ideas with concrete materials and diagrams as well as symbols  Teachers new to the department are trained

Minding the gap: Transition from grade 8 to 9 Knowledge of one another’s curriculum (Table 5 - p. 29) Frequency of meetings (Table 3 - p. 27) What happens at the meetings Different cultures  Classroom practices (e.g. Table 10 - p. 34)  Beliefs - about math teaching and learning, students (Table 15 - p. 39)

Further research on transition- focused case study Family of schools  Teachers see risks and are hesitant  Administrative support is essential  Focus at meetings is shifted  Learning about and respecting one another’s cultures takes time  Developing a collaborative culture takes time

Questions and your responses

Who are the teachers and what are their practices?

Who are the teachers who responded to the questionnaire? FrequencyPercent Grade 7 and 8 teachers50646% Grade 9 and 10 teachers55951% Other313%

Mathematics teaching qualifications organized by panel Grade 7/8Grade 9/10 Intermediate mathematics24%77% Senior mathematics5%74% Honours Specialist (math)1%31% P/J Math - Part 14%1% P/J Math - Part 21% P/J Math - Specialist1%0% Other math qualifications7%4% No math qualifications69%11%

How comfortable are you with the following aspects of the curriculum for this class? The content of the course Very Grade 10 Academic84% Grade 9 Academic80% Grade 10 Applied73% Grade 9 Applied71% Grade 10 Essential/Locally Developed61% Grade 861% Grade 757% Grade 9 Essential/Locally Developed55%

Of the following, which group has the least experience in teaching math? A. Grade 8 B. Grade 9 Applied C. Grade 9 Academic D. Grade 10 Applied

Who are the Grade 8 teachers? Intermediate and/or senior qualifications 30% Some university math courses 58% Degree in math 5% Less than 5 years teaching experience 34%

Who are the Grade 9 Academic teachers? Intermediate and/or senior qualifications 75% Some university math courses 98% Degree in math 47% 5 years or less teaching experience 42%

Who are the Grade 9 Applied teachers? Intermediate and/or senior qualifications 75% Some university math courses 98% Degree in math 47% Less than 5 years teaching experience 41%

Who are the Grade 10 Applied teachers? Intermediate and/or senior qualifications 73% Some university math courses 97% Degree in math 30% Less than 5 years teaching experience 51%

Beliefs about practice

Beliefs about practice: In this class, how important is each of the following? Very important Providing students with opportunities to practice skills 87% Providing students with many examples69% Providing engaging problems58% Providing opportunities for students to explain their reasoning 58% Encouraging student discussion of mathematical ideas 50% Promoting the use of multiple representations of ideas (concrete materials, technology, etc.) 48%

But we see that different grade levels have different beliefs about what is important to do in a classroom

Which grade has the least number of teachers reporting that the discussion of mathematical ideas is very important? A. Grade 7 B. Grade 8 C. Grade 9 D. Grade 10

In this class, how important is encouraging student discussion of mathematical ideas? Very important Grade 860% Grade 757% Grade 9 Academic54% Grade 9 Applied42% Grade 10 Academic40% Grade 10 Applied34%

Classroom practices

Teacher practices: In this class, how often do the following occur? Most or every lesson The teacher explains, demonstrates or provides examples93% Students work on practice questions91% Students provide solutions to problems74% The teacher provides solutions to problems67% Students justify their answers and explain their reasoning66% Students work on investigations to determine relationships or mathematical ideas 36% Students work on problems with multiple solutions34% The teacher works with small groups of students33% Students work with concrete materials or manipulatives24% Students use computer software or graphing calculators13%

Teacher practices: In this class, how often do the following occur? Most or every lesson The teacher explains, demonstrates or provides examples93% Students work on practice questions91% Students provide solutions to problems74% The teacher provides solutions to problems67% Students justify their answers and explain their reasoning66% Students work on investigations to determine relationships or mathematical ideas 36% Students work on problems with multiple solutions34% The teacher works with small groups of students33% Students work with concrete materials or manipulatives24% Students use computer software or graphing calculators13%

Looking closely at reform practices

In this class, how often do the following occur? Students work on problems with multiple solutions NeverSome lessons Most or every lesson Grade 71%50%49% Grade 81%56%43% Grade 10 Academic2%69%29% Grade 9 Academic6%68%26% Grade 9 Applied6%70%24% Grade 10 Applied6%79%15%

In this class, how often do the following occur? Students work with concrete materials or manipulatives NeverSome lessons Most or every lesson Grade 71%55%43% Grade 81%71%28% Grade 9 Applied6%75%20% Grade 10 Applied10%82%8% Grade 10 Academic20%74%7% Grade 9 Academic14%84%3%

In this class, how often do the following occur? Students use computer software or graphing calculators NeverSome lessons Most or every lesson Grade 727%57%17% Grade 820%66%15% Grade 10 Applied0%85%15% Grade 10 Academic10%83%9% Grade 9 Academic5%86%9% Grade 9 Applied4%89%8%

There appears to be a difference in teaching practices between Grade 7/8 teachers and Grade 9/10 teachers. Why? School culture Math background View of mathematics

Professional development What does it mean and what does it take to “shift practice”

The critical role of the teacher Recent research has identified the role of the teacher as the critical element in the development of learners ’ mathematical understanding (Ball, 2003; Ball & Bass, 2002; Ball & Even, 2004; Boaler, 2002).  International Commission on Mathematics Instruction (ICMI - Study 15)  Canadian Mathematical Society Math Education Forum, 2005  Rand Education/Science and Technology Policy Institute

However, The kinds of changes teachers are being asked to undertake are not simple and require a substantive re-orientation of their basic beliefs about the world in general and mathematics education in particular. Such a re-orientation can only occur (if at all) over time and requires ongoing and iterative cycles of professional engagement.

