Supporting English Language Learners in Trigonometry (Texas)

Trigonometry punishes students whose English is still developing more than almost any other math topic. The mathematics is a set of ratios, but the questions arrive wrapped in angle of elevation, adjacent, bearing and line of sight, and a student who cannot decode the sentence never reaches the ratio. In a Texas classroom where the ELPS run alongside the math TEKS, the job is to grow the language without thinning the content, and those two goals are less in tension than they look.

Separate the three languages in the room

There are three vocabularies operating in a trigonometry lesson and students conflate them. Technical terms have one meaning only: hypotenuse, tangent, ratio. Semi-technical terms carry a math meaning that differs from the everyday one: adjacent, opposite, solve, degree. Context words belong to the story rather than the math: ladder, mast, kite, surveyor. Emerging bilingual students most often fail on the second group, because they have met the everyday meaning and have no reason to suspect a second one. Sort the vocabulary of your unit into these three columns before you teach it, and give class time to the middle column only. The first column can be taught with a labeled diagram in two minutes; the third can be glossed as it appears.

Staging the vocabulary across the unit

1. Label before you name. Students mark the sides of a right triangle relative to a marked angle for a whole lesson before the words sine, cosine or tangent appear. The relationship comes first; the label is attached to something already understood.
2. Fix the reference angle. Opposite and adjacent are meaningless without an angle to refer to. Rotate the triangle on the board and have students relabel it three times. This single routine removes the most common error in the topic.
3. Introduce the ratio names last. When they arrive, they name something students can already point at, which is what makes them stick.
4. Only then add the story. Word problems come after the language of the diagram is secure, never as the introduction.

The whole sequence rests on ratio being solid underneath. If a student is unsure what it means for two quantities to be in a fixed ratio, no amount of trigonometric vocabulary will help, and the Algebra Basics – Ratio, Proportion and Percentage | Math Foundations Workbook | GRADE 5–9 pages are worth two lessons before the unit starts rather than a remediation scramble in the middle of it.

Sentence frames that carry mathematical reasoning

Frames get a bad name because they are often used to produce sentences with no thinking in them. Written well, they do the opposite: they require a claim and a reason in the same breath. Use three, posted permanently. "The side opposite the angle is ___ because ___." "I chose ___ because I know the ___ and I need the ___." "My answer is about ___, which is reasonable because ___." The second one is the workhorse; it forces students to state which two sides they have before choosing a ratio, which is the actual decision the problem asks for. Require the frame out loud in pairs before it is written, since speaking is where the language actually develops. Visual supports matter as much as verbal ones, and graph-based work such as the Algebra – Linear Functions and Systems of Equations | Foundations & Problem Solving Workbook | GRADE 7–10 material helps students connect a picture to a relationship, which is the same move trigonometry asks for on a triangle.

Assessing the math, not the English

When you score a constructed response, decide in advance which part of the answer is a language demand and which is a math demand, and do not let a missing article cost a mathematical point. Allow diagrams as evidence of reasoning. Permit a student to explain a method orally and record it as met. At the same time, do not lower the mathematical bar, because emerging bilingual students who are given easier math fall further behind every year. The bar stays; the route to it widens. Keep a personal word list going in the back of each student's notebook, three columns as above, added to weekly rather than issued at the start. Underlying number work should stay in circulation too, and the Algebra Basics – Real Numbers Explained | Number Sets and Foundations Workbook | GRADE 5–9 workbook keeps the vocabulary of number types alive while the geometry runs. The unit has gone well when a student who arrived in your class in October reads a problem about a ramp, sketches it, labels it relative to the marked angle, and tells her partner in her own words which ratio she needs.

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