mathematics teachers’ educational beliefs web viewthe survey is a part of joint comparative...

NorBa mathematics teachers’ belief survey, Fall 2010

Proposals are marked with colours as following:- to omit- proposals what to change or add - new version/added items

NorBa-TM New Open Research: Beliefs about Teaching Mathematics.

Mathematics teachers’ educational beliefs/Introduction should be modified for different participating countries/Dear teachers,

We invite you to fill a survey on your satisfaction with your work as a teacher, effective/good teaching of mathematics, usage of textbooks, and few other questions. The survey is a part of joint comparative research project on mathematics teachers’ educational beliefs. It is created by the network of Nordic and Baltic researchers in math education.

There is evidence that beliefs are culturally informed and impact differentially on classroom practice. Cross-cultural differences in teacher beliefs and belief structures can provide important information regarding classroom practice and teacher inclination to different teaching approaches. Moreover, knowledge of teacher beliefs may indicate to specificity of teaching approaches and thus inform pre-service and in-service teacher education or curricular reforms. The main aim of this survey is to clarify the Latvian mathematics teachers’ beliefs on teaching mathematics. Identical surveys will be administrated in several Baltic and Nordic countries.

Your participation in this study is voluntary and refusal to participate will involve no penalty. You can withdraw from this study any time. Please, answer these questions thoroughly and thoughtfully, by choosing relevant answer (part A), drawing a circle around the chosen number in line with provided scale (parts B,C, D, E, F) or presenting textual answer (part G). Filling out this survey could take approximately 30 minutes. Your privacy and research records will be kept confidential. All data will be securely kept in a locked file and only the researchers will have access to the data. Upon your request after the finishing of research the researhers will send you the feedback on the results of this survey.

If you receive this survey by e-mail, please, respond in two week’s time from the day of reception. If you have any questions about this research study, contact the researchers by e-mail …………….(e-mail

of national coordinator).


A. Background information

Add gender item

1. My age is …. Years

2. Gender: male

female

3. What is the highest level of formal education you have completed? (mark one alternativeHigh school............... Bachelor’s degree..... Master’s degree......... A doctorate ..............

4. Mathematics was my major subject in my degree : Yes / No

5. I fulfil the formal requirements for a mathematics teacher: Yes / No

6. By the end of this school year, I have been working as a teacher .........years.

7. By the end of this school year, I have been working as a teacher in mathematics for the grades 7-

9 for …....years.

Add item on professional development: the first option below is most probably too general; so may be the

second and the third?

8. I attend courses or workshops for professional development in mathematics

Less than once a year

About once or twice a year

About three or four times a year

More often than that

9. In all, how many days of professional development did you attend during the last 18months?Please round to whole days, write 0 (zero) if none: .....days

10.How many days of professional development mentioned above were about math education?Please round to whole days, write 0 (zero) if none: .....days

B. Your overall satisfaction with your teacher job

Reorder items!

+Add more items about emotional feelings (develops another scale)1 (Fully disagree)...2...3...4...5 (Fully agree)


1. There is a great deal of cooperative activity among the staff 1 2 3 4 5

2. I sometimes do not get cooperation from the people I work with 1 2 3 4 5

3. Physical surroundings in my school are unsatisfactory 1 2 3 4 5

4. Necessary materials (e.g., textbooks, supplies, copy machine, library/media

materials, etc.) are always available as needed by the staff (to shorten!) 1 2 3 4 5

5. Teachers in our school have a big influence in making important school

decisions and designing school policy 1 2 3 4 5

6. I prefer to have others assume responsibility 1 2 3 4 5

7. The work of a teacher consists of routine activities 1 2 3 4 5

8. Teaching encourages me to be creative 1 2 3 4 5

9. In our school, staff members are recognized for a job well done 1 2 3 4 5

10. No one tells me that I am a good teacher 1 2 3 4 5

11. I know that the administrators are ready to help me with classroom problems,

should they arise 1 2 3 4 5

12. I look forward to each teaching day 1 2 3 4 5

13. My physical illnesses may be related to the stress in this job 1 2 3 4 5

New version of module B (developed by Anita and Martin)1) including the items left in accordance with our common decision in Tallinn (09.13)

2) reordering items as much as possible as to separate items belonging to one factor and to alternate

positively and negatively worded items;

3) reducing examples in brackets for item 3;

4) adding three “emotional items” as decided in Tallinn and their sources.