Why do you understand math teaching and learning the way you do?

Open space discussion Given yesterday’s discussion and presentation, what’s on your mind now? Write this down on a piece of chart paper (include your name). Post these on the walls in the room

Open space discussion Move around the room and read what people have expressed. Begin finding themes similar to yours and negotiate and move your paper together with papers that have a similar topic Keep gathering papers until you have a group of 5-6 people and when you do, you are a group Find a table and begin your discussion Use a new piece of chart paper to record the ideas generated in your group

Sharing the discussions

What does the data tell us about what helps teachers

Choose which one of the following you think teachers would say has most helped their implementation of the curriculum A. Curriculum documents B. Professional development workshops C. Teacher resource books D. Dialogue with their colleagues E. Textbooks

To what extent have the following resources or learning opportunities helped your implementation of the mathematics curriculum in this class? Top 6 choices Somewhat/ A lot Mathematics textbooks81% Dialogue with colleagues70% Ministry curriculum documents60% Teacher resource books that accompany a textbook53% Other teacher resource books49% Professional development workshops46% Table 2, p. 146

How often do you use each of the following resources when planning for this course? Top 5 choices Often or Very often Mathematics textbooks86% Dialogue with colleagues78% Ministry curriculum documents71% Other teacher resource books57% Teacher resource books that accompany a textbook52% Handouts from professional development workshops46% Table 1, p. 145

Teacher collaboration How often do you meet with other teachers to discuss and plan mathematics curriculum or teaching approaches for mathematics? Grade 7/8Grade 9/10 Never6%1% Once or twice a year32%13% Every other month16%8% Once a month24%18% Once a week13%20% Two or three times a week6%20% Almost every day4%19% 23% meet once a week or more 59% meet once a week or more Table 3, p. 147

Teacher responses to open-ended question about PD Q42: Please describe a professional development activity that has positively influenced the way you teach mathematics 757 teachers responded to this item Data was organized into information about formats for PD, topics of PD, providers of PD

Please describe a professional development activity that has positively influenced the way you teach mathematics Formats for PD  Workshops  Conferences  Leadership roles  Courses  Classroom observation/lesson study

Role of collaboration comes up in all of these formats - formal or structured “I was involved in the PRIME workshops... It got the same grade teachers together to share ideas and that hadn’t happened in years.” “One school I had previously taught in required all teachers to observe other colleagues as they teach. This was great to go and see other approaches, methods of motivation, and classroom management.”(03017)

Informal settings “I think the biggest key is being able to have a good math department with good colleagues so that you can bounce ideas off of each other.”(15110) “I have found that time spent with colleagues is most valuable with a free exchange of ideas over a longer period of time. Spending our lunch hours together talking about math questions and problems is one of the most valuable uses of our time.” (22794)

Topics of their positive experiences Teaching practice in general Use of manipulatives Technology TIPS How students learn Curriculum Assessment

Comments about these topics - Manipulatives “I went to one workshop where I was taught how to use fraction tiles. I had never really understood the ideas behind the subtraction of fractions, I simply knew how to apply the correct algorithm to solve the question. Using the manipulatives I learned the concept and actually saw why the algorithm works. I truly learned the value of using manipulatives first hand myself. It was very powerful and now I feel more comfortable and confident using fraction tiles in my classroom.”(22232)

Comments about these topics - Technology “I recently had a SmartBoard put in my classroom. It has revitalized the way I teach mathematics and my students are fascinated with the new technology.” (08177)

Comments about these topics - TIPS “The TIPS seminar profoundly changed the way that I view the learning of students and how I should be focusing on problem solving... (29672) “The best PD I’ve undergone in the last 2 years has been informal and unofficial. It consisted of becoming familiar with TIPS, implementing TIPS in my class, analyzing the results and adapting it for subsequent years. Having seen the impact of open-ended, contextual problems coupled with students groupings and a lot of manipulatives, I’ve become dedicated to this type of math teaching... (19597)

To what extent do you feel that further professional development in these areas would help support you in implementing the curriculum in this class ? Top 7 choices Somewhat/ A lot Teaching through problem solving79% Understanding how students learn mathematics72% Teaching strategies70% Use of manipulatives67% Assessment in mathematics66% Using group work in mathematics61% Facilitating investigations60% Table 5, p. 149

So, what do we know?

Thank you!