MATH DEBATE
By:
PERSPECTIVES
PARENTS Vs Educators
• Individual Work Vs Collaborative Learning.
• Basics Vs Problem Solving.
• Technology, Visuals and Writing.
• Homework.
Individual Work Vs Collaborative Learning
Parent’s Perspective
• Parents believe that students learn better alone than in a
group.
• Teacher should lecture students
Educator’s Perspective
• Students get engaged and motivated working w/ math in
small groups.
• Learning is fun in collaboration than in isolation.
• Students could learn from each other and not only from the
teacher.
Individual Vs Collaborative
Teacher:
• Groups will be formed in the beginning of the class. A problem will be
introduced through lecture to the students while motivating them to solve the
problem among themselves with guidance.
•Once the students are motivated, they will become involved with one another
and help each other solve the problem. As a teacher, we can observe and help
the students solve the problem by assisting with ideas, former lessons, and
giving hints. This will help prepare the children for the day’s lesson.
•Students become more proficient when they understand the underlying
concepts of a math problem with the help of their peers and teacher guiding
them to the correct solution. After the students have worked on the problem
among themselves, we as teachers will go over the problem that will then lead
into the uncovered lesson planned for that day.
Parent:
•We are not comfortable with your approach in class work
because our children will become distracted form working with
other children.
•All the students have the same mathematical knowledge when
solving a problem so we would prefer the children to be lectured
on the day’s lesson and then be given problems individually.
Working individually will reduce the chance of misbehavior,
misguided information, and increase a controlled learning
environment.
•The students performance will advance because they will be
more focused on their own work than the other students who
may cause distractions. With the students working individually,
it will shape them into independent learners that can solve
mathematical problem both numerically and through problem
solving.
•There are many ways that a child can practice this. One way is
through note taking, class work that is assigned individually,
and through visual memorization.
Teacher:
• Students could learn from lecture and note taking, but they have the chance
to become more involved in their own learning when active. When students
are more involved in their learning they can grasp the concept that is being
presented to them. This can help them become independent thinkers through
collaborative learning.
•A student can learn from note taking and lectures in a controlled
environment, but the information that is covered in a child’s notes is the only
information that they have. If a child only depends on their notes for studying
and homework that information cannot always assist a child apply it to
problem solving.
•Their learning could be limited to pencil and paper. There will be a lack of
experience in working with math. Math is best learned when it is applied and
having the students solve problems in a group helps them not only become
thinkers, but how to contribute in a group and develop their communication
skills.
Parent:
• Yes, learning math is about application, but we want to
promote a well behaved classroom. The chances of a child
being distracted is higher in group work than a child working
on their own. Therefore, group learning is an alternate way of
learning, but the task of keeping the children focused is an
issue.
• We want our children to be good thinkers. Class lectures
does not really require a child to think. Their attention is
required. The child should be centered back to focus in
lecture. The lessons should be coherent in their notes. The
notes should cover the mathematical concepts of the day so
that they can refer to them.
• Group work should not take the time of lecture. The time
spent during a lesson should be spent efficiently. A math
lesson could be divided in different activities but we insist on
lecture in a controlled environment.
Teacher:
• A math lesson is carefully planned. All the time and information is crucial.
We want a well behaved classroom as well. We will teach the students. We
cannot simply dictate the math concepts. We will teach them the concepts
through each step consecutively.
•Group work also allows us to test their understanding of what they have
already learned. It is only an alternate way to review the previous day’s lesson.
The work is a link to the present day’s lesson.
•We do not only leave the children in group work. It is only an exercise to
warm them up and encourage them to learn new concepts. It will help them
become involved with their independent learning, their peers, and the teacher
as well (whether it is by asking questions or listening to the instructions).
•They can refer to their notes for the lessons and more so on how to solve a
concrete numerical problems. It is easier to refer back to the collaborative
activities through memory, therefore note taking is not highly best for such
learning. Their notes are required to be reviewed for homework and test
reviews.
Agreement:
• Teachers can facilitate group work among students to review the previous
day’s lesson and to introduce the present day’s lesson; however, time will also
be set aside for lectures and group work will not interfere with lectures.
