Monitoring The Status Of Students' Journey Towards Science And Mathematics Literacy

Monitoring The Status Of Students' Journey Towards
Science And Mathematics Literacy
A major focus of the current mathematics and science education reforms is on
developing "literacy;" that is, helping students to understand and use the
languages and ideas of mathematics and science in reasoning, communicating,
and solving problems. In many ways, these standards documents are far more
voluminous and complex than any scope and sequence in place in school systems
today. But these documents are meant to be used as frameworks which provide
guidance in education reform - they are not the definitive sources articulating to
teachers how education reform must occur in their classrooms.
Our plan in this discussion is to lay out the components of mathematics and
science literacy as set down in the major reform documents and then, using
selected how-to articles, to show how strategies and activities tried by math and
science teachers have been used, or can be used, to promote math and science
literacy among students. For pragmatic reasons only, our discussions often focus
either on mathematics or science reform recommendations and examples. In
doing this, we do not mean to imply that the elements of literacy in these

disciplines are somehow separate or different. In fact, the separate discussions
show how both the mathematics and science education communities, coming
from different directions at different points in time, independently arrived at
similar positions and many of the same recommendations regarding the ideas of
literacy.
In support of this discussion of the components of literacy, we also provide
samples of resources, materials, and services that teachers might find useful in
promoting mathematics and science literacy in their classrooms. The how-to
articles are meant to be quick-reads that can be applied or adapted to classrooms
directly. These articles are included to make it easier to decide which ones might
be of special interest. Other articles and documents are intended as sources of a
more general background. These documents provide some of the research bases
and rationales behind some of the reform recommendations. Finally, we have
included other references and information on databases which are not directly
cited in the discussion but might prove valuable as additional sources of
classroom ideas.
During the last decade, the mathematics education community appeared to lack
clear focus and a sense of direction. Although many conferences were held,
papers written, and reports produced, there was not a general consensus
regarding which direction mathematics education should head.
The Standards offer an organization of important mathematical topics and
abilities by grade-level groups (Kindergarten - grade 4, grades 5 - 8, and grades 9 -
12). Throughout the Standards the emphasis is: "knowing" mathematics is "doing"
mathematics. Knowledge should emerge from problem situations so that
students have a strong conceptual basis for reconstructing their knowledge at a
later time. Furthermore, problem solving situations develop mathematical literacy
by: (a) providing motivation for developing concepts by establishing a "need to
know;" (b) providing opportunities to read, write, discuss, and explore
mathematical ideas; and (c) providing opportunities to make conjectures, test,
and build arguments about a conjecture's validity. In short, the Standards
describes a new curriculum for school mathematics in which students learn more,
and often different, mathematics and in which methods of mathematics
instruction are significantly different.

This notion of what a mathematics-literate American learner might be is parallel
to that of a science-literate student. Similarly to the mathematics education
community, science educators and scientists also began to grapple with the
lackluster performance of our students relative to students world-wide.
Both the science education and mathematics education communities have in
common the image of what discipline literacy requires for this century. Both have
pushed the concept of literacy beyond that used in the reading literature.
Whereas in reading it is common to find literacy defined by functional grade level
performance, in science and mathematics the essence of literacy is increasing
sophistication over the course of schooling. This represents a fundamental shift
from literacy as a status notion to one of literacy as relative to the context of
knowing - that is, the real world, the domains of the discipline, and specific
applications. For teachers, this non-static notion of literacy presents considerable
challenge and opportunity. And, when presented with standards documents that
are not linear, not sequential, and not hierarchical in their recommendations, the
teacher or teacher-advocate has the responsibility of translating the image
statements into instructional materials, textbooks, learning activities, and
pedagogical practices.
A major premise of both the mathematics and science standards is that what a
student thinks, knows, and can do is greatly dependent upon how the student
learned it. Research across a variety of disciplines indicates that students may
learn best when they construct their own understanding of the material. This
implies that teachers do not, and cannot, pass understanding to their students;
instead, teachers can only engage students in activities from which students
construct their own meaning. In short, learning is an individual activity fostered
within the social context of teaching. This does not imply, however, that students
must always "reinvent the wheel." For example, basic computation and
algorithms were invented precisely so that people would not have to count on
their fingers and toes to solve each problem. Formulas in science serve similar
practical purposes. However, such activities should not dominate the
mathematics or the science curriculum. Furthermore, computational procedures
should be developed in contexts so that students perceive them as tools for
solving problems not as problems to be solved.

