How does this help support your students’ learning about math and science?

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Readings:
-New Jersey Student Learning Standards for Math & Science
-Adams & Hamm, Chapter 1
-Pitler et al., Chapter 1
Assignments:
Discussion Board #1:
Having read the selections for this week and reviewed the NJSLS(NJ) for mathematics and science, begin to identify how
you incorporate technology into the lessons with your students.
Share with your classmates any technology or digital tools that you use in your classroom when teaching math or
science. How does this help support your students’ learning about math and science? In what ways does technology
support your teaching of math/science learning objectives? How can technology or digital tools help you provide
feedback to your students?
Your post should be between 500-550 words in length
Chapter One
Helping All Students Learn About
Math and Science
In wealthy schools and poor ones, I encountered the same recurring patterns:
considerable variation among classrooms in the degree to which students were
challenged; an emphasis on procedural knowledge at the expense of analysis,
reflection, and understanding; a tendency to focus more on students who were
“easy to teach” rather than those who were struggling.
—Richard Elmore
Achieving an adequate national level of numeracy and scientific literacy
requires educating all students up to a level of reasonable competency.
It would be wise for every citizen in a democracy to have some idea of
where math, science, and their technological offspring are taking us. Take the
example of algorithms. They may be thought of as a set of math-related rules
for solving a problem in a certain number of steps. They can also be used to
tell a computer what to do and how to do it.
In the future, any job or activity that can be reduced to an algorithm
probably will be. Still, when asked about understanding even one of the
many implications of math and science, a surprising number of people in
every generation say that their comprehension and appreciation are limited.
The Common Core State Standards recognize the need for changing societal attitudes toward numeracy and literacy. They also suggest that in a wired
world, students of all ages need to learn about previously understated dimensions of math and science (Common Core State Standards, 2013).
In spite of their obvious importance, math and science are just about the
only topics for which more than a few well-educated adults will freely admit.Chapter 1
ignorance. Teachers reflect the general population. So it is little wonder that
when it comes to teaching these subjects, many of the characteristics of
effective instruction fall by the wayside.
Lack of mathematical and scientific interest in the broader society has a
corrosive effect on the young. Some simply do not like math and science;
others do not think they can be successful. We identify such students as
struggling or reluctant learners. Only a few will become mathematicians or
scientists, but all need some understanding of math and science to succeed in
school, in the workplace, and in life.
Some struggling students may have special needs, but all students in the
typical classroom are capable of responding to well-designed active learning
approaches (Sherman et al., 2009). The principles of play, purpose, and
teamwork can help make good things happen. Clearly, how we teach is as
important as what we teach.
When teaching math and science, asking disaffected learners to reason,
solve problems, and maintain a positive disposition may be a tall order. So
we should not be surprised when teachers sometimes pay more attention to
procedural knowledge than they do to reflection and understanding.
In spite of the difficulties, the primary goal of instruction should be getting every student in the classroom to develop and use the higher-level thinking skills associated with problem solving and inquiry.
Online learning opportunities are developing in ways that offer some
intriguing possibilities. But the current crop of online lessons and courses has
not helped as much as some had hoped (Dudley-Marling, 2012). The use of
shared blogs, for example, may help students get better at working together
but seems to have little effect on content mastery.
Active offline collaboration between students at different skill levels can
help generate imaginative problem-solving and inquiry experiences for everybody. Like adult experts, all children can profit from the intellectual ferment that happens when they have to collaborate in person and bounce ideas
off each other.
No one approach or method of teaching math and science has been found
to meet the needs of all students all of the time. But various kinds of active
and collaborative learning experiences certainly increase the odds of success.
Although we think of learning as something that happens in school, what
happens in the home and social environment is critical. In the final analysis,
connecting all students to productive math and science experiences has a lot Helping All Students Learn About Math and Science 3
to do with using all the tools available at school and at home to support
multiple student needs.
Attending to individual student needs and interests has always been key
to quality instruction, because, after all is said and done, both children and
adults interpret their experiences through unique patterns of ideas, values,
and beliefs. To paraphrase the poet Anais Nin, “I don’t see the world as it is;
I see it as I am.”
MATH AND SCIENCE INSTRUCTION FOR ALL STUDENTS
Some students tend to avoid challenge, some do not complete tasks, and
some are simply satisfied to just get by. Whether you use the term “struggling students” or “reluctant learners,” some have the potential to do well but
do not care much about learning certain subjects. The challenge is to turn
around negative attitudes.
Identifying some of the reasons behind the reluctance to learn math and
science is essential if we are going to engage student interest and help them
succeed. The key is finding something that will spark every student’s interest. The next step is turning that spark into a flame.
Even the most reluctant learners are naturally curious and able to learn.
Most want to get their hands and minds around objects of interest as much as
anybody. Even the most disaffected student is capable of learning math and
science but has trouble making certain approaches work for him (Small,
2012).
Just as it is never the wrong day to do the right thing, it is never too early
to get started planting the seeds of academic success. Quality instruction has
to begin at the early childhood level and be cultivated throughout elementary
school.
By the middle grades, teachers like to build on a solid base and move
children on to deeper mathematical, statistical, and scientific understandings.
The students who reach secondary school without grade-appropriate numeracy and literacy skills are the ones most likely to drop out.
Since a learner’s mental, emotional, and physical needs have a direct
impact on her schoolwork, exploring individual student needs should be near
the top of the teaching agenda (Van de Walle and Lovin, 2006). Curriculum
reform is often geared more to academically oriented children and young
adults, and not to students who have different interests.Fortunately, most K–8 teachers (our focus) try to teach math and science
concepts and skills in a way that helps struggling students (along with everyone else) understand and remember what is being taught. Although we assume that secondary school teachers make the same effort, elementary and
middle-school teachers often pay special attention to small-group work and
motivating reluctant learners.
