connecting research and practice ciim: themes, results, implications

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OMCA Winterlude Retreat

January 10-11, 2008

Connecting Research and PracticeCIIM: Themes, results, implications

Dr. Chris SuurtammDr. 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

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 8 1995, 1999, 2003 - Canada ranked in top 10 countries 1999, 2003 - Ontario students scored significantly

higher than the international average in all 5 content areas

PISA 2003 - Ontario students performed significantly better

than the international average, particularly in problem solving

2006 - 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 504Source:http://www.pisa.oecd.org/

Not statistically different from OECD average

Germany 504

Sweden 502

Ireland 501

France 496

United Kingdom 495

Poland 495

Statistically significantly below OECD average Slovak Republic 492 Hungary 491 Luxembourg 490 Norway 490 Lithuania 486 Latvia 486 Spain 480 Azerbaijan 476 Russian Federation 476 United States 474 Croatia 467 Portugal 466 Italy 462 Greece 459 Israel 442 Serbia 435 Uruguay 427

Turkey 424 Thailand 417 Romania 415 Bulgaria 413 Chile 411 Mexico 406 Montenegro 399 Indonesia 391 Jordan 384 Argentina 381 Colombia 370 Brazil 370 Tunisia 365 Qatar 318 Kyrgyzstan 311

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 7 - 10

"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 ContributorsLead 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 AddisonAnn ArdenNicola BentonArlene CorriganAdrian JonesMartha KochJennifer HallTom Hillman

Queen’s UniversitySteven KhanJill LazarusKate Mackrell

Research Design Focus groups interviews with leaders in

mathematics education (Winter 2006)

Web-based questionnaire for math teachers in grades 7 - 10 (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 91 - 98% 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? Frequency Percent

Grade 7 and 8 teachers 506 46%

Grade 9 and 10 teachers 559 51%

Other 31 3%

Mathematics teaching qualificationsorganized by panel Grade 7/8 Grade 9/10

Intermediate mathematics 24% 77%

Senior mathematics 5% 74%

Honours Specialist (math) 1% 31%

P/J Math - Part 1 4% 1%

P/J Math - Part 2 1% 1%

P/J Math - Specialist 1% 0%

Other math qualifications 7% 4%

No math qualifications 69% 11%

How comfortable are you with the following aspects of the curriculum for this class? The content of the course Very

Grade 10 Academic 84%


Grade 10 Applied 73%

Grade 9 Applied 71%

Grade 10 Essential/Locally Developed 61%

Grade 8 61%

Grade 7 57%

Grade 9 Essential/Locally Developed 55%

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%


Degree in math 47%

5 years or less teaching experience 42%

Who are the Grade 9 Applied teachers?



Degree in math 47%


Who are the Grade 10 Applied teachers?



Degree in math 30%


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 examples 69%

Providing engaging problems 58%

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 8 60%

Grade 7 57%


Grade 9 Applied 42%


Grade 10 Applied 34%

Classroom practices

Teacher practices: In this class, how often do the following occur?

Most or every lesson

The teacher explains, demonstrates or provides examples 93%

Students work on practice questions 91%

Students provide solutions to problems 74%

The teacher provides solutions to problems 67%

Students justify their answers and explain their reasoning 66%

Students work on investigations to determine relationships or mathematical ideas

36%

Students work on problems with multiple solutions 34%

The teacher works with small groups of students 33%

Students work with concrete materials or manipulatives 24%

Students use computer software or graphing calculators 13%

Looking closely at reform practices

In this class, how often do the following occur?Students work on problems with multiple solutions Never Some

lessonsMost or every

lesson

Grade 7 1% 50% 49%

Grade 8 1% 56% 43%

Grade 10 Academic 2% 69% 29%


Grade 9 Applied 6% 70% 24%


In this class, how often do the following occur?Students work with concrete materials or manipulatives

Never Some lessons


Grade 7 1% 55% 43%

Grade 8 1% 71% 28%





In this class, how often do the following occur?

Students use computer software or graphing calculators

Never Some lessons


Grade 7 27% 57% 17%

Grade 8 20% 66% 15%





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 textbooks 81%

Dialogue with colleagues 70%

Ministry curriculum documents 60%

Teacher resource books that accompany a textbook 53%

Other teacher resource books 49%

Professional development workshops 46%

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 textbooks 86%

Dialogue with colleagues 78%

Ministry curriculum documents 71%

Other teacher resource books 57%

Teacher resource books that accompany a textbook 52%

Handouts from professional development workshops 46%

Table 1, p. 145

Teacher collaborationHow often do you meet with other teachers to discuss and plan

mathematics curriculum or teaching approaches for mathematics?

Grade 7/8 Grade 9/10

Never 6% 1%

Once or twice a year 32% 13%

Every other month 16% 8%

Once a month 24% 18%

Once a week 13% 20%

Two or three times a week 6% 20%

Almost every day 4% 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 PDQ42: 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 solving 79%

Understanding how students learn mathematics 72%

Teaching strategies 70%

Use of manipulatives 67%

Assessment in mathematics 66%

Using group work in mathematics 61%

Facilitating investigations 60%

Table 5, p. 149

So, what do we know?

Thank you!

connecting research and practice ciim: themes, results, implications

Documents

ciim research

international averagebelow

math results countries

international averageabove

ciim reportwho

enacted curriculum

written curriculum

current mathematics