Posted: May 25th, 2022

Algebraic concepts & polynomials factoring

Jeffery Case Study

Background for Jeffery

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Jeffery has problem understanding algebraic concepts such as polynomials and factoring. Jeffery doesn’t require any special aids and his learning capabilities are normal for his age.

Ability to solve polynomials and factorization with the help of Mnemonic device such as FOIL

develop the ability to understand order in which polynomials are solved

Become familiar with complex algebraic terms with the help of vocabulary teaching.

Supporting information for set goals

John Steele (2003) explains that children having difficulty with mathematical concepts can be helped with the use of mnemonic devices because “Mnemonics are useful for memorizing rules, steps, and procedures.” (p. 624)

Vocabulary teaching is also critical for developing good understanding of algebraic concepts. This has been proven by Richard Drake’s research of 1940 and was later supported by studied carried out by others. Myszczak found that vocabulary learning is significant because it teaches students the ability to focus on the question and what is being asked as “students often search the problem for numbers rather than attempting to comprehend what is truly being asked in the problem” (p. 28)

Schoenberger and Liming (2001) focused on the teaching of a specific list of words that could help students learn mathematical concepts. They believed that “Students should be able to use and understand vocabulary in order to think about and discuss mathematical situations” (p. 27).

Apart from teaching vocabulary, it was also found that simply communicating with students while teaching mathematical concepts could help facilitate better understanding of the concepts. In other words, students could communicate the problem and seek the solution by talking to their teachers. “Language is a major medium of teaching and learning mathematics; we serve students well when we support them in learning mathematical language with meaning and fluency” (Rubenstein, 2007, p. 206).


First Jeffery needs to understand that any two sets in parenthesis without any sign in the middle means multiplication. Once he understands that he needs to understand the order in which each term is multiplied. For this he can use the FOIL method. FOIL means FIRST OUTSIDE INSIDE LAST. This order can help erase the confusion that arises with understanding of order in which equations are to be solved. This technique falls in the category of Mnemonics which was one of the strategies recommended for Jeffery’s case. Mnemonics are any sentences or pictures that help students make connections and understand concepts.

Students often are befuddled with the use of complex terms in mathematics and hence it’s recommended that they become familiar with some commonly used terms before they are used in the context of mathematics or algebra. For example students can be told what a variable is without actually referring to any mathematical equation. Variable is simply any letter in which a value can be stored. 4x for example would be the number 4 with a variable x that also contains a value though hidden from us.

Students should be explained what a variable in their everyday life context so they become more comfortable with the use of such terms in mathematics. For example x is the most common variable used. When we talk about other things in our general lives, we do use variable like saying “She has that X factor,” or “In his case, it was the X factor that worked.” Now X is something but the value is hidden. In mathematics, it is up to us to discover the value of that X variable.


Marcee M. Steele and John W. Steele (2003). Teaching Algebra to Students with Learning Disabilities. Mathematics Teacher, Volume 96, Number 9; December, 2003; pp.622-624.

Blessman, J., & Myszczak, B. (2001). Mathematics vocabulary and its effect on student comprehension. Saint Xavier University & Skylight Professional Development. (ERIC Document Reproducion Service No. ED455122).

Rubenstein, R. (2007). Focused strategies for middle-grades mathematics vocabulary development. Mathematics Teacher, 10(4), 200-207.

Schoenberger, K., & Liming, L. (2001). Improving students’ mathematical thinking skills through improved use of mathematics vocabulary and numerical operations. Saint Xavier University and Skylight Professional Development. (ERIC Reproduction Service No. ED455120).

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