Students often become motivated to learn about math and science as a
result of influences outside of school. The better organized and directed these
influences, the better the chance of success for the student.
Helen’s Student Teaching Log
At the beginning of the school year my daughter was quite reluctant to ask her
peers for help. She feared that other students would tease her because it takes
her longer to understand concepts and organize her thoughts. Math and science
were scary subjects. What to do? I applied the strategies I learned in my
college mathematics and science education classes to the daily homework
sessions I have with my daughter. These new strategies worked with the differentiated problem sets and in convincing my daughter to work with her peers.
This turned her attitude around. Her performance improved so dramatically
that she began tutoring some of the other students!
Students all have different needs, and these needs have a tremendous
influence on their achievement. What can teachers do to ensure academic
success? To begin with, they can assess each individual’s ability. The next
step is choosing teaching strategies that best match students’ learning
strengths and difficulties.
Questions teachers have (such as “How does this child learn best?” or
“What kind of learning environment can best bring out a student’s natural
learning abilities?”) are part of this diagnostic process. The focus should be
on understanding the child as a learner and making choices about structuring
the learning environment through innovative teaching strategies and methods.
Effective teachers internalize responsibility for students’ learning and examine their practices critically if they are not reaching some students. They
realize that most students want to succeed, but many do not find success
when taught from the traditional teaching model.
Students who have difficulties with math and science frequently need
alternative approaches and remedial strategies that are designed to promote
academic success. The math and science success plan is one technique thatwe developed to help improve student achievement. It builds on students’
strengths and can serve as an assessment tool.
EVERYONE NEEDS TO UNDERSTAND MATH AND SCIENCE
The public’s failure to understand chance phenomena, statistics, probability,
and the nature of numerical assertions opens the way for all manner of belief
in nonsense. Perhaps more important, it leads to distortions in the making of
public policy.
—John Poulos
The need to understand and use math and science in everyday life has never
been greater. Personal satisfaction and confidence come with making wise
quantitative decisions, whether it is buying a house, solving problems on the
job, choosing health insurance, or voting intelligently. In many ways, mathematics and science are part of our cultural heritage.
Our careers, our workplace, and our community all require a foundation
of sound mathematical and scientific knowledge. Although it may not be
readily apparent, proficiency in these subjects can open doors to future
achievements and sound citizenship. More important than a classroom being
online or full of digital devices is having a teacher who appreciates what the
new forms of math and science instruction are about.
A quick high-tech fix cannot solve many of the most important human
challenges. In fact, thinking that all problems have clean and clear solutions
just because we have the technological tools to get rid of them is an illusion.
The most genuine problems we face may require drawn-out personal, institutional, and social responses.
Data-enhanced decisions are more than ever part of human decision making. Statisticians and data analysts pay more attention to correlations than
human predispositions (Mayer-Schonberger and Cukier, 2013).
Everyone needs to understand mathematics, science, and technology to
make decisions about important societal issues in our democracy. Even mass
media are not that reliable. Take the example of global warming. For a long
time, the story was reported in a way that suggested some scientists took it
seriously and some did not. And this was after a large number of the scientists had recognized the reality of the problem.
Advances in medicine have sometimes been reported in another problematic way. Exciting breakthroughs are sometimes reported when only small
advancing steps have been taken. Whatever the scientific issue, a better understanding of the mathematical significance of statistical results would
help everyone (from the media to the typical student) understand the situation, whatever their age.
When we asked several struggling learners in a sixth-grade class why
they were not interested in math and science, many replied that it was “not
interesting” or “too difficult,” or that it “never made much sense.” These
explanations and other reasons might be classified as students’ personal or
environmental situations.
No matter what gets in the way of learning, teachers have to know what to
teach and how to teach it. Four or five years of college and continuous
professional development help. So do the suggestions and recommendations
that can be found in the math and science standards and state and school
district guidelines. Even many textbooks are helpful.
Wherever you get instructional ideas, activities often have to be adapted
for different students. Everyone in the classroom has to be involved in building knowledge by asking relevant questions, reasoning, making connections,
and solving problems.
The Characteristics of Struggling Students
All students of math and science have individual strengths and weaknesses.
However, struggling students often have similar learning problems (Armstrong, 2012). Being able to identify individual problems and knowing some
helpful teaching strategies certainly helps.
Struggling students may be passive learners, who have little motivation
or interest in becoming active participants in math and science learning.
Some students who struggle may think that math and science achievement is
a matter of luck. They may think it is too easy, too difficult, or too boring.
They may also believe that achievement in these subjects is beyond their
control: “I’m just not good at math” or “Science is boring.”
Students with negative feelings about math, science, or technology may
prefer not to acknowledge that their lack of success might have something to
do with personal discipline, hard work, and persistence. They may mistakenly believe that you succeed in math and science through some combination of
luck and level of intelligence.
The home and school environments matter a great deal; if poor achievement is expected, then that is the most likely result. Whatever the reason,
when students are discouraged or disinterested, their ability to move forward
is limited.Teachers can learn to do a good job with struggling students without
simplifying problems or always telling them exactly what to do. It is important to get learners actively involved in interesting and relevant situations. So
the teacher has to encourage reluctant learners to construct ideas and communicate their thoughts.
Graphic wall charts can help individual students see how they are doing
and track their achievement. Such visual displays give students, teachers, and
parents very powerful ways to see the progress of a student’s learning (Jackson and Lambert, 2013). Remember, the ultimate goal is reaching all the
students in your classroom.
Some reluctant learners may have difficulty remembering basic math and
science facts. Let us start with math. Remembering simple math combinations, even basic facts such as addition, subtraction, multiplication, and division, is difficult for many. There is no reason to be alarmed—strategies to
improve recall skills can be taught.
