Critical Issue of All Students Being
Mathematically Proficient:
Standards-Based or Reform Practices
Pamela R. H. Bailey
George Mason University
Critical Issue of All Students Being
Mathematically Proficient:
Standards-Based or Reform Practices
Most mathematics teaching and
learning is based on a specific textbook and driven by assessment and
procedures. This is in direct contrast
to the standards set forth by the National Council of Teachers of Mathematics
(1989, 2000) which stresses the process standards: communication,
collaboration, reasoning and justification, representations and problem solving,
and the Ontario mathematics curriculum (Lim, 2004). The focus of standards-based teaching and
learning is the process standards. With
the technological advances in the world, mathematical needs by employers and
society are very different from the past and are changing rapidly every
day. Mathematics instruction however has
not progressed at the same pace. A
majority of teachers around the world are still focusing on procedures versus
the conceptual understanding so our students will become productive citizens. The critical issue is why the world has not
insisted on a standards-based approach to mathematics.
Teaching and Learning of Mathematics
Hong Kong wants a quality education
for all their students but there are issues with the attitudes of teachers
toward a standards-based curriculum (Taplin & Chan, 2001). Fourteen preservice mathematics teachers were
observed by Taplin and Chan with respect to their ability to view themselves as
problem solvers. Research has been
positive for the standards-based approach but how does a school system or
educational system encourage, demand, or promote its implementation so that the
change in teaching and learning mathematics may take place. Malouff and Schutte (2008) discuss the issue
of standards-based teaching and learning with a focus on problem solving in
Australian schools. They felt that
teachers were already teaching problem solving strategies but that they are
specific to the type of problem or mathematical concepts the students are
learning. Australian schools, in
general, believe that they are on the road to a more standards-based approach
and that what the teachers are currently doing just needed to be fine tuned. Handal (2003), also from Australia, investigated
the beliefs held by teachers and how their beliefs predicted instructional
practices. Teachers fell in to holding
either constructivist or behaviorist beliefs with their approaches to teaching
mathematics. Beliefs held by each are
complex and multi-faceted. He expressed
the need for students and teachers to be more student-centered and
standards-based but their beliefs are one aspect that interfered with their
growth. Samuelsson (2010) takes Handal’s
(2003) comment about beliefs leading to instructional practices one more step
by stating that what happens in the classroom has an effect on student’s
capacity to learn mathematics. His work
with elementary students in Sweden showed that their conceptual understanding
was affected by the teachers approach to instruction.
Parents, Teachers, and Students
Teachers are feeling the effects of
the push for a more standards-based curriculum because they are entering in to
a realm of uncertainty since they have never experienced a classroom that is
student-centered (Taplin & Chan, 2001).
The preservice teachers in Taplin and Chan’s study were requested to
reflect in journals about their experiences in the classroom and the problem
solving that took place, what the teachers did and what the students did. The teachers need to experience success and
positive feedback just like their students will need as they begin the journey
in to standards-based learning. Not only
do teachers need to be reflective but also the students (Malouff & Schutte,
2008). Student reflections should be
more on the problem solving process and relating their new ideas to other
subject areas and situations outside of the school environment.
Handal (2003) elaborates on teachers
that hold a constructivist philosophy as believing that all students had the
ability to learn mathematics and would approach topics by doing mathematics
instead of a sit and lecture atmosphere.
Students would be exposed to more real-world problems with a focus on
their thinking and the problem solving process.
Constructivist teachers in Australia were more likely to employ a
thematic approach with their mathematics instruction which helped students to
see the relevancy in their efforts and understanding.
Samuelsson’s (2010)
study looked at the gender issues with elementary students in an area of Sweden
with low socio-economic status. When
students entered school for the first time they participated in an assessment
which disclosed that there was no difference in their mathematical ability. The
results after five years showed that the mathematical growth of the students in
the problem solving classes were significantly lower on conceptual
understanding, strategic competence, and adaptive reasoning than the students
in the traditional classes. In addition
the student’s disposition toward mathematics was lower for the problem solving
classes but no differences were shown with procedural fluency. When Samuelsson compared the boys to the
girls after five years he found that there was still no difference between
them. So should parents considered as having
a low socioeconomic status insist on the traditional setting? Students in a high school in California were
analyzed with groups in standards-based classrooms and others in traditional
classrooms (McCaffrey, Hamilton, Stecher, Klein, Bugliari, &
Robyn, 2001). This study showed the
opposite of Samuelsson’s in that the more teachers
employed reform practices then their student’s scores were higher than those in
the traditional classes.
Assessing Students’ Understanding of Mathematics
Preservice students that changed
their attitudes toward the standards-based approach did so when they realized
how the alternative assessments were making a difference with the students (Taplin
& Chan, 2001). However the Hong Kong
schools need to readdress how they report student progress with the new
approach and the new types of assessment.
Handal (2003) mentions assessment practices in the standards-based
classroom as being diversified to include portfolios, presentations, and
writing about the problems and the process.
A new approach to teaching leads to new types of assessment but the
reporting practices of schools do not correlate with the assessments. Schools in Ontario (Lim, 2004) encountered
several issues that related to the diversity of assessments that meet the goals
of standard-based instruction such as time to create, give, and grade the
different types; the content of the curriculum especially if procedural in
nature; students with varying academic levels being assessed differently; and
the need to report student progress to parents along with the rationale behind
the assessment and the student grade. Administrators
as the instructional leaders in their buildings are a huge influence on the
type of assessment given by the teachers (Kulm & Li, 2009). Their concern is state and local assessments
and how the public perceives the school academically
Classrooms of the Future
In an attempt to assist preservice
teachers with their understanding of a standards-based lesson, Taplin and Chan
(2001) found that some of the teachers began with a positive attitude which
remained positive; the opposite was also true as well as those that changed
from the negative to the positive.