In the mathematics and science reform literature, meaningful learning is
promoted when students actively inquire. Inquiry in the reformed mathematics
and science classrooms is more than just doing activities; it involves interacting
with peers, teachers, people outside of the classroom and the school, and all
kinds of resources. In the inquiry classroom prescribed in the reform literature,
students work collaboratively on problems that are engaging and relevant; they
ask questions; they access and use information from a variety of resources; and
they challenge the ideas of others. Teachers, in turn, challenge their students
about their observations, hypotheses, explanations, procedures, and evidence.
We refer to this interactive kind of inquiry as "Inquiry" (i.e., inquiry with a capital I
and in italics) to emphasize the importance of interacting orally and in writing as
recommended in the reform movements. Inquiry is not restricted by student age,
content, or context. Students at the earliest grade levels can use and develop the
skills of mathematical and scientific Inquiry.
There should be a lot of investigation and debate going on in the science
classroom. Inquiry in science is characterized by its demand for evidence, reliance
on a blend of logic and imagination, expectation that scientists try to identify and
avoid bias, rejection of authoritarianism, and recognition that science is a
complex social activity. These characteristics of scientific inquiry are translated
into instructional goals and standards in the reform literature. Similarly in
mathematics, the theme of Inquiry is manifested in the standards and in the
instructional activities. Whole-class discussions can provide students
opportunities to synthesize, evaluate, and summarize strategies, ideas, and/or
hypotheses. Small group discussions can provide opportunities to discuss and
exchange ideas with peers, and individual work can help students to develop
confidence in their own mathematical abilities. Different instructional
approaches and activities such as those which develop students' Inquiry abilities
will be discussed in the following sections.
In both mathematics and science, Inquiry can be "issues-based." This approach
heightens the interest level, and therefore, the engagement of students.
Throughout the Standards the importance of connecting mathematics to real-
world problems (and hence utilizing an issues-based approach in teaching) is
emphasized. Real-world problems with 'messy' numbers or too much or not

enough information or that have multiple solutions, each with different
consequences, will better prepare students to solve problems they are likely to
encounter in their daily lives. The key to the effectiveness of the issues-based
approach is to use a learning prompt which is appropriate and interesting to the
learners. Teachers must also take care to use open-ended tasks for which there
are multiple correct solutions. These open-ended tasks will then promote
experimentation and exploration on the part of each student and will avoid the
recall of particular facts, algorithms, or procedures.
An example of a series of issues-based lessons is Mathematics in Baseball in
which students work in small groups investigating baseball statistics as well as
other aspects of the game. Stimuli for small group discussions are provided in the
article, which encourage students to exchange ideas, offer and receive
constructive criticism, develop and test hypotheses, and make and correct
mistakes in their small groups. Another example of a teaching module utilizing the
issues-based approach is Involve the Community which confronts misconceptions
students may have about the usefulness of mathematics and science in their own
lives outside of school. Students go into the local community and interview
someone to find out how that person uses mathematics on the job. Students are
then responsible for developing mathematical problems described during their
interviews, scheduling the person to speak to class, and writing a term paper
concerning what they learned during their interview.
In science, the unity of perspective is not as evident. There are those who
interpret science literacy to mean that life skills and citizenship are the key
elements, not the rigorous scholarship or mastery of any specific science content
or processes. This is countered by those who advocate for a focus on conceptual
learning in the context of real-world problem solving.
Those who advocate for a life-skills and citizenship approach to science
instruction are exemplified by Hurd's statement, "Modern science is driven more
by societal needs than by theory." This societal perspective with its emphasis on
life learning and citizenship places greater value on "knowing how" than on
"knowing that" in defining science literacy.

