Structured Word Inquiry and Making Math Real® Part 1: Formal Language

Lisa Klipfel, MA, Educational Therapist

August 9, 2019

Structured Word Inquiry (SWI) looks at the English writing system through a scientific approach. SWI uses tenets from linguistic rather than education. Making Math Real® (MMR®), developed by David Berg, reveals the incremental steps of mathematical conceptual development to gain a true understanding of accurate math code. While these two approaches focus on different content areas, this article is a comparison of their similarities and their importance on accuracy. Both SWI and MMR® use formal language. This first article explains the importance of formal language and why both SWI and MMR® insist upon its use.

Formal Language

One of the damages that happens in education today is the avoidance of formal language. Formal language is avoided in many content areas because it is felt that is formal language is “too much” for a student to understand or comprehend. While it may seem initially that formal language can be difficult to understand, that is often because the language and the concept have not yet been connected. Educators bridge the abstract of formal language with the use of informal language to help create a picture, a concept, but informal language is not precise and should be considered temporary or transitory. Informal language can have multiple meanings, be ambiguous, or grounded in fantasy/imaginary concepts. Its purpose is only meant to connect the concrete concept with an abstract concept. Informal language should only be in used as a transition to the formal language. It creates an association in learning. As soon as the abstract concept is grasped, then informal language should be abandoned. Pairing both the informal language with the formal language until the association is made can be helpful during this process. Formal language of a concept was developed to name the construct specifically and concisely. The length of time that informal language is used will vary by student need and complication of the subject matter at hand.

Examples of Formal and Informal Language

A few examples of informal language are, “minus five,” “flip the second one,” “word ending,” and “sound.” All of these are not quite precise enough language, which can lead to misunderstandings. Does the “minus five” have to do with an operation such as ten minus five, or is it a negative number, such as negative five? Is the “word ending” really a suffix? Or maybe it is a base that occurs finally in a word? Perhaps what is being referenced isn’t a morpheme at all, such as *<ture>, *<tive, or *<tion>.

In language arts, informal language uses the word, “sound,” whereas the formal language might be, “phoneme,” or even, “phone.” An educator might say, “What sound do you hear at the end of <fox>?” The educator may be wanting /ks/ as an answer, yet the final “phone” would be /s/ which is also a “sound”. This is the ambiguity of the word “sound”. A more precise question would be: “What is the final phoneme in <fox>?” Here, the precise answer would be /ks/. Why does this matter? A child with good phonemic awareness might differentiate between /ks/ and /s/ and not really know what is being asked. Is the answer a phoneme of /ks/ or a phone of /s/, as both could (inadequately) be defined with the vague use of the term “sound.” So, using informal language of “sound” is unclear. Asking a student using formal language, “What is the final phone in <fox>?” will yield a different answer, “/s/“ as it asks with specificity. This is an example of how informal language is not precise enough to create the right picture and can be quite confusing.

Extended Informal Language with no Formal Language Shift

One of the problems with the use of informal language is that it is often used too long. Quite frequently, the formal language is never introduced. Or, if the formal language is introduced, it is a brief side note of the formal title rarely to be uttered again to reference the concepts in the future. With lengthy informal language use, students start to believe that the informal language is the formal language. Many times, teachers or parents are concerned that their student/child cannot “handle” the formal term when often student ask about the longest words possible in our language.

The problems with avoidance of formal language are multifaceted. While clarity is one problem, another is the connection of formal language that is used in books, textbooks, other subjects and/or on a standardized test. A student may understand a certain concept, but if they are not able to associate their known concept to an unknown formal term then the problem/word may be lost. For example, if a textbook starts, “What is the quotient…” and the child cannot relate the formal word of <quotient> to division and this is the amount each person gets, then it doesn’t matter if they’ve “mastered” division. Essentially, their mental picture is lost because it was never transferred to the formal language.

Lack of formal language knowledge

Another more serious problem exists within the pedagogical community and that is when informal language is so pervasive that formal language was never introduced to educators during their training programs. Some informal terms have been used for such duration that some educators don’t know the formal terms at all because they were never taught. It is not their fault, but it is something for educators to recognize, be open, and seek out formal accurate terminology. An example in literacy is “the magic <e>.” This is the pervasive informal language that kids and adults alike use. Most native speakers know exactly what I’m talking about when I use that term. What makes it magical? What spell does it possess? What does mysticism have to do with the writing system? When studying Spanish, French, German or Latin, have you ever encountered a “magical” letter in those languages? The <e> is not magical in <give> or <have> but it is doing a job, a different job, a job that can be found when studying linguistics. In fact, the final single <e> that is not pronounced (also called non-syllabic) has over 10 different jobs. The point is that some informal language is so immersed in not only our schools but our culture that we don’t question its use and we don’t even realize that it is informal. The informal language has also skewed our ability to view and consider that the <e> could have other roles, jobs, and duties. This is the danger of excessive and extensive informal language.

