Secondary school mathematics teachers’ views of manipulatives and their use in the classroom

Adrian Jones

M.A.(Ed.) Candidate

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Motivation Mathematical Manipulatives Research Perspective What’s Really Happening in the Classroom? Challenges Influence of Teachers’ Views on Practice Conceptual Framework Research Questions Data Analysis dimensions Timeline

THE MOTIVATION

Introduced to mathematical manipulatives during my teacher education program in 2006.

– Challenged my own ‘understanding’ of mathematics– Many “ah-ha” moments, new insights (larger mental repertoire?)– Opportunity to develop understanding of their use with pre-service teachers

during Math Camp– Helped my children in their own understanding by…:

connecting manipulation of algebra tiles to algebraic operations (e.g.: collecting like terms, factoring and reforming quadratics, multiplying binomials…).

helping to make concrete and meaningful connections to abstract mathematical concepts

shifting the locus of understanding from the teacher to the student– So why aren’t my children’s (and other) teachers, especially in high-school

mathematics, using them for their students’ (and potentially their own) benefit?

I want to gain a better understanding of…– why and how ‘experienced’ teachers use manipulatives in their classrooms– benefits of and challenges in their use in secondary-school mathematics– the educational research process (CIIM+)

MATHEMATICAL MANIPULATIVES

Manipulatives can be considered as concrete representations. Other external representations include pictorial, language, experiential, symbolic. (as proposed by Lesh, Post, & Behr, 1987)

Manipulatives are “designed to represent explicitly and concretely mathematical ideas that are abstract” and a catalyst in building representations of math concepts

– real-world objects (e.g.: coins, cube-a-links) used for a variety of concepts, or

– specifically designed materials (e.g.: algebra tiles, fraction circles) used to teach particular mathematical concepts.

– to be touched, moved about, rearranged, and handled by students (Moyer, 2001; Kennedy, 1986; Pimm, 1995)

The understanding and value of manipulatives comes from being used by students and teachers engaged in shared and meaningful practices that involve strong and multiple connections to underlying mathematical concepts

(Meira, 1998; Moyer, 2001)

RESEARCH PERSPECTIVE

Studies report declining use of manipulatives as students progress through school years resulting in little use in high-school mathematics classes (e.g.: Howard, Perry & Lindsay, 1996; Suurtamm & Graves, 2007;

Weiss, 1994)

Why the decline of manipulative use in high-school when:– The use of manipulatives is strongly recommended by current

curricula for all students, across all grades (NCTM, 2000; OME, 2005).

– Researchers find that long-term use of manipulatives: increases mathematics academic achievement (Ernest, 1994) improves attitudes towards math (Leinenbach & Raymond, 1996) has value to students in all school grades (LeNoir, 1989)

THE REALITY

Questionnaire data from 1,096 Ontario Grade 7-10 teachers, CIIM Report, Suurtamm & Graves (2007)

Very

Important

Grade 7 60%

Grade 8 53%

Grade 9 Applied 50%

Grade 9 Academic 37%

Grade 10 Applied 47%

Grade 10 Academic 30%

How important is promoting the use of

multiple representations of

ideas?

THE REALITY

Questionnaire data from 1,096 Ontario Grade 7-10 teachers, CIIM Report, Suurtamm & Graves (2007)

Very

ImportantA Lot

Grade 7 60% 46%

Grade 8 53% 43%

Grade 9 Applied 50% 48%

Grade 9 Academic 37% 30%

Grade 10 Applied 47% 35%

Grade 10 Academic 30% 27%

How important is promoting the use of

multiple representations of

ideas?

In this class, how comfortable are you with using concrete materials to teach

mathematics?

THE REALITY

Questionnaire data from 1,096 Ontario Grade 7-10 teachers, CIIM Report, Suurtamm & Graves (2007)

In this class, how often do students use

manipulatives?

Very

ImportantA Lot Never

Use

Grade 7 60% 46% 1%

Grade 8 53% 43% 4%

Grade 9 Applied 50% 48% 12%

Grade 9 Academic 37% 30% 40%

Grade 10 Applied 47% 35% 21%

Grade 10 Academic 30% 27% 48%

How important is promoting the use of

multiple representations of

ideas?

In this class, how comfortable are you with using concrete materials to teach

mathematics?

THE CHALLENGES

Teachers face many challenges in their use of manipulatives in the classroom:

– Perceived value (Sherin, Mendez, & Louis, 2004)– Math meaning behind their use (Moyer, 2001)– Uncertainty how to use them (Suurtamm & Graves, 2007)– Time and curriculum coverage pressures (Weiss, 1994)– Changes to class environment (Howard et al., 1996)

But they are worth facing because:By demonstrating how to use the manipulatives as tools for better understanding, teachers open doors for many students who struggle with abstract symbols.(Moyer & Jones, 2004, p. 29)

However, research on how and why teachers use of manipulatives within secondary school mathematic classrooms is lacking (Howard et al., 1996, Moyer, 2001)

INFLUENCE OF TEACHERS’ VIEWS ON PRACTICE

Teachers’ teaching practice is grounded in their beliefs and understandings of mathematics and their perceptions as to how children learn (Thompson, 1984).

Teachers’ beliefs of mathematics in general, and specifically in the value of manipulatives, influence the way in which they are used (Sherin, Mendez, & Louis, 2004).

So, to examine views and practice…If teachers’ characteristic patterns of behaviour are indeed a function of their views, beliefs and preferences … then any attempt to improve the quality of mathematics teaching must begin with an understanding of the conceptions held by teachers and how these relate to their instructional practice(Thompson, 1984, p. 106)

Social Context of Teaching

Teach

ers View

s & B

eliefs

Cu

rrent C

urricu

lum

TeacherPractice

Teach

er Kn

ow

ledg

e

PedagogicalContent

SubjectContent

StudentLearning

Teaching of Mathematics

Learning of Mathematics

Classro

om

Nature of Mathematics

Students aslearners

Theories of learning

Curriculum

Pedagogy, practice &

subject knowledge

MultipleRepresentation

Underpinningbeliefs and rationale

Concrete reps.(Manipulatives) Enacted

curriculum

Theories and

research

Reflection

Reflection

Section 1Influences on, and state of current mathematics

curricula and pedagogical direction

Section 2Influence of teachers’ belief and knowledge on

teacher practice

Section 3The enacted curriculum

CONCEPTUAL FRAMEWORKExamine views and knowledge to better understand practice

The catalyst

THE RESEARCH

RESEARCH QUESTIONS: To gain insight into why and how secondary school

mathematics teachers choose to use or choose not to use manipulatives in their classrooms, the research is guided by the following questions:

– How do secondary school teachers view the use of manipulatives in teaching mathematics?

– How do secondary school teachers describe their use of manipulatives in teaching mathematics?

DATA INSTRUMENT: Data collected through semi-structured interviews with 8 (max.)

secondary school mathematics teachers; with the key focus of:– teachers’ views and beliefs about mathematics, and mathematics

teaching and learning– teachers’ views of the use of manipulatives for teaching

mathematics– teachers’ descriptions of their use of manipulatives in the

classroom.

DATA ANALYSIS

Key dimensions from research– Perceived value for all students– Math meaning behind their use– Uncertainty how to use them– Time and curriculum coverage pressures– Changes to class environment, control issues..– Support environment (peer, dept. admin.)– Logistics, availability, $$...– …

TIMELINE…

Awaiting Ethics Approval Recruitment through open invitation to

participate sent by COMA (and/or directed to willing candidates)

Data collection through interviews

Data analysis

Thesis

Now

End May

JuneJuly

Fall

Many thanks for your attention

Adrian Jones