1. I consider teaching very pleasant (Lester, 1987)

2. I sometimes do not get cooperation from the people I work with

3. Necessary materials (e.g., textbooks, supplies, etc.) are always available as needed by the

staff

4. Teachers in our school have a big influence in making important school decisions and

designing school policy

5. No one tells me that I am a good teacher

6. There is a great deal of cooperative activity among the staff

7. I am glad that I have selected teaching as my career (Teacher Burnout Scale)

8. Teaching encourages me to be creative

9. I sometimes feel that trying to do my best as a teacher is a waste of time (Perie et al.,

1997)

10. In our school, staff members are recognized for a job well done


11. Physical surroundings in my school are unsatisfactory

12. I know that the administrators are ready to help me with classroom problems,

should they arise

13. I look forward to each teaching day

C. Your views of two teaching approaches

Please, read the descriptions of two teachers and choose one approach answering the following four

questions.

New wording, more math related, bring content in, not so obvious

Approach A

Teacher Hill was leading the class in an animated way, asking questions that students could answer

quickly; based on what they had been taught before. After this review, the teacher taught the class new

content, giving them an example on the board, again using questions to keep students attentive and

focused at what was presented.

Approach B

Teacher Jones’ class was also having a discussion, but many of the questions came from students

themselves. The teacher facilitated discussions and group activities, clarified students’ questions and/or

suggested how to approach the questions. The teacher hardly ever answered the questions

himself/herself, and some of the questions were left open.

1. Which type of class discussion you would be more comfortable having in class? 1 2 3 4 5

2. Which type of discussion do you think most students prefer to have? 1 2 3 4 5

3. From which type of class discussion do you think students gain more knowledge? 1 2 3 4 5

4. From which type of discussion do you think students gain more useful skills? 1 2 3 4 5

Alternative answers:

1. Definitely teacher Hill

2. Tend toward teacher Hill

3. Cannot decide

4. Tend toward teacher Jones


5. Definitely teacher Jones


D. Your view about good/effective teaching

F1(constructivism) add or change items to differentiate more

F2 (traditionalism) needs more items

1 (Fully disagree)...2...3...4...5 (Fully agree)

1. The students' real-life problems and future life serve as a meaningful context

for the development of their knowledge. (two separate aspects in one item?) 1 2 3 4 5

-to omit

2. Instruction should be built around problems with clear, correct answers,

and around ideas that most students can grasp quickly. (devide into two?) 1 2 3 4 5

-to leave as it is (TALIS item)

3. How much students learn depends on how much background knowledge

they have -- that is why teaching facts is so necessary. (into 2 items?) 1 2 3 4 5

-to leave as it is (TALIS item)

4. Effective/good teachers demonstrate the correct way to solve a problem 1 2 3 4 5

5. My role as a teacher is to facilitate students' own inquiry. 1 2 3 4 5

6. Students learn best by finding solutions to problems on their own. 1 2 3 4 5

7. Students should work on practical problems themselves before the teacher

shows them how they are solved. 1 2 3 4 5

8. Teacher should direct students in a way that allows them to make their

own discoveries. 1 2 3 4 5

9. In order to facilitate student's conceptual understanding the teacher

should vary methods accordingly (according to the situation). 1 2 3 4 5

10. Students should engage in collaboration in small groups explaining newly

developing ideas and listening to other students' ideas. 1 2 3 4 5

11. Thinking and reasoning processes are more important than specific

curriculum /learning mathematical content. 1 2 3 4 5

12. Most activities require the use of previous knowledge and skills in new ways. 1 2 3 4 5

13. Teacher should emphasize the use of knowledge and skills obtained in other


disciplines to solve problems and address issues. (change the order of those two items!)

1 2 3

4 5

14. Students and their teachers create the assessment criteria and/or tools together. 1 2 3 4 5

15. Assessment should include practical problems, projects and investigations. 1 2 3 4 5

16. A quiet classroom is generally needed for effective learning. 1 2 3 4 5

17. Teacher should emphasize the use of knowledge and skills obtained in other

disciplines to solve problems and address issues. (was No 13 before)

Add some traditionalist items from the list below:

There is always some procedure which one ought to exactly follow in order to get the resultMuch will be learned by memorizing rulesThere should be as much repetition and training of routines as possibleTo do mathematics requires much practice and correct application of routinesUsually in math instruction we use the tasks which have just one proper way to solve itThe teacher always tells the pupils exactly what they ought to do

Quizzes or tests based on recall of procedures and facts should be carried out regularly

Add some stronger constructivist items from the list below:

It is important to let students go outside the classroom to investigate a mathematical problem

It is important to make students collect data through measuring, investigating or asking around

