In 1989, the National Council of Teachers of Mathematics (NCTM) published
its ideas for the reform of school mathematics via the Curriculum and
Evaluation Standards for School Mathematics document. It was the view
of NCTM that there should be a shift towards communication, connections,
problem solving, and reasoning in mathematics. Changing the way mathematics
is taught required that assessment practices be adapted to meet the instruction.
The traditional mathematics tests that measured a student's ability to perform
skills of manipulation and memorize facts and theorems were not suitable
to assess thought processes and problem-solving skills. For this reason,
NCTM also suggested alternative assessment tools to parallel the new vision
of school mathematics.
During my student teaching in the winter of 1995, I tried to develop my tests to assess understanding and the ability of my students to communicate their ideas mathematically. I used open-ended questions that asked the students to explain or describe what happens in certain situations. I was proud of the kind of questions that I was using on my tests. This feeling of pride did not last very long. I ran into a problem when I administered the first test. I had four Asian students in my class who were also in the English as a Second Language (ESL) class. These students were highly skilled at the algebraic manipulation needed to solve problems, but they all had difficulty with the open-ended questions they were presented with. I do not know if the obstacle was the nature of thequestion or the inability to communicate their ideas mathematically. I think it was the latter of these explanations. These ESL students were struggling to learn the English language, and I believe that the mathematical language only added to their struggles. I felt helpless to the questions of these students during the test. Did they really know what they wanted to say and just did not know the vocabulary to communicate? Should I tell them the words they were trying to use? If I did this, was this fair to the other students? I originally thought my test would be a diagnostic assessment tool for the students' understanding of mathematics. What the test turned out to be was a signal that raised questions of equity in regard to assessment that I had not thought about previously. This dilemma really troubled me, so I started looking for answers.
Before I left the University for student teaching, I was given the assignment to find an area of interest in mathematics education to research for a Senior Project. This situation with the ESL students presented itself as the perfect area for me to investigate. The first thing I did was talked to my students' ESL teacher and observe her classes. After talking with this teacher and getting some information from her, I realized that finding resources for my study was not going to be easy. This teacher's response when I asked her how to help these students in mathematic was that ESL students usually do not have any problems in mathematics since it was not an English-dependent subject. To this teacher, mathematics was calculations and a set of steps to memorize that does not require written or verbal communication. What I observed in my class was an obvious contradiction to this comment. My Asian students were definitely faced with English becoming an obstacle in mathematics.
It was not a big surprise to me after talking to this teacher that I did not find a lot of resources addressing ESL students and mathematics. I found some things that addressed subtle things to do to enhance instruction, such as using cooperative groups and peer helpers, communicating clearly, and being more visual. I found very little information about assessment, which was my main focus of my inquiry. The most that was suggested concerning testing was to find an interpreter to help explain questions to the student. I still did not have the answers that I was in search of.
Since I had not had much success with my research, I was very excited when I received during the summer of 1995 the Assessment Standards for School Mathematics published by NCTM. One of the Standards outlined in this document was an Equity Standard. I thought to myself, "Finally, what I have been looking for." I was able to get suggestions that will help me the next time I am faced with a similar situation.
One of the things that I learned was how to modify open-ended questions to accommodate the ESL student. The question and the student's response can be given in the language with which the student feels most comfortable. This may be beyond the scone of the teacher, but another student could take on this responsibility. Another modification that can be made is to allow for the use of various forms of response and representations to answer a question. Some alternate representations might be pictures, graphs, or tables. Both of these adjustments are less English-dependent and therefore the student is able to communicate their ideas without the stress of using the correct English word. Teachers should make allowances while the ESL students are developing their written and oral use of the English language.
I thought my assessment tool was sufficient for measuring the students' reasoning and mathematics knowledge. From reading the Assessment Standards, I see that assessing these things can be surveyed better by using several forms of assessment. I relied solely on a test to determine achievement. I think it would be more reliable to utilize alternative activities to evaluate a student. I think this is especially true for students with limited English proficiency who may not do well with written or oral activities. Perhaps for these students, portfolios, projects, or observations are more fitting.
I believe the most important thing that I learned about assessment and ESL students is to be aware of the situation. If I am not aware that non-English speaking students in my class might have difficulties, I cannot make adaptations. Once I am alerted to the circumstance, my next duty is to become informed of the special needs of the student. All students are different and learn differently, so assessment should reflect these differences. All assessment types are not appropriate for all students. It is the responsibility of the teacher to modify their assessment practices so that "each student has the opportunity to demonstrate his or her mathematical power" (NCTM, 1995).
One of the questions that I posed when I was faced with this predicament was whether or not the modifications that I made for the ESL students was fair to the other students. I have come to the conclusion that the things done for these language-minority students, such as using various forms of assessment, can benefit the class as a whole. It does not have to be perceived as something done to help only a few students. Mathematics instruction is changing to meet the needs of all students and so should assessment.
National Council of Teachers of Mathematics. Curriculum and Evaluation
Standards for School Mathematics. Reston, VA. 1989.
-----Assessment Standards for School Mathematics. Reston, VA. 1995.