Learning what influenced the teachers to remain advocates of
standards-based learning or to change their beliefs toward it was studied by Taplin
and Chan. They found that the teacher’s
beliefs changed when they saw students perform different types of assessments
and get involved in learning and doing mathematics. Beliefs are seen to play a part with how
Ontario teachers create and use assessments (Lim, 2004). This includes if and when technology should
be used along with the how teachers balance their time within the curriculum
with instruction and assessment. In
order for the classroom of the future to be student-centered with instruction
being facilitated using a standards-based approach then principals need to be
educated in the approach as well (Taplin & Chan). Many of the Hong Kong school leaders are not
accepting of noisy classes nor are the classrooms favorable for group
activities. Australian principals were
also mentioned as an essential element for the teachers to implement a
different approach to learning mathematics for the future (Malouff &
Schutte, 2008). A domino effect happens
when administrators support the teachers who then support their students by encouraging
their efforts which leads to improved confidence.
Handal (2003) envisions the classroom
of the future as one not centered on the textbook. The teachers that are standards-based, using
relevant problems for their students, will develop their own resources to meet
their specific student needs. Samuelsson
(2010) cautions teachers and administrators to consider their school population
when deciding the approach to be taken in the mathematics courses so that all
student needs will be addressed.
The Critical Issue and My Personal Theory
I do not see that educators have much choice but to consider their
student’s needs when deciding how to approach mathematics instruction. As stated previously, we need to do what is
necessary for our students to become productive citizens in this global
society. If we bore the students, expect
exact answers with no consideration for thinking processes, and demand that
students just sit and get the material then our society will decline. My interests lie in teachers receiving and
participating in professional development that encourages standards-based
instruction. The issue for me is how I
can meet the teacher’s needs with forces such as the administrators, state and
local assessments, peer pressure, and the teacher’s beliefs not in alignment
with the goals.
Scholarly Suggestions for the Critical Issues
The needs of students necessitate a
change in teacher education (Taplin & Chan, 2001). Many of our teachers avoid change because of
a lack of knowledge about what they are expected to do. Taplin and Chin revealed through their
research that teacher strategies can be developed in a relatively short amount
of time given the opportunity to observe expert teachers and to receive input
from peers or instructors. Also key to
implementing a standards-based approach is changing attitudes and building
confidence in the teacher’s ability so they will want to continue to grow. This can begin with the education of preservice
teachers. More schools of education need to address this
issue and provide students with the experiences to assist them in changing
their viewpoints on how students should learn mathematics and how teachers should
present or facilitate the learning of mathematics. Schools of education are a definite place
where change does need to take place but it needs to be at all school levels so
that the preservice teachers will already have been indoctrinated in the
approach.
For teachers already practicing professional
learning, sessions should be encouraged in each of the schools followed with
discussions among the participants (Malouff & Schutte, 2008), Malouff and
Schutte felt that all of the Australian teachers did not need to participate in
the sessions because over several years all of the teachers would see the need
to come on board. I disagree. It could pose huge conflicts of student
placement, traditional or a standards-based classroom, as well as internal conflicts
among teachers. All teachers need to
educated with the approach but stressing that instruction is a balancing act of
all strategies. McCaffrey et al. (2001)
posit that professional development sessions need to include time for teachers to
become familiar with the curriculum and the instructional practices that will
support the written document.
Standards-based instruction is not textbook driven but entails teachers
as active facilitators of the planning and implementation process for success
student growth.
Changes in curriculum need to be
examined at different levels according to Kulm and Li (2009). China and the United States approach
curriculum and instruction issues with different lens. When considering the culture and society of
both countries with respect to education we also need to look at the history of
the each as well as the expectation of academics. Change is effected by the culture of the area
which may embrace new ideas or stand firm with past actions. China has a national curriculum which
provides the structure within their culture to promote change to more inquiry,
problem solving, and instruction that is student-centered. The United States educational system is a
culture where the schools are controlled by administrators, are textbook
driven, and have teachers that are lone rangers within their classrooms. Parents of children in China and the United
States in general have very different values.
Our students do not value their education so we, as educators, need to
find ways that will encourage them to do so.
With technology and various types of internet and video games, students
are used to immediate gratification. It
will take time for educators to encourage the students to think.
Conclusion
Samuelsson (2010) states that instruction
should be delivered using a diverse selection of methodologies so that the
needs of all students will be met regardless of their economic standing or gender. We cannot forget procedural fluency. The automaticity of basic facts and certain
concepts is necessary for students to be able to concentrate and understand
additional mathematical topics. Developing
or purchasing a standards-based approach to mathematics is only the
beginning. Educating the teachers,
whether it is in schools of education or with professional development, needs
to begin. The implementation process of
a standards-based curriculum will not happen within a school year which must be
realized by all. It takes time to
experience the unexpected, to make the connections, and to assist the public in
accepting the change. Assessments and
the expectations of the assessments on the local, state, and federal level will
need to be developed to match the instruction.
This is a huge adjustment for our nation but decisions need to be made
as to whether assessment should continue to drive curriculum and instruction or
will it, should it, be the other way.
We, as educators, are in the classrooms for our students. Decisions need to be made that is in our student’s
best interest so they can truly learn mathematics.
References
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