Mathematics Reformbased Instruction: Hearing Teachers Voices Mary C. EndersonAzita Manouchehri Middl

1
Mathematics Reform-based InstructionHearing
Teachers VoicesMary C. Enderson Azita
ManouchehriMiddle Tennessee State University
Central Michigan UniversityMathematical
Sciences Mathematical Sciencesmcenders_at_mtsu.edu
Azita.M_at_cmich.edu
2
Messages from research on implementation of
reform in schools

• reform-minded teaching remains a novelty in
  school settings (Ball Cohen 1998).
• many teachers are unaffected by the reform and
  continue to teach in a traditional manner (Tobin
  2001).

3
Factors contributing to this problem

• teachers lack of familiarity (and comfort) with
  a gradual development of the subject matter which
  prevents them maintaining instructional coherence
• teachers inability to present mathematics as a
  chain of interpenetrating concepts rather than as
  isolated skills due to their narrow understanding
  of the subject

4
Factors (continued)

• teachers reluctance to conform to new methods of
  teaching due to a mismatch between their own
  beliefs about the nature of mathematics and the
  philosophies that guide the reform
  recommendations
• teachers reliance on locally driven theories
  about practice rather than current research on
  learning and teaching

5
Critique of research on reform-based teaching and
teachers

• The results of these studies represent the
  researchers (research teams) perceptions of
  what ought to happen in classrooms, what teachers
  do not or can not do and the value they attach to
  the teachers choice of pedagogy or student
  learning.

6
Critique (continued)

• These studies evidence the absence of teachers
  voice in deepening our understanding of the
  complexities associated with instructional change
  and in shaping the direction of research within
  the discipline (Goodson 1996).

7
Critique (continued again)

• Most studies have focused on elementary and
  middle levels. Studies that concentrate on high
  school mathematics teachers and their practices
  are rare.
• Omission of teachers perspectives and views is
  problematic (Clark 1996).

8
Issues in need of attention

• What do mathematics teachers think about the
  recommendations of the reform for teaching and
  learning?
• What value mathematics teachers attach to
  research in mathematics education?

9
Issues (continued)

• How do teachers characterize their needs and
  their expectations of research in helping them
  meet those needs?

10
Goals of current research

• document teachers views on the current
  recommendations for reform in curriculum and
  instruction.
• elicit teachers assessment of the usefulness of
  current research in mathematics education in
  advancing their skills in implementing
  reform-based practice.

11
Goals (continued)

• identify those elements, from the teachers
  perspectives, that facilitate instructional
  change.
• Focus
• High School Mathematics Teachers

12
Process

• Survey-Design and pilot
• Content
• Biographical information
• Teachers rated their confidence with innovative
  instructional roles and techniques.
• Teachers ranked their level of proficiency in
  implementing aspects of reform minded practice.

13
Content (continued)

• 4.   Teachers identified areas in which they felt
  they needed professional development.
• 5. Teachers rated their familiarity with current
  research in mathematics education, whether they
  found such research reports beneficial to their
  work, and to identify areas that they felt must
  gain research attention.

14
Process (continued)

• Interviews
• Classroom Observations

15
Data analysis

• Factor analysis
• Number of years of teaching, age, gender,
  post-graduate training, school district, types of
  professional development activities in which they
  were engaged within the last 5 years, courses
  they taught, and their level of knowledge about,
  and support of, reform based curriculum and
  instruction as well as research in mathematics
  education

16
Sample

• 500 surveys mailed in both states, 212 were
  returned
• Mean teaching experience 21 years
• 32 teachers had less than 10 years of teaching
  experience.
• 87 teachers taught in rural schools
• 66 in urban schools

17
Sample (continued)

• 54 in suburban school districts
• 161 were white
• 39 teachers taught upper division mathematics
  courses (Pre-calculus, calculus, and statistics).
  
• Others taught courses ranging from fundamentals
  of mathematics, geometry, Algebra I and II.

