Valerie Daugherty
Ltcy 444
June 21, 2002
Strategic
Learning in Mathematics
A math teacher, or any teacher for that matter, will come across so many
different students it will be amazing. Along
with the different students will be different learning styles.
Teachers will have to be able to identify these different learning styles
and adapt each individual student. Most
learning styles will be grouped into one or more of these following four
categories:
-
Perceivers
Ÿ
concrete
these students have to absorb information through hands on learning.
such as
doing, acting, sensing, and feeling
Ÿ
abstract
these students pick up information through analysis, observation, a and
thinking
- Processors
Ÿ
active
these students can use new information in order to pick up the material
at once
Ÿ
reflective
these students have to think and reflect on the material before they are
able to get it
http://funderstanding.com/learning_styles.cfm
Once a teacher has identified a student’s learning style, he/she has to
get the student interested and motivated. Here
are a few quick ideas a teacher can use to help.
Ÿ
From the
first day, demonstrate and talk about your own enthusiasm for the course
material, and how it effects you personally.
Ÿ
Look for
ways to connect the material to the lives of your students.
Ÿ
Think of
questions you can ask about the material that make students think about the
subject matter, even if they have not read the material.
Ÿ
Create a
“need to know“.
Math may be tricky for some students to get a grasp on.
Here are a few tips and suggestions geared toward teaching math to your
students.
*
Read over the unit - take time to go over the unit with the students
before and after
each of the lessons.
*
Develop a sound math foundation - math is cumulative.
If a student does not get the
basic, he/she will not be able to continue successfully.
Make the student has a
good understanding of the material before moving on.
*
Time management - it is important for the students to do their reading
and homework
assignments as soon as possible after each lesson.
Try to enforce this as much as
possible.
* Have students to show their work - it is very important for students to show
their work
when it comes to solving math problems.
This will help them to identify where
they are making mistakes at.
*
Always write legibly - students will not be able the read their handwriting if
it is not
legible. Stress the importance of slowing down and writing neatly.
*
Be prepared - Being prepared for each course involves several important factors:
·
complete any previously assigned homework
·
compile a list of questions about the previous
assignments to ask the instructor
·
preview the material to be covered that day
·
take your textbook and/or workbook to class
·
carry the proper supplies to each class - calculator,
pencils, erasers, lined or graph paper, etc.
There are many ways for students to organize information in order for
them to learn the necessary basic.
^ Flash cards- Flash cards are useful for organizing all forms of math
information.
^ Running concept list- Running concept lists organize all forms of math
information.
^
Flow charts- Flow charts are useful for organizing sequential information such
as the steps for solving a problem.
^
Matrices - Matrices may be used to organize math symbols, equations, and
definitions.
http://muskingum.edu/~cal/database/math1.html
A math course is not only learning how to solve problems.
There are several ways for students to communicate and see the connection
of why math is so important to learn. These
are good strategy tips provide for teachers at www.education-world.com.
In grades 5-8,
the study of mathematics should include opportunities to communicate so those
students can--
·
Model situations using oral, written, concrete,
pictorial, graphical, and algebraic methods;
·
Reflect on and clarify their own thinking about
mathematical ideas and situations;
·
Develop common understandings of mathematical ideas,
including the role of definitions;
·
Use the skills of reading, listening, and viewing to
interpret and evaluate mathematical ideas;
·
Discuss mathematical ideas and make conjectures and
convincing arguments;
·
Appreciate the value of mathematical notation and its
role in the development of mathematical ideas.
In grades 5-8,
the mathematics curriculum should include the investigation of mathematical
connections so those students can--
·
See mathematics as an integrated whole;
·
Explore problems and describe results using
graphical, numerical, physical, algebraic, and verbal mathematical models or
representations;
·
Use a mathematical idea to further their
understanding of other mathematical ideas;
·
Apply mathematical thinking and modeling to solve
problems that arise in other disciplines, such as art, music, psychology,
science, and business;
· Value
the role of mathematics in our culture and society.
http://www.education-world.com/standards/national/math/5_8.shtml
This article is “straight from the horse’s mouth,” which I found
very interesting and I thought it had many wonderful learning strategy tips for
students.
