ASSESSMENT OF STUDENTS IN MATHEMATICS COURSES
DR. JAMES WILSON
FOR COURSE EMT 705
THE UNIVERSITY OF GEORGIA
DEPARTMENT OF MATHEMATICS EDUCATION
ATHENS, GA 30602
ASSESSMENT OF STUDENTS IN MATHEMATICS COURSES
The concept of assessment refers to the accounting of knowledge of a student
or a group of students. It is a tool that helps a teacher to ascertain whether
the goal of a curriculum has been achieved. There have been a lot of changes
in the methods of assessment in the classroom. Problems have been a central
part in mathematics curriculum but problem solving has not. Recently the
mathematics educators accepted the idea that the ability of problem solving
needs special attention.
Assessment is changing for many reasons. Changes in the skills and knowledge
needed for success, in our understanding of how students learn, in relationship
between assessment and instructions are changing our learning goals for
students and goals for students and schools. So we must change our assessment
strategies to tie assessment design and content to new outcomes and purposes
Assessment has five common features: assessment situation, response, interpretation,
meaning to the interpretation of student's response, and reporting and recording
the findings from the assessment. In this paper I shall discuss the features
I have used in my classroom. This paper is organized as follows: section
I will deal with the review of literature, section II will deal with the
assessment of my classroom teaching in a secondary school, and section III
will deal with summary and conclusions. References will be provided at the
end of the paper.
Review of Literature
Swan (1993) argues that collecting students' work, mark the answers for
correctness, and then write a numerical or letter grade by a comment have
some shortcomings. First, the purpose is confused. Second, the focus of
attention is too narrow. He discussed assessment for two different outcomes:
using mathematical and general strategies and achieving positive attitudes
Nagasaki and Becker (1993) discussed the classroom teaching in Japan. They
observed that Japanese mathematics lessons involve whole-class instructions.
The teachers appreciate the students' ways of thinking and the importance
of formative evaluations. But many teachers depend on summative evaluation
using paper-and-pencil tests. The classroom practice and assessment techniques
are also used by teachers. They agree that even a problem has only one solution,
there may be several ways to find the solution. So the students are encouraged
to use different techniques to arrive at the solution. So this generates
incentives to different ways of thinking.
Marshall (1988) discussed some current approaches to the assessment of problem
solving. They discussed some procedures that require how knowledge is accessed,
stored, and retrieved in human memory. They observed that in most testing
situations, we want to know whether an individual has a good understanding
of the basic principles that govern the domain of knowledge, and the whether
the individual can use that domain. They argued that our testing procedures
must be aimed at larger and broader conceptual structures. They recommended
two procedures that shift from statistical or psychometric models to cognitive
models of learning and memory. They argued that their procedures make explicit
and direct links among the testing, teaching and learning process.
Classroom Assessment in a Secondary School
Teaching in a high school classroom is quite different than teaching an
undergraduate course. The students in high school are mostly teen agers
and many of them are immature. I taught in high school in overseas during
1961-1974. Then I started to teach in a university. I came to USA in 1980
and taught undergraduate courses in SUNY at Albany in 1981-82 academic year.
I moved UGA and taught undergraduate courses during 1983-1989. Then I taught
in college during 1989-1993. I taught in a public school in Georgia during
1994-1995 academic year. I was assigned to teach courses on algebra, geometry,
and general mathematics. The classroom environment in public school is quite
different than the classroom environment in schools in overseas or colleges
in USA and overseas. Soon after I started to teach in a public school in
Georgia, I realized that classroom discipline is the most important part
of teaching. Classroom control is the key to success in teaching in secondary
schools. The team of management, parents, teacher and the students can handle
the discipline problem in the best possible way. In many cases the students
are from single or no parent or no direct guardian situation. These students
create most of the discipline problems and cannot be corrected completely
even with the intervention of the administration. The students of the school
represent the minority section of the population. The two classes of general
mathematics composed of the students who need special help. Two sections
of algebra students and one section of geometry students have the potential
to do well in the courses.
I applied different methods of assessment in different courses. In all courses
I wanted the students to get involved and participate in problem solving,
and create similar problems in the book. This created interest and enthusiasm
among the students. I used to assess the students using five different methods:
class participation, class work, homework, quizzes, and tests.
Assessment in Algebra Course
The algebra class composed of the students mostly from ninth and tenth grades.
