“Failure–When your best just isn’t good enough” probably accurately captures the feelings of many newcomer English Language Learners (ELLs) after they take a high-stakes mathematics test, write two researchers in a recent study on the linguistic demands of these tests in the journal Language Policy.
Even though it is a coffee-mug parody of motivational slogans on success, this statement describes the experiences of many newcomer ELLs who take math tests with linguistic demands on students that go far beyond what many educators realize, the researchers say. The two researchers performed a linguistic analysis of a 5th grade Texas Assessment of Knowledge and Skills (TAKS) Math test to more closely examine just what are the linguistic challenges of a math test on a newcomer ELL.
“NCLB’s allowances for newcomer ELLs to be excluded from state reading tests, but not math tests, appears to be based on the view that of all the academic content areas, math poses the least linguistic difficulty for ELLs. This is a major misconception,” writes the author. “Research shows that math tests have high academic language demands posing significant difficulties for ELLs.”
Here are some of the linguistic challenges faced by newcomer ELLs who take TAKS:
Superlatives are usually crucial for answering math word problems. TAKS had two questions that used superlatives, including this one: If the shelf is 3 feet long, what is the greatest number of videotapes that Stella can store on the shelf? Without understanding superlatives, it is impossible for an ELL to answer the question correctly, the authors write.
Words that must be converted into numbers
In the following question from TAKS, students would need to know that dozen means 12: Roses are $1.00 each or $10.00 per dozen. Sharla’s mother needs to buy 3 dozen roses for Sharla’s sister’s wedding. How much will she save by buying the roses by the dozen instead of individually?
Common words with different meanings in math.
Words such as feet, point, face, table and place (such as in place value) are familiar to ELLs, but have different meanings in math problems.
TAKS had 18 uses of the infinitive in complicated sentence structures, the authors report. For example, one question asked, “To determine whether they are halfway to their goal of $450.00, what should the students do?” Students must understand the meaning of the infinitive, “to determine” to answer the question.
There were nine comparatives in the TAKS test. Comparatives always involve crucial information for problem solving, the authors write. For instance, one question presented students with this problem: “His brother Tom is 2 years older than Jon, and their brother Henry is twice as old as Tom. Which number sentence could be used to find h, Henry’s age?”
TAKS had 9 items with adverbial clauses. For instance, one question asked, “What is the least number of boxes he can buy so that each fifth grader gets at least 1 ice-cream bar?” Without understanding the adverbial clause, it would be extremely challenging to answer the question, the authors write.
Negation in questions
Negation in questions presents a major syntactic challenge for ELL students, the authors write. The following questions in TAKS used this syntactic feature: Which of the following combinations of supplies does she NOT have enough money to buy? Which is NOT a way to find how much money Leanne spends on lunches each week? Such questions are beyond the reasonable range of capability for most newcomer ELLs, they write.
Other challenges ELLs face when taking a math exam include:
Word order may differ from the way numbers and symbols appear in a numeric sentence (e.g. “the square of the sum of x and y (x + y)2).
Mathematical symbols may differ from the way they are used in the home country. For example, in Cambodia, a comma is used instead of a decimal point for number values less than one and a period is used instead of a comma to separate place value. So the number 4,232.56 would be written 4.232,56 in Cambodia.
“There has been some research on the potential of creating linguistically simplified mathematics tests, which attempt to remove difficult lexical and syntactic features such as those discussed in this article,” write the researchers. “However, such research is still in its infancy, and it is unclear to us how a written math test in English could ever completely eliminate a student’s lack of English as a source of construct irrelevance. But even if this is possible, it still ignores the other important factor raised in this article–the opportunity for students to learn the material before they are tested.”
A reasonable policy for ELLs, takes into account the following:
- The quality of education in the students’ home countries
- students’ opportunities to learn the content being taught in the classrooms of U.S.-born students
- the language barriers that prevent equal access to core curriculum instruction in the U.S. classrooms
Students from other countries may not have had the same exposure to math concepts as their U.S. peers, the authors write. The researchers worked with two sisters from Cambodia as part of their study. The girls faced language barriers in math test-taking, and also lacked the math background their peers had because of conditions in their home country.
The researchers note that in the girls’ home province, over two-thirds of elementary school teachers had less than a high school education. The 573-page American math textbook used in their U.S. class was six times longer than the thin paperback textbook typically used in Cambodia for their grade level.
The sad reality, say the researchers, is that in many rural schools, students do not have textbooks at all. The country’s educational system, severely disrupted by the Khmer Rouge regime, which persecuted educated members of society, had to be rebuilt by scratch in the last 30 years.
“High-stakes math tests and newcomer ELLs,” by Wayne Wright and Xinoshi Li, Language Policy, Volume 7, Issue 3, September 2008, pp. 237-266.