The issues-based, societal perspective is the basis of the Science-Technology-
Society approach. With its learn the science you need to know when you have a
need to know it philosophy, there is no such thing as a fixed science curriculum or
mandatory content or set of process skills. Students in an classroom identify
personal, school, or community problems and issues and work collaboratively on
a solution, learning and using appropriate science content and skills in the process
of solving the problem or resolving the issue. Proponents claim that the approach
develops science literacy more effectively than a content-driven curriculum
because the problems are real and the learning is relevant to the students. The
"medium is the message;" concepts and principles of science, however well-
learned outside the context of a societal or personal issue, are not science at all,
or at least not the kind of science worth learning. Teachers have reported
numerous issues-based instructional activities across a range of issues.
Advocates of conceptual change learning view the elements of understandings
and habits of mind in the definition of science literacy as key and argue for Inquiry
that promotes meaningful learning of critical content and process knowledge in
science. Teachers emphasize the importance of both the students and the teacher
knowing what the student already knows and uses in everyday life situations and
applications to engage students and provide context for learning science
concepts and processes.
The major difference between the issues-based Inquiry and Inquiry for conceptual
change is that specific ideas are targeted for instruction. For example, in science,
playground equipment and amusement park rides are used to explore basic laws
of force and motion. The properties of liquids and gases are investigated when
students make their own carbonated soft drinks; or the life cycle of a common
house fly is learned by studying the droppings of the classroom guinea pig.
Teachers have used state-of-the-art technologies such as high-speed trains,
entrepreneurial interests of students, "who-dunnit" detective scenarios and The
Great Tape Robbery, and even current hit movies to capture student interest and
to teach for conceptual change with regard to basic science concepts.
Similarly, important mathematics content is described throughout the Standards.
For example, all three grade-level divisions include probability and/or statistics
standard(s) as well as a geometry standard; and two grade-level divisions include

measurement, estimation, algebra, and functions standards. As in science, Inquiry
is a central theme in classroom instruction: throughout the Standards, verbs such
as explore, justify, represent, solve, construct, discuss, investigate, describe,
develop, and predict are used to convey this active physical and mental
involvement of children in learning the content of the curriculum.
As in conceptual change learning in science, specific ideas, skills, and/or
mathematical concepts can be targeted for instruction. For example, teachers
have used common materials such as popcorn for developing data analysis skills,
calculators to discover number patterns and hone estimation skills. Teachers have
integrated math and art to develop geometric concepts, and math and science to
develop geometric concepts and measurement and estimation skills.
In another lesson, students learn to apply probability models as well as use
simulations to estimate probabilities concerning boy/girl birth ratios and the
average number of children in a family. And student development of spatial
imagery is targeted in the lesson Promoting Visual Imagery in Young Pupils. The
magazines are useful resources for Inquiry for conceptual change-type
instructional activities.
The challenge of managing Inquiry learning environments without sacrificing
intellectual vigor is not insignificant. Student-centered learning is grounded in
moderating the Inquiry-based classroom, which is prompted with exploration and
stimulated with manipulatives in a way that is connected to the students' real
world. By reflecting on students' growth in the disciplines, teachers will
understand what pedagogical techniques work well to move students along on
their learning journey.
Because the standards themselves represent the possibilities for instructional
focus rather than the requirements for instructional focus, the teacher is placed in
the important leadership role of selecting the optimal content to engage each
particular group of students in the work of the discipline. The selection process
must take into account local content goals, learning goals that ensure that the
"habits of mind" of the disciplines are reinforced, resource availability, and the
interest levels and developmental characteristics of the students. In short,
optimizing learning in mathematics and science is not an algorithmic process.

The role of teacher as facilitator of learning begins to take on real meaning as the
standards are implemented. And teachers seeking a cookbook for effective
mathematics and science teaching will be sorely disappointed.
In clear and unequivocal ways, the role of the teacher as implementer of either
the science or mathematics standards becomes more important in defining the
learning journey for students than ever before. Because the standards documents
are to be used as frameworks to guide mathematics and science education
reform, teachers' professional judgment becomes more and more powerful as a
force in defining the schooling experience for students. For this reason, those
teachers who choose to or are chosen to teach mathematics and science must
have an in-depth understanding of that which they are teaching.
In order for teachers to make decisions about what, when, and how to teach
science and mathematics, they must have a rich understanding of the content and
appreciate how knowledge in a content area is created, organized, linked to other
disciplines and applied to real-world settings.
Teachers who effectively use the standards documents to guide daily instructional
decisions must have specialized knowledge of how to teach the content (i.e.,
content-pedagogy), and they must recognize misconceptions and background
knowledge that may make growing sophistication problematic. They must, of
course, also be able to modify and reorganize to meet the needs of all learners.
The emphasis in the critical response skills is on argument and evidence. We
contend that some or all of these "symptoms" should be used more or less as
"ground rules" for Inquiry in (and out of) the classroom. For example, making
activities such as checking that statements (both oral and written) do not
intermingle fact and opinion or that celebrities aren't used as authorities in
arguments part of what routinely happens in science class will develop the "habits
of mind" so valued by reform proponents and reinforce the use of these same
habits of mind beyond the classroom walls and school years.
Teachers who use an issues-based approach usually have little trouble creating an
Inquiry environment. Personal and societal issues (e.g., landfills, toxic waste, AIDS,
pollution) are readily controversial and lend themselves to investigation and
argument. It is generally not difficult to find students who will take opposite sides