For teaching multi-digit multiplication, teacher-researcher Magdelene
Lampert created a series of lessons in which she taught a heterogeneous group of
28 fourth-grade students. The students ranged in computational skill from
beginning to learn the single-digit multiplication facts to being able to
accurately solve n-digit by n-digit multiplications. The lessons were intended
to give children experiences in which the important mathematical principles of
additive and multiplicative composition, associatively, commutatively, and the
distributive property of multiplication over addition were all evident in the
steps of the procedures used to arrive at an answer (Lampert, 1986:316). It is
clear from her description of her instruction that both her deep understanding
of multiplicative structures and her knowledge of a wide range of
representations and problem situations related to multiplication were brought to
bear as she planned and taught these lessons. It is also clear that her goals
for the lessons included not only those related to students' understanding of
mathematics, but also those related to students' development as independent,
thoughtful problem solvers. Lampert (1986:339) described her role as follows:
My role was to bring students' ideas
about how to solve or analyze problems into the public forum of the classroom,
to referee arguments about whether those ideas were reasonable, and to sanction
students' intuitive use of mathematical principles as legitimate. I also taught
new information in the form of symbolic structures and emphasized the connection
between symbols and operations on quantities, but I made it a classroom
requirement that students use their own ways of deciding whether something was
mathematically reasonable in doing the work. If one conceives of the teacher's
role in this way, it is difficult to separate instruction in mathematics content
from building a culture of sense-making in the classroom, wherein teacher and
students have a view of themselves as responsible for ascertaining the
legitimacy of procedures by reference to known mathematical principles. On the
part of the teacher, the principles might be known as a more formal abstract
system, whereas on the part of the learners, they are known in relation to
familiar experiential contexts. But what seems most important is that teachers
and students together are disposed toward a particular way of viewing and doing
mathematics in the classroom.
Magdelene
Lampert set out to connect what students already knew about multi-digit
multiplication with principled conceptual knowledge. She did so in three sets of
lessons. The first set used coin problems, such as "Using only two kinds of
coins, make $1.00 using 19 coins," which encouraged children to draw on
their familiarity with coins and mathematical principles that coin trading
requires. Another set of lessons used simple stories and drawings to illustrate
the ways in which large quantities could be grouped for easier counting.
Finally, the third set of lessons used only numbers and arithmetic symbols to
represent problems. Throughout the lessons, students were challenged to explain
their answers and to rely on their arguments, rather than to rely on the teacher
or book for verification of correctness.
Lampert
(1986:337) concludes:
. . . students used principled
knowledge that was tied to the language of groups to explain what they were
seeing. They were able to talk meaningfully about place value and order of
operations to give legitimacy to procedures and to reason about their outcomes,
even though they did not use technical terms to do so. I took their
experimentations and arguments as evidence that they had come to see mathematics
as more than a set of procedures for finding answers.
Clearly,
her own deep understanding of mathematics comes into play as she teaches these
lessons. It is worth noting that her goal of helping students see what is
mathematically legitimate shapes the way in which she designs lessons to develop
students' understanding of two-digit multiplication.
http://books.nap.edu/html/howpeople1/ch7.html
The following areas also need to be placed on the top of the list when it
comes to student learning. If the
curriculum, instruction, and assessment are not carefully planned out, the
student will suffer not matter the learning strategies.
1.
Curriculum - Teachers need to place emphasis on hands on material as well as the
thinking processes of the students.
2.
Instruction - When teaching their lesson, teachers have to include all learning
style in order to reach the students. They
also have to be sure to vary their teaching tools in the classroom.
3.
Assessment - It is also important to use a wide range of assessment.
Resource
books for further research
Boaler,
J. (2000). Multiple Perspectives on
Mathematics Teaching and Learning
(International Perspectives on Mathematics
Education, V. 1).
Ablex Pub Corp; ISBN:
156750535X.
Driscoll,
M. ( 1999). Fostering Algebraic Thinking:
A Guide for Teachers, Grades 6-10.
Heinemann (Txt); ISBN: 0325001545.
Hiebert,
J. (1997). Making Sense : Teaching and
Learning Mathematics With
Understanding. Heinemann (Txt); ISBN: 0435071327.
Sobel,
M. & Maletsky, E. (1998). Teaching
Mathematics: A Sourcebook of Aids,
Activities, and Strategies (3rd Edition).
Allyn & Bacon; ISBN: 0205292569.
Stigler,
J. & Hiebert, J. (1999). The Teaching
Gap: Best Ideas from the World's Teachers
for Improving Education in the Classroom. Free
Press; ISBN: 0684852748.