Strategies
Instruction of this unit will begin within the first one or two days of the semester. The first question I will ask my new students is, "Have you ever seen a number?" If they say yes, then "What did it look like?" I hope to promote a discussion centered around the idea that numbers are adjectives that modify nouns (the units). Written numerals are merely symbols that represent numbers, and we need to know what they describe to assign meaning to them. In order to operate on them (i.e. add or subtract, etc.) the numbers must be modifying the same noun. I may use PowerPoint slides created by Herb Gross and Richard Medeiros 7 to illustrate this adjective-noun relationship in mathematics. I expect Precalculus students to see the adjective-noun connection to algebra - adding "like terms." I plan to start with this adjective-noun relationship to be able to refer to it throughout the semester in different contexts.
Based on weaknesses that I have observed in my students, and supported by my readings and seminar discussions, I have selected weekly mathematical topics for Warm-up/Bell-Ringer activities. For the past several years, I have prepared my Warm-up activities using computer software so that they are displayed on the interactive white board when students enter the classroom. All activities in this unit will be calculator-free, and I expect students to attempt to solve each problem in more than one way. Wherever possible, I would like them to perform mental arithmetic, although they will record their mental thought process. These activities should be completed independently in the first five minutes of class, and followed by a full-class discussion. I will expect students to share their own strategies and listen and learn alternate strategies. I may demonstrate some strategies that are described in the Background section of this unit, if no students use them.
In my classroom, students receive a template every Monday that they fill in each day of the week and turn in on Friday. The template has space to copy the daily Essential Question (objective for the class period) and to copy and work out the daily Warm-up problems. I do put a grade on them (a very small percentage of their course grade), typically for completeness, and return them to be kept in their notebooks. I have found that this system keeps students accountable, organized, and provides a record of what they have studied throughout the semester. I will continue with this strategy with one addition - I will add a space on Friday's section for students to summarize what they learned from the weekly Warm-up activities. At the end of the semester, I will ask students to review all of the weekly Warm-up activities and, again, summarize strategies and concepts they learned throughout the semester.
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