of an issue or classrooms of students to find public groups with opposing
positions. Teachers have used a variety of issues-based topics with great success,
for example, investigations of ecological problems; Integrating Science,
Mathematics, and Environmental Education Resource and Guidelines; The
Curriculum File; Computerized Simulation as an Inquiry Tool, or problems dealing
with death and aging; Debates: Verbal Encounters in the Science Classroom. What
is challenging for the teacher who utilizes an issues-based approach is to keep
students focused on those aspects of the argument that can be resolved with
scientific and/or mathematical evidence, and/or which utilize scientific and/or
mathematical reasoning, and to minimize those aspects of the argument that are
strictly emotional, political, and/or personal. One must also keep in mind that just
because an activity is issues-based does not imply that students will use or
develop Inquiry skills. Students must generate and evaluate arguments on the
basis of the scientific and/or mathematical evidence they gather and evaluate
their conjectures using the rigorous standards of mathematical and scientific
inquiry.
In classrooms where the emphasis is on understanding specified content and
process outcomes, controversies are not at all obvious to students (or to most
teachers) and any disagreements that arise are usually not as sensational as they
are in an issues-based classroom activities. But the potential for argument and for
debate nonetheless exists. Facilitating Inquiry when there is no "hot" social issue
requires that the focus shift to the controversy embedded in science and
mathematical ideas themselves. The alternative conceptions and/or
misconceptions that students hold in a given topic or area are excellent sources of
controversial ideas that can be investigated. For example, controversies from the
history of science such as the phlogiston theory of heat or the geo-centric model
of our solar system - can be used to stimulate Inquiry for conceptual change.
Common misconceptions of mathematical concepts can be also confronted and
explored, as can common student mathematical errors.
The strategy of simply suspending judgment or withholding the correct answer is
very effective at stimulating discussion. Challenging students who hold different
ideas to produce evidence of their respective positions is one way to stimulate
debate, discussion, and investigation and turn routine lessons into Inquiry

sessions. Simple modifications of cookbook activities (e.g., adding an open-ended
question or posing an extra-credit question) or project work that requires
students to work collaboratively is another effective way of facilitating Inquiry.
Inquiry can also be facilitated directly by using variations of the "student-
teaching-students" idea. A strategy that has been around for centuries but still is
effective today is "cross-age tutoring." But tutoring must be done in a hands-on
rich environment so that legitimate Inquiry can take place. When older students
inquire with younger students, both benefit from the experience.
As it does in any language, the ability to communicate well requires more than
the knowledge of vocabulary and grammatical rules - one must also be fluent in
using the language in both speaking and writing. Both the mathematics and
science standards identify learning to communicate mathematically as an
important goal for all students. As students communicate their ideas, they learn
to clarify, refine, and consolidate their thinking. In other words, communication
helps students to enhance their understanding of mathematics.
Learning the language of mathematics or science is not a simple task. For young
children, representing is an important way of communicating mathematical ideas.
Physical models can be used to represent and develop mathematical concepts.
Furthermore, with young children the connections between thought and spoken
word are usually stronger than those between thoughts and written symbols.
Thus, children should be encouraged to relate their everyday language to
mathematical language and symbols and to verbalize their thoughts and thinking
processes.
As students progress in school, their mathematics communications should
become increasingly sophisticated, that is, become more formal and symbolic.
The introduction and use of technical symbolism should, however, evolve as a
natural extension and refinement on the students' own language. Moreover,
great care must be taken to ensure that students are aware of the connections
between mathematical concepts and symbols, otherwise students are likely to
view symbols as disparate, empty objects which are to be memorized and/or
manipulated. All students should be provided opportunities to listen to, read
about, write about, speak about, and reflect upon their mathematical ideas. It is

