“In an age of exponential change, we need the power of diverse thinking, and we cannot afford to leave any talent untapped.” - Cathy Englebert
Do your students become disengaged in class? Have deficits in standards taught in previous years? Are you always trying to find ways to remediate the skills that they struggle with during class time? I can assure you, I experience these problems every year. As summer comes to an end and a new school year is on our horizon, there are several hundred thousand students excited to return to their classrooms. Most students at this time are still excited about school and have deep love for Math Class. They haven’t begun to experience the anxiety that comes from the new concepts that they will soon encounter. Somewhere around third or fourth grade when they're introduced to fractions and decimals, mathematical anxiety is something that many of my students have expressed. For most of my students, this is when they said they either grew to appreciate and love math or cringe and do the bare minimum to get by. Students often fall through the cracks with no real understanding as to what fractions and decimals are and their place in our number system; nor do they truly understand the place value for a decimal fraction. They then continue their young careers as math students being taught to manipulate and apply operations to these numbers and are left clueless as to what the values of these numbers actually are. This curriculum unit will aim to address some of those misunderstandings while exposing them to a new standard of algebraic representation.
This unit will introduce an innovative way to decompose numbers, identify their characteristics, and use Base 10 to introduce the Law of Exponents. Throughout my experience as a teacher, I have seen that many students can often apply the various properties of exponents but, are lacking a solid understanding around what exponents define, especially negative exponents. I'm hoping to use the property of negative exponents to model that negative powers are the reciprocals of positive powers, and also to make connections with the Base 10 model and place value.
As the curriculum progresses, students are often asked to demonstrate their understanding of the properties of exponents by representing them in various forms. These properties of exponents can also be represented in graphical form, tabular form, and written as equations. This is also what students are expected to do after mastering the basic laws of exponents. These types of questions can often include open-ended and inquiry-based questions which require students not only to show their mathematical skills but relate them to a real-world concept and/or situation. My students will be expected to answer a collection of questions that will be written on different levels and designed to assess multiple aspects of content knowledge.
By teaching my students to compare the process of applying the basic exponent rule combined with the negative exponent rule, I aim to broaden their understanding of positive and negative integers, inverse operations, and the value of tiny numbers/decimals on a number line. This will allow my students to solve problems more fluidly, and a number of the mathematical procedures will become innate. Through this process, my students will be able to compare the value of small numbers, which will not only enhance their abilities to make more accurate approximations and estimations as they arise, but also, they’ll be able to describe the relationship between one number and another with more accuracy and meaning. I will be encouraging students to invent new ways of accessing the material & encouraging them to share their thoughts with their peers. Through this level of constructivism in their math classroom, all my students will encounter increasing levels of success, by being able to persevere through outside distractions and make personal connections with the content. Through these experiences’ students will strengthen their knowledge concerning what one number means in relation to another.
Lastly, my unit will provide my students several different ways to show their understanding of what is taught. Especially, I will be requiring them to do a little more writing than their average math class. This writing will permit the unit to be presented through questioning and inquiry-based problems. This will allow me to facilitate mathematical discourse around what is being covered. By creating this safe space, I will make my students feel more comfortable, addressing any misunderstandings that they may have or had and allow for new learning to happen. Because dealing with negative exponents becomes more and more important as you progress through high school, students must be given a fair chance to unlearn any bad practices and learn new and fluent ways of manipulating these small numbers.