(Sometimes) Teacher should change the plan of a lesson because a student has a mathematical idea/

problem/ question worth following up

Teacher should use specific brainstorming techniques in order to collect as many and as various ideas on

a topic as possibleStudents work on projects that require at least one week to completeActivities involving searching for patterns and relationships should be used as often as possible

Students hold a debate and argue for a particular point of view


E. Your view about good/effective teaching and learning of mathematics


1. One has to pay attention to students mathematical language (e.g. one should distinguish

between an angle and the magnitude of an angle, between a decimal number and

a decimal notation). 1 2 3 4 5

2. In a mathematics lesson, there should be more emphasis on the practicing phase than

on the introductory and explanatory phase. 1 2 3 4 5

3. Mathematics has to be taught as an open system that will develop via hypotheses

and cul-de-sacs. Develop into System aspect?

Mathematics has to be taught as a rigorous system based on exact definitions 1 2 3 4 5

4. Working with exact proof forms an essential objective of mathematics teaching. 1 2 3 4 5

5. Sometimes teaching should be realized as project-oriented (beyond subject limits),

and prerequisites for it should be created. (An example of a project: to buy and

maintain an aquarium.) 1 2 3 4 5

Teaching should include projects that go beyond subject limits (An example of a project: to plan the

program and finances for an excursion)

6. In mathematics teaching, one has to practice much above all. 1 2 3 4 5

7. The proof of the Pythagorean theorem has to be worked in a mathematics lesson. 1 2 3 4 5

8. The irrationality of the number 2 has to be proved. 1 2 3 4 5

9. In mathematics teaching, learning games should be used. 1 2 3 4 5

10. As often as possible, pupils should work using concrete materials

(e.g. cardboard models). 1 2 3 4 5

11. In particular, the use of mathematical symbols should be practiced. 1 2 3 4 5

12. In teaching, one should proceed systematically above all. 1 2 3 4 5


13. The learning of central computing techniques (e.g. applying formulas) must be stressed. 1 2 3 4 5

14. Pupils should above all get the right answer when solving tasks. 1 2 3 4 5

15. Above all the teacher should try to get pupils involved in an intensive

teaching discussion. 1 2 3 4 5

16. A pupil need not necessarily understand each reasoning and procedure. 1 2 3 4 5

The justification of mathematical knowledge isn’t always needed

All mathematical knowledge presented in the classroom needs solid justification

17. As often as possible such routine tasks should be solved where the use of the

known procedure will surely lead to the result. 1 2 3 4 5

18. Abstraction practice should be stressed in mathematics. 1 2 3 4 5

19. Above all mathematical knowledge, such as facts and results, should be taught. 1 2 3 4 5

20. Mathematics teaching should emphasize logical reasoning. (cross loadings) 1 2 3 4 5

Fundamental to mathematics is its logical rigor and preciseness

21. Pupils should develop as many different ways as possible of finding solutions, and

in teaching they should be discussed. 1 2 3 4 5

22. Pupils should formulate tasks and questions themselves, and then work on them. 1 2 3 4 5

23. In assessment (classroom performance), above all the presented solutions of the

tasks should be taken into account. 1 2 3 4 5

24. As often as possible, the teacher should deal with tasks in which pupils have to think

first and for which it is not enough to merely use calculation procedures. 1 2 3 4 5

25. Above all pupils should learn how the mathematics can be used in everyday life 1 2 3 4 5

26. Students don’t need to drill mathematical routines that can be done by computer 1 2 3 4 5

As computers can do most mathematical routines, their extensive practice is no longer needed


F. How do you use textbook? PROBLEMATIC MODULE- to leave out


1. I have chosen the textbooks I use for teaching 1 2 3 4 5

2. The textbook is the primary tool to plan and prepare my lessons 1 2 3 4 5

3. The pedagogical strategies I use are often influenced by the instructional

approach of the textbook 1 2 3 4 5

4. The tasks in the textbook are well adapted to fit both weak and strong students. 1 2 3 4 5

5. Overall, I am very satisfied with the textbooks I use 1 2 3 4 5

Alternative responses to the items on this pageNever (1), Some lessons (2), About half the lessons (3),(Almost) every lesson (4)

6. How often do students in your class use textbooks for the following activities:

(a) to study new concepts individually 1 2 3 4

(b) as the only source for exercises 1 2 3 4

(c) as a source for group work tasks 1 2 3 4

(d) to find additional material about the content

covered by teacher during the lesson 1 2 3 4

(e) as the only source for homework tasks 1 2 3 4


G. Your typical classroom practices

In teaching mathematics to the students how often do you usually ask them to do following:

1. Memorize formulas and procedures 1 2 3 4

2. Apply facts, concepts and procedures to solve routine problems 1 2 3 4

Add more items on Traditionalist practices

3. Work on problems for which there is no obvious method of solution 1 2 3 4

4. Relate what they are learning in mathematics to their daily lives 1 2 3 4

5. Decide on their own procedures for solving complex problems 1 2 3 4

6. Work together in small groups 1 2 3 4

7. Work in an investigative manner: to try to find patterns, formulate

statements and prove them 1 2 3 4

8. Work with computers or graphical calculators- Not related to our scales?

Add more specific items on ICT in math ed 1 2 3 4

Never (1), Some lessons (2), About half the lessons (3),(Almost) every lesson (4)

To use the following scale for grading (from TIMSS):

(1) Never or hardly ever(2) In about one-quarter of lessons(3) In about one-half of lessons(4) In about three quarters of lessons(5) In almost every lesson

Add items from the following:TIMSS items:a) Listen to me explain how to solve problemsb) Memorize rules, procedures, and factsc) Work problems (individually or with peers) with my guidance d) Work problems together in the whole class with direct guidance from mee) Work problems (individually or with peers) while I am occupied by other tasks f) Apply facts, concepts, and procedures to solve routine problems g) Explain their answers h) Relate what they are learning in mathematics to their daily livesi) Decide on their own procedures for solving complex problems j) Work on problems for which there is no immediately obvious method of solution


k) Take a written test or quiz

More items to consider:I present new topics to the class (lecture-style presentation).I ask my students to remember every step in a procedure.I administer a test or quiz to assess student learning. Students work individually with the textbook to practice newly taught subject matter.

Students hold a debate and argue for a particular point of viewStudents work in groups based upon their abilitiesUse computer software for mathematics instruction Explain their answers to other studentsHelp another student with mathematics


H. Please think and write down a metaphor characterising a teacher. Please explain your

metaphor.

Teacher is like…_____________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

My brief explanation of the metaphor is as follows: __________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

I. Possible other comments:____________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________

____________________________________________________________________________________


To develop new scale about computer based math

Chan proposed the following questions related to perception on using technologies (including computer)

to learn or teach mathematics:

1. Integrating technologies into learning and teaching mathematics has been proposed in recent

education reform. What do you think?

2. Is computer useful for teaching or learning mathematics? What is the major function? / Why is it

not useful?

3. What is the advantage or disadvantage of using computers in teaching or learning mathematics,

especially geometry?

4. Some people like to use technologies (such as computer or calculator) to help them solve

mathematics problems. What do you think? Do you regard this activity as doing mathematics? Why or

why not?

TIMSS items:

Do the students in this class have computer(s) available to use during their mathematics lessons?

Yes No

How often do you have the students do the following computer activities during mathematics

lessons?

Check one option for each line:

- Every or almost every day

- Once or twice a week

- Once or twice a month

- Never or almost never

a) Explore mathematics principles and concepts

b) Practice skills and procedures

c) Look up ideas and information

d) Process and analyse data

e) Use interactive software or computer animations to illustrate math conceptsItems above could be added to our module about typical classroom practices of teachers. The statements there started : “ In

teaching mathematics to the students how often do you usually ask them to do following:”


More ICT related items:

New technologies change the nature of mathematics

Change what kind of mathematical knowledge is important/ Because of new technology the content of

school math should be changed

New technologies have changed the way I teach mathematics

Essential part of mathematical competences is to learn to use mathematical software (computer algebra

systems, Geogebra etc.)

The students should be able to solve mathematical problems also without mathematical software

When students become fluent with mathematical software there is no need for them to learn solving

problems using paper and pencil.

Doing mathematics with computers does not develop a good comprehension of mathematics


Develop the new scale: Teachers’ perception about mathematics- ready-made scales availableGrigutsch et al. used in their study a test consisting of 75 statements. They classified the statements according to the

orientations. A shortened version of this test, consisting of 20 statements, was used in Mathematic Teaching in the 21st

century (MT21) –study (Schmidt, Blömeke & Tatto, 2011). These 20 statements are listed in Table. They reveal in more

detail what different orientations mean with respect to the nature of mathematics

Formalism-related orientation Scheme-related orientation

Mathematical thought is characterized by abstraction and logic.

Hallmarks of mathematics are clarity, precision and unambiguousness.

Essential for mathematics is definitional rigor, i.e. an exact and precise mathematical language.