not enough for students to merely write a response to an exercise or to "show all
their work" on a problem. It is equally important that students be able to explain
how they arrived at their responses as well as describe the difficulties they
encountered during problem-solving processes. Students must constantly be
encouraged to clarify, paraphrase, or elaborate on their mathematical ideas and
relationships. These are means by which students enhance their mathematical
understanding and teachers monitor their students' mathematical progress and
understanding.
In reformed mathematics and science classrooms, literacy means being able to
express oneself, defend one's ideas, and critically analyze claims both orally and in
writing. Journaling, logging, and keeping a portfolio are as much a part of the
reformed science and mathematics classroom regimen as they are of any arts or
humanities classroom. Portfolio assessment strategies are especially effective in
promoting Inquiry. When students have to explain, argue, and reflect on their
work rather than simply to select responses, answer questions, and complete
standard form assignments, both their writing and Inquiry skills are enhanced.
Portfolio scoring rubrics based on evidence and logic of argument communicate
to students the value and importance of Inquiry skills.
Student problems and misunderstanding can be revealed and corrected. Teachers
can use student writing to identify which instructional techniques did/did not
work and modify their techniques accordingly. Furthermore, through student
writing teachers can examine what students have learned versus what those
students think they have learned and use this information in assisting students in
developing their metacognitive skills ("knowing how to learn"). However, it
should be noted that the utilization of information gained from student writing is
dependent upon the quality of both the writing prompts and the teachers.
Teachers must collect, read, and give feedback to students frequently. And
teachers must be ready to receive and use constructive (and perhaps not-so-
constructive) criticism.
The move to emphasize patterns of argument and thought in the language of
mathematics and science Inquiry has payoff potential across the curriculum. For
example, there is strong evidence that analyzing the language and layout of good
expository material enhances the general reading, comprehension, and critical

thinking skills of younger students. High school science and mathematics teachers
report great improvement in creative writing skills, critical thinking, student
attitudes toward the subjects, and conceptual understanding when students keep
journals and are encouraged to compose creative writing reports (e.g., case
histories and resumes) in place of standard laboratory reports or other
conventional tasks. However, it should be noted that attempts by teachers to
translate results of alternate assessments, journal writings, and other creative
writing into letter grades can be difficult and that racial differences may affect
students' performance on open-ended items on standardized tests as compared
to multiple-choice items was found.
The current reform agenda has the potential to dramatically alter the experiences
that children have in science and mathematics classrooms in America. The
standards documents themselves set the tone for a new understanding of science
and mathematics literacy for all Americans. They present an image of the
classroom that is Inquiry-oriented, activity-based, and engaging. The role of the
teacher changes from that of disseminator of information to one of a mentor-
scholar as children present ideas, challenge ideas, and reconceptualize these
ideas.
This shift in the image of what a learning environment should look like calls upon
teachers to take risks and to incorporate new instructional strategies into
established pedagogical practices. The standards themselves, as a replacement
for a scope and sequence or hierarchical curriculum, challenge the teacher to
make professional judgments about what the appropriate content and context
vehicles are for each group of students to maximize their learning. Teachers must
take on instructional leadership roles. To do this, they must have both content
and content-pedagogical knowledge. Background in the disciplines of
mathematics and science is essential to support an effective Inquiry-oriented,
student-centered classroom consistent with the standards documents. This
expertise is also essential to the appropriate and reasonable assessment of
whether or not students are becoming increasingly sophisticated in their
understanding of important science and mathematics. This view of what quality
work is in mathematics or science does not come from the standards. This
understanding can and should come only from the expert professional classroom

teacher. Thus, the ultimate challenge of the reform goals for classroom practice is
for teachers to increase in their understanding of mathematics and science so
that they have the appropriate frame of reference for identifying appropriate
learning goals, selecting instructional resources to support students' construction
of meaning, sequencing and pacing the activities in the learning environment to
support learning, and monitoring the status of students' journey towards science
and mathematics literacy.
Jeff C. Palmer is a teacher, success coach, trainer, Certified Master of Web
Copywriting and founder of https://Ebookschoice.com. Jeff is a prolific writer,
Senior Research Associate and Infopreneur having written many eBooks, articles
and special reports.
Source: https://ebookschoice.com/monitoring-the-status-of-students-journey-
towards-science-and-mathematics-literacy/

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