•The students are required to take notes during the teacher’s lesson. Whether
the notes be given on the black board or specifically told to be taken verbally by
the teacher. It is optional for student to write their notes during group work.
•The teacher is responsible for making sure the class is focused on a
collaborative problem and assists students in solving it without giving the
answers.
•The teacher should also give the students time to work individually on
numerical drill problems. This time should not really be collaborative and
should be a brief moment just after the teacher has delivered the present day’s
lesson.
•The math lesson must be divided up wisely and in a timely manner. By the
end of the lesson the students should be ready for the homework given for the
evening.
Basics Vs Problem Solving
Parent’s Perspective
The basic concepts in math should be
learned by memory and by repetition of
arithmetical problems.
Teacher’s Perspective
Students needs to understand a math
problem in order to solve it.
Students become a better problem solvers.
Student’s internalize knowledge by
understanding not by memorization.
Basics Vs Problem Solving
Parents
• Children in school are familiar with the basic mathematical concepts. Addition,
subtraction, multiplication, and division have been learned by kids for a long time.
The best way they learn is through memorizing the equation of basic math. It can
help them learn and save time when they begin learning more advanced
mathematics.
• Students learning through memorization would have a easier time in
standardize test. It will save them time in their homework, class work and tests.
• The best methods the students can learn through memorization is to be given
notes, flash cards, and reciting whether it be through song or rhyme.
• The students must know their basic math so that that can advance in more
complicated math. Problem solving is a more confusing way to learn
mathematical concepts. Problem solving diverts the focus of learning the value of
the numbers the they work with in math. The child should be working with more
numerical problems than writing out their math.
• Math classes should involve numbers not writing exercises involving an
excessive amount of writing that should really be assigned in an English class.
Teacher
• We support the same notion of helping the students know and be familiar
with basic math. There are just a few things we disagree with. We do wan to
the children to remember what we teach them. They can remember all of
their basic math and concepts, but they must be versatile and comfortable
with the math they are learning. In class we do problem solving to assist
them in their knowledge of math.
• It is fine that they memorize all their basic math such as addition,
subtraction, multiplication, and division. That is a good way of learning, but
once they have memorized what 2+2 is and so forth – as teachers we need
know how much they understand of what they know. For instance, do they
know what the value of 2 is? Or do they know how many two of something
looks like.
• Problem solving helps us to know what the children know. It gives us a
sense of where they are in their learning and a sense of where we need to
intervene. Once we know where to intervene, we can pick up their learning
process to a point of understanding the entire mathematical concept. It is that
the children know what to solve in any problem, but especially word problems.
Teacher Continued:
• Problem solving does not negatively effects the students. Problem solving
involves applied math. Each problem is strategically set to introduce realistic
problems life has. The applied math causes them to be comfortable and
proficient with problem solving. They are able to function in a world that has
realistic problems that require mathematical knowledge. Whether it is counting
money, dividing work among a group, or how to put something together.
• Students who are learning only by memorization cannot always explain or be
fluent in explaining there step by step approach in solving a word problem. The
same numerical math is applied in word problems which means the students are
not being diverted from learning math. They are required to record their step by
step process. This does require for them to write extensive notes on their
progress. Math does not turn into an English class, the only difference is they
are sharing their progress on paper rather than presenting it to the class in
discussion.
• The problem solving helps distinguish where one child is in learning than the
other. It is not a public notification, just for the teacher. We are aware that
some children grasp concepts better than another. Knowing where they are
helps us help them.
Parent
• If the same numerical math is applied to word problems then there is no
need for problem solving. Problem solving belittles the potential of the
children’s understanding. The teacher should know where the child’s
understanding in math is through their home work.
• Applied math is not really required to kids in middle school. It is more in
high school when their math does become more complicated. The child should
already be familiar with their basic math. It should not be reviewed as much
as the math they are learning before high school. The math they are learning
in middle school should be easy.
• If the teacher is aware that a child does not understand the math the
teacher should notify the parent or tutor them.
• The teacher should prepare the children for specialized tests. The ideal
problems should be presented and broken down so that the children can
understand what will be asked of them. When they are familiar with the tests
they will have a better chance of passing. Problem solving should be briefly
reviewed, not an every day practice.