The assessment of the students in algebra course has five parts: class participation,
class work, home work, quiz and tests. For class participation the students
were given the basic knowledge about a topic and review of the contents
of the previous day materials. I used to solve some problems from the book
and then make up some problems similar to those and solve them. I asked
each students to generate their own problems and solve them. They were also
asked to solve some problem from the book. At the end of class I would collect
the work and then grade them. The next day some students were asked to show
their work on the board. Those who did not do good were asked to generate
a problem and solve it on the board. All the students put their efforts
to find the solution of their own problems. This increased their creativity
and thinking ability. I found that it was the most effective way to generate
the interest of the students in mathematics. I scored their works and I
would discuss their performance with them individually at a later time.
I used to give them homework. The most difficult situation in homework was
copying from one another. But many students tried to solve their own problems
and learn with the help of their parents. This was a good part on homework.
I used to give them quizzes and grade them. The tests were given every two
to three weeks. The students of this school preferred to take multiple choice
tests. They have a very poor writing habit. As a result, multiple choice
tests were adding to this habit. I used give tests in which they have to
actually show their work. The tests also included some multiple choice questions.
In first few tests they were not doing good but over time they were used
to it and they were doing better. I used to compile all the grades and averaged
to get the final grade. The students would do better in the class participation
part of the assessment. I would put more weight on this part. I found that
this way of assessing the students was very efficient.
Assessment in Geometry Courses
This class composed of the students from tenth to twelve grades. These students
are more matured than the students of algebra course. I started to teach
the basic elements in geometry with proof. Soon I discovered that I should
not teach any proof in the informal geometry course. The book prescribed
for this course discussed two column proofs in detail. Most of the students
were interested in simple proof but as it was not required they were reluctant
to do it. In this course I used to assess the students using five methods
of my assessment techniques. The students tried to draw different geometrical
figures and solve their problems. They were not used to construct geometric
figures. They were reluctant to use compass and ruler. But I helped them
to use them in the class room. Finally they became interested in construction
of geometric figures. The homework, class-work, quizzes, and tests composed
of problems relating to geometric figures. The students liked the multiple
choice tests better than the tests in which they have to draw or write something.
It would take a large amount of time to grade the essay type tests but it
was very useful to the students. I would also give some multiple choice
questions in the quizzes and tests. So the tests were a mixture of multiple
choice and essay type questions. The students liked the class participation
part of my assessment technique. This improved their creativity and skills
to express their ideas. I used to average their scores and give a final
Assessment in General Mathematics Course
This class comprised of the students from ninth and tenth grades. These
students need to learn basic operations in mathematics: addition, subtraction,
multiplication, and division. They are also exposed to decimals, symbols,
and simple algebraic operations. These group of students have serious behavioral
problems. So the most important task was to keep them involved in the class
lessons. I used to provide worksheet at the beginning of every class. I
would explain similar problems on the worksheet. Then I asked a student
to create a similar problem and solve it on the board. Every student has
to do some problem on the board as a part of their class participation.
When every student is familiar with the concept of the problem, I would
ask them to generate few problems and solve for class work. The worksheet
was to be solved as a part of homework. Many of the students would not finish
the worksheet. So I would give them time to solve the worksheet problems
in the next class. I would give them a quiz at the end of every week and
a test at the end of every two weeks. The students became very interested
in making up their own problems. I would put more weight on the class participation
part of my assessment criteria. I would average the scores and give a grade.
Summary and Conclusions
Assessment of students achievement is changing, largely because today's
students face a world that demand new knowledge and abilities. In the global
economy of the 21 st century, students will not only need to understand
the basics but also need to think critically to analyze and make inferences
from the analysis. Helping students develop these skills will require changes
in assessment at the school and classroom levels, as well as new approaches
to large-scale high states assessment.
Assessment in a mathematics course is a complex and changing situation.
The students are exposed to a wide variety of technologies and they need
to relate mathematical problems with the real world situation than before.
So the assessment techniques are also changing over time. It has been observed
that the involvement of the parents in the learning process is very important.
The conference with the parents increased the level of involvement of many
students in the learning process. So the parents need to be informed in
different stages of the progress of a student. If the parents are interested
in the level of learning of their children and they have control over their
children, conferences with them improve the performances of those children
Charles, R. and Silver, E. (1988), "The Teaching and Assessing of Mathematical
Problem Solving", Vol. 3, NCTM, 1906 Association Drive, Reston, VA
Webb, N. and Coxford, A. (1993), "Assessment in the Mathematics Classroom",
NCTM, 1906 Association Dr., Reston, VA 22091.
Assessment Standard for School Mathematics, NCTM, May 1995
1906 Association Drive, Reston, VA 22091.
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