Fundamental to mathematics is its logical rigor and preciseness.

Mathematics is characterized by rigor, namely rigor of definition and rigor of formal mathematical argumentation.

Mathematics is a collection of rules and procedures that prescribe how to solve a problem.

Mathematics involves the remembering and application of definitions, formulas, mathematical facts and procedures.

When solving mathematical tasks one has to know the correct procedure else one is lost.

To do mathematics requires much practice, correct application of routines, and problem solving strategies.

Mathematics means learning, remembering and applying.

Process-related orientation Application-related orientation

Usually there is more than one way to solve mathematical tasks and problems.

Mathematics means creativity and new ideas.

In mathematics many things can be discovered and tried out by oneself.

If one engages in mathematical tasks, one can discover new things (e.g., connections, rules, concepts).

Mathematical problems can be solved correctly in many ways.

Every person can discover or rediscover mathematics.

Mathematics entails a fundamental benefit for society.

Mathematics is useful for every profession.

Many aspects of mathematics have practical relevance.

Mathematics helps solve everyday problems and tasks.

According to Ernest (1989), mathematics can be seen either as a static but unified body (Platonist view), as “a set of

unrelated but utilitarian rules and facts” that are needed in the pursuance of external ends (instrumental view), or as “a


dynamic, continually expanding field of human creation and invention” (problem-solving view) (p. 250). The Platonist view

corresponds to the formalism-related orientation, the instrumental view to the scheme-orientation and the problem-solving

view to the process-related orientation. Ernest’s classification does not include any corresponding view to the application-

related orientation.

Ernest, P. (1989). The impact of beliefs on the teaching of mathematics. In P. Ernest (Ed.), Mathematics teaching: the state of

the art (pp. 249-253). New York: Falmer.

Felbrich, A., Müller, C. & Blömeke, S. (2008). Epistemological beliefs concerning the nature of mathematics among teacher

educators and teacher education students in mathematics. ZDM Mathematics Education, 40, 763–776.

Grigutsch, S., Ratz, U. & Törner, G. (1998). Einstellungen gegenüber Mathematik bei Mathematiklehrern. Journal für

Mathematikdidaktik, 19, 3–45.

Wong suggested:

Conceptions of Mathematics Questionnaire

1. For me, mathematics is the study of numbers

2. Mathematics is a lot of rules and equations

3. By using mathematics we can generate new knowledge

4. Mathematics is imply an overcomplication of addition and subtraction

5. Mathematics is about calculation

6. Mathematics is a set of logical systems which have been developed to explain the world and relationships in it.

7. What mathematics is about finding answers through the use of numbers and formulae

8. I think mathematics provides an insight into the complexities of our reality.

9. Mathematics is figuring out problems involving numbers

10. Mathematics is a theoretical framework describing reality with the aim of helping us understand the world

11. Mathematics is like a universal language which allows people to communicate and understand the universe

12. The subject of mathematics deals with numbers, figures and formulae

13. Mathematics is about playing around with numbers and working out numerical problems

14. Mathematics uses logical structures to solve and explain real life problems

15. What mathematics is about is formulae and applying them to everyday life and situations

16. Mathematics is a subject where you manipulate numbers to solve problems

17. Mathematics is logical system which helps explain the things around us

18. Mathematics is the study of the number system and solving numerical problems

19. Mathematics is models which have been devised over years to help explain, answer and investigate matters in the

world

Fragmented: 1, 2, 4, 5, 7, 9, 12, 13, 16, 18

Cohesive: 3, 6, 8, 10, 11, 14, 15, 17, 19


References

Crawford, K., Gordon, S., Nicholas, J., & Prosser, M. (1994). Conceptions of mathematics and how it is learned: The

perspectives of students entering university. Learning and Instruction, 4, 331-345.

Crawford, K., Gordon, S., Nicholas, J., & Prosser, M. (1998a). Qualitative different experiences of learning mathematics at

university. Learning and Instruction, 8, 455-468.

Crawford, K., Gordon, S., Nicholas, J., & Prosser, M. (1998b). University mathematics students' conceptions of

mathematics. Studies in Higher Education, 23, 87-94.

There is another popular one by Schoenfeld

Schoenfeld, A. H. (1989). Explorations of students’ mathematical beliefs and behavior. Journal for Research in Mathematics

Education, 20, 338-355.

New: metaphor about mathematics

Mathematics is like ……………………………..

My brief explanation of the metaphor is as follows: ………………………..

mathematics teachers’ educational beliefs web viewthe survey is a part of joint comparative...

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