Planning a research project on teacher beliefs

Markku S. HannulaUniversity of Helsinki

Ontologies of affect (Hannula, 2007)Physiological Psychological Social

Affect as a state

Concepts: Neural activation, physiological adaptation.Methods: Facial expression coding systems, brain imaging techniques

Concepts: Feeling, emotion, thought, meaning, goalMethods: think-aloud protocols, video-stimulated recall interview

Concepts: Social interaction, communicationMethods: Observation, interview

Affect as a trait

Concepts: Brain structure, neural connectionsMethods: Brain injury case studies, reaction time measures

Concepts: Attitude, value, belief, motivational orientationMethods: Interviews, questionnaires

Concepts: Norms, social structuresMethods: Discourse analysis

Beliefs• Beliefs have been described as messy construct

(Pajares, 1992)• The term has not yet been clearly defined (Furinghetti &

Pehkonen, 2002)• Mathematical beliefs are considered as personal

philosophies or conceptions about the nature of mathematics and its teaching and learning (Thompson, 1992)

• Beliefs can be interpreted as „mental constructs that represent the codification of people‘ s experiences and understandings” (Schoenfeld, 1998).

Belief System• Beliefs must always be seen as part of a belief

system and these are characterized by quasi-logicalness, psychological centrality, and cluster structure (Green, 1971).

• Belief systems have a structure. Constitutive dimensions are object, self, and context. (Op ’t Eynde, De Corte & Verschaffel, 2002)

• The framework by Op ‘t Eynde et al. (2002) was mainly confirmed by analysis of our teacher student data, also one emotional scale could be found (Hannula et al., 2005a)

Beliefs are

• Individual constructs• Based on individual experiences

• Socially shared• Social constructs

Beliefs are

• Individual constructs• Based on individual experiences

• Emphasis in Finnish belief research

• Socially shared• Social constructs

• Cross-cultural studies important

Teacher beliefs

• About …– oneself as a learner of mathematics – oneself as teacher of mathematics– mathematics– teaching and learning of mathematics

• Use of technology– the social context of learning and teaching mathematics

• Have a cognitive and an emotional aspect• Teacher values

Teachers beliefs

• The traditional teacher – emphasises basic teaching techniques and

extensive drill• The innovative teacher

– emphasises student thinking and deeper learning • Many (but not all) have differentiated beliefs

about boys and girls in mathematics

Perry, Howard, & Tracey, 1999, Mathematics Education Research Journal, Vol. 11, No. 1,39-53

• Transmission: the traditional view of mathematics as a static discipline which is taught and learned through the transmission of mathematical skills and knowledge from the teacher to the learner and where "mathematics [is seen] as a rigid system of externally dictated rules governed by standards of accuracy, speed and memory" (National Research Council, 1989, p. 44);

• Child-centredness: students are actively involved with mathematics through "constructing their own meaning as they are confronted with learning experiences which build on and challenge existing knowledge“ (Anderson, 1996, p. 31).

Beliefs about the nature of mathematics

Beliefs about the nature of school mathematics

Instrumentalist Platonist Problem-solving

Instrumentalist

No conflict School mathematics is about learning basic skills that will later allow learning higher, more interesting math

You need basic skills before you can be creative in math. Creativity after school.

Platonist

School math is hierarchical knowledge that you need to learn in order to apply it

No conflict School math is hierarchical knowledge that you need to learn- Gifted few can eventually be creative

Problem-solving

Problem solving motivates students to learn the basic skills they need

Problem solving motivates students to learn ”real mathematics”

No conflict

(Beswick, 2009 PME)

Teacher’s professional identity measure (Beijaard, Verloop & Vermunt, 2000)

Factor α Sample items

Pedagogical interest

.845 I think I have the right qualities for working as a teacher

Security seeking

.736 Work at school means a secure state job and salary

Change agent

.852 Working as a teacher is an opportunity to change the young and society for the better

Social reasons

.647 My family and friends have advised me to consider a career in teaching

Beijaard, D., Verloop, N. & Vermunt, J. D. (2000). Teachers’ perceptions of professional identity: an exploratory study from a personal knowledge perspective. Teaching and Teacher Education 16, 749-754.

Teachers’ beliefs about girls’ and boys’ essential differences as math learners (Soro, ICME 2004)

Girls Total 145 Boys Total 105

f f % f f %

conscientious 35 24 % lazy 17 16 %

diligent, hard-working 34 23 % reasoning, clever 13 12 %

rote-learner 12 8 % careless 11 10 %

lack of self confidence 12 8 % insight, creative 9 9 %

routine-doer 10 7 % self-confident 8 8 %

rule-follower, copies 8 6 % venturesome 7 7 %

Exercising 5 3 % problem-solver 5 5 %

persistent 4 3 % not persistent 5 5 %

• JOHNSON & McCLURE Constructivist Learning Environment Survey (CLES) 5 scales (Learning Environments Research 7, Number 1 / January, 2004)

• Beswick. 9 “nine crucial beliefs” Educational Studies in Mathematics Volume 65, Number 1 / May, 2007

A model for generation of teachers’ mathematical beliefs

Local school context

Individual experiences

Individual beliefs

Culturally shared beliefs

Contextual experiences

Culturally shared experiences

Local beliefs

Individual charactersitics

Cultural context

Data collection methods

• A- learning rules and solving routine exercises• B- understanding mathematical concepts and

ideas• C- the ability to solve problems and appy

mathematics

        

 

 

A       

   

B C

 

Teachers beliefs visually: beginning of the project

A

CB

Teachers beliefs visually: beginning and end of the project

And now to discuss what we wish to study