Teachers are masters of their subject, with in depth knowledge far exceeding the basic skills and knowledge that students are expected to master. This provides teachers with the confidence to teach and scaffold across the discipline as well as the ability to identify and avoid learner misconceptions. It also assists in creatively teaching the subject in memorable ways.
Goal:
I will use correct mathematic language and vocabulary and expect my students to do the same so they may be successful in future mathematics classes.
Goal Reflection:
I decided this goal was important when the majority of my students incorrectly used the word "reflection" to describe what was actually "symmetry." on a common formative assessment. As I reflected on their response, I realized it was likely because I would say "mirror image" to describe the symmetry seen in parabolas, so it made sense they would connect "mirror image" with "reflection." As the year progressed, I focused more and more on vocabulary because understanding vocabulary allows students to correctly communicate mathematics. I created vocabulary lists and included vocabulary in quizzes and tests. I taught my students to break down words to better understand their meaning so when they encounter a mathematical word that is a bit foreign to them, they can break it down to smaller words with familiar meanings. Since understanding correct vocabulary is important to communicating, I emphasized speaking with the correct words. When students would ask or answer questions in class, they were allowed to express themselves freely. And then, once I understood their train of thought, I would help them communicate using the correct vocabulary and ask them to repeat their thoughts using the proper mathematical terminology to emphasize the importance of mathematical precision and so they could practice communicating their ideas correctly. It is my hope, that because of the emphasis on vocabulary, my students will be able to not only effectively communicate mathematically in future classes, but understand new concepts by using the skills I taught them.
Evidence:
Below you will see lesson plans with vocabulary words, as well as a copy of class notes showing a discussion of vocabulary words, including a compare-and-contrast of the meanings of the familiar but often misused words.
Reflection:
Although using student-friendly language is important, using proper mathematical language and vocabulary will help students gain a deeper understanding of the math. Teachers sometimes fall into the trap of teaching shortcuts or tricks. It may be memorable to refer to factoring quadratics as "hippo-butts" or "the box thing," and students may understand "flip" better than reflection, and it may be easier to remember "A squared plus B squared equals C squared" than actually understand the Pythagorean Theorem as a relationship between the lengths of the legs of a right triangle and its hypotenuse. Unfortunately, as soon as the student moves on from a teacher who uses these tricks to a teacher who doesn't, the student feels lost, not understanding the mathematics and the language used to communicate that math. I realized that this is really a slippery slope as I discovered I fell into the trap of using non-mathematical language in an attempt to help students understand. For example, when describing symmetry of parabolas, I often times would use the words "mirror-image." I realized my mistake when my students chose the word "reflection" to describe what was actually symmetry on a common formative assessment. It was then I decided to force myself to use correct mathematical language as would be seen in the Utah Core Standards for Mathematics, the SAGE, and other mathematics texts. As I became better at using the correct language, I encouraged proper usage from my students as well. I would often say, "I know what you are trying to say. This is the way we say it mathematically..." and then I would have the student repeat her thought process using the correct language.
To continue to improve our use of correct mathematical vocabulary, I would create and spend time on vocabulary lists to help solidify new words. Sometimes, the mathematical meaning of a word is diluted through common use in the English language. For example, the word "similar" has a precise definition in mathematics that is lost through common use in everyday language. Without addressing the difference in common everyday use, students will not fully understand the precision required for the mathematical definition, so we often discuss the non-mathematical understanding of a word and how it relates to the precise mathematical definition. I would also help students understand meanings of words using root words. Breaking down "trigonometry" to the root words of "triangle" and "measure" makes trigonometry much less scary. And teaching students that "quartic trinomial" comes from the Latin- and Greek based words meaning "character of four" and "three terms" helps them to understand we are referring to a fourth degree polynomial with three terms.
Students who understand mathematical language will do better in other math and science classes as the language across the discipline is standardized, while tricks are specific to individual teachers. Tricks are used by magicians to deceive and defy logic. Mathematics serves to logically explain the world around us. I am teaching my students to be mathematicians, not magicians.
To continue to improve our use of correct mathematical vocabulary, I would create and spend time on vocabulary lists to help solidify new words. Sometimes, the mathematical meaning of a word is diluted through common use in the English language. For example, the word "similar" has a precise definition in mathematics that is lost through common use in everyday language. Without addressing the difference in common everyday use, students will not fully understand the precision required for the mathematical definition, so we often discuss the non-mathematical understanding of a word and how it relates to the precise mathematical definition. I would also help students understand meanings of words using root words. Breaking down "trigonometry" to the root words of "triangle" and "measure" makes trigonometry much less scary. And teaching students that "quartic trinomial" comes from the Latin- and Greek based words meaning "character of four" and "three terms" helps them to understand we are referring to a fourth degree polynomial with three terms.
Students who understand mathematical language will do better in other math and science classes as the language across the discipline is standardized, while tricks are specific to individual teachers. Tricks are used by magicians to deceive and defy logic. Mathematics serves to logically explain the world around us. I am teaching my students to be mathematicians, not magicians.