Repetition games such as having the teacher call out a fact combination
problem like “4 × 3 = __” and asking students to solve it, and then repeating
with a new combination (such as “2 × 7 = __”), is one example. The game
continues as each player calls out a new fact and each student responds with
an answer. Students’ ability to organize their thinking and use it to recall
basic combinations will affect their success.
Quite often struggling students also have attention problems. They have
trouble sustaining attention, avoiding distractions, and controlling their impulses. Some reluctant learners are easily distracted and have difficulty focusing on complex problems. It helps many students if the teacher arranges a
structured, consistent classroom where clear expectations are carefully
spelled out.
Although clear expectations can help, it is important to have space available for creative and critical thinking. It is not always necessary to tell students how to do a task. Let them come up with new ideas in different ways
and monitor their progress.
Structure is often useful, but too much can stifle the imagination. Sometimes, it is best to supply the possibilities and let students decide how to
reach various objectives.
Don’t tell people how to do something. Tell them what to do and let them
surprise you with their ingenuity.
—Anonymous Effective use of visuals, manipulatives, and learning aids often help overcome various problems. Working in pairs or small groups is a good motivator. Peer involvement expands and strengthens language skills and increases
students’ confidence.
Struggling students with attention difficulties often have trouble with time
management and changes between subjects and classes. They may also benefit from opportunities to be physically engaged in learning. Giving students
many chances to move and interact with peers in structured situations is one
of the keys to success.
Language problems can result in a bad attitude toward math and science.
Even students whose first language is English are often confused by the
vocabulary of these subjects. Words that have special meanings, such as
“equals,” “divisor,” “sum,” “cycle,” or “properties,” often slow down students’ ability to focus and understand the terms being used.
When students fail to see the connections among concepts, math and
science become a rote exercise, and understanding is limited. As experienced
teachers will tell you, simply memorizing terms without knowing what they
mean is not useful. Comprehension is the goal.
Student language understanding is helped by discussing important vocabulary, using creative writing strategies, and asking pertinent questions. Student learning is also assisted by reviewing previous concepts and demonstrating connections in problem-solving situations.
Metacognition is the ability to think about thinking. Students need to
reflect on their own thinking in order to be aware of what they need to know
(self-knowledge) and how they can go about acquiring information (procedural knowledge). As students become better at figuring out their own reasoning, they can also observe their own learning. This process includes evaluating whether they are learning, using helpful strategies when needed, and
making changes when necessary.
As children grow and develop, they become better at thinking about their
own thinking and how they think. This helps them move beyond their own
personal perspective and better understand how others might think about a
topic. These are critical skills for a math or science problem-solving situation.
Many struggling students do not understand that being successful in math
and science involves employing problem-solving strategies. Teachers have to
teach them how to be metacognitive learners and help them recognize the
thinking strategies they are using. Metacognition strategies can amplify self- reliance and creativity for struggling learners. Teachers who model thoughtfulness and encourage students to share problem-solving strategies with each
other can go a long way toward fully engaging struggling students.
Students with a vast array of special needs are now found in the regular
classroom (inclusion). In addition, the levels of language and cultural differences represented in elementary and middle schools continue to grow. The
result is that today’s classrooms include students with a very broad range of
learning needs (Tucker et al., 2006).
A typical classroom today may include struggling students such as José,
Maria, Jason, and Carlos. José struggles with a language-based learning
problem. Maria has attention difficulties. Jason’s inadequate reading skills
interfere with his learning in all areas. And although Carlos has excellent
cognitive abilities, he still has difficulty with math and science.
Whatever the reason for poor performance, youngsters need opportunities
to learn about their individual strengths and weaknesses. The successful
teaching of struggling students is most likely when teachers utilize culturally
relevant materials, use collaborative instructional activities, and recognize
that learning can take many forms through many modalities.
There are many ways to go about using collaborative activities in ways
that build on the natural learning dispositions of a wide variety of cultural
groups. Engaging in problem-solving strategies that are similar to those used
in real-life situations certainly helps. And yes, celebrating individuality and
working together to build successful learning communities certainly complement each other.
COLLABORATIVE INQUIRY IN MATH AND SCIENCE
All students can flourish when good teaching is combined with collaborative
inquiry and an engaging curriculum (Tomlinson and Imbeau, 2010). Collaborative inquiry is a form of reasoning and peer cooperation that begins with a
problem and ends with a solution. It generally involves asking questions,
observing, examining information, investigating, arriving at answers, and
communicating the results.
A collaborative inquiry approach to the teaching of math and science has
been found to work well with struggling learners. Among other things, it helps these students experience the excitement of mathematics and science activities in learning groups Knowledge of math and science has always been constructed in association with others. At all levels, mathematical and scientific inquiry is much
more than an individual endeavor. So it is best if elementary and middleschool students employ procedures similar to the collaborative procedures
that mathematicians and scientists actually use when they work.
The collaborative inquiry approach is a student-centered process of cooperative discovery. The teacher often gives the students directions and materials—but does not tell the small group exactly how to go about doing their
work. The teacher encourages conversation and provides activities that help
students understand how math and science are applied in the world outside of
school. The teacher might also give a brief whole-class presentation and then
move from small group to small group, encouraging questions and guiding
student observations.
As students interact with materials and their peers, they can interact with
math-science problems and jointly recognize the results of their investigation. The next step is applying what has been learned and recognizing that the
knowledge acquired through inquiry is subject to change.
Learners certainly have different talents and interests, but they should all
have access to high-quality math and science instruction. All students can be
motivated with concrete materials, differentiated instruction, and cooperative
experiences. But all these resources are especially important for students who
are struggling with basic math and science concepts and skills.
