I am teaching the third subunit of the second unit in Mathematics I. The third subunit focuses on rational and radical expressions. The goal of my unit was to make the students feel like radical and rational expressions are not scary, and in fact pretty fun. When I was told what unit I’d be teaching, the first sentence out of the teacher’s mouth was, “Good luck, the kids hate fractions.” I am hoping that I can change the student’s perceptions regarding rational and radical expressions.
The first day I am teaching, we will be working through and discovering rational expressions using polynomials in the Just Jogging Learning Task. The learning task is a great way to let the students discover how to manipulate rational expressions. The students are given something familiar that they have seen before, the distance formula, and simply manipulate it by adding variables. In order to increase conceptual understanding, the students can work in pairs and communicate math to each other.
We have four days allotted for operations on rational expressions. Although the resources I were given were extremely procedurally based, I have added conceptually challenging questions and thought provoking statements in my lessons. I am hoping for the students to not just accept what the text book tells them and try and fully understand the material. To support conceptual understanding, I have reworked some of the Lassiter worksheets and instead of 30 “procedural” problems; the students will have a limited number of problems to do outside of class that will still check for understanding of the material. The first week is wrapped up with a Jeopardy game to review the operations of rational expressions. Although the worksheets and exercises may appear to be conceptual, students will continually be challenged to think why they are doing steps of solving rational expressions, rather than just following the textbook’s rules.
The second half of my subunit deals with radicals. I never really thought about how fun radicals could be. The students and I will be discovering the rules of the radicals through many trial and error steps. We will discover why rationalizing a denominator is helpful, and why simplifying radical expressions can help mathematicians. Helping the students understand why teachers ask them to simplify will hopefully help motivate the students to actually want to learn how to simplify.
The unit conforms to the GPS and NCTM standards by continually challenging the students to reason through their problems. Instead of just listing the excluded values in a rational expression, the lessons challenge the students to know what the excluded values tell us about the expression. I am a huge technology person and wish there was more I could do with technology. If this were my own classroom, I would try and do as much possible with technology. I believe that technology is one of the best ways to keep students entertained and keep their focus in mathematics.
I have been met with some resistance regarding procedural and conceptual understanding. By going into a very successful school that has taught procedural for years, it is hard to justify the importance of conceptual understanding; however I believe that after my unit the students will desire to know why they are performing operations, rather than just performing them. If this were my own class, I would rather create future mathematicians, and not just mathematical robots.
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