Informal Language in Making Math Real

Making Math Real® introduces informal language to name visual concrete representations of math. The idea is that the informal language is something familiar and relatable to the student. While some of the language may be seen globally is some textbooks, most of the MMR® informal language is proprietarily exclusive to MMR®. Informal language in MMR® serves the purpose for students to hold a picture of a concept. As soon as a student can pull up and maintain that picture, the formal language is introduced to begin its transition. Because the picture has created meaning for the abstract concept (with many layers of scaffolding in between), the student can connect the formal language to the informal. While MMR® doesn’t require students to utter the formal language, they must be able to recognize, comprehend, and understand the formal language as part of the process of learning the math concepts. Because the instructor is using the formal language, they can recognize it in textbooks and tests as needed.

Words such as dividend, quotient, subtrahend are not part of everyday conversational vocabulary unless, perhaps, you live in the world of math. People will use words such as “the answer” or “the second number” instead of precise descriptive terms. Ambiguity creates confusion. Quotient plus its remainder is accurately “the answer” of a division problem. Latin is rarely studied but if morphology and etymology were part of the study of the word <quotient>, it would be easier to decipher as would subtrahend and addend for that matter. The ambiguity of “the second number” creates positional confusion as well as gives no clarity of the function of “the second number.” Using a term like, “operator” which gives the clue that this is the number doing the action in the equation. If you have a reverse number sentence, such as 2= 5-3, which one is the operator there? Is it still the second one? In this case, “the second one” is not even informal language but completely inaccurate language. There are precise names for even <operator> in the four operations: addition, subtraction, multiplication, and division.

Informal Language with Structured Word Inquiry

Structured Word Inquiry (SWI) relies heavily upon formal language: morphemes, graphemes, phonemes. This is just the start. Representations of synthetic and analytic word sums and matrices are also often new terminology. These are just the basics to get started. Once one dives deeper into SWI, many additional terms may arise including synchrony, diachrony, metathesis, excrescent, allomorphs, nominative, genitive, marker, portmanteau, phonotactic, and the list goes on. SWI uses little informal language which is one of the biggest criticisms of SWI. Most of the pedagogical language around spelling and reading uses informal language with little formal language and one of the roles of SWI is defining the written language more precisely. The high objection of the precise terminology in SWI by pedagogues is a clear indicator that the pedagogical terminology is almost all informal with little overlap.

Often SWI practitioners reject informal terminology like “sound” very early on to bring clarity and signal literacy study will be a completely different way to understand language. It’s not that “sound” is not studied. Orthographic phonology is studied, in-depth, but it is studied in a different manner and different sequence. Using terms like, “the <ch> sound” is confusing as the phrase is naming a grapheme to describe a phoneme. The <ch> (grapheme) has lots of difference pronunciations (phonemes): <chair>, <Christmas>, <chef>. So the phrase “the <ch> sound” is confusing when discussing <Christmas> and <chrome>. The actual phoneme pronunciation is useful instead of that graphemic phrase. The precision in formal terminology is to define and classify concepts rather than conflate concepts which is what is happening in the above phrase.

Benefits of formal language

Besides clarity of terms, formal language can also help to connect content areas. Another benefit is the expansion of language vocabulary. This can not only be seen in writing but oral language. When formal language is used connections are made from the formal language in content areas with leisure reading, conversations, movies and, yes, even video games. Students are also able to more clearly explain what they mean when they have the language to be able to describe it. It can assist them in deciphering test questions, not only with their teachers in class but state tests, formal test and later with standardized tests, such as the SAT. Formal language in math and literacy should be looked at as a gift in bringing accuracy and true understanding freeing them from false impressions.

About the author: Lisa Klipfel is an educational therapist who specializes in working with students with dyslexia. She has been studying SWI for over five years. She has a master’s degree in psychology. She has taken Making Math Real ® courses of 4 Operations, 9-lines, Fractions, Geometry I and Pre-algebra. She can be reached at www.leveluped.com and on Instagram/Facebook @leveluped.

Disclaimer: Lisa Klipfel is in no way affiliated with, a member of, or employed by Making Math Real Institute (MMRI), and does not represent or reflect MMR® or David Berg in any way whatsoever.