Since student motivation is a major concern, it is important go beyond
rote skill building to challenge reluctant learners. This means helping them
deal with interesting, difficult, and ambiguous problems in which they are
expected to discuss, question, and resolve problems themselves.
COLLABORATION, INQUIRY, AND RELUCTANT LEARNERS
Inquiry is sometimes thought of as the way people study the world and
propose explanations based on the evidence they have accumulated. It involves actively seeking information, truth, and knowledge. When collaboration is added to the process, it helps build the positive relationships that are at
the heart of a learning community.
Collaborative inquiry may be thought of as a range of concepts and techniques for enhancing interactive questioning, investigation, and learning.
When questions that connect to student experiences are raised collectively ideas and strengths are shared in a manner that supports the struggling students’ search for understanding (Snow, 2005).
Teachers have found that using a collaborative approach to connect math
and science instruction is a way to involve disinterested students in active
small-group learning. When students work together as a team, they tend to
motivate each other. Accomplishing shared goals benefits all of the individuals in a group and makes it more likely that collaboration will become a
natural part of the fabric of instruction. The teacher provides a high degree of
structure in forming groups and defining procedure, but students control the
interactions within their groups. Building team-based organizational structures in the classroom makes it easier for teachers to reach out to students
who have problems and ensure that all students are successful.
A shift in values and attitudes may be required for a collaborative learning environment to reach its full potential. Some traditional school environments have conditioned students to rely on the teacher to validate their thinking and direct learning. So getting over years of learned helplessness takes
time. As they share and cooperate rather than compete for recognition, many
children find more time for reflection and assessment. Although collaborative learning helps teachers achieve a number of motivational and social
objectives, it also aims to improve student performance on academic tasks.
By tapping into students’ social nature and natural curiosity, collaborative
inquiry can go a long way toward helping struggling schools achieve academic and social goals. It is a disciplined and imaginative way of exploring
and coming together in community with others. As they work in pairs or in
small mixed-ability groups, students can take more responsibility for helping
themselves and others learn. As teachers learn when and how to structure
group lessons, collaboration can become a regular part of the day-to-day
instructional program.
A Sample Collaborative Activity
This science and math example is designed to help students discover the
diversity of seeds by using the process skills of predicting, comparing, categorizing, collecting data, organizing, recording, interpreting, and communicating. It is a collaborative inquiry activity that sets out to examine the
tremendous diversity of plants and their seeds. Math and Science Standards
• Math and science as inquiry—use appropriate tools to gather, organize,
and interpret data.
• Think critically and logically to classify data and make connections between categories.
Materials: Science/math journal, brown paper bag, and pencil
Objectives
1. Students will work collaboratively.
2. Students will make predictions (guesses) about where the seed might
be categorized.
3. Students will describe the categories verbally and in writing and the
reasons for putting the seeds in them.
4. Students will classify seeds and describe the properties of seeds.
5. Students will compare and order their seeds.
Procedures
1. Introduce the concept of the great variety in plant seeds. Tell students
that they are going to go on a seed hunt with a small group of two or
three other classmates. Their task is to try to find and collect samples
of one seed for each of the following categories: seeds that float, seeds
that blow, seeds that hitchhike, helicopter seeds, seeds that twirl, and
seeds that are cycled through animals or need animals to grow.
2. Instruct students to record where the seed was located in their math/
science journals. Students may wish to describe, draw, or write their
feelings about finding the seeds.
3. Upon returning, students will be asked to guess where the seed may be
categorized. Encourage them to write their predictions in their journals.
Evaluation
1. Have student groups bring their seeds back to the class to compare
their findings and test their predictions with other groups.
2. Have students divide and save the seeds in their portfolios 3. Have students reflect on this activity.
Reflections
1. Allow students time to discuss and write their reflections.
2. Students may wish to imagine they are the seeds their group collected
and compare themselves to their seeds.
3. Ask students how the group felt about being seeds.
4. Ask students how this activity relates to their lives.
MAKING INSTRUCTIONAL DECISIONS
WITH DIFFERENTIATED LEARNING
Because we know that students learn in different ways and at different rates,
it is important to consider differentiating instruction. The basic idea is to
provide individual students with different avenues for learning content. Differentiated learning is an organized approach through which teachers and
students work together in planning, setting goals, and monitoring progress. In
such classrooms, the teacher draws on the cultural knowledge of students by
using culturally and personally relevant examples. They show respect for
learners by valuing their similarities and differences, not by treating everybody the same.
Teachers are the main organizers, but students often help with the design.
It is the teacher’s job to know what is important and to analyze and offer the
best approach to learning. Students can let teachers know when materials or
assignments are too hard or too easy and when learning is interesting (or
when it is not). As a collaborative effort in shaping all parts of the learning
experience, students will assume ownership of their learning.
Understanding how students adapt to learning environments and classroom structure is crucial. When teachers focus on students’ strengths, students become more interested and work to achieve. Learners who struggle
are frequently rebellious and out of sorts in a learning environment that does
not adequately address different teaching strategies and learning styles. This
can result in failure for these students, starting with inaccurate diagnosis and
remedial work, or sometimes even withdrawal from school.
The most useful teaching approach for the struggling learner is often
well-organized differentiated instruction (Tomlinson and Cunningham Eidson, 2003). A teacher who is organized examines the conditions surrounding the child, such as curriculum content, the classroom environment, and the
student’s academic and social behaviors. The ways students react to information and respond to feedback are also important. Planning for manageable
units of classroom time and including as many teaching and behavioral approaches as possible certainly help. But teachers know that no approach is
effective in every situation, so it is important to be flexible. They also know
that when they depend too much on rote memorization (devoid of meaningful applications), many students have trouble recognizing and retaining math/
science facts and drawing conclusions.
