Mathematics

Graphic Organizers

In math, sequences and processes must be followed in exact order to achieve a correct result. The most common graphic organizer used is a series of steps, or sequence, chart. However, abstract concepts of math can also use graphic organizers and visual displays in order to enhance understanding. 

Examples:

  • To show information graphically through the use of a circle, line, bar, or coordinate graph
  • The concept of rational numbers including integers, wholes, and naturals (circles within circles)
  • A concept web of the properties of proportions
  • Sequencing how to fnd the slope of a line when given two coordinates
  • Comparing how to find inverse operations of an equations, like the Pythagorean Theorem (finding c vs. finding a or b)

Word Walls

While math is typically thought of as a universal language, this is not the case. It takes awareness of mathematical concepts and their related vocabulary in order to comprehend word problems. Often times, struggling readers and ESOL students have difficulty because of this vocabulary. Structuring word walls in clusters by similar conceptual processes or topics can benefit students by helping identify connections between the words as synonyms or a different relationship. Even playing a small game of choosing two words from the wall and discussing their relationship can support this understanding. Word sorting of a manipulative set of word wall vocabulary is also a productive tool for making connections between words and concepts. Students should use the correct vocabulary when describing orally or in writing the math processes needed to solve a problem.

Writing in Math

The use of an unedited learning log for notes and practice equations during teacher instruction is beneficial for students to have as a reference of processes and real-time examples provided in class. The use of a color-coded note-taking system can benefit all students, however, it is especially helpful for the lowest quartile of students who may need additional strategies that are not language-based. When a teacher can trace how 3x - 5 = 1 (see example) with color, the student can successfully track how to complete the steps as the problem is being solved. If the student's own note-taking includes the color coding system, the reference is beneficial for future practice as well. 

Example: 3x - 5 = 1

Step 1: Combine the constants. 3x - 5 + 5 = 1 + 5 ⇒ 3x = 6

Step 2: Isolate the variable. 3x ÷ 3 = 6 ÷ 3 ⇒ x = 2

Step 3: Check for accuracy. 3(2) - 5 = 1 ⇒ 6 - 5 = 1 ⇒ 1 = 1 yes

Writing in math should also be used as an extension of real-world learning problems involving math equations. Collaborative groups should be provided with an inquiry-based lesson in which they must use their knowledge of a mathematical concepts in order to solve a real-world problem. After discussing and determining a solution that works mathematically, students should compose their rationale alongside their answer, utilizing vocabulary from the unit's math wall to support their discourse. Language frames can the student's connection between the matematical concept and how to express it in an organized way.

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