Teacher
• Basic knowledge goes hand in hand with the advance math that they will
learn. For example, if the student is learning how to add fractions, the child
should already know the basic mathematics. What we would cover is the basic
to adding fractions, what a fraction is, and how to add them. The element of
fractions that are being covered will be submitted with problem solving that the
student can relate with. As was said earlier it will learned as applied math.
• Students are not always going to fully understand a concept without
practicing how to use mathematics. Memorization limits this practice. In
middle school, the students should already know their basic math. By middle
school they are not learning how to add numbers or double digits, but it is
important the remember the rules of the equation they are solving. That’s
where memory can take an effective part, but insist that the student remember
problems does not help[ them have a full understanding of what kind of
problem it is, what is being asked of them, and how to solve the problem.
• Students will be able to understand the concepts by practicing how to solve
them. Once they actively solve them they will have a better understanding of
the math because they thoroughly work in problem solving.
Teacher Continued
• We are always preparing students for their specialized tests. We do break
down the problem and review what math must be applied. We don’t only
show them what kind of problems it is. We also solve the problem step by
step. That is usually what breaking the problem down is. For instance, we use
the Poly approach when problem solving.
• The problem is examined and evaluated for what it is and what is being
asked. To know what is being asked they must understand the problem first.
When the student is understand what is being asked of them they will know
what plans to make to solve the problem. It is basically how they will
approach it step by step. They follow those steps that will lead them to solving
the problem with a mind that is familiar with the math. When they carry out
the plan, they will go over what they have done step by step.
• When the student follows the steps he has taken he may see the mistakes he
made giving them the chance to correct their mistakes. Looking back at what
they have done that in is self is note taking on how to solve a problem with
that kind of math. When they look back they will remember what they have.
Teacher Continued
• The student is using memory through practice. Drill problems can be used
as a substitute for numerical problems. This can also help, but if the student
uses only drill to learn they will be a little more confused if they find that
they do not know how to apply the math to there what they do almost every
day.
• As teachers we use by any means to determine the status of the student’s
understanding of math. We always will and that is necessary for us to know
how and where to help the student. There is no problem with contacting the
parents. In fact we encourage the parents to involve themselves and assist
their children in learning.
• Middle school is key and a preparation for high school. If we were to
disregard applied problem solving, we as teachers will not be doing our job
as teachers.
• Problem solving does not belittle the potential of the students ability in
math. In fact it enhances their thinking ability. It develops their ability to
use math in there realistic lives. All of which shapes them into critical
thinking citizens.
Parent
• After applying the math to realistic problems, the students can take there
notes. Their notes can be used to assist them with the drill problems. The
children should also have drills to help jog their memory of what they are going
to review.
• Find a way of managing how many problem solving approaches vs.
numerical drill exercises should be taken into consideration. The children must
spend their time reviewing their lesson. The notes taken in the class should
assist them with this.
• The children must learn the rules of solving mathematics. Although we
believe problem solving takes too much time, it is important that they know
the rules of the math given.
• We suggest that problem solving be done with the teacher’s advisement.
• The teacher should notify the parents if they are aware of a child who has
difficulty with a math lesson after numerous attempts of review and testing.
Agreement
• Both parent and the teacher will observe the learning progress of the
student. Consistent communication will be relayed between the teacher and
parent to schedule a conference or by formal writing.
• The teacher can apply numerical problem solving and apply it to
investigative problem solving related to realistic examples that the students
can relate to. The teacher should use the numerical drill problems from the
text book.
• The students do learn a lot better from word problems and investigative
learning. They are more aware of what is being asked of them therefore, they
can approach the problem with a plan. It is a good way to introduce drill
problems. Their memorization can be drawn from their experience in problem
solving.
• Repetition and review are key in boosting the memory and understanding of
the student. Both means of written problem solving and numerical drills are
both very important for the child, the outcome makes more comfortable and
versatile in math.
Technology, Visuals and Writing.
Parent’s Perspective
• Limited use of manipulative.
• No use of technology in a math class.
• No calculators.
Teacher’s Perspective
• The use of manipulative in math class helps to understand the
math concepts.
• Manipulatives are used to reinforce the multi-intelligence of
learning.
• Technology and calculators enhance the students learning.