In general, today’s standards-driven curriculum provides many opportunities for students to develop a real understanding of mathematics and science content. As learners become more skillful and experienced, math and
science ideas can be built upon and related to previous learning. Disaffected
students, too often, are assigned uninteresting drill work each year to help
them learn “basic skills.” Yet we know that students who did not understand
the concept the first time are not likely to “catch on” the next time. Limiting
their chances for math and science reasoning and problem solving puts struggling students at a serious disadvantage (Karp and Howell, 2004). It does not
take long for youngsters to get the message that teachers have low expectations when it comes to their academic achievement.
Achievement gaps often result when math and science content is not
connected to students’ ability levels and experiences. What conditions will
foster improved achievement? Research has not provided many clear-cut
answers. Some suggest student absences or movement between schools may
account for some of the problems. Other factors include the child’s developmental environment and the home and school learning conditions. Gaps exist
not only in the curriculum but also between the student and some of the
challenging content of math and science.
What works for reluctant learners? Among other things, working with
peers can help disaffected students focus and feel good about themselves.
Opportunities to communicate with others, as part of interesting math and science activities, can make also these subjects more motivating. Such a team-based approach is particularly powerful when student efforts are rewarded by peers and the teacher DISCOVERING WAYS TO DIFFERENTIATE INSTRUCTION
In a differentiated classroom, the teacher accepts students as they are and
helps them succeed considering their unique circumstances. Differentiated
classrooms are places where the teacher carefully designs instruction around
the important concepts, principles, and skills of each subject. The helpful
teacher makes sure that struggling learners focus on essential understandings
and important skills. The subject is introduced in a way that each student
finds meaningful and interesting. Although the teacher intends to have all
students attain these skills, he or she knows that many will not achieve all
there is to know (Tomlinson, 1999).
Recognizing individual learning styles and adapting a differentiated
teaching style can make learning easier. With differentiated learning, the
teacher provides specific ways for each student to learn deeply, working
energetically to ensure that all students work harder than they imagined and
achieve more than they thought possible (Tomlinson, 2001).
What is clear is that struggling students seem to have the hardest time
with the traditional classroom setting (straight desks, teacher lectures, textbooks, worksheets, lots of listening, waiting, following directions, reading,
and writing). In other environments, students who struggle have much less
difficulty, for example, in an art classroom, a wood shop, a dance floor, or
the outdoors. In these differentiated classroom settings where students have
opportunities to engage in movement, hands-on learning, arts education, project-based learning, and other new learning approaches, their interest and
desire to learn have been shown to be at or above average (Gardner, 1993).
There are ways that teachers can differentiate or modify instruction to
guarantee that each student will learn as much and as competently as possible: Teachers can modify the content of what is taught and the ways in
which they give students information. They can also help students understand the process of how they learn important knowledge and skills. Did they
use manipulatives to aid in their understanding? Did they ask others? Teachers want to know what the student understands and is able to do. Did the
student show his or her work? The teacher is also interested in discovering
students’ thoughts and feelings in the classroom. How did students react to
the learning environment or the way the class atmosphere worked?
There are several student characteristics that teachers respond to as they
design differentiated lessons. They include readiness (what a student knows, understands, and is able to do today), interest (what a student enjoys learning
about), and learning profile (a student’s preferred learning style).
Several Sample Strategies for Differentiating Instruction
Readiness
Provide books at different reading levels.
Use activities at various levels of difficulty but focused on the same
learning goal.
Interest
Encourage students to use a variety of media arrangements such as video,
music, film, and computers to express their ideas.
Use collaborative group work to explore topics of interest.
Learning Profile
Present a project in a visual, auditory, or movement style.
Develop activities that use many viewpoints on interesting topics and
issues.
Today’s classrooms are challenging environments for teachers. Designing
lessons that are responsive to the individual needs of all students is not an
easy task. Teaching math and science in a differentiated classroom can be
challenging, especially when teachers are trying to increase the emphasis on
math and science inquiry process skills. Skills such as communicating, observing, reasoning, measuring, making connections, experimenting, and
problem solving are only a few of the processes of doing mathematics and
science.
MEETING THE PRINCIPLES AND STANDARDS
The six principles discussed below describe important issues of the mathematics and science curriculum standards. Used together, the principles will
come alive as teachers develop comprehensive school math and science programs.
• Equity: High-quality mathematics and science require raising expectations
for students’ learning. All students must have opportunities to study and learn mathematics and science. This does not mean that every student
should receive identical instruction; instead, it demands that appropriate
accommodations be made for all students. Resources and classroom support are also a large part of equity.
• Curriculum: A curriculum must be coherent, focused on math and science,
and articulated across grade levels. Interconnected strands effectively organize and integrate mathematical and scientific ideas so that students can
understand how one idea builds on and connects with other ideas. Building deeper understandings provides a map for guiding teachers through the
different levels of learning.
• Technology: Technology today is an essential part of learning and understanding math and science. The effectiveness of mathematics and science
teaching is dramatically increased with technological tools. Tools such as
calculators and computers provide visual images of math and science
ideas. They facilitate learning by organizing and analyzing data, and they
compute accurately. Technology resources from the Internet to computer
programs like Logo provide useful tools for mathematics and science
learning.
• Assessment: Assessment should support the learning of math and science
and provide useful information to students and teachers. This enhances
students’ learning while providing a valuable aid for making instructional
teaching decisions.
