• Identify linguistic demands of instructional contexts;

• Plan instructional activities to teach natural language and the mathematical language of texts;

• Adjust instruction to accommodate cultural, socioeconomic, and linguistic changes occurring in ESL student populations.

“More than 40 percent of all teachers in the nation report that they taught students who are limited in their English proficiency, yet only 12 percent of those teachers had eight or more hours of training in how to teach those students”: 

Nieto, S. (2004). Affirming diversity: The sociopolitical context of multicultural education (4th ed.) Boston: Pearson Education.

A genuine, and typical, word problem

The Laundry Problem

Sandy’s family does its laundry at a coin-operated laundromat. It costs $1.25 per load to use the washing machines and 25¢ per load to use the dryers for 10 minutes. Sandy’s family has 5 loads of laundry to do and each load will need to be in a dryer for 30 minutes. Which expression will give Sandy’s family the total cost of doing these loads of laundry?

A. ($1.25 + $0.25) × 3 × 5

B. [$1.25 + (3 × $0.25)] × 5

C. [(3 × $1.25) + $0.25] × 5

D. 3 × ($1.25 + $0.25) × 5

From the 2002 Washington Assessment of Student Learning (WASL) for Mathematics.

A reasonable problem for seventh graders?

About half (49.9%) of more than 70,000 students who took the test were unable to manage the cognitive demands of this problem to select the correct answer. (Choice B)

About one-third (33.9%) of the students linked the information within the second sentence (Choices A and D) instead of linking information from the second sentence with information from the third sentence.

Students’ lack of prior experience with laundromats could be expected to impact their success rate.

What is really being tested by this problem?

Linguistic challenges

Use of the pronoun it in the sentence, “It costs $1.25 per load to use the washing machines and 25¢ per load to use the dryers for 10 min,”

Compounding & cognitive demands; “and 25¢ per load,” links the “25¢ per load” with the washing machine load until the end of the sentence -prior experience with laundromats signals the reader to interpret the sentence differently.

Spanish speakers, for example, may interpret the words to do as make.

Knowledge assumptions: a student may be familiar with wash clothes in English but not with the word laundry, and students whose families do laundry at home may not understand the word laundromat.

Load is usually first learned as a verb and when second-language learners read the word expression, they may, for example, think about what someone’s face looks like.

For many ESL students, English first names are not easily recognized; “What is a Sandy?”

Another one for you to think about …

The Soccer Problem

Jorge’s town has a soccer league. He helped sign up players for the different divisions. The table below shows the total number of players who signed up this year.

Jorge needs to figure out the total amount of money from sign-up fees.

Which of the following expressions will give him the correct amount?

A. (49 + 54) × $20 + (67 × $30)

B. (49 × $30) + (54 × $20) + (67 × $30)

C. (49 + 54 × $20) + (67 × $30)

D. (49 + 54 + 67) × ($20 + $30)

Underestimating what students know

How students use everyday knowledge to answer mathematics test items that use “realistic” contexts to frame the test question.

Cooper, B., & Dunne, M. (1998). Anyone for tennis? Social class differences in children’s responses to national curriculum mathematics testing. Sociological Review, 46, 115–148.1998;

Lamon, S. (2003). Beyond constructivism: An improved fitness metaphor for the acquisition of mathematical knowledge. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 435–447). Mahwah, NJ: Lawrence Erlbaum

Underestimation of students’ actual capacities with respect to mathematics may occur as a result of second-language learners’ lack of familiarity with the context of a problem.

When a teacher and students do not share the same language, previous experiences, or culturally based assumptions about what it means to teach and learn mathematics, the teacher’s resulting mental model of student learning may have little to do with the students’ actual understanding and construction of mathematical concepts and processes.

A check list for mathematics teachers