Technology, Visuals and Writing.
Parent
•Students should be limited to the use of manipulatives on their
own. The teacher should use manipulatives as a visual
demonstration for the students to understand the math concept.
The manipulatives should not really be used by the children.
• Manipulatives can be devices of distraction. Visual learning
should be monitored and controlled. Preferably, manipualtives
should be removed from the class room.
• The use of computers do not help the children grasp
mathematical concepts. The class work, home work, and the
time spent should be substantial enough for the children to
understand a given lesson. The use of computers could make it
challenging for a the teacher to monitor the children.
Parents Continued
• The students should not use calculators to solve their work. Preventing
a student from becoming dependant on a computer is important. Children
should take the time to solve their with pencil and paper. The use of long
problem solving would be easier for a child to check their work. It is
impossible to retrace their steps through a calculator.
• Technology in a class room can divert the child from wanting to sit and
learn as they should. The children should be actively involved in wanting
to learn.
Teacher
• The students should not be deprived of mulipulatives. The use of
malipulatives should be reduced (especially as they age), but not completely
eliminated. Manipulatives are useful tools that the children use in their math
class as visual devices that represent the math that they will be learning in a
class room environment.
• Computers can not be used as primary resources to teach math, but they
are helpful not only in teaching, but in tutoring a child of what he has already
been introduced to in a mathematics class room. The children’s mathematics
software is scanned for what it offers to a child in elementary school.
Children are not entirely left alone with the computer, they are carefully
monitored.
• We do not encourage that a student relies on a calculator in solving math.
We allow the children to used them when they are reviewing and/or checking
their work. We use calculators to assist them with large infinite numbers that
would take too much of the lesson’s time to manually write down.
Teacher Continued
• The use of calculators are a good way to help introduce the students to
the world that is dominantly operated by technological inventions.
Calculators and computers are only small advances before they are
introduced to greater things.
• As teachers we often demonstrate what we wan to to teach the students.
It can be presented as through a visual, or manipulatives. The
manipulative is not used in every lesson that is planned. It is used for
lessons that are first introduced or with more complicated units of a lesson.
We do want the children to used them too often, but they are used if we
must.
Agreement
• The use of manipulatives could help the students understand a
mathematical concept better. The use of manipulatives should be decreased
as the children grow older. When they are older the teacher should use the
manipulative themselves and demonstrate with the manipulative so show.
Teachers can have the students use the manipulatives if they must.
• Computers are helpful tools to tutor the children on concepts they have
already been introduce to. The computers should really be use to tutor the
children. It will open the student to the use of techonology and dominate
technological world.
• Calculators should not be used to solve mathematical problems. They
should be used to check and review their work. The use of calculators among
students should be monitored.
• The students should be encouraged to solve their word and numerical
problems through writing out what they do step by step and keeping their
notes from the class.
Homework
Parent’s Perspective
• Homework should be assigned every day.
• More worksheets.
• Homework is an extension of a daily lesson.
Teacher’s Perspective
• Homework should reinforce problem solving approach.
• Homework should reinforce the classroom learning.
• Every day homework is not a must.
Parent
• Home work should be assigned every evening. Review home work
should be assigned for the weekends. The quantity of the homework
should equally effective as the quality of the home work.
• The children should be assigned a substantial amount of home
work that covers and reviews what was covered in the class room of
that present day. The homework should consist of worksheets of
numerical problems and along with home work from the text the
children use in math.
Teacher
• Home work will cover what the student has learned in the class
room. Numerical drill will be assigned. Along with the numerical
drills, problem solving will be assigned. Problem solving may be
word problems form the test book or assigned the teacher directly.
• The problem solving problem will consist of word problems that
will have the math that was covered in the lesson, but will involve a
relavant problem that is related to the math that was learned in the
day’s lesson.
• The home work will also consist of writing. The children will
have to write how a problem could be solved rather than actually
solve a problem. This will show us how much the student
understand from the days lesson.
• The homework also consist of one or two problems that will have
a new component to the math that will be covered in the class
room the following day.
Agreement
• Home will be assigned every day.
• The homework will be an extension and reinforced what was
covered I the day’s lesson.
• The home work will have both numerical and word problems.
• Students will write how the math is solved and why.