18
Sample (continued)

• 62 teachers had participated in content specific
  professional development activities (technology
  in instruction, using new textbooks, and
  authentic assessment techniques.
• 108 teachers had completed at least one graduate
  course at the university within the last three
  years.
• 79 teachers had completed a masters degree in
  curriculum and instruction within the last ten
  years.
•   

19
General results

• 143 teachers were familiar with PSSM. Nearly a
  half of this population was supportive of their
  agenda.
• 25 teachers were familiar with Professional
  Standards for Teaching Mathematics.

20
General results (continued)

• There was a positive correlation between the
  level of mathematics preparation of the
  participants and their degree of support of the
  NCTMs guidelines for practice. Those teachers
  with a more sophisticated mathematics background
  (more coursework in mathematics education) were
  more supportive of, and confident in their
  ability to implement innovative curriculum and
  instruction.

21
More results

• Female teachers were more supportive of
  recommendations of reform for learning and
  teaching mathematics.
• Teachers in suburban school districts were more
  familiar with the standards and found them more
  applicable to their work.
• 126 of teachers who taught in rural and urban
  schools found the current guides for
  instructional change impractical for their
  settings.

22
Results (continued)

• Age, number of hours of involvement in
  professional development activities, and years of
  teaching experience did NOT serve as significant
  factors on participants level of support of the
  reform based instruction.
• No significant changes were detected according to
  geographic location (state).
• Only three teachers in the entire sample found
  merit in current research findings for advancing
  their professional efforts.

23
Teachers reports of their level of comfort with
fostering reform-based learner behaviors
24
Teachers reportslearner behaviors (continued)
25
Teachers reports of their level of comfort with
reform-based instructional behaviors
26
Teachers reportsinstructional behaviors
(continued)
27
Some general areas of concern included

• State-wide testing
• How am I supposed to do innovative things with
  my students when all teachers hear is you must
  prepare your students to do well on the test!
  DAN
• Testing has everything to do with me keeping my
  job! Why shouldnt I feel pressure? SALLY

28
Areas of concern (continued)

• Support by school administration
• I am able to do the things I do because my
  principal supports me in the process. This gives
  me a great deal of comfort knowing he is behind
  me. RUTH

29
More areas of concern

• Mathematics preparation prior to High School
  taking
• a closer look at the foundation students
  possess
• How am I supposed to teach students if they
  dont even have the basic skills needed for an
  Algebra II course? I dont know what they are
  doing in the middle schools these days. TONY

30
Areas of concern (continued)

• School and classroom conditions classroom
  environment, class size, availability of aids or
  assistants (to meet the needs of all students),
  materials/tools
• Instructional preparation time collaborating,
  mentoring, planning, assessing
• Curricular issues content and coverage of
  content

31
Areas of concern (continued)

• Available resources to help with instruction how
  do I go beyond what the textbook has?
• How to motivate students
• Finding TIME to do it all
• How to keep good teachers in the profession

32
Areas of concern (continued)

• When (and how) to reflect on my own teaching?
• They keep telling us about this Japanese lesson
  study, but they dont help us get there. When
  are we given time to really think about what
  happened in our lessons? When do we have time to
  go visit other teachers classrooms to see what
  they are doing? All these reports are good, but
  they dont seem to work here in our situation!
  JERRY

33
Assessment of past professional development
opportunities

• 165 teachers rated their professional development
  experiences as ineffective. 109 of these
  teachers claimed the content of the sessions they
  had attended was either too difficult, or too
  trivial.
• 63 teachers from this category expressed the
  content of their workshops either too narrow to
  have practical merit for long term instructional
  planning, or too general to have mathematical
  merit.

34
Assessment (continued)

• 32 teachers rated those workshops that focused on
  the use of technology in instruction as extremely
  helpful.

