Prior to reading any articles, I typically read titles, subtitles, and skim for basic information.  This technique is useful for any reader.  Of course the anxiety potential is heightened when seeing words such as polynomial, linear equation, and factoring trinomial.  My thoughts become twisted and stomach begins to knot up.  Immediately, thoughts go toward giving up and throwing the articles in the trash. There will be no reflection on this week.  None the less, I trudged on determined to connect and relate to the articles in some way reading again and again until there is some way found to connect and relate mathematics to language instruction and literacy.  Eventually a relation, a connection is realized regarding using concrete models to introduce concepts, increase and learn important vocabulary, and using alternative approaches to provide students access to mathematics understanding

Annette Leitze and Nancy Kitt believe learning algebra is possible for all persons by using concrete models such as the algebra tiles mentioned in the reading.  The authors suggest this technique gives students a series of levels to learning: concrete, pictorial and abstract or symbolic. This is true for all subjects and pertains to not only mathematics instruction but language based courses also.  Young children especially gain experience going through various levels and stages of learning beginning with concrete and progressing to the abstract.  When working with students who have various learning styles and special education services, concrete is a great first stage of presentation.  For example when working with a deaf student on vocabulary building, I can say the word cup, sign the word cup, show the printed letters for the word cup, but unless I show a picture of the cup or an actual cup the concept of cup may not be acquired or fully established.  Although a child may have been shown how to use the cup, without being able to relate the cup to everything, pictures, sign, print and tactile – full understanding of the concept or meaning is not established.  It would be interesting to do a study and collect data with deaf students implementing all steps or methods of language or vocabulary acquisition.

Next, Rhela N Rubenstein focuses on strategies for increasing and learning mathematics vocabulary.  Students with limited vocabulary as a result of language delays may easily become confused during instruction, for example when math words such as sum and some are used during instruction.  A deaf student relying on speech reading and lip reading skills may have difficulty understanding which word is being used if enough clarification is not provided.  Although students using sign language will understand the differences in meaning, students using speech reading and listening skills may become confused or misunderstand these two words since they both look exactly the same on the lips.  This article in particular states the importance and the need for early language and vocabulary work.  It is important for parents and teachers to show, explain, describe, print, and give details and concepts as early as possible with students having language delays.  This suggestion does not come from knowledge gained through research, but as a parent these are issues that popped up from time to time when my daughter was young. Children born with hearing loss or deafness are at an instant disadvantage. Without sound may of the ways early language is acquired such as environment, parents, radios, television, and other siblings are not available.  Language stimulation is acquired from one on one and face to face interactions.  This is but one challenge children with hearing loss face in the classroom.

Another challenge in language acquisition is having access to skilled interpreters.  Interpreters do not always have a good grasp on conceptual signing. Using the same sign for two words with different meanings such as some and sum could seriously impair a child’s understanding of mathematical concepts.  This unfortunately occurs more often than I care to discuss. Additionally, these authors asked “how do we help students recognize these nuanced differences of usage?”   The idea of the need for understanding the difference in meaning is enormous.  Students using speech reading and or sign language need to be exposed to all meanings.  Signs must be conceptually correct; Interpreters must have an understanding of mathematical concepts and meaning as well as parents.  These concepts must be expressed, signed, spoken, practices, and shown to ensure the correct meaning is acquired.

Last, John W. Coburn discusses using various approaches to teaching algebra.  This article seems similar to several of the earlier articles read this semester regarding students invented algorithms and teachers teaching from the same, old approach.  Although, I have solved inequalities, graphed quadratic equations and factored polynomials, my heart races and anxiety increases while reading this article.  I look at some of the text and feel as if I am reading a foreign language.   There are pieces of my mind wanting to shut down and give up.  Equally, the intrinsically motivated side of my mind is determined to give this another chance, to reread over and over until something stands out.   When Coburn discusses students using certain uncommon styles, I am intrigued and continue reading.  I absolutely agree with this discussion.  There is a lot of information which seems to support providing students multiple ways for solving mathematical equations.  It is essential  to use every available resource in an education setting and these resources should be used until the concept is acquired.