• Teaching: Effective teachers understand mathematics and science, comprehend what underachieving students know and need to learn, and challenge and support them through learning experiences. Teachers need
multiple kinds of knowledge: knowledge of the subject, pedagogical
knowledge, and an understanding of how children learn. Different techniques and instructional materials also affect how well their students learn
mathematics and science. Struggling learners are often inundated with
only practice materials trying to help them master the “basic skills.” They
often lack the conceptual foundations of real understanding. Students frequently forget procedures and are referred back to the same uninteresting
skill-based drill work. The learner is not the focus; rather, the basic skill
drill is the center of attention.
• Learning: Math and science must be learned with understanding. Students
actively build new knowledge from prior experience. Students should have the ability to use knowledge in a flexible manner, applying what is learned, and melding factual knowledge with conceptual understand-ings—thus making learning easier. The learning principle is used when all
students are involved in authentic and challenging work. Struggling students’ interest is sparked, and they create a strong understanding of the
basic skills, regardless of whether it is through games, peer involvement,
or simple quiz situations.
STRUGGLING LEARNERS AND THE MATH
AND SCIENCE STANDARDS
The new millennium has ushered in extraordinary changes. In mathematics
and science, new knowledge and new ways of learning, doing, and communicating continue to evolve. Today, inexpensive calculators are everywhere.
Powerful media outlets widely disseminate information as mathematics and
science continue to filter into our lives.
If students can’t learn the way we teach, we must teach them the way they
learn.
—Carol Ann Tomlinson
We want all students, particularly struggling learners, to be involved in
high-quality engaging mathematics and science instruction. High expectations should be set for all, with accommodations for those who need them.
As students become confident about engaging in math and science tasks, they
learn to observe, explore evidence, and provide reasoning and proof to support their conclusions. As they become active and resourceful problem solvers, students learn to be flexible as they participate in learning groups (with
access to technology).
Students value mathematics and science when they work productively
and reflectively—communicating their ideas orally and in writing (NCTM,
2000; NRC, 1996). This is not a just highly ambitious dream but also a
successful effort to influence instruction. Here we reference some of the
principles behind the new standards and offer suggestions for effective teaching.
The National Council of Teachers of Mathematics and the National Science Foundation have developed standards that serve as guides for focused and enduring efforts to improve students’ school mathematics and science education. These content standards provide a comprehensive set of standards for teaching mathematics and science from kindergarten through grade 12.An Overview of the Curriculum and Evaluation Standards for
School Mathematics
The principles and standards for school mathematics recommend that all
students
• understand numbers and operations and estimate and use computational
tools effectively.
• understand and use various patterns and relationships.
• use problem solving to explore and understand mathematical content.
• analyze geometric characteristics and use visualization and spatial reasoning to solve problems within and outside mathematics.
• pose questions, collect, organize, represent, and interpret data to evaluate
arguments.
• apply basic notions of chance and probability.
• understand and use attributes, units, and systems of measurement and
apply a variety of techniques and tools for determining measurements.
• recognize reasoning and proof as essential to mathematics.
• use mathematical thinking to communicate ideas clearly.
• create and use representations to model, organize, record, and interpret
mathematical ideas.
(These are brief selections. For a full descriiption, see NCTM, 2000.)
An Overview of the National Science Education Standards
Principles that guide the standards:
• Science is for all students.
• Learning is an active process.
• School science reflects the intellectual and cultural traditions that characterize the practice of contemporary science.
• Improving science education is part of a systemic educational reform.
The science standards highlight what students should know, understand, and be able to do. Examples include the following:
• Becoming aware of physical, life, earth, and space sciences through activity-based learning.
• Connecting the concepts and processes in science.
• Using science as inquiry.
• Understanding the relationship between science and technology.
• Using science understandings to design solutions to problems.
• Identifying with the history and nature of science through readings, discussions, observations, and written communications.
• Viewing and practicing science using personal and social perspectives.
(National Academy Press, 1996)
As far as the subjects of math, science, and technology are concerned,
even the experts often have no idea of future directions. Oddly enough, the
ambiguity of what is going to come next meshes with the spirit of scientific
inquiry, technological innovation, and mathematical problem solving.
GOING BEYOND SKILL MASTERY
Students who complete their math and science lessons with little understanding quickly forget or confuse the procedures. For example, in doing a long
division problem, suppose that students cannot recall if they are supposed to
divide the numerator into the denominator, or the reverse, in order to find the
correct decimal. They can do the problem either way, but they may not
understand what they are doing or be able to explain their reasoning.
Understanding and skill mastery go together when students build on ideas
they already know in a discovery process. In science, step-by-step directions
for an experiment often are quickly given and extra time is not provided for
explanation. Again, the goal should be to understand what is going on well
enough to know how it can be applied in the world outside school.
Understanding important ideas and accurately completing problems are
some of the first steps in becoming mathematically and scientifically skillful.
Mathematics and science learning contains five strands of thought:
1. Understanding ideas and being able to comprehend important content.
2. Being flexible and using accurate procedures.
3. Posing and solving problems.
4. Reflecting and evaluating knowledge.
5. Reasoning and making sense and value out of what is learned.
Oftentimes, the struggling student has experienced little success in the
five strands. Math and science success can be expected and achieved as adaptations are made to the students’ curriculum. This can happen when
teachers relate problems to real-life student interests and provide time for
collaborative work.
Organizing Successful Lessons
Students reach higher rates of proficiency when they are involved in organized lessons that pay special attention to their individual learning needs.
Stage 1: Review
Students connect new math and science concepts to old ideas they are familiar with when they are actively engaged at a concrete level of understanding.
Math and science manipulatives such as counters, eye droppers, rulers, and
blocks are used to answer questions that represent interesting real-life problems. For example, students are asked to show how many more cupcakes
need to be made for a class picnic if seven are already made for the class of
sixteen students (each student gets one cupcake). Connections are made to
former lessons, such as relating subtraction to the mathematical idea of how
many more. Questions are asked, and students discuss their understanding of
the mathematical ideas.
Stage 2: Demonstrate Knowledge or Skill
Next, students show their thinking by drawing a picture of the problem. For
example, the set of cupcakes might be shown like this: “I have 7 cupcakes.
How many more do we need to get 16?” Have students draw a basket to
show their results.
Stage 3: Guided Practice
Students form a number sentence to match their drawings. 7 + __ = 16.
(Answer: 9). We needed 9 more than 7 to get 16. Students fill in numerals
and number sentences.
Stage 4: Check for Understanding
In the last part of the lesson, students practice skills and problems through a range of activities and supporting lessons. The teacher provides ongoing feedback at each step so that procedural errors can be corrected Organized Strategies to Support Students with Learning Problems
1. Review important concepts—make connections between familiar and new information.
2. Demonstrate knowledge or skill—increase student engagement
and promote independent student activities.
3. Provide guided practice—reinforce language skills, partner, and
share. Students do a variety of problems.
4. Check for understanding and provide feedback—summarize
strategies and evaluate.
5. Teacher provides continuous reinforcement at each stage so that
errors can be found and corrected.
Assessing Students’ Strengths
Math and science content knowledge, student learning styles, behaviors, and
reinforcement that affect learning are all considered in assessment. Assessment data is gathered from teacher observations, performance on daily assignments, math and science quizzes, homework, and in-class work. This
information is recorded on a student data sheet. The value of assessment is
that it leads to an overall analysis of a student’s strengths and weaknesses.
Student Data Sheet
1. Learning setting—indicates the physical environment in which
the student works.
2. Content—includes the subject matter in which the child is engaged.
3. Process—involves strategies, methods, and tools that students
are engaged in (e.g., listening and speaking).
4. Behavior—refers to academic and social behaviors that students demonstrate.
5. Reinforcement—looks at responses from the learning environment that cause behaviors to occur.
Recording Behavior Patterns
Behaviors that are consistent are called likely behaviors. They might include
the desire to play video games or use the computer. Unlikely behaviors
describe behaviors that usually occur below an average rate or at a very
minimal level. For example, a classroom environment that is conducive to
student achievement could be rated with a “1” symbol. If a student is having
problems in the classroom environment, the teacher would mark this category with a “2” symbol. Collecting and reviewing this information with students allow teachers to focus on recognizing which classroom activities foster positive behaviors.
Creating Math and Science Success Plans
Math and science instruction focuses on student learning while building on
students’ strengths and identifying error patterns. The teacher judges the
students’ data sheets, recording the type of learning environment that students were involved in. The content of the lessons is also recorded. The
learners’ preferred learning style and how they accept and express themselves (including listening, speaking, writing, or drawing) are also recorded
information.
The teacher notes if the student works well with others or works best
alone. The students’ academic and social participation are other factors considered when evaluating the students’ data sheets. Learners’ responses are
documented. Examples of learner responses that are recorded include “likes
being with friends,” “enjoys helping in class,” “likes being in front of class,”
“does not turn in work on time,” “cannot stay focused,” or “talks out of turn.”
Based on identifying how students learn, the Sample Math and Science
Success Plan is designed to recognize and move students toward more positive behaviors and academic success. In this way, the Sample Math and
Science Success Plan serves as a guide for an organized and well-planned
learning approach for struggling learners.
Instruction now tends to be more research based and standards driven. It
often involves learners constructing deeper content knowledge through collaborative inquiry. Modern math and science learning is much more than
memorizing a collection of isolated rules and procedures. Understanding and
application involve certain levels of reasoning, problem solving, and imagination. Chance and uncertainty play major roles along the path to developing
cultures of intellectual curiosity and innovation Sample Math and Science Success Plan
There are, after all, multiple ways of charting the way forward—and very
different ways to successfully go about solving problems. So it is little wonder that so many of us have trouble dealing with the arbitrary nature of
individual and societal destiny.
Building Creative Understanding and Academic Success
Creativity, originality, and exploring future possibilities are often a matter of
perspective. Sometimes it involves digging up new ground—and sometimes
it is going over old ground differently.
Recognizing the learning characteristics of all students and finding instructional methods that motivate them are important steps in math and science instruction. The basic idea is to use strategies that consider all aspects of
the learners’ instructional needs so that they can use their imaginations and
be successful.
The instructional methods mobilized for reluctant learners must not get in
the way of the students who are already doing well in math and science.
Differentiated learning and collaboration help reach the unmotivated, while
providing meaningful opportunities for everyone in the classroom (Hehir and
Katzman, 2013).
Math and science certainly do not attract universal affection. In fact,
anything even faintly mathematical or scientific engenders fear in many.
Such an attitude has long been referred to as an “American phobia” (Burns, 1998). Still, regardless of whether they know it, all individuals use and are affected by math and science in their day-to-day lives. In many respects,
these disciplines cannot be avoided.
In order to do well in any subject, students need to have a fairly positive—or at least disciplined—attitude toward achieving mastery. Also, both
students and teachers may have to be willing to adapt and change to maximize learning.
The educational process involves much more than what happens at
school. One way or another, everyone is involved in the education of children and young adults. So when it comes to who is to blame for educational
problems, it goes well beyond the classroom door.
Educators need to be aware of how social forces (including the family)
influence what is learned in the classroom. This does not mean that parents
have to teach math and science outside of school, although that would not
hurt. It is just that the home and social environment matter when it comes to
learning.
The self-esteem and spirit of individuals and groups are often expressed
through culture. All students are helped when community resources, issues,
events, and topics connect to what happens in the classroom (Van de Walle
and Lovin, 2006).
Past and present experiences outside of school can serve as powerful
resources for learning. In addition, purposeful classroom linkages with the
home environment can be created and sustained by the math/science curricula and by the actions of the teacher. There are even situations, especially at
the early childhood level, in which parents may have to be coached and
rewarded for becoming better caregivers.
As teachers use an organized approach to assess their students’ math/
science strengths (and error patterns), they can put into practice learning
strategies that connect a student’s predisposition to a positive classroomlearning environment. One of the things that helps is having students explore
the practical applications of math and science in their lives.
Math/science rules need to be connected to student understandings in a
way that offers them an authentic invitation to interesting problems. This
organized approach may well be the best way to get struggling students to
express their reasoning in ways that can lead to academic success (Muschla
et al., 2012). While opening doors to understanding for reluctant learners,
teachers must not slow down those who are already motivated and doing well Getting young people to work as part of a team is one thing, but getting
them to appreciate math and science can be more difficult. Experienced
teachers know a lot about making the classroom a positive experience. They
also know that for many disaffected students, it helps if they can work with
others.
Effective teachers frequently use interactive mixed-ability group strategies as they adapt techniques from a wide repertoire of methods.
Since it is best to use all the tools available, technologies like the Internet
can prove useful when it comes to encouraging collaborative inquiry and
learning by doing. For example, some teachers like students to work in pairs
as they write on classroom wikis and websites (editing each other’s writing is
part of the process).
SUMMARY, CONCLUSION, AND LOOKING AHEAD
Mathematics and technology are tools of science and they are subjects in
their own right. All three topics influence and feed off of each other. Thriving in an innovation-driven world requires generating high-quality learning
experiences at the earliest possible level.
It is difficult to overstate the impact of the technological products of math
and science. A good example is the set of virtual global connections and
social structures that are changing how we think, live, and work. It is important for young people to develop the ability to mitigate the potential risks as
technology pushes out to new frontiers.
As students grow and master more advanced skills they will interpret
their experiences through many of the patterns of ideas, values, and beliefs
that they learned early on.
At every age level, it is important to think big and risk failure to make
new ideas and positive change possible. It does not all have to happen at
once—teachers can think big and start small as they weave new ideas into the
educational fabric.
As a larger proportion of the population is able to meet higher educational
standards, it is bound to lead to more innovation, higher incomes, and a more
productive economy. It does not take a university degree to be successful and make a social contribution. But everyone does need to have at least some post-secondary training. (Take a look at how Germany conducts its apprenticeship programs.) In an innovation-driven changing world, we may never fully succeed in
providing exactly the same opportunities for everyone. But we can do better,
much better, by providing high-quality instruction for all students—especially unmotivated learners and others who may be struggling to master math or
science content.
When bringing technology into the math/science classroom, it is best to
build on what you already do well. At the K–8 level, that probably means
small collaborative groups and student activities or projects.
Humans are not designed to get their basic understanding about subjects
by sitting alone in front of a computer or video screen. Although online
education has gotten off to a rocky start, hybrid courses that include a mix of
face-to-face learning and online work show some promise.
At least a fair amount of offline social interaction is needed for imaginative new ideas and innovation to fully flower. There are, after all, many
situations in which academic success requires face-to-face problem-solving
activities in combination with online experiences or virtual reality simulations in order for active learning to reach its full potential.
Even in a technology-rich classroom environment, creativity and innovation are processes that are sometimes difficult for the teacher to get across to
their students. However, building on the social nature of learning (in which
everyone involved comes together) makes it possible to improve the odds.
The most important and innovative applications of math, science, and
technology involve communities, networks, institutions, and changing social
attitudes. With or without technology, overall educational success has a lot to
do with the level of support in the surrounding culture.
Improving student outcomes is most likely to happen at the intersection of
individual imaginative processes and the collaboration associated with generating new ideas.
Numerous aspects of good teaching exist in a gray zone where there are
no black and white answers. Educational research and the content standards
matter, but an overreaching reliance on experts and nebulous metrics can get
in the way of positive change. Many things that can be counted or measured
do not matter all that much. And many of the things that matter cannot be
counted.
The process of teacher evaluation and improvement has to be built on what teachers actually do and how their students learn (Darling-Hammond, 2013). For a teacher to grow and change in a way that enriches what goes on in the classroom requires combining professional development with partici-pation in the professional community. Within schools, collegial help and
activity have to go hand in hand with mutual respect and support.
When it comes to student learning, there is no substitute for a good
teacher who develops lessons that combine thinking and feeling in a way that
reaches both the head and the heart.
Clearly, a student’s academic success is strongly influenced by the teacher’s energy, knowledge, character, sense of humor, and ability to relate to
young people. If we want all students to master math and science, there has
to be a highly skilled teacher in every classroom.
Major changes in the productivity of American schools rest on our ability to
create and sustain a highly prepared teaching force for all, not just some, of
our children.
—Linda Darling-Hammond
QUESTIONS FOR TEACHERS AND PROSPECTIVE TEACHERS
1. Interview four peers. Ask them if they ever had difficulty learning
math and science. Have them identify their reasons and explain.
2. How would you identify a struggling learner and include him in smallgroup work?
3. What are some teaching ideas for connecting math and science to
students’ needs and interests?
4. Are digital technologies barging into the classroom before we have the
ability to understand their implications or possibilities?
5. How does learning mathematics and science today differ from how
you were taught? Provide examples.
REFERENCES AND RESOURCES
Armstrong, T. (2012). Neurodiversity in the Classroom: Strength-based Strategies to Help
Students with Special Needs to Succeed in School and Life. Alexandria, VA: Association for
Supervision and Curriculum Development.
Burns, M. (1998). Math: Facing an American Phobia. White Plains, NY: Math Solutions
Publications.
Common Core State Standards Initiative. (2013). “Mathematics Standards.” Available online at

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