35
Areas in need of professional development

• Topics most frequently cited by teachers
  included
• writing lessons that utilize applications of
  mathematics (n137),
• using calculators in lessons (n201),
• using computers in lessons (n182),
• implementing discovery learning activities
  (n173),

36
Areas in need of prof. development (continued)

• ways to maintain productive discussions about
  mathematics among students (n162),
• ways to involve/engage all students in
  mathematics learning (n195),
• dealing with diverse abilities and background
  students bring to class (n191),
• convincing students that mathematics is important
  and useful (n143),

37
Areas in need (continued)

• implementing open-ended exploratory activities
  (n86),
• establishing interest in mathematics and
  mathematics learning among students (n191),
• helping students take charge of their learning
  (n94),
• need for assistance in finding meaningful
  activities to use in instruction (n73),

38
Areas in need(continued)

• organizing and monitoring cooperative group
  activities (n88),
• using students life experiences in my
  instruction (n88),
• using assessment techniques other than standard
  tests (n59),
• need for further training in how to facilitate
  learning rather than telling students what to do
  (n23),

39
More Areas in Need

• do long term instructional planning (n4),
• explaining why mathematical algorithms work
  (n44),
• deciding which mathematical conventions are
  important for students to know (n26),
• connecting mathematics to other subject areas
  (n57),
• making connections among various mathematical
  topics (n21).

40
Areas in need of prof. dev. (continued)

• All teachers from urban schools ESL and
  Absenteeism.
• 65 of the teachers in rural schools were
  concerned with learning about how to work with
  limited resources in classroom.

41
Views on research in mathematics education (3
questions)

• First question asked teachers to rank their
  familiarity with findings of current research in
  mathematics education from very high (4) to very
  little (0).
• M3.1 ? 0.4
• See next slide for note

42
Views on research (continued)

• NOTE It was determined through some interviews
  that many teachers interpreted documents and
  articles (like those in the MT) as mathematics
  education research rather than something specific
  from a research journal (like JRME)

43
Views on research (continued)

• Second question asked teachers to rate the
  findings of current research along a continuum
  from very useful (4) to not useful at all (0).
  They were also asked to state the reasons for
  their rating.
• M 0.2 ? 0.8

44
Explanations Offered

• current research does not address the level of
  mathematics they taught (n137).
• research reports difficult to understand (n121).
  
• failure to provide concrete guides for practice
  (119).
• research studies did not focus on answering
  questions that related to their particular
  settings (n123). Nearly 95 of this population
  taught in rural and urban school districts.

45
Explanations (continued)

• research reports did not make sense to them
  (n86).
• research settings artificial, thus, their
  findings not applicable to their own particular
  situation (n74).
• Twenty-five teachers made statements that
  indicated a lack of trust for those conducting
  research in mathematics education (i.e.
  University people like to tell us what to do).

46
Views on Research (continued)

• The third question asked the participants to
  identify areas in which they felt additional
  research was needed.
• Responses
• how to motivate all students in learning (n181).
  
• methods to bridge informal explorations to formal
  mathematics (n139).

47
Other categories identified by teachers

• Long term student outcomes of teaching concepts
  (n51),
• the influence of block scheduling on learning
  (n37),
• the impact of technology on mathematics learning
  (n46).
• Fourteen teachers stated that they did not know
  how to respond to the question.

48
Where do we go from here?

• Need-driven research vs. curiosity-driven
  research A balancing act
• Authoritarian voice of research
• Making research reports useful and meaningful
  Ownership of results
• Early intervention Teacher preparation
• Action research

49
Where do we go from here? (continued)

• What do we do with reform in Urban and Rural
  school districts?
• Components of effective professional development
  designs for HS teachers?

50
Closing comments Pronouncing the teachers
voice

• Here we deal with kids that have no vision of
  what is out there they come from environments
  tough environments I mean, they go home and
  there is no one there they work to support their
  families, school is not an important
  consideration for them. I have kids that cant
  read. I have kids that dont speak a word of
  English, and I have kids that come to school only
  to have a quiet place to sleep. These are tough,
  I mean, tough things to deal with. I dont
  believe anyone has talked about what to do in
  these conditions. Good teaching in a place like
  this is hard-- it is really hard not to give up.
  (Amy)

51
Closing Comments (continued)

• I really want to help all my students be
  successful. Finding the time to do this is a
  whole nother thing. (Carolina)
• I believe the reform movement is important, but
  when are administration and public officials
  going to place some value in what teachers think?
  My principal appears to be more concerned with
  state testing than if students really learn or
  retain the information. This makes it really
  difficult for me to